Con - Macquarie University

1

Spontaneous emission in GaN

Contents

1 Introduction 5

2 Recombination processes in the bandgap region 7

2.1 Free excitons . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Bound excitons . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Free to bound transitions . . . . . . . . . . . . . . . . . . . . 11

2.4 Band to band transition . . . . . . . . . . . . . . . . . . . . . 12

2.5 Donor-acceptor pair spectra . . . . . . . . . . . . . . . . . . . 13

2.5.1 Temperature evolution of photoluminescence signatures 15

2.5.2 Photoluminescence intensity dependence on excitationpower . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.5.3 PL intensity and dopant concentration . . . . . . . . . 19

2.5.4 Lineshape . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.6 Lifetime and recombination time . . . . . . . . . . . . . . . . 21

2.6.1 Background . . . . . . . . . . . . . . . . . . . . . . . . 21

2.6.2 Non-radiative recombination . . . . . . . . . . . . . . 22

2.6.3 Examples of applications . . . . . . . . . . . . . . . . 23

2.6.4 Recombination rates and excitation dependence of emis-sion intensity . . . . . . . . . . . . . . . . . . . . . . . 27

2.6.5 Photoluminescence excitation spectroscopy . . . . . . 28

2.7 Strain e�ects . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3 Common deep emission bands in GaN 41

3.1 Yellow emission of GaN . . . . . . . . . . . . . . . . . . . . . 41

3.1.1 Models of the yellow emission process . . . . . . . . . 42

3.1.2 Empirical features of the yellow emission band . . . . 44

3.1.3 Microscopic origins of the centre responsible for theyellow emission . . . . . . . . . . . . . . . . . . . . . . 47

3.2 Blue emission in acceptor doped GaN . . . . . . . . . . . . . 52

4 Piezoelectric e�ect in GaN and its in uence on emission 65

4.1 Fundamentals of piezoelectric e�ects in perfect crystalline GaN 65

4.2 Film surface polarity . . . . . . . . . . . . . . . . . . . . . . . 67

3

4 CONTENTS

4.3 Piezoelectric phenomena in real structures . . . . . . . . . . . 684.4 Implications of piezoelectric e�ects for devices . . . . . . . . . 70

5 Dislocations and their e�ects on emission 81

5.1 Spatially-resolved studies . . . . . . . . . . . . . . . . . . . . 835.2 Recombination at dislocations . . . . . . . . . . . . . . . . . . 87

References 99

Part 1

Introduction

The technological potential of GaN as an opto-electronic material was an-ticipated for the last 30 years, but only in the recent decade, improvedcrystal growth techniques have allowed several leading groups to achievedevice-quality �lms. Progress was due to reduction of the high backgroundelectron concentration, persistent in the GaN grown in the seventies, andthese reduced electron concentrations were accompanied by enhanced car-rier mobilities. The problems with p-type doping delayed, however, practicaluse of this material. A real breakthrough came when the low resistivity ofacceptor doped material became available. In recent �ve years many sub-sequent challenges in the area of materials science and device fabricationwere successfully resolved. Following the commercialisation of light emit-ting diodes (LEDs) in 1994, the mass production of the present GaN-basedLEDs yields devices with quantum eÆciency exceeding 10 %, comparable tothe most eÆcient semiconductor light sources on the market today. In 1999we witnessed another industry breakthrough, the commercial introductionof the blue laser diode. It can be expected that this event will revolutionisethe optical memory devices by considerably increasing the amount of infor-mation that can be stored in optical disks.

The advantages of high bandgap energy and good thermal properties inGaN and related III-V nitrides are still accompanied by a relatively poormaterial quality. GaN materials grown using both MBE and MOCVD meth-ods was proven to contain high densities of dislocations, partly related toa lack of suitable substrate material with matching lattice constants andthermal expansion coeÆcients. The successful utilisation in electronic andopto-electronic industry of materials with such high dislocation density, ispuzzling. Consequently in this review we concentrate on the optical prop-erties of GaN and related nitrides. We start with a basic discussion ofvarious recombination processes important in GaN. We describe the ways ofdistinguishing between these processes. This is very important in the case

5

6 PART 1. INTRODUCTION

of GaN, because due to large di�erences between materials a given photo-luminescence (PL) transition is often observed at quite di�erent spectralpositions. Next, we discuss the relationship between structural (morpho-logical) properties of GaN �lms and optical transitions. We survey the roleof dislocation in radiative and nonradiative recombination transitions andthe in uence of piezoelectric e�ects on rate of radiative recombination andemission energy. Finally, we analyse two deep emissions of GaN - the yellowand blue emission, observed in acceptor doped samples.

Part 2

Recombination processes in

the bandgap region

In this part we discuss examples of photoluminescence processes in galliumnitride selected to exemplify the di�erent types of recombination. The non-radiative as well as radiative centres will be considered. We will concentratein this section on methods that use photoluminescence and other emissiondata and on quantitative information about GaN �lms and their defect struc-ture and processes that can be obtained from these studies.

The term photoluminescence denotes the radiation emitted by a crystal afteran optical excitation. It is produced as a result of recombination of pho-toexcited electron-hole (e-h) pairs. From the analysis of the luminescencespectrum as a function of di�erent parameters (temperature, excitation en-ergy, excitation intensity, temporal evolution, external �elds, etc), generalinformation on the material quality can be gained. It may give some insightinto the defects involved in the growth process or produced by typical pro-cessing steps and by post-growth treatments. It gives information mainly onminority carrier properties and their in uence on, or relationship to, defects.For example, the minority carrier lifetime, di�usion length, and quantum ef-�ciency can be deduced from the study of the recombination pathways. Allthese quantities are a�ected by the defects as well as the doping level. Im-portantly, photoluminescence spectroscopy is capable of distinction betweenthe chemical species of impurities. Owing to its sensitivity, photolumines-cence may be used at very low defect densities, sometimes even as low as1013 � 1014 cm�3.

It is not always straightforward to extract quantitative information from thephotoluminescence measurements alone. The values of the doping densityor the trap concentration may require a very accurate calibration or carefullineshape studies. Sometimes extensive analysis and supplementary mea-

7

8PART 2. RECOMBINATION PROCESSES IN THEBANDGAP REGION

surements using other techniques are required. The important non-radiativerecombination processes can be studied only indirectly and accessed throughtheir e�ect on transition rates for the radiative processes. For example, thenon-radiative processes are more pronounced in the proximity of extendeddefects and thus may be visualised in the topographic distribution of theluminescence intensity. Owing to this e�ect, the imaging techniques, andmore particularly cathodoluminescence, have provided detailed informationon dislocations and other extended defects and their spatial distribution.

In an idealised semiconductor at least four coupled radiative recombinationchannels may be active, these are band-to-band, free exciton, bound exci-ton, and impurity to-band transitions, as illustrated in Figure 2.1. Thesechannels may or may not be spectrally distinct in a particular �lm. We nowpresent some background information on these four processes.

2.1 Free excitons

Free excitons assemble from the excited electrons and holes as a result ofthe Coulomb interaction. The Wannier-Mott free exciton can be describedwithin the e�ective mass approximation, and its bound states (in the caseof non-degenerate band extrema and at the exciton wavevector k = 0) havebinding energies En given by [1]:

En =1

n2�

m0

1

�20RH : (2.1)

In Equation 2.1 RH is the Rydberg constant of the hydrogen atom, m0 is theelectron mass, �0 is the static relative dielectric constant, and the excitonreduced mass � is given by

� =memh

me +mh

:

The free excitons at non-zero wavevectors can not be directly observed in theemission spectra. The emission of the recombining free excitons (at k = 0)occurs below the band gap energy Eg, at the energy EX given by:

EX = Eg �RH

n2:

GaN in wurtzite structure has its valence band split into three subbands.The splitting is caused by the axial crystal �eld and the spin-orbit interac-tion. The valence band splitting leads to three free excitons A, B and C,

2.2. BOUND EXCITONS 9

associated with each of the three subbands. The exact energy of these threeexcitonic transitions was obtained from re ectance and photoluminescence(PL) studies performed on thick GaN epilayers and homoepitaxial epilay-ers [2{7]. Accurate values of energies of the excitonic transitions have beendetermined due to full strain relaxation in such epilayers. The highest pre-cision measurements were carried out in homoepitaxial GaN samples, wherevery sharp PL lines are observed, with linewidths below 1 meV [8, 9]. Thevalues of exciton energies of 3.478 eV (A exciton), 3.484 eV (B exciton) and3.502 eV (C exciton) have been obtained with the accuracy of about 2 meV[10]. Consequently, the binding energy of all three (A,B,C) free excitons inGaN is determined to be about 25-27 meV [10, 11].

With technological advances in GaN layer quality resulting in sharp spectralfeatures, it became possible to observe �ne structures in the excitonic tran-sitions. Examples of such �ne structures inlude the polariton longitudinal-transverse splitting and the singlet-triplet exchange splitting. The �ne struc-ture of the A exciton was determined from re ectivity and polarised PL in-vestigations by Ho�mann and co-workers [11, 12]. Ho�mann et al. [11] haveidenti�ed the PL peaks at 3.47904 eV and 3.47892 eV with the lower trans-verse branch of the spin singlet state and with the spin triplet state of theA exciton, respectively. Such identi�cation gives the value of the exchangesplitting of about 120 �eV with the accuracy of about 100 �eV. The PLpeak at the energy of 3.48000 eV was assigned to the longitudinal branchof the spin singlet state of the A exciton [11]. This identi�cation yields thevalue of the longitudinal-transverse splitting of the A exciton to be about1.0 meV, with the uncertainty of 0.1 meV [11, 12], while other authors [13]quote the value of about 1-2 meV.

2.2 Bound excitons

A free exciton can be bound at a neutral or ionised donor or neutral acceptor,giving rise to an exciton-impurity complex. An exciton bound to an ioniseddonor is a complex of an ionised donor ion, an electron and a hole; an excitonbound to a neutral donor consists of an ionised donor ion, two electrons anda hole, or otherwise of a neutral donor, an electron and a hole. An ioniseddonor-bound exciton can only be formed if the e�ective mass of a hole isconsiderably larger than the e�ective mass of an electron, as in the case ofGaN. By analogy, ionised acceptor-bound ecitons can be stable only if thee�ective mass of electrons is larger than that of holes. This situation is notrealised in GaN. Thus, excitons bound at neutral acceptors are stable, whileionised acceptor-bound excitons may not be formed in GaN.

Recombination of bound excitons is an important process in the near-gapspectral region. It becomes more pronounced with an increasing impurity

10PART 2. RECOMBINATION PROCESSES IN THE BANDGAP REGION

concentration. In GaN, as in other semiconductors, bound excitons oftendominate the low temperature band-edge spectra. They appear as sharpspectral lines in close proximity of the band edge, particularly at low donorand acceptor concentrations. The sharp bound exciton emission lines arefound at the energies �h! given by:

�h! = EX �EBX ; (2.2)

where EBX is the exciton binding energy required to remove the exciton fromthe impurity centre. The binding energy of donor-bound excitons obtainedfrom spectroscopic measurements is 11.7 meV, while the thermal activationenergy is 10.7 meV [14]. The binding energies of excitons bound to acceptorsare slightly larger, namely 19� 4 meV for the Mg acceptor, and 34� 4 meVfor the Zn acceptor [15]. According to the Haynes' rule, well establishedin semiconductors such as silicon and gallium phosphide [16], the excitonbinding energy is a linear function of the donor binding energy. We notethat the Haynes' rule is, strictly speaking, not applicable to all semiconduc-tors. Nevertheless, a linear relationship for common intentional donors andacceptors in GaN has been empirically identi�ed, as shown in Figure 2.2.Exciton binding energies correlate well with ionisation energies for shallowdonors in GaN, and also for the substitutional Mg and Zn acceptors withbinding energies of 200 meV and 340 meV, respectively. The latter valuesare associated with ionisation energies for substitutional Mg acceptor of 200meV, and for Zn acceptor of 340 meV. Such correlation suggests that theempirical Haynes' rule [17] can be applied to GaN.

In pure materials, with low impurity densities, individual bound excitoncomplexes interact relatively weakly. Mutual interaction becomes impor-tant when the average impurity separation approaches the bound excitonradius given by

aBX =�h

(2m�EBX);

where m� is the reduced e�ective mass of the bound particles. Values ofaBX in excess than several or even tens of nm are common. In the absenceof interactions, the bound exciton lines can be spectrally very narrow. Suchsharp bound exciton lines may serve as useful indicators of strain. Theirsensitivity to local strains in the sample is often exploited to reveal the mi-croscopic stresses, and particularly their nonuniformity.

Bound excitons can recombine either directly or through other associatedrecombination channels such as the "two electron" or "two-hole" transitions[17]. The low intensity two-electron (hole) satellites re ect the recombina-tion of bound excitons in which the donor (acceptor) is left in an excitedstate. The two-electron (hole) transitions, if observable, provide a wealth

2.3. FREE TO BOUND TRANSITIONS 11

of detailed information on the donor and acceptor centres. Their spectralsignatures appear on the low energy side of the main exciton line and theysometimes coincide with the high energy tail of other (for example the donor-acceptor pair) transitions. The two-electron (hole) satellite spectra in GaNare diÆcult to be observed, possibly because the overall level of uninten-tional defects/impurities is typically too high and strain-induced broadeningprevents observation of sharp low-intensity lines. The two-electron transi-tions were identi�ed in GaN only very recently [18]. Selective excitationto the no-phonon absorption lines associated with a given defect specieshas been successfully used in other semiconductors [17, 19] to enhance the"two-electron" luminescence, and may be attempted in GaN. The presentauthors are con�dent that this research direction will be further developedonce better quality GaN material becomes available.

In addition to two-electron (hole) transitions, radiative recombination ofexcitons bound at neutral donors or acceptors competes with a highly eÆ-cient, non-radiative Auger process, in which the energy of exciton recombi-nation is transferred to a second carrier bound at the site [17]. This strongcompetition prevents the use of bound exciton transitions in any practicallight-emitting devices.

2.3 Free to bound transitions

Free to bound transitions are observed as broad spectral features, also lo-cated in close proximity of the band gap energy. The spectrum of a free-tobound transition is described by the following relationship (given here in thecase of an electron-acceptor transition) [20]:

IeA / (�h! �Eg +EA)1=2 8

p2

�2a3Am

3=2

H

�h3� exp

��h! �Eg +EA �EF

kT

�:

(2.3)Here, EA is the acceptor energy, EF is the Fermi energy, aA is the acceptorBogr radius, mH is the e�ective mass of holes, and other symbols have theirusual meanings.

The free to bound transitions are often seen emerging from the donor-acceptor pair spectra as the temperature is raised, provided that the shallowdefect ionisation energy is small enough. The free to bound transitions wereidenti�ed for example in GaN:Mg [21] at 3.21 eV, where they are associ-ated with the shallow impurity Mg. The same authors show another free tobound transition at 2.95 eV. Kaufman et al [22] identi�ed a free to boundtransition at 3.242 eV (see Fig 2.3), and they were able to preferentially ex-cite either the free to bound or the donor-acceptor pair transition by varyingthe excitation energy.


The deep defect-related band at 2.8 eV in GaN:Mg was studied in Ref.[23] and the band was attributed to a free to bound transition involving adeep donor and the valence band. The PL excitation intensity dependenceand temperature dependence of PL emission measurements were carried out.Under high excitation the band was shown to undergo a blue shift of 200meV and potential uctuations were found to be responsible. The lumi-nescence quenching is observed at high temperatures with the activationenergy of 0.3-0.4 eV. This identi�cation of the blue PL (BL) in Mg dopedGaN is however still controversial and it contradicts the results of severalother groups. The nature of BL will be discussed in detail in a separatesection.

The free to bound transitions can be used to optically determine a degree ofcompensation [20]. Such studies in GaN:Mg has been carried out by Oblohet al [24]. In their work the Mg-related photoluminescence bands have beeninvestigated as a function of Mg concentration. The hole density was foundto reach a maximum at the Mg level of 3� 1019cm�3 and then continued todecrease with increasing Mg content, suggesting self-compensation. At thesame density of Mg, the dominant radiative recombination mechanism wasfound to change, from a free-to bound to a donor-acceptor pair transition.The authors suggest that the deep donor involved in self-compensation is anearest neighbour associate of a MgGa acceptor with a nitrogen vacancy. Wewill return to this model later in the discussion of compensation mechanismin highly p-type doped GaN.

2.4 Band to band transition

Band to band transitions are commonly observed in other direct gap semi-conductors. The theoretical description based on the Fermi golden rule andassuming a parabolic density of states and a single hole band gives the fol-lowing expression for the radiative recombination rate Rsp[25]:

Rsp / (�h! �Eg)1=2 exp

��h! �Eg

kT

�: (2.4)

The peak energy (�h!p) and the half-width (�E) of the band-to-band re-combination is given by:

�h!p � Eg +1

2kT; (2.5)

�E � 1:8kT: (2.6)

The exponential energy dependence in Equation 2.4 makes it possible to de-termine the carrier temperature, by the analysis of the high energy slope ofthe emission spectra. The carrier temperature can be used to evaluate the

2.5. DONOR-ACCEPTOR PAIR SPECTRA 13

rate of energy thermalisation under high excitation conditions, important,for example, in laser operation.

Band to band transitions dominate at room temperature, and they are alsoone of the key processes thought to be responsible for gain in GaN bluelasers [26]. The identi�cation is not trivial, as the binding energy of theother prospective candidate - the FE emission - is about kT at RT (20 meV)[27{29]. Under high carrier injection conditions the competing processes ofbiexciton and excitonic molecules formation are not very eÆcient.

2.5 Donor-acceptor pair spectra

The recombination processes involving donors and acceptors compete stronglywith the bound exciton processes at high compensation ratios, and partic-ularly when the concentration of both donor and acceptor species is high.The early work by P.J. Dean [16] o�ers a comprehensive review, focussedon properties of GaP, where the donor-acceptor spectra are particularlypronounced. The donor-acceptor pair spectra are explained by Coulombinteraction of ionised donor-acceptor pairs in the �nal state, leading to thefollowing dependence of the transition energy �h! on the pair separation r:

�h! = Eg � (EA +ED) +e2

�r�EvdW : (2.7)

Here, ED is the donor binding energy. The van der Waals polarisationinteraction term can be modeled as:

EvdW =6:5e2

�r

�aD

r

�5

; (2.8)

where aD = �hp2meED

is the Bohr radius of the shallower impurity in the pair.

The intracentre distance takes only discrete values leading to a structureddonor-acceptor band. In consequence, a �ne structure of donor-acceptorpair transitions can be observed at the high energy wing of the PL band, asobserved in GaN in homoepitaxial epilayers [30]. At higher donor - acceptorseparations r, the individual spectral components merge and form a wideasymmetric band. The envelope of this unresolved band is given by [20]:

I(�h!) =

Z 1

0

4�r2ND

�0

e2�h!W (r)

ND �NA

Wnr +WDA(r)�exp

�4�NDr

3

3

!Æ [�h! � �h!(r)] dr:

(2.9)Here ND(A) is the donor (acceptor) concentration, W (r) is the overlap inte-gral between the donor and acceptor wavefunctions, WDA(r) is the donor-acceptor pair transition rate at a separation r, and Wnr is the non-radiative


recombination rate. The radiative rate for hydrogenic donor and acceptorimpurities is given by WDA(r) = WDA(0) exp(�2r=aD) and it was foundto correctly describe the close donor-acceptor pairs in GaN:Mg [31]. Therecombination rate quickly decreases with relative distance, and, therefore,distant pairs, while numerous, have very low recombination rates. Suchpairs are thus very easily saturated, and, consequently, the DA pair bandshifts to higher energies at increasing excitation levels by as much as severalmeV per decade. The blue shift of the PL is often considered as a proof ofthe donor-acceptor pair origin of the emission. This argument was used toidentify the yellow emission in wurtzite phase GaN [32] and red emission incubic phase GaN [33].

The intensity J dependence of the peak of the donor-acceptor transitionscan be described as [34]:

J / (EDA �E1)3 exp [�2ED=(EDA �E1]

ED + 2E1 � 2EDA

; (2.10)

where E1 = Eg � (EA + ED), with EA and ED. With an increasing exci-tation level, the donor-acceptor band maximum saturates at the energy of�h!1 + ED

2:

An important special case relevant to GaN is that of donor-acceptor pairsinvolving a shallow centre as well as a deep centre. Due to a localised char-acter of deep impurities, their electronic states may couple strongly to thelattice. As a result, optical transitions may involve strong phonon coopera-tion. Such transitions between a ground state of a strongly lattice-coupleddefect and another weakly coupled or uncoupled defect at a �xed separationr produce a PL spectrum with a zero phonon line and phonon sidebands.The relative strength of the zero-phonon line and the sidebands is given bythe Huang-Rhys factor S [35]. The lineshapes for increasing values of S vary,and, for strong lattice coupling, the vibrational contributions give rise to aGaussian shape of the PL band. In these conditions the zero-phonon line istoo small to be observable. The maximum of the broad band does not cor-respond to the electronic transition energy, but is related to the energy of ahigher phonon replica. The half-width of the band varies with temperatureas:

�(T ) =

�8 ln 2 (�h!ph) 2S coth

��h!ph2kT

��1=2: (2.11)

Here, �h! is the energy of the participating phonon.

The analysis of the donor-aceptor pair luminescence decay in Mg-dopedGaN was reported by Shin et al [36] and Godlewski et al [37]. The resultsof the latter studies are shown in Figure 2.4. This �gure shows the energy


dependence of the measured PL decay time for the blue and yellow PL ob-served in lightly Mg doped GaN, re ecting the donor-acceptor origin of thetwo emissions. Closer donor-acceptor pairs, contribute to the PL at the highenergy side of the Gaussian band and they show shorter PL decay times, inagreement with the outlined theory. Thus, the PL decay studies help iden-tify the donor-acceptor pair processes, through their characteristic energydependence of the PL decay time.

2.5.1 Temperature evolution of photoluminescence signatures

Band gap

Temperature evolution of spectral features in emission is often taken as astrong indicator of their origin. Central to this concept is the evolution ofenergy gap with temperature. The temperature dependence of energy gapEG is generally described by the Varshni's semi-empirical relation [38]:

�EG(T ) = EG(T )�EG(0) = ��T 2

� + T; (2.12)

where � and � are parameters. This formula provides a benchmark forthe bandgap evolution with temperature. The best experimental tech-niques to study bandgap variations with temperature include re ectanceand its derivatives - photo- and electro-re ectance [39{41]. The parameters� = 8:32�10�4 eV/K and �= 835.6 K were obtained from photo-re ectancestudies [39, 40]. There appears to be some degree of inconsistency betweenthe band gap evolution measured in GaN grown by di�erent techniques.While the Varshni formula appears to be generally applicable, the detailedtemperature studies of the bandgap reveal specimen-related variations. Thetemperature dependence of the fundamental band gap in heteroepitaxialGaN on sapphire was studied, for example, by Herr et al [42] through thePL study of excitons. They have obtained the Varshni expression with �=7.3�0:3�10�4 eV/K and � = 594�54K. Similar sample dependency was shownin the study by Manasreh and Sharma [43]. The Varshni parameters in bulkGaN obtained from the temperature dependence of the fundamental absorp-tion edge [44] were found to be � = 10:8�10�4 eV/K and �= 745 K. Thesevalues di�er considerably from those reported for epilayers grown on latticemismatched substrates, indicating a strong in uence of strain conditionson bandgap properties of GaN. The di�erences between various �lms werefurther explored by Buyanova et al [45] who revealed variations between�lms grown on SiC and those grown on sapphire, due to di�erent thermalexpansion/contraction. These di�erences are presented in Figure 2.5. De-spite these sample-dependent di�erences, the donor-acceptor pair transitionsand excitonic emissions are easily distinguished by their temperature evolu-tion, as the latter decrease in energy with increasing temperature, while thedonor-acceptor pair bands shift to higher energies.


Bound excitons

The bound exciton lines rapidly decrease in intensity with increasing tem-perature, whereas the free exciton emission is observable up to room tem-perature. This behaviour re ects the small localisation energies of boundexcitons.

The PL intensity as a function of temperature I(T ) may often be analysedusing a two-channel dissociation Arrhenius model:

I(T )

I(0)=

1

1 + c1 exp(��E1=kT ) + c2 exp(��E2=kT ); (2.13)

where c1 and c2 are the prefactors, and �E1 and �E2 are the activationenergies. The two activation energies are easily understood if we examinethe process of bound exciton creation. Excitation above the band gap cre-ates either free excitons or free carriers. The process of their localisation atneutral donors involves the localisation energy. At elevated temperatures lo-calisation at neutral donors reduces the number of available neutral donors,a process competing with thermal ionisation. Therefore the donor bindingenergy should also be involved in the process of thermal deactivation ofbound exciton emission. The temperature dependence of the PL intensityof a bound exciton complex can be used to identify the kinetics of its ther-mal dissociation and thus provides a valuable insight into the origin of thecomplex. Such analysis is, however, possible only if two activation energiesdi�er noticeably. Otherwise, both ionisation processes occur at the sametemperature range, and their separation is not possible.

Sometimes it may not be easy to distinguish a priori whether a given excitonis bound at a neutral donor or at an ionised donor. In the latter case, thedissociation energy corresponds to the break o� of a loosely bound hole. Inthese circumstances, the temperature dependence of PL emission may beanalysed using a single-channel dissociation model:

I(T )

I(0)=

1

1 + c1 exp(��E1=kT ): (2.14)

The same single-channel model is sometimes applied to the excitons boundat neutral donors, if the emission is examined only in a limited temperaturerange. While this approach may be justi�ed for individual defect-boundexcitons, the conclusions as to the nature of the recombination processesneed to be treated with caution. It is known, that in excitons bound tocertain isoelectronic traps in GaP [46] thermal release of the hole may befavoured over exciton delocalisation. Therefore if the single-channel modelis to be applied a priori, close agreement is required between the activationenergy of thermal dissociation with the exciton binding energy, obtained for


example from the wavelength separation of the observed emission line withrespect to the free exciton line. The reference [14] describes a recent studyof thermal evolution of bound exciton emission in GaN carried out alongthese lines.

Phonon replicas

The phonon replicas of free exciton transitions are associated with theexciton-photon (polariton) coupling. The relative strength of the phononreplicas is a measure of phonon scattering needed to get across the bottle-neck in the lower exciton-polariton branch to the radiative branch of thedispersion curve [47]. A linear temperature dependence of the ratio of onelongitudinal optical (1LO) phonon replica of the free exciton emission to thetwo-phonon replica (2LO) is expected in the temperature range below 100K [48] and observed in Ref. [13], supporting the classical exciton/polaritonmodel. Monemar notes the relatively strong no phonon free exciton linecompared with the 1LO and 2LO phonon replicas [13]. This e�ect points toan enhanced scattering rate of exciton polaritons into the radiative branch ofthe no-phonon A exciton. High defect density may o�er a plausible explana-tion as it assists in polariton scattering and provides the required momentumtransfer.

Investigations of phonon-assisted photoluminescence in wurtzite GaN werereported by Liu [49]. They studied the free exciton linewidth due to exciton-phonon interaction. The LO-phonon assisted satellite lines associated withbound excitons were also observed. Their study of the 2LO phonon replicasprovided information on the recombination lifetime of free excitons in GaN.

2.5.2 Photoluminescence intensity dependence on excitation

power

Excitation intensity dependence of individual spectral emission componentsmay help identify the corresponding recombination processes. Two quanti-ties may be analysed, these are energies of the spectral features and theirintegrated intensities. The excitonic energy does not vary with increasingexcitation power, but the peak energy of donor-acceptor pair transitionsdoes, as described in Equation 2.10. This di�erence can form a basis of atest to identify the nature of unknown recombination processes. The inte-grated intensity may be analysed with a varying degree of sophistication. Ina simple analysis, a power law may be applied to all near-gap emission lineswhere the intensity of the line, I and the excitation power, J are relatedthrough:

I / Jk: (2.15)


The coeÆcient k may also depend on J if the excitation intensity is variedby many orders of magnitude. This relationship is underpinned by a setof rate equations describing details of the relevant recombination processes,and the relationships between them. Typically, simplifying assumptions arenecessary.

The excitation intensity dependence may not be the most precise tool toidentify a given transition, nor to analyse the nature of the recombinationprocesses, but some general properties have, nevertheless, been identi�ed[50]. It was found that in the case of above-gap excitation the exponentk in Equation 2.15 for free and bound excitons is generally between 1 and2. A strictly linear dependence of the free exciton recombination on theexcitation level was shown by Smith et al [51]. At low excitation intensi-ties, where the e�ects of photoneutralisation are insigni�cant, the exponentk is the same for free and bound excitons. On the other hand, for free tobound and donor-acceptor pair recombinations, the exponent k is less thanunity. The di�erence in the ensuing spectra is illustrated in Figure 2.6 (a).Measurements of the emission intensity to identify the exponent k need tobe done in the wide spectral region, as sometimes the excitation-inducedchanges include large spectral shifts (Fig. 2.6 (b)).

A more detailed analysis was used by M�ullhauser et al [52]. They plot-ted the intensity and quantum eÆciency (taken as the ratio of intensity ata given temperature to the intensity at 4K) of the near band-edge lumines-cence against the excitation intensity (see Fig 2.7, where a clear deviationfrom the power-law dependence is easily noted). The data have been �ttedwith the model based on rate equations [53] and an estimate of non-radiativelifetimes was obtained. This work sets an example on how to extract quan-titative information about the nonradiative processes by using the radiativeemission data.

Excitation dependence and temperature dependence were used jointly toidentify the cathodoluminescence emission lines in cubic and hexagonal GaNgrown on GaAs (001) by MBE [54]. The peak energies in the cubic materialat 5K were: 3.263 eV (bound exciton), 3.234 eV (donor-band), 3.208 eV(acceptor-band), 3.150 eV (D-A pair). Similar photoluminescence studiesof cubic GaN on (100) GaAs by MOVPE [55] identi�ed the bound excitonemission at 3.274 eV, the donor-acceptor pair emission at 3.178 eV and twoadditional lines at 3.056 eV and at 3.088 eV, also tentatively attributedto donor-acceptor pairs, possibly with other residual acceptors. Such dif-ferences in bound exciton and donor-acceptor pair energies are commonlyfound and not fully explained at present, and it is believed that poor controlof strain and strain relaxation conditions may play a role.


Smith et al [56] have shown that at room temperature the band-to-bandtransitions dominate in their high quality undoped (n=5�1016 cm�3) wurtziteGaN grown by low pressure MOCVD. The temperature evolution in its ownright is insuÆcient as grounds for distinction between the (free) excitonicand band-to-band mechanisms, as the line is too broad. However, additionalidenti�cation is feasible by varying the excitation intensity. For band-to-band transitions the peak position of the emission line shifts towards lowerenergies with increasing excitation intensity, due to enhanced many-bodye�ects and screening of free carriers. The analysis of the exchange energy ofelectrons and holes lead to the expression for the PL peak emission energyE to be:

E = Eg(n = 0)� �I1=3exc ; (2.16)

where � is the proportionality constant [56]. The experimental data arein excellent agreement with the above formula. The excitonic transitionsdo not obey this type of relationship, so it provides a criterium for theiridenti�cation. The value of the bandgap energy at n = 0, Eg(n = 0), is de-termined as 3.429 eV. Additionally, the excitation dependence, Iexc, of thetotal PL intensity yields IPL / I�exc with �=2.32, consistently with band-to-band transitions. The full width at half maximum (FWHM) also increaseslinearly with Iexc, as expected for band-to-band transitions, since increasingIexc would increase the energy distribution of the electrons and holes andhence the linewidth. Smith et al argue that the radiative recombinationrate for band-to-band transitions should be comparable with the recombi-nation rate of excitons. They also suggest that band-to-band transitionsmay actually be more probable in less pure or less perfect crystals wherelocal �elds can lead to exciton dissociation into free carriers. The oppositeview was held by Monemar et al [13] who argued that a band-to-band tran-sition would be manifested as a new peak at about 25-30 meV higher thanthe energy of the A exciton, and this peak would gradually take over themain PL intensity at the expense of the excitonic transition with increasingexcitation level. However, in their work the PL studies as a function ofexcitation intensity were not carried out.

2.5.3 PL intensity and dopant concentration

It is diÆcult to establish the dopant concentration by measurements of thephotoluminescence intensity alone. Firstly, experimental measurements ofabsolute intensity are diÆcult and require the use of specialised techniques.Secondly, di�erences in the nature and strengths of recombination channelsmay play an important role in �lms with the same dopant concentration, butwith di�erent defect structures. The photoluminescence intensity saturatesonce the concentration of a particular type of a centre is increased to apoint where the recombination through it accounts for the generation rateof free carriers. In typical conditions such as the lifetime of 1 ns, typical of


exciton states, this concentration may be as low as 1015 cm�3. However, theratio of spectral signatures of free and bound excitons turns out to be anacceptable measure of the impurity content. A careful analysis of the ratioof the bound exciton to the free exciton emission intensity in Si yielded thefollowing relationship [57]:

IBE

IFE= Nm

I (2.17)

where IBE is the bound exciton intensity, IFE the free exciton intensity,and NI is the ionised donor concentration, m is a constant close to unity.It needs to be noted that this empirical relationship applies only to �lmswith relatively low compensation level. To the best of our knowledge similarwork in GaN has not yet been reported.

2.5.4 Lineshape

We have presented the expressions for the energy-dependent PL intensity inthe important recombination mechanisms, however they need to be treatedwith some caution. The measured emission spectrum may depart from theo-retical predictions if a�ected by the reabsorption e�ects and photon recyclinge�ects. The reabsorption is easily quanti�ed, and the measured spectrumImeas and the emitted spectrum Iem are related through [58]:

Imeas(�h!) = [1�R(�h!)] Iem(�h!)1� exp [��(�h!)d]

�(�h!)d: (2.18)

Here d is the �lm thickness, R(�h!) is the sample re ectivity and �(�h!) isthe energy - dependent absorption coeÆcient. Owing to the high bandgapabsorption coeÆcient of GaN, in excess of 1� 105cm�1, the reabsorptione�ects in typical GaN �lms in the micrometer thickness range are very pro-nounced, and many authors discuss their in uence on the �ne details of theemission spectra [59].

In principle, the free exciton emission spectrum can be obtained from its ab-sorption spectrum through the van Rosbroeck-Shockley formula 2.19. Thisformula relates the absorption coeÆcient �(�h!) to the spontaneous emissionspectrum I(�h!):

I(�h!) =8�n2(�h!)2�(�h!)

h3c2 [exp ((�h! ��EF )=kT )� 1]: (2.19)

Here �EF is the energy di�erence between the electron and hole quasi-Fermilevels, n is the refractive index. The simulation of the emission spectrumfrom the absorption spectrum is, however, possible only for highly perfectmaterials with a homogeneous PL line width and provided excitons are notlocalised [60]. If localisation e�ects are strong then the absorption or re- ectivity probes the density of free excitons, whereas the PL emission is

2.6. LIFETIME AND RECOMBINATION TIME 21

dominated by recombination of localised excitons, i.e., the PL emission isrelated to the density of localised states and its energy distribution. In suchcase there is no simple relation between absorption spectrum and the re-sulting PL emission spectrum. Fortunately, such complications can easilybe identi�ed from the comparison of the absorption/re ectivity and the PLspectra, since their spectral positions are shifted by an averaged localisationenergy (Stokes shift). Localisation of excitons, caused by alloy uctuationsor quantum well width uctuations, is a common property of excitons inquantum well structures of III-V [60] and II-VI semiconductors [61]. It isalso critical for excitons in InGaN and GaN epilayers, and will be discussedseparately.

The extrinsic broadening of exciton lines caused by crystal imperfections,strain and impurities results in a Gaussian shape of the exciton line [62, 63].The e�ect dominates in strongly localised excitons.

2.6 Lifetime and recombination time

2.6.1 Background

The photoluminescence eÆciency is an important measure of quality ofa semiconductor material. It is therefore not surprising that signi�cantamount of research is devoted to its studies, particularly through time-resolved emission measurements. The photoluminescence eÆciency is de-termined as:

� =1=�r

1=�r + 1=�nr; (2.20)

where �nr is the non-radiative lifetime and �r is the radiative lifetime. Acritical parameter in determining the PL eÆciency is the total lifetime �tot:

1

�tot=

1

�nr+

1

�r: (2.21)

In lightly doped materials in the low injection limit the radiative recombi-nation time is given by a simple rule

�r =1

BND

; (2.22)

where B is the radiative recombination coeÆcient. The value of B canbe determined using a detailed balance principle and the van Roosbroeck-Shockley formula [64]. The approach is based on computation of the sponta-neous emission spectrum from the measured absorption spectrum followedby �tting of the result to the experimental PL spectrum. If the two matchclosely, then the absolute calibration of the measured PL intensity can be


carried out. Consequently, the integral of the spontaneous emission spec-trum renormalised to the absolute value of the emission intensity gives thetotal radiative recombination rate [65]:

Rrad = Bnp: (2.23)

Using this method, Muth et al [66] calculated B to be 1:1� 10�8cm3/s andthe radiative lifetime for the electron concentration n = 1 � 1017 cm�3 tobe 0.9 ns, in contrast with GaAs where the radiative lifetime for the sameconcentration is in the order of 100 ns. The value of the radiative constantB of 4.4�10�11cm3=s at 300 K is given in Ref. [67]. The upper bound valueof B in Ref. [68] was given as 2.4�10�11cm3=s at 300K. Such analysis ofthe excitonic decay time is not valid in the case of exciton localisation, ascommonly encountered in InGaN and GaN epilayers and in their quantumwell structures. The in uence of localisation e�ects on exciton dynamics inlow dimensional structures is discussed in Ref. [69].

2.6.2 Non-radiative recombination

In addition to radiative recombination, the photoexcited carriers may re-combine non-radiatively through a variety of processes such as trapping andrecombination at defects, surface recombination, di�usion away from theexcitation spot and Auger recombination. As a result, the PL decay time isoften regarded as one of the most sensitive tests of �lm quality. Generallyspeaking, any imperfection of the crystal/�lm results in reduction of the PLdecay time of free excitons, due to the increased importance of localisationand/or non-radiative processes.

The non-radiative recombination time, �nr is determined by the non-radiativerecombination centres, these are typically mid-gap levels involved in theSchottky-Read-Hall recombination [70]. An insight into the nature of thenon-radiative recombination centres was given by Klann et al [71] who sug-gested that structural defects such as edge dislocations and stacking faultsdo not act as non-radiative centres but are electronically inert. The en-hanced non-radiative recombination in the proximity of dislocations can beexplained by their decoration with impurities. The role of dislocations inrecombination processes in InGaN and GaN will be discussed later.

At low injection conditions, when the photoexcited e-h density is smallerthan the doping density, �tot is dominated by recombination of minoritycarriers. These conditions are often met in experiments at higher tempera-tures. In such circumstances a certain simpli�ed analysis may be applicable,as shown by Hangleiter et al [68]. They have measured the temperaturedependence of the bandedge PL intensity I(T ), assumed the quantum eÆ-ciency �(0) at low temperatures as unity and taken �(T ) as I(T )=I(0). If


the measured decay time is approximately equal to the non-radiative time,then the radiative time is approximately given by:

�rad = �nr

�1

�� 1

�: (2.24)

The radiative time thus obtained can be plotted as a function of tem-perature and compared with models. The conventional theory [72] pre-dicts a T 3=2 dependence for free excitons, however the experimental data ofHangleiter et al show some deviations at higher temperatures (see Figure2.8). These deviations were explained by thermal dissociation of excitonsinto free carriers. Since electrons and holes forming an exciton are stronglylocalised, free excitons are expected to have a much smaller radiative life-time than free carriers at a given carrier density. The quantitative theory ispresented in Ref [73]. The �t yields the free exciton dissociation energy of27 meV.

The signi�cance of non-radiative recombination can, to some extent, becontrolled by the excitation intensity as it may be possible to (partially orfully) saturate the non-radiative channels, or to occupy the localised states,if their density is low. It needs to be noted that the experimentally observedPL decay time �PL may also be a�ected by the e�ects of sample geometry,and particularly, by surface recombination. In the case of a parallel slab ofa thickness d, the observed decay time is given by:

1

�PL=

1

�r+

1

�nr+2S

d: (2.25)

Here, S is the surface/interface recombination velocity. This formula isapplicable if the di�usion constant De is much larger than the product ofSd. At low surface/interface recombination velocity S, the measured �PLapproaches the bulk minority carrier lifetime �tot. It is known that photonrecycling can, in general, change the carrier lifetime �tot to give:

1

�tot=

1

�nr+

1

�(d)�r: (2.26)

where �(d) is the recycling factor [74].

2.6.3 Examples of applications

The radiative and non-radiative relaxation of excitons in GaN was exam-ined in Ref. [75]. The excitonic quantum eÆciency was studied as a functionof the specimen parameters such as the sample and bu�er thickness, bu�ermaterial, and residual oxygen content. Predictably, thicker and less contam-inated samples gave improved quantum eÆciencies, and homoepitaxial GaN[6] gave better values than GaN on an AlN bu�er. Interestingly, in GaN


epilayers the quantum eÆciencies were generally in the 20 % range, whereasbulk GaN shows 25 % quantum eÆciency for the free A exciton and 50 %for the neutral donor bound exciton complex. The latter result indicates arather reduced role of Auger-type non-radiative recombination in excitonsbound at neutral donor centres. Similar conclusions were reached by Pau et

al [76] who found that the free exciton decay dynamics at the front surface ofthe �lm and at the interface side were signi�cantly di�erent. The interfacedecay time was much shorter, in concert with an increased density of thenon-radiative centres.

The time-resolved photoluminescence measurements of exciton recombina-tion at low temperatures [6, 77] show a broad perspective of the excitonbehaviour and illustrate the methods available in time-resolved emissionstudies. The observed emission channels consist of free excitons and donorand acceptor bound excitons. At low temperatures, bound excitons arefound to dominate, but are subject to quenching at 50 K and above. Athigher temperatures free excitons are the most pronounced feature. Gen-erally, non-radiative processes dominate in epitaxial layers, and the decaytimes of about 100 ps are typically observed [6, 77]. In thick bulk samples,the free exciton lifetime of about 200 ps is observed, close to the radiative de-cay time of free excitons [77]. The donor and acceptor bound excitons decaymore slowly, with the decay constants of 250 ps and 1200 ps, respectively.Bergman [77] and Godlewski et al [6] observed that at increasing tempera-tures the donor bound exciton emission is quenched, but at the same timethe free exciton recombination increases, giving an almost constant total PLintensity. This e�ect illustrates a strong interaction between free excitonsand donor bound excitons through an important free exciton recombinationmechanism of capture to a donor (or acceptor). An interesting e�ect is ob-served with increasing excitation intensity, where an increase in the free ex-citon recombination time is observed [77]. This phenomenon is interpretedas due to partial saturation of the non-radiative recombination channels,most likely dislocations. Further increase of the excitation intensity make itpossible to observe the actual radiative recombination time. Saturation oftraps at dislocations with increasing number of injected carriers has recentlybeen invoked to explain high performance of GaN optoelectronic devices de-spite the abundance of dislocations [78]. We will return to this problem later.

The temperature dependence of the free exciton lifetime re ects the captureof free excitons at deep defects, donors and acceptors. This temperaturedependence is also a�ected by exciton localisation, due to poor crystallinequality of GaN epilayers. At low density of structural imperfections anddefects, only a weak temperature evolution is observed. If the free exci-ton decay time is purely radiative, then it should increase with temperaturedue to thermal redistribution of excitons, caused by scattering with acoustic


phonons. This e�ect reduces the relative number of excitons with small mo-mentum, the only excitons involved in radiative recombination. Bergman[77] found that the free exciton decay time increases only up to 20 K and, athigher temperatures, it starts to decrease due to the onset of non-radiativeprocesses.

The donor bound exciton and the free exciton decay curves have a dif-ferent character, free excitons are characterised by a rapid rise followed byan exponential decay, while donor bound excitons have a longer rise time,following the free exciton decay. Bergman [77] concluded that this indicatesthe population increase of donor bound excitons formed by the capture offree excitons. This result indicates that impurities should be avoided in ac-tive parts of the opto-electronics devices, since donor and acceptor boundexcitonic recombination processes compete with free excitonic transitions.

The value of 200 ps for the radiative time of free excitons in GaN is muchshorter than in GaAs (3.3 ns at 2K [79]). An increase in the recombinationprobability in GaN compared to GaAs is related primarily to the higherbandgap photon energy. The free exciton decay time � depends on thephoton energy �h!, the exciton absorption coeÆcient �ex and the refractiveindex n as:

� / 1

(�h!)2 n2�ex: (2.27)

This expression explains the factor of 1/20 compared to GaAs.

The recent value of 200 ps for the radiative exciton lifetime in GaN is pos-sibly one of the longest reported (other authors give the values of 35 ps forFE and 55 ps for BE or even about 5 ps [80]), but still it falls well shortof the actual theoretical prediction for the radiative lifetime. These werepresented in Ref. [81]. The expression for the radiative lifetime is [82, 83]:

�r = 2��0m0c3=ne2!2f; (2.28)

where f is the oscillator strength, and other symbols have their usual mean-ing. The oscillator strength for the free excitons, calculated within thee�ective mass approximation, is given by:

f =Ep

��h!� (V=a3x); (2.29)

where Ep is the Kane matrix element, V is the volume of the unit cell andaX is the e�ective Bohr radius of the free exciton. The e�ective Bohr radiusof the free exciton in GaN was estimated by aX = 0:528(m0�=��0) �A, where� = n2 � 5:8�0 and � is the reduced e�ective mass of � 0:16m0. With the


value of aX = 20�A thus obtained and Ep � 18 eV, the oscillator strengthf is 0.012 and �r � 800=f (ps). For bound excitons an estimate only isgiven, and, assuming that the oscillator strength is in the range of unity,the radiative lifetime of approximately 1 ns is obtained. We note here thatthese theoretical predictions show an opposite trend to that observed in [77],where the bound exciton lifetime is longer than that of free excitons. Thisis a clear indication of non-radiative relaxation processes for free excitonswhich, at low temperature, are trapped at donor/acceptor centres, formingbound excitons. The capture of excitons, in addition to trapping of carriersby non-radiative centres (defects and impurities) thus plays a major role inthe population decay of free excitons examined in [81].

The dynamics of fundamental optical transitions probed by picosecond time-resolved photoluminescence was also studied by other authors, for exampleby Jiang and Lin [84] and Mair et al [85]. The latter work is focussed onthe properties of ionised donor-bound excitons in GaN doped with both Mgand Si at concentrations 5�1018cm�3 and 1.5 �1017cm�3, respectively. Theionised donor-bound exciton is identi�ed approximately 11.5 meV below theneutral acceptor bound exciton and 20.5 meV below the free exciton peak.The free excitons decay rapidly, within 20 ps, as a result of rapid captureby acceptors and ionised donors. The ionised donor bound excitons decaymuch more slowly than the acceptor bound exciton (with the decay time of180 ps), suggesting that the state is stable at low temperatures. Reductionof the acceptor bound exciton PL decay time by a competing Auger-typetransition provides a possible explanation. In the process, the energy of therecombining e-h pair is transferred to a second hole bound at the same cen-tre. The hole is then excited into a valence band state. Such process leadsto ionisation of acceptors while the exciton energy is dissipated by phononthermalisation.

The temperature dependence of radiative lifetime in GaN was also examinedby Brandt et al [86]. They carried out the lifetime analysis in conditionswhere di�erent recombination processes (band-to-band, free exciton, boundexciton) could not be spectrally resolved. In such circumstances, the mea-sured radiative lifetime is a composite of individual lifetimes. The observeddecays showed a bi-exponential behaviour, with the decay times in the or-der of 250 ps. Such bi-exponential decays are typical of capture processesin multilevel systems, and require a nonstandard analysis. Brandt et al

have taken the radiative decay rate as equal to the peak intensity of thetransient PL signal divided by the incident uence. This approach is valid,provided the exciting pulse is much shorter than any recombination pro-cesses in the sample. To normalise the radiative rate at 0K, the value of250 ps was used as calculated using the theory of Rashba [87]. The rateequations described the formation and dissociation of free excitons, capture


and emission of free excitons by neutral donors and capture and emissionof electrons by charged and neutral donors. As all capture coeÆcients areunknown, the authors assumed that capture is much faster than recombi-nation; under these conditions the population in each level decays with acommon time constant. They also used the principle of detailed balanceto obtain analytical expressions for the common radiative decay rate eff .Importantly, these expressions make it possible to quantify the contributionof each of the recombination channels. Below 20K the bound excitons dom-inate the recombination, and between 20 K and 50 K the bound excitonshave largely dissociated and free excitons become dominant. The free car-riers become important at 100 K, but even at room temperature the freeexcitons contribute to the radiative rate. The free excitons spectrally dom-inate in all samples except in the highly doped case, where high electronbackground reduces the free exciton decay rate. Free to bound (donor-hole)transitions are insigni�cant in all �lms except in the highly doped, wherethey contribute between 100 K and 300 K. The temperature dependence ofthe radiative lifetime and the result of the �t to the analytical formula isshown in Figure 2.9.

2.6.4 Recombination rates and excitation dependence of emis-

sion intensity

The importance of various recombination mechanisms can be identi�ed throughthe calculations of recombination rates which have appeared in recent liter-ature. One of the examples is described in the work by Griesbacher et al[88] who discussed competition between the edge and yellow luminescence inGaN. The principal claim in this work was that the yellow band emission isthe principal recombination channel competing with the bandgap emission.This is a rather common assumption, since yellow emission in GaN is con-sidered parasitic, however, surprisingly, it has not yet been experimentallyveri�ed. The rate equation model introduced by Griesbacher et al took intoaccount the electron/hole populations in the bands and on shallow donorstates, and the population of deep stats involved in the yellow PL. Contraryto the accepted view, the authors assumed that the transition takes placefrom a band to a deep level. This assumption was supported by the absenceof saturation at higher intensities; we will show further that such characterof the yellow PL is observed only in bulk GaN samples with metallic n-typeconductivity. The rate equations gave the power law dependence of the PLintensities on the generation rate:

I / Gn; (2.30)

where n can assume the values of 0.5, 1 or 1.5, depending on the dopinglevel and excitation conditions. It was found experimentally that the band-to-band emission increases linearly with the excitation level over the entire


range of excitation intensities. The yellow emission follows a linear depen-dence at low intensities and changes to a square root dependence at highintensities. Such behaviour is consistent with the proposed rate equations.Similar model was put forward by Banas et al [89]. Further works [90, 91]revealed that the observed yellow and bandgap emissions are coming fromdi�erent regions of the �lm; the bandgap emission is reabsorbed and comesfrom the top layer of the �lm (within a fraction of a �m), while the yellowemission is particularly strong at the interface. These e�ects are ignored bythe rate equation model [88].

2.6.5 Photoluminescence excitation spectroscopy

The photoluminescence excitation spectroscopy yields information about theintrinsic excitonic strucure, also available through re ectivity and absorptionmeasurements. It provides information on the relaxation dynamics towardsthe impurity-related photoluminescence lines. If the energy transfer pro-cesses are eÆcient, then, for example, excitation of free excitons leads tobound excitonic or other impurity-related PL emissions. Such observationis then considered a direct proof of the energy transfer. In the case of GaN,such transfer was observed from A excitons to the centres active in the yel-low emission, but only at elevated temperature [92], which complicates thediscussion of the role of the yellow emission as a parasitic transition in GaN�lms.

The PL excitation spectra give a direct estimate of the localisation energyin a given material. A typical value of the localisation energy in commonsemiconducting materials is about few meV [61]. It was thus highly unex-pected that the values of more than 100 meV were reported in structureswith InGaN quantum wells. The origin of such large Stokes shifts and theaccompanying e�ects, such as the temperature-induced PL blue shift andthe red shift of time resolved PL with time is still disputed and was discussedby several authors (see for example Refs [41, 93{103]). It is now understoodthat the e�ect comes from both piezoelectric �elds in the structure and verystrong uctuations of the In fraction in InGaN quantum wells caused by thephase separation e�ects. This issue will be discussed separately.

2.7 Strain e�ects

A particular recombination process in a semiconductor is typically expectedto give rise to a sample-independent emission line (band) at a certain sample-independent photon energy. In GaN �lms grown on lattice mismatched sub-strates this is no longer the case. Di�erences in the lattice constants andin thermal expansion coeÆcients induce strain in the �lm. The associatedhydrostatic strain component modi�es the band gap energy compared to

2.7. STRAIN EFFECTS 29

bulk GaN, and, consequently, the position of all emission lines associatedwith the band edges. Variations of the bandgap as high as 25 meV canoccur. The in uence of strain on the A, B and C excitonic transitions inGaN was systematically examined by Bigenwald et al [104]. The strain inthe samples can be modi�ed by variations in growth conditions, leading toa substantial scatter of the reported free and bound exciton energies. As aresult it is often impossible to judge the identity of a recombination processfrom the energy of the spectral feature alone and reliable assignments arepossible only through additional studies. This explains a large number ofworks devoted to general photoluminescence studies of bandgap emission,for example Ref. [105]. In this work, growth of undoped and Si-doped �lmswas carried out by magnetron sputtering on (0001) sapphire. Donor andacceptor bound excitons were observed at low Si levels at 3.488 eV and at3.456 eV, respectively. Two donor-acceptor and band-acceptor transitionswere observed at 3.364, 3.368, 3.375 and 3.383 eV and explained by twoacceptor ionisation energies of 120 meV and 135 meV, while a donor ionisa-tion energy of 14 and 18 meV was obtained. The temperature dependenceof the yellow band yielded an activation energy of 11 meV, consistent withthe shallow donor energy. Other works focussed on identi�cation and classi-�cation include Ref. [106] and numerous others. The benchmark values forvarious emission energies are available from studies of homoepitaxial nomi-nally strain-free GaN [107]. The values are: 3.483 eV for the free exciton B,free exciton A - 3.4785 eV, donor bound exciton - 3.4718 eV, donor boundexciton (second donor) - 3.4709 eV, acceptor bound exciton 3.4663 eV. InRef. [107] the identity of donors and acceptors remains undetermined. It isimportant to note that homoepitaxial �lms can also be partly strained de-pending on the contamination level of the �lm and substrate or due to thefact that Ga- and N-side grown �lms exhibit di�erent properties. Moreover,the GaN bulk crystals grown at high pressures have a relatively high densityof dislocations, in the order of 104 to 105cm�2 [108].

A valuable study performed on �lms grown with controlled in uence of strainwas reported by Lee et al [109]. These authors made use of the fact thatdoping (with Si) is accompanied by a systematic change in strain conditionsas measured by X-ray di�raction. The residual strain �c=c0 varied between1.1�10�3 to almost zero. This change led to variation of the in-plane stressestimated from the simple expression based on the elasticity theory [110]:

�k = [�c=c0]BM=�; (2.31)

where c0 is the strain-free lattice constant of the bulk GaN, �c is the changein the lattice constant, BM is the bulk modulus, and � is the Poisson ratio.The bound exciton peak energy was found to vary approximately linearlywith the compressive in-plane stress at a rate of 42 meV/GPa (see Figure


2.10). The bound exciton in undoped layers was already shifted with re-spect to its bulk value by 17 meV, due to large di�erences of the thermalexpansion coeÆcients of sapphire and GaN. The overall shifts of about 20meV have been reported.

Advances in understanding of lattice-mismatched �lm growth have iden-ti�ed a number of other growth parameters that a�ect strain in the �lms,and, consequently, the excitonic energies. It was found, for example thatGaN �lms grown on (0001) sapphire but using two di�erent bu�ers, GaNand AlN, are subjected to di�erent strain, and �lms deposited on AlN aremore strained [111]. Variations of the V/III ratio in a MOCVD growth pro-cess have a pronounced e�ect; if this ratio decreases, the exciton featuresand the bandgap can blue shift by as much as 20 meV [111]. Finally, GaNlayer thickness is an important factor, and the thicker is the layer the smallerits residual strain. Some factors are still not well understood, for examplerecrystallization of the bu�er prior to growth a�ects the strain as well [111].In addition to shifts of peak energies, other e�ects, such as strain-inducedvariations of the oscillator strength of the B and C exciton have also beenreported [112].

2.7.STRAINEFFECTS

31

hvalence band

conduction bande

NR

donor

NR

donor free to bound

donor-acceptor pair

acceptor free to bound

acceptor bound exciton

acceptor

Figu

re2.1:

Basic

recombination

processes

induced

byshallow

donor

and

acceptor

species

inasem

iconductor.


5 10 15 20 25 30 350

50

100

150

200

250

300

350

Zn

Mg

OSi

acceptor bound excitons

donor bound excitons

Bin

ding

ene

rgy

(meV

)

Localisation energy (meV)

Figure 2.2: Localisation energy as a function of binding energy for acceptorand donor bound excitons. After Ref. [114].


2.0 2.5 3.0 3.5

0.0

0.2

0.4

0.6

0.8

1.0

GaN:Mg[Mg]=

1.2x1019cm-3

RT

Φ/6 Φ3.

405

XF

Mg0,e3.242

D-A2.83

PL

inte

nsity

(ar

b.u.

)

Photon energy (eV)

Figure 2.3: Photoluminescence spectra of a GaN:Mg sample recorded withtwo di�erent excitation intensities and normalised to the same peak intensity.After Ref [22].


0 5 10 15 201xe

0

1xe1

1xe2

1xe3

1xe4

1xe5

1xe6

1xe7

1xe8

1xe9

ln P

L In

ten.

(ar

b. u

nits

)

GaN:Mg heavily doped

Time (µsec)

Figure 2.4: Energy dependence of PL decay time measured of the blueemission in magnesium doped bulk GaN crystals. The PL decay curveswere taken at maximum of blue emission band (top curve), at two positionsalong the low energy wing of the PL (second and third curve) and at thespectral position of the yellow PL (bottom curve). After Ref. [37].


0 50 100 150 200 250 300 350

3.42

3.43

3.44

3.45

3.46

3.47

3.48

3.49

3.50

3.51

3.52

3.53

E1(GaN/SiC)

Ea(GaN bulk)

Ea(GaN/Al

2O

3)

Eb(GaN/Al2O3)E2(GaN/SiC)

Ec(GaN/Al2O3

Ene

rgy

(eV

)

Temperature(K)

Figure 2.5: Temperature dependent energies of intrinsic excitonic transitionsdetermined by PL spectroscopy in GaN/SiC epilayers and bulk GaN. Forcomparison data from Ref. [113] obtained in a GaN/sapphire heterostruc-ture using re ectance measurements are also shown.


2.6 2.8 3.0 3.2 3.4 3.6

1 W/cm2

0.1 W/cm2

0.01 W/cm2

0.001 W/cm2

(a)

Inte

nsity

(ar

b.u.

)

Photon energy (eV)

2.6 2.8 3.0 3.2 3.4 3.6

(b)

10 W/cm2

1 W/cm2

0.1 W/cm2

0.01 W/cm2

Inte

nsity

(ar

b.u.

)

Photon energy (eV)

Figure 2.6: Photoluminescence spectra at 15 K for nominally undoped GaN(a) and highly doped GaN:Mg (b) with various excitation densities. AfterRef. [115].


-0.5 0.0 0.5 1.0 1.5 2.0 2.5

-1

0

1

2

3

4

5

6

log(

inte

nsity

)(ar

b.u.

)

log(excitation intensity) (W/cm2)

-0.5 0.0 0.5 1.0 1.5 2.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

log(

quan

tum

eff

icie

ncy)

log(excitation density) (W/cm2)

Figure 2.7: Intensity (top) and quantum eÆciency (bottom) of the near-band edge luminescence against excitation density (symbols) compared tomodel calculations. Squares - hexagonal GaN, circles: cubic GaN. After Ref.[52].


1

2

3

4

5

T3/2

27 meVfree excitondissociationradiative lifetime

GaN/Al2O

3

4002001005020

log

(rad

iativ

e lif

etim

e) (

ps)

log(temperature) (K)

Figure 2.8: Temperature dependence of the radiative lifetime. The dashedline indicates the T 3=2 dependence expected for free excitons or free carriersin a direct gap semiconductor. The full line is the result of theory presentedin Ref [68]. After Ref [68].


0.5 1.0 1.5 2.0 2.5

-0.5

0.0

0.5

1.0

1.5

2.0

log(

radi

ativ

e lif

etim

e) (

ns)

log(temperature) (K)

Figure 2.9: Measured (symbols) and calculated (lines) radiative lifetimeversus temperature for four GaN samples. After Ref. [86].


-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.73.46

3.47

3.48

3.49

gradient=42 meV/GPa

Bou

nd e

xcito

n pe

ak e

nerg

y (e

V)

Compressive in-plane stress

Figure 2.10: Bound exciton peak energies for undoped (I2 line) and Si-dopedGaN �lms as a function of the compressive in-plane stress. The triangledenotes the value for a fully relaxed sample. After Ref. [109].

Part 3

Common deep emission

bands in GaN

In addition to the edge emission comprising of various excitonic and othertransitions, GaN �lms usually show deep emission bands. The most com-monly studied deep emissions include the yellow PL band (YL), recognisedin very early studies in the sixties. The precise nature of this band has notbeen clearly identi�ed yet. Another deep emission of interest, blue PL (BL)is observed in heavily acceptor doped GaN samples. Below we discuss thenature of these two PL emissions of GaN, emphasising a close relationshipbetween material properties, such as growth and doping conditions, and thenature and strength of these two PL recombination transitions.

3.1 Yellow emission of GaN

Under photoexcitation GaN often emits a broad yellow luminescence bandcentred near 2.2 eV. The YL band appears in GaN grown by various tech-niques, under dissimilar growth conditions and on di�erent substrates. Sincethe YL is commonly found in GaN samples regardless of their growth tech-nique, it is widely regarded that intrinsic defects such as vacancies, inter-stitials or antisites may participate in its formation. The contribution ofinadvertently introduced chemical species, such as C, O and H can not beeasily ruled out as these contaminants are found in many GaN �lms. A vari-ety of technological procedures was found to a�ect the YL band, for exampleion implantation signi�cantly increases its intensity [116]. The YL band inwurtzite GaN is particularly pronounced in poor quality layers [117], andit is also observed in doped �lms, where it seems to be correlated with thedoping level.

41

42 PART 3. COMMON DEEP EMISSION BANDS IN GAN

3.1.1 Models of the yellow emission process

The microscopic models of the yellow emission band in wurtzite GaN re-main the subject of a continuing debate. All models assume that there isone yellow emission common in all types of GaN samples studied. We willlater show arguments why this may not always be the case, as many ex-perimental results indicate that there are several overlapping PL emissionbands, occurring in the YL spectral region.

An important early work by Ogino and Aoki [32] was based on lumines-cence studies, and attributed the yellow band to transitions between shal-low donors and deep acceptors strongly coupled to the lattice. A schematicdiagram of energy levels in relation to con�gurational coordinates is givenin Figure 3.1. The Ogino and Aoki model assumes radiative recombinationof an electron from a shallow donor (with binding energy of about 25 meV)with a hole on a deep acceptor located 860 meV above the valence band [32].This model was further supported by PL studies under hydrostatic pressure[118] where the YL band was observed to shift to higher energies with in-creasing pressure. This shift follows the pressure-induced movement of theband edges and it indicates that a shallow hydrogenic state takes part in theYL recombination. Such observation is consistent with the Ogini and Aokimodel, but also with the free (electron)-to-bound (hole on deep acceptor)or deep donor-shallow (hydrogenic) acceptor origin of the YL. Thus preciseidenti�cation of a detailed microscopic mechanism exclusively through highpressure studies is not feasible. A similar pressure-induced shift was ob-served in the YL measurements in bulk heavily n-type samples and in GaNepilayers.

An alternative model presented in the work of Glaser et al. [119] wasbased on the results of optically detected magnetic resonance (ODMR) mea-surements. According to this work, the principal transition responsible forthe yellow emission takes place from a deep donor to a shallow acceptor.The Glaser model [120] implies a two-step process: a non-radiative electrontransfer from a shallow donor to a deep double donor followed by radiativetransfer from the deep donor to a shallow acceptor. The Glaser model issupported by results of ODMR investigations of Mason et al [121]. BothGlaser et al and Mason et al reported that a deep donor signal was observedin their ODMR studies. This signal appeared as an enhancement of theYL intensity at the magnetic resonance and interpreted as a proof of thedonor-acceptor pair origin of the YL. Thus it was concluded that the YLdonor-acceptor pair process involves the deep donor - shallow acceptor pairrecombination.

Other models of the yellow emission have also been proposed. A most

3.1. YELLOW EMISSION OF GAN 43

popular approach assumes broadening of the participating defect levels andformation of large potential uctuations in doped samples. For example,Banas et al. [89] proposed that the YL arises from an ensemble of midgapstates and the relevant transition is from these states to the valence band.Their photoluminescence excitation shows a strong peak at 3.36 eV suggest-ing that a donor state takes part as an intermediate step in the relaxationprocess. The excitation power dependence of the YL is found to be propor-tional to the square root of power, a similar dependence is predicted by therate equations in the midgap state model. A prominent role of potential uc-tuations in heavily doped samples was also reported for Si-doped GaN [122].

The recent ODMR studies of Godlewski et al [123] and Bayerl et al [124]in Mg doped bulk GaN samples indicate another possible mechanism of theYL emission, which explains its behaviour in heavily oxygen-contaminatedsamples codoped with acceptors. In Figure 3.2 we show the ODMR signalsobserved in heavily Mg doped bulk GaN detected in the spectral region ofthe YL. An anisotropic ODMR spectrum is composed of a group of reso-nance lines around g = 2 and another group at about g = 4. Such ODMRspectra were previously observed for excitons bound at neutral complex cen-tres and explained by the spin triplet resonance [125]. We thus propose thatthe new ODMR spectrum observed by us has a similar origin. If so, theODMR investigations indicate a contribution of a new recombination chan-nel, namely recombination of an electron and hole at a closely associateddonor-acceptor pair forming a neutral complex centre. A detailed analysisof the angular dependence of the spectrum could not be performed, dueto a large width of the observed resonance. We could not thus identifythe microscopic model of the complex active in the YL. However, recentcalculations suggest a possible explanation of the observed triplet ODMRspectrum. Recently, the Mg-O complexes were found theoretically to havea fairly low formation energy [126]. The Mg-O complex consists of a singledonor, which compensates a single acceptor, thus it is a close analogue of adonor-acceptor pair and a prime candidate for the neutral complex centreobserved in the ODMR experiments. If this hypothesis is con�rmed, theintroduction of Mg into the crystals may not only compensate the chargeon oxygen donors, but could also deactivate oxygen centres acting as singledonors, if found in close proximity.

The above analysis of the ODMR data leads to an alternative interpretationof the YL in Mg doped samples. The model is based on high probability of�nding close donor-acceptor pairs. In such pairs, due to exchange interac-tion of an electron bound at a shallow, oxygen-related donor with a hole atan acceptor the PL can be no longer described in terms of donor-acceptorpair transitions and the bound exciton model should be introduced [125]. Atthis stage the identi�cation is tentative and it needs to be further supported


by calculations of energy states of the Mg-O complex.

Currently, most of experimental evidence con�rms the original model byOgino and Aoki [32], at least in GaN samples which are not heavily doped.In such samples only minor modi�cations of the model are being proposed.For example, the time-resolved PL and ODMR measurements [127] sug-gested a double donor rather than a double acceptor, as the centre partic-ipating in the YL. The Ogino and Aoki model of the YL is also supportedby photocapacitance studies [128], which show a trap at 0.94 eV above thevalence band, detected only after light excitation at above 2.5 eV. The pho-tocapacitance signal correlates well with the YL intensity pointing to thistrap as a recombination path for the YL. Below we list further properties ofthe YL emission as observed in various experiments.

3.1.2 Empirical features of the yellow emission band

a) Temperature evolution

Various authors report di�erent evolution of the YL with temperature Ac-cording to Seitz et al. [129] the yellow band increases in intensity between30 and 100 K and then it starts to decrease. This feature is not found in allsamples, in some �lms the YL stays relatively constant and then it thermallyquenches at above 120 K. The time-resolved spectroscopy at varying tem-peratures enabled these authors to distinguish a second band overlappingwith the YL with the maximum at 2.35 eV but characterised by a muchslower decay time. This is another indication of a more complex nature ofthe YL.

A more involved mechanism of the YL is also suggested by the PL decaystudies. The average lifetime of the YL measured as a function of tem-perature shows two time constants, a dominant decay of 0.2 ms is almosttemperature independent, while the second component with a value of 3ms at 10 K varies with temperature following an exponential law with theactivation energy of 13.7 meV. The same activation energy can be used tomodel the intensity variations. Such property of the PL decay is easy toaccount for if we assume that two recombination processes contribute to theYL. The temperature independent and fast component can be attributedto free-to-bound recombination, whereas the slow component with a longerdecay time and with the activation energy of about 14 meV, to a shallowdonor-deep acceptor pair recombination. At high temperatures these twoPL recombination processes should be deactivated by thermal ionisation ofa deep acceptor. According to Ogino and Aoki [32] the YL emission intensity


decreases at high temperatures and is well described by the expression

I(T ) =I(0)

1 + C exp �E�

kT

: (3.1)

Here C is a constant and E� is the activation energy of 860 � 40 meV [32].The observed activation energy was consequently related to the ionisationenergy of a deep acceptor and the model of shallow donor-deep acceptor wasproposed. Considering, the proposed shallow donor-deep acceptor model ofthe donor-aceptor pair transition, the YL emission should also decrease whenshallow donors are ionised. The energy of 13.7 meV reported by Seitz et al[129] can indeed be explained by shallow donor ionisation. Such deactiva-tion process was however not observed by Ogino and Aoki, we believe thatthis may be due to a strong contribution of free-to-bound transition to theYL in their �lms.

b) YL halfwidth

The YL can be approximately described by a Gaussian line shape, andthe PL halfwidth is typically in the order of 0.4-0.5 eV. The PL halfwidthvaries with temperature according to the equation:

Wem(T ) =Wem(0)

scoth

�h!e2kT

: (3.2)

Here �h!e is the energy of the e�ective vibrational mode of the excited state(� 40 meV). Such temperature dependence is only expected for the donor-acceptor pair mechanism of the YL, thus it provides a strong argument infavour of such origin. However, the two models of shallow donor-deep accep-tor and deep donor-shallow acceptor pair recombination can not be distin-guished in these measurements. A similar PL halfwidth may be observed forfree electrons localised by potential uctuations near the conduction bandedges to a deep acceptor strongly coupled to the lattice.

c) Excitation intensity dependence

The yellow band shifts to lower energies with increasing excitation inten-sity, by about 10 meV as the excitation level is decreased by a factor often. This result supports the donor - acceptor pair origin of the YL. Withincreasing excitation density, the distant donor-acceptor pairs are saturatedand their relative contribution to the PL decreases. This e�ect leads to ane�ective spectral shift of the YL towards the recombination of close pairs.

The intensity dependence of the YL in a wide range of excitation pow-ers with the focus on competition between the YL and the bound excitons


was examined by Grieshaber et al. [130]. They formulated a detailed rateequation model including the conduction and valence states, deep states in-volved in the YL and shallow donor states. The YL in their �lms is found tofollow a linear power dependence at low excitation intensities, changes to asquare root dependence at higher excitation densities and does not saturate.Surprisingly Grieshaber et al. [130] did not observe any change in the widthof the YL for excitation intensities up to 50 W/cm2.

d) Photoluminescence excitation spectra

The photoluminescence excitation spectrum of the yellow band reportedby Ogino et al. [32] is dominated by the bandedge peak, where, at low tem-peratures, the three main excitonic transitions, A, B, and C can be resolved.There is also a low energy tail extending down to about 3.4 eV at 4.2 K.In carbon-doped samples with a strong YL, a characteristic excitation bandbelow the bandgap can be observed with the maximum at about 3.19 eV andthe width of 0.40 eV. Comparison of the PL and PL excitation bands yieldsa zero-phonon transition energy of 2.64 � 0.05 eV. A similar PL excitationspectrum taken at 1.8 K is reported by Hofmann et al. [127]. In additionto a structured edge emission where the three free excitonic transitions A,B and C, as well as an acceptor and donor bound exciton peaks can be ob-served, a characteristic band extending to 2.4 eV and with a maximum near2.8-3.0 eV is seen. The most detailed PL excitation studies reported so farwere carried out by Colton et al [131]. Using selective PL excitation theywere able to resolve the contributions of at least two PL transitions to theYL emission. These authors conclude that with their bandedge excitationthe excited YL is dominated by recombination of distant donor-acceptorpairs. However, a new type of YL emission can be selectively excited. Thisnew PL shows a �ne structure and is attributed to the recombination ofelectron-hole pairs at closely associated donor-acceptor pairs. Thus, the PLexcitation studies con�rm our results of the ODMR investigations, in whicha triplet resonance was observed and attributed to the recombination of ex-citon bound at closely associated donor-acceptor pairs.

e) Time-resolved spectroscopy

The time-resolved studies of YL in GaN epilayers formally agree with thedonor-acceptor pair recombination model of this emission, since the resultscan be analysed using the model of Thomas and Hop�eld [132]. Recently,Hofmann et al. [127] showed that the photoluminescence decay of the YLmatches closely that expected for pair transitions and that a shallow donoris implicated. However they also underline the apparent lack of Coulom-bic interaction between the two centres active in the recombination process.The authors failed to observe any shift in energy between the YL observed


at short and long time delays and at di�erent time windows. This led themto conclude that the YL mechanism involves a shallow donor-deep donorrecombination. Similarly, Seitz et al. [129] did not observe any shift intheir time-resolved spectra. The anticipated shift can be calculated usingthe shallow donor concentration and the value between 5 meV and 10 meVcan be estimated for samples used in Ref. [127]. We emphasise here thatin our own measurements on cubic GaN [33] a shift of similar magnitudewas, in fact, observed with shorter delay and gate times (see Figure 3.3).We believe that inadequate (too long) time delays and time windows wereresponsible for the negative result in Refs [127, 129].

In n-type GaN our PL kinetics studies indicate that the free-to-bound re-combination process, which we attribute to recombination of delocalisedelectron with holes at deep acceptors, increasingly contributes to the YLemission. The relevant PL decay curves taken on bulk GaN samples areshown in Figure 3.4. In the nominally undoped highly n-type bulk GaNan energy-independent decay of YL is observed with the PL decay timein the ns range, which we explained by degenerate n-type conductivity ofuncompensated bulk crystals [123]. We thus conclude that in the sampleswith shallow donor concentration, above the Mott transition limit, the YLshows the characteristics of the free-to-bound transition and thus di�erentPL kinetics and temperature dependencies. Due to small ionisation energyof shallow donors, the free to bound transition is observed nearly at thesame spectral region as the donor-acceptor pair YL emission.

A very di�erent dependence is observed both for the YL and BL bandsin acceptor compensated crystals. The PL decay spectra taken at 2 K inheavily Mg doped crystal show a non-exponential PL kinetics. The fast de-cay is followed by a slow decay component, with a time constant up to 500�s. The PL decay time is photon energy dependent. Longer decay times areobserved at the low energy tail of the PL emission, a characteristic propertyof donor-acceptor pair recombination transitions [132].

3.1.3 Microscopic origins of the centre responsible for the

yellow emission

The studies of deep traps often give a variety of trap energies that maysupport almost any model of YL. A variety of thresholds observed in pho-toemission capacitance spectroscopy and optical transmission ranges from0.87 to 3.1 eV [106, 133, 134]. Deep level transient spectroscopy and photo-capacitance data taken by Calleja et al. [128] show two clear thresholds at2.5 eV and at 1 eV. The capacitance step amplitude at 1 eV correlates wellwith the YL intensity. The latter value agrees relatively well with the 1.2eV energy of the 3� charge state of gallium vacancies in GaN predicted the-


oretically [135]. Other authors give, however, di�erent values for the samestate, for example 0.3 eV above GaN valence band is predicted in Ref. [136].Thus coincidence of energies can not be treated as a de�nite identi�cationof deep acceptors responsible for the YL. Recently Fleischer et al. proposeda modi�cation of this model. They suggested that a complex of gallium va-cancy and oxygen forms a deep acceptor active in the YL [137]. The energyposition of this state in the GaN bandgap is not known yet.

Calleja et al. [128] invokes the concept of a broad band of trap states to ex-plain long times needed for capacitance stabilisation. A similar distributionof states was suggested by Qiu et al. [138] to account for the photoconduc-tive response of undoped GaN to photon energies between 1.5 and 3.0 eV.The surface photovoltage spectroscopy in conjunction with PL was recentlyemployed to shed light on the energy distribution of the YL-related levels[139]. The surface barrier height (surface charge density) was found to cor-relate with the ratio of the yellow to band edge PL intensity, and the surfacestate density increases with increasing YL/bound exciton ratio.

The donor and acceptor species active in the YL emission could be dueto native defects or impurities, or, alternatively, to extended defects such asdislocations or grain boundaries and practically all these alternatives wereproposed and analysed. For example, numerous reports point to the YLbeing enhanced by or associated with extended defects. However, the factthat the YL is present and often very strong in bulk GaN �lms with a muchlower extended defect density than GaN in thin �lm form strongly suggeststhat the extended defects themselves are not a unique source of YL. The as-sociation can be explained by the well-known aÆnity of extended defects toattract native defects or impurities forming the Cottrell atmosphere. Thise�ect is stimulated by strain �elds surrounding the extended defects, whichmay facilitate the formation of other native defects or getter impurities. Therelative enhancement of the YL with respect to the edge PL emissions canalso be due to the destructive in uence of local electric �elds at chargeddislocations on the formation rate of excitons. It is thus possible that a fre-quently observed anticorrelation between the intensity of the YL and densityof extended defects (dislocations) may be due to this indirect in uence.

Assuming the shallow donor to deep trap model, no signi�cant changes inthe YL signal should be expected with increasing level of n-type doping asthe deep trap density should be the limiting factor. However certain dop-ing procedures clearly modify the deep trap concentration. The e�ects ofdoping on the PL bands in doped, codoped and undoped GaN provide avery strong argument for the donor-acceptor pair recombination characterof the YL (2.2 eV) and also of other red (1.8 eV) and blue (2.8 eV) lu-minescence bands [140]. According to this report, doping with Si donors


enhances the YL, while Mg acceptor doping generates the blue band and,upon codoping with Si and Mg simultaneously, the red band is induced. It issuggested that the two former bands are self-activated, that is a fraction ofthe dopant atom is converted into deep centres of with the opposite electri-cal activity by association with vacancies (self-compensation). The degreeof self-compensation in Si doping is small, but it is signi�cant for Mg dop-ing. We will return to this point later, here we only point out that severalother authors tried to examine the anticipated correlation between dopingprocedures and strength of the YL, with varying degree of success. Suchstudies have, for example, shown that the YL can be suppressed by p-typedoping of GaN [141]. This indicates that the YL is associated with a defect,with a low formation energy in n-type material but high formation energyunder p-type conditions. This behaviour is characteristic of acceptors; theseare more easily formed in n-GaN than in p-GaN due to energy gained bypartly compensating donors. By the same argument, donors are more easilyformed in p-type GaN. The compensation e�ects will be discussed again inthe context of blue PL in Mg-doped GaN.

The studies of the YL as a function of doping density [142] also show thatthe density of the compensating centres is proportional to the doping den-sity. This behaviour is consistent with simple acceptors or donors, such ascarbon, silicon or oxygen contributing to the YL. We can not reject such in-terpretation of the YL, but we point out that both p-type and n-type dopingshifts the position of the Fermi level in the sample and thus it dramaticallya�ects the formation rate of di�erent intrinsic defects in GaN [136, 143{145].This fact is often ignored in the explanation of the observed results.

Several acceptor centres were proposed to be responsible for the YL. Theassociation of YL with carbon was suggested by Ogino and Aoki [32] andsupported by others. This model of the YL has been theoretically investi-gated by Neugebauer and Van de Walle [143]. They have found that carbonhas very high formation energies in a variety of sites, for example at the Gasite where it acts as a donor, and also at interstitial sites. The only con�gu-ration with a relatively low formation energy is that of a shallow acceptor ata substitutional N site. As such, carbon can not be directly involved in YL.It can not form complexes with Ga vacancy; as they are both acceptors, theyoccupy a negative charge state in n-GaN and thus repel each other. Thisresult rules out the involvement of carbon in the YL. The results of Neuge-bauer and Van de Walle were also con�rmed by Boguslawski and Bernholc[146]. These authors con�rmed that carbon at a gallium site should behaveas an e�ective mass shallow donor, whereas carbon at a nitrogen site is ex-pected to be a shallow acceptor, with the binding energy below that of aMg acceptor.


The involvement of nitrogen vacancies in the YL has also been discussedby other authors [147]. In this work the YL band was studied as a functionof deposition temperature in the MOCVD process and the microstructure,carbon, oxygen and hydrogen contamination were examined. The YL wasfound to be stronger at grain boundaries, where high concentrations of hy-drocarbons are present. The latter result was not, however, con�rmed byother authors. Thermal annealing to 1000oC was found to increase the YL bya factor of 1.5, accompanied beyond 850oC by GaN decomposition throughevaporation of nitrogen molecules. This suggests that nitrogen vacanciesmay play a role in the YL mechanism. The direct involvement of nitrogenvacancies in the YL is not, however, supported by theoretical calculations.Neugebauer and Van de Walle [143] proposed that a native defect, either aGa vacancy or a related complex is responsible for the YL. Their calcula-tions indicate that a Ga vacancy produces a triply-charged (V3�

Ga) acceptor

level which acts as a compensating native defect in n-type GaN. A varietyof complexes such as VGa-O and VGa-donor [137] (see Figure 3.5 ) gener-ate close deep acceptor states in the range 0.9 - 1.1 eV. These results restcomfortably with the picture of YL as due to several closely spaced deepacceptor states.

Neugebauer and Van de Walle [143] have calculated the equilibrium con-centrations of defects in n-GaN in a Si-doped material in the presence ofoxygen. They found a signi�cant concentration of VGa - ON complex ac-ceptor centres, about one order of magnitude less than the shallow donorconcentration. The concentration of VGa was also signi�cant. The associ-ation of YL with Ga vacancies either isolated or in complexes can explainwhy the YL is observed only in n-GaN. This is because the equilibrium con-centration of VGa-related defects decreases rapidly as the Fermi level movesaway from the conduction band. Likewise, in Ga-rich growth conditions theGa vacancies are less likely to form, leading to a reduced YL intensity.

The works by Saarinen et al [148, 149] and Mattila and Nieminen [150] givefurther evidence that cation vacancies and/or their complexes are common inn-type samples. The concentration of these defects increases with increas-ing V/III molar ratio. The concentration of gallium vacancies is relatedclosely to the intensity of the YL band. Mattila and Nieminen [150] un-derline that complex formation between cation vacancies and substitutionaloxygen donors is a very likely process. The dominant charge-state is doublynegative and its energy state in the gap is dominated by the vacancy level.

The nature of shallow donors in GaN was discussed by many authors, andresults of earlier doping studies are somewhat contradictory. For exampleOgino and Aoki [32] showed that Si and O doping did not a�ect the relativeintensity of YL to band edge emission, while C doping clearly enhanced it.


According to Nakamura et al. [151] an increased doping with Si and Geproduced a moderate decrease of the YL to band edge emission ratio. Theseresults are very surprising, since oxygen [143, 152, 153] and silicon [146, 154]are the two most common shallow donors in GaN and in GaN epilayers andoxygen was shown to be involved in both YL and BL emissions in bulk GaNsamples [123]. It is often forgotten that silicon at a nitrogen site acts asa deep acceptor in the GaN lattice. Its energy position is predicted to beabout 1.2 eV above the valence band edge [146], i.e., at or very near theposition of the deep acceptor active in the YL. The formation energy of SiNis, however, relatively high [146] and thus Si prefentially occupies galliumsite and acts as a shallow donor only.

The direct support of the role of oxygen in the YL was furnished by Tothet al. [155]. In this original experiment, cathodoluminescence kinetics wasused to study electron-beam-induced impurity di�usion. These studies weresupplemented by cathodoluminescence imaging and wavelength-dispersiveX-ray spectrometry.

The issue of oxygen-related donor in GaN was recently revisited by Chen et

al. [156]. These authors reported a striking similarity between the local vi-brational spectra of the deep oxygen donor in GaP and oxygen in GaN. Theyalso argue that the 0.88 eV PL of GaN is, in analogy to GaP, due to captureof an electron by an excited shallow state of the oxygen donor (substitutingnitrogen) followed by radiative recombination to a deep ground state of theoxygen donor. This model requires further experimental support to be fullyveri�ed.

A study of YL in Se-doped GaN �lms has been reported by Chen et al.

[157]. Unlike Si, selenium substitutes on N site. An equivalent of the yellowband was observed in the photoconductivity spectra. The persistent pho-toconductivity e�ect was found for photon energies down to 2.3 eV, thatis within the range of yellow emission. It should be emphasised that GaN�lms without the YL do not show the persistent photoconductivity e�ects[158].

Spectral signatures of defects associated with the yellow emission have beenalso observed in Raman spectroscopy measurements [159], and several lowenergy peaks with a Raman shift between 10 meV and 30 meV were identi-�ed. These peaks are enhanced in resonance with the YL transitions and arebeing attributed to electronic excitations of donors, while the lowest peakis identi�ed as a quasi-local vibrational mode. This study indicates that allshallow donors in GaN may be involved in the YL emission.


3.2 Blue emission in acceptor doped GaN

The blue photoluminescence (BL) band is present in acceptor doped GaNlayers. In heavily Mg-doped samples an asymmetric PL band can be ob-served with a maximum at approximately 3 eV and a low energy wing ex-tending down to about 2 eV. This PL gradually replaces the YL, as shownin Figure 3.6 where we present the PL spectra of bulk GaN samples compen-sated with di�erent acceptors. The decrease of the YL intensity with p-typedoping was explained earlier, and is related to the Ga vacancy generationrate being correlated with the Fermi level position.

In GaN layers grown on sapphire the peak position of the BL varies with thedoping level and shifts to lower energies with increasing Mg concentration[22, 160]. Such a shift was attributed to either large potential uctuationsin heavily doped samples [21, 115, 160] or to deep donors in the GaN latticecreated during doping with acceptors [23, 160, 161] by the self-compensationprocess [22, 160]. By self-compensation we understand here the process ofspontaneous generation of donor or acceptor defects, which counteracts theattempt to increase the intentional p- or n-type doping level. The simpleexplanation of the process is that the energy required to promote one orseveral electrons (holes) from the Fermi level to the impurity level may be-come smaller than the formation energy of a given intrinsic defect. If so,the formation of a native defect results in compensation of the sample andin lowering of the system energy. Since intrinsic defects (vacancies, intersti-tials, antisites) are created as a consequence of doping, the doping processmay result in a change of �lm stoichiometry, as discussed by Boguslawski etal. [136].

The model of strong potential uctuations was recently supported by theresults of Oh et al [115]. They observed that the BL strongly shifts to higherenergies with increasing excitation density, similarly to the reports by Eckeyet al. [160]. The BL at low excitation intensities has a maximum at about2.85 eV and progressively shifts to about 3.2 eV at high excitation condi-tions. The authors also claim that the observed temperature dependence ofthe BL is consistent with free to bound (electron to acceptor) recombinationtransitions. Such assignment of the BL agrees with the results of the PLkinetics investigations of Smith et al. [21].

The model of potential uctuations was earlier proposed to explain theemission properties in heavily doped GaAs [162, 163]. These potential uc-tuations are due to charge compensation e�ects and large concentration ofionised impurities. We point out, however, that the results of Oh et al. canalso be explained within the model of donor-acceptor pair transitions. Thereported strong blue-shift of the PL maximum with increasing excitation

3.2. BLUE EMISSION IN ACCEPTOR DOPED GAN 53

density is also expected for the donor-acceptor pair process. The blue-shiftitself does not provide distinction between these two models of the BL.

The ODMR investigations of Glaser et al [164] also do not con�rm theimportance of self-compensation processes in their samples. The red-shift ofBL is observed in samples with high Mg concentration. The BL in the sam-ple with Mg concentration below 1019 cm�3 is due to shallow donor-shallowacceptor pair recombination and has a structured form with a well-resolvedzero-phonon line and three LO-phonon replicas. With increasing acceptorconcentration, the PL broadens, while the �ne structure is not resolved atthe Mg concentration above 1019 cm�3. Such broadening can be explainedby potential uctuations in the structure caused by nonuniform distributionof charged impurities. In addition to broadening, the PL red-shifts from itsinitial position with the band maximum moving to 2.7 eV at the Mg concen-tration of 5 � 1019 cm�3. The ODMR studies indicate the same origin of theBL in lightly and in heavily Mg-doped samples. The magnetic resonancesof shallow donors and Mg acceptors were detected through the change inintensity of the BL emission indicating the donor-acceptor origin of the PL.Thus the shift of the PL maximum can not be explained by the change ofdefects active in the PL process, but it is consistent with the potential uc-tuation model. The same authors report that the g-factors of shallow donorand Mg-acceptor vary from sample to sample. The latter observation wasalso con�rmed in other works [165]. It was reported that the g-factor of theMg acceptor in GaN epilayers varies between 2.102 and 2.005 for gk and 1.94and 2.00 for g?. This result is not yet fully explained. In other materialsthe electron spin resonance and ODMR measurements are commonly usedfor defect identi�cation, since the g-factor and its anisotropy are treated asa unique feature of a given defect. Apparently this is not the case in GaNepilayers, with large potential uctuations in �lms, large nonuniformities ofthe material and uctuations of strain and/or electric �eld.

Several other groups indicate that deep donors in addition to shallow donorsare involved in the BL transition. Following the PL and deep level transientspectroscopy investigations it was proposed that doping with Mg acceptorsis accompanied by generation of at least three deep donors [22, 160, 162].Thus, the term "Mg-related deep donors" was coined [160]. The energies ofthese donors were estimated to be 240 meV, 350 meV and 850 meV [160], or265 meV, 400 meV and 615 meV [162]. We point out, however, that similardeep donor levels were also observed in samples not doped with acceptors.For example, the 234 meV, 578 meV and 657 meV donors were recently ob-served in n-type MBE-grown GaN samples, which were not Mg doped [166].

The multi-band character of the BL and involvement of deep donors inthe emission is con�rmed by ODMR investigations by Godlewski et al. We


studied the origin of BL in bulk GaN samples, which are metallic n-typeprior to acceptor doping. In Figure 3.6 we show the 2 K PL spectra ob-served in the as-grown GaN sample (not compensated with acceptors), theZn doped sample, the Ca doped sample and in two Mg doped samples, onelightly doped and the other heavily doped. The PL spectrum of the as-grownsample is dominated by the YL emission with the maximum at 2.26 eV. Theacceptor doped samples either show a two-band PL with YL still well re-solved or, in the case of the heavily doped �lm, an asymmetric and intenseBL with a long, low energy tail. In the latter case, the YL is not resolved asa separate PL emission, but likely to contribute to the low-energy wing ofthe BL. The ODMR signals were detected via the intensity increase of eitherthe entire BL emission band, or by selecting di�erent spectral regions usinga set of optical �lters. We identi�ed at least three slightly anisotropic andoverlapping ODMR signals (D1, D2, A1), with g-factors of: gk=1.995 (D1),gk=1.982 (D2), and gk=2.042 (A1), as shown in Figure 3.7. All values aredetermined with the accuracy of (� 0.005) The �rst two signals (D1 and D2)are relatively narrow (10 mT (D1), 19 mT (D2)) and slightly anisotropic,with g-factors close to 2. They show typical features of deep donor-relatedODMR signals in GaN [121, 167, 168]. The shallow donor-related signal(slightly anisotropic with g-factors of gk=1.9514, g?=1.9486 [169]), whichwas reported previously [121, 164, 167, 169], is not resolved in this work. Theshallow donors are however, apparent in the observed fast components of thePL decay, and can also be deduced from the temperature dependence of thePL intensity, not discussed here. We thus expect that, similarly to the sit-uation reported by Glaser et al. [164], shallow donor-shallow acceptor pairrecombination contributes to the high energy wing of the BL. The thirdanisotropic signal (denoted as A1) has a g-factor larger than 2 (gk=2.042 �0.005) and shows the characteristic of an acceptor-related signal. Such valueof the g-factor agrees with range of g values reported for the Mg acceptor inthe GaN lattice [165]. We thus tentatively associate the A3 resonance withMg acceptors. The relative intensity of the D1 and D2 ODMR signals varieswithin the spectral region of the BL (see Figure 3.7), but the A1 signal wasdetected within the whole spectral region of this emission, which means thatthe same acceptor (Mg acceptor) participates in all PL transitions responsi-ble for the BL. These properties of the ODMR signals con�rm a multi-bandnature of the BL and the contribution of donor-acceptor transitions to thisPL, as both donor- and acceptor-related signals are observed.

The PL spectroscopy and PL kinetics investigations of bulk GaN samplesfully support the multi-band character of the BL. We can not, however,conclude whether doping with Mg (and also with other acceptors) is accom-panied by self-compensation processes, in which deep donor levels are intro-duced. Our studies only prove that the BL and possibly self-compensationis not a unique property of Mg doping. Doping with Ca or Zn also leads to


an asymmetric PL band, in close analogy to the BL in Mg-doped crystals.We also point out that the YL emission is still observed in acceptor dopedsamples, but becomes weaker in Zn doped and in lightly Mg doped samples.In heavily Mg doped samples the YL is no longer resolved, but is likely tocontribute to the low energy wing of the broad BL band.

The donor-acceptor contribution to the BL, as concluded from the aboveODMR study, is also con�rmed by our PL kinetics measurements. The PLdecay curves for acceptor doped samples (see Figure 2.4) are strongly non-exponential and show that the slow components of the decay are energydependent. As already mentioned, such properties of the PL kinetics arecharacteristic for donor-acceptor pair recombination.

The origin of deep donors active in the BL emission and their relation toMg doping are still not fully explained. But if created as a consequenceof doping (self-compensation) these donors are most likely to be related tonative point defects either directly or indirectly, for example as a complexwith an intrinsic defect [170, 171]. The formation energy of a given intrinsicdefect strongly depends on the Fermi energy and thus a particular defectformation can be stimulated by p-type doping. The theoretical calculations[136, 144, 145, 152] indicate that depending on doping conditions nitrogen orgallium vacancies or Ga interstitials can be formed. The antisite defects,so important in other III-V semiconductors, are also formed in the GaNlattice. For example, in Ga-rich conditions self-interstitials and antisites arefavoured. In both Ga-rich and N-rich conditions the most important defectsare vacancies [135]. Recent theoretical calculations indicate that upon dop-ing with Mg the Fermi level is pushed down, which can considerably increasethe formation rate of nitrogen vacancies [172, 173]. Thus nitrogen vacancies,which can occur in the 3+ and 1+ charge states, can act as compensatingdefects in p-type doped GaN [126]. The vacancies can also form complexcentres with impurities. Mg-VN complexes are thus good candidates fordeep donors created by Mg doping [174].

Intrinsic defects can also form complexes with hydrogen, present in largequantities in MOCVD-grown samples. The role of hydrogen complexes inYL and BL emissions and the in uence of annealing processes related toacceptor activation in MOCVD �lms on the stability of Mg-H and VN -Hcomplexes remains unclear but is being pursued with increasing interest[152, 174, 175]. It is too early to make de�nite statements about the originand eÆciency of self-compensation processes and on the role played by hy-drogen in these phenomena.

The recent theoretical calculation of Reboredo and Pantelides [174] indicatethat compensation processes in Mg-doped GaN can include self-compensation


of the Mg acceptor by the Mg donor (interstitial magnesium). The authorsconclude that complexes involving self-interstitials and interstitial impuritiescan play a major role in compensation processes responsible for low p-typedoping eÆciency. This point requires further experimental evidence.


Initial state(shallow donor)

Configurational coordinate

(deep acceptor)

Final stateEmission

Valence band

Acceptoractivationenergy

Ene

rgy

Figure 3.1: The con�gurational coordinate diagram of the transitions re-sponsible for the YL after Ref. [32]


��

GRQRU DQG DFFHSWRU

UHVRQDQFH

*D1�0J �.

�� *+]

∆06 �

∆06 �

3/�,QWHQ��DUE��XQLWV�

0DJQHWLF�)LHOG�>*@

Figure 3.2: Anisotropic spin triplet resonance detected in the spectral regionof the YL emission in a heavily Mg compensated bulk GaN sample.


2.0 2.1 2.2 2.3 2.40

1x104

100-140 µs

0-0.2 µs

PL

inte

nsity

(a.

u.)

Energy (eV)

Figure 3.3: The PL spectra accumulated at selected delay times, between 0and 0.2 �s and between 100�s and 140 �s in undoped cubic GaN. After Ref[33].


� ��

�

�

�

*D1�DV�JURZQ

*D1�0J��FRPSHQVDWHG

GHW��DW��H9

GHW��DW��H9

�

�

7LPH��µV�

OQ�3/�,QWHQ��DUE��XQLWV�

Figure 3.4: The PL kinetics of the YL emission observed at 2K in undopedand in Mg-compensated bulk GaN sample. Nonexponential and energy de-pendent decay is observed in the latter case.


N N

N

NN

V VGa Ga

10.6 %

11.8 %

14.9 %

9.8 %N

N

N

Figure 3.5: Atomic geometry of the Ga vacancy and of the VGa-ON complexin the 3� and 2� charge state where all defect levels are fully occupied. Thenumbers give the increase of the bond length in %. The bulk bond lengthis 1.94 Angstrom. Adopted from Ref. [143]


��

�H�

�G�

�F�

�E�

�D�

3/�,QWHQVLW\��DUE��XQLWV�

3KRWRQ�(QHUJ\��H9�

Figure 3.6: The 2K PL emission of undoped (a) and acceptor compensatedwith Ca (b), Zn (c) and Mg (d, e) (lightly doped (d) and heavily doped (e))bulk GaN samples.


� ��

%__F

∆06 �

∆06 �

$��'�

$�'�

�� H9 /3

�� H9 /3

�� H9 /3

�� H9 /3

3/�,QWHQ��DUE��XQLWV�

0DJQHWLF�)LHOG��*�

Figure 3.7: Optically detected magnetic resonance spectra detected viabroad and asymmetric BL emission of heavily Mg compensated bulk GaNcrystal. The spectra were detected by selecting di�erent spectral regionswith low-pass (LP) �lters.

Part 4

Piezoelectric e�ect in GaN

and its in uence on emission

It has recently been realised that strong piezoelectric e�ects in GaN andrelated compounds may have a signi�cant impact on a range of materialand device properties. The area is developing rapidly, and many issues haveonly provisionally been addressed. First reviews of the piezoelectric e�ectsin the nitrides, and GaN in particular, have appeared in the last few years,see for example Ref. [176] and Ref. [177].

4.1 Fundamentals of piezoelectric e�ects in per-

fect crystalline GaN

GaN typically crystallises in wurtzite structure. Its basic unit cell is de�nedby the edge length a of the basal hexagon, the height c of the hexagonalprism and the parameter u, the anion-cation bond length along the (0001)axis in units of c; in GaN a = 6:040 bohr, c=a = 1:6336 and u = 0:376.The wurtzite structure lacks inversion symmetry and thus yields sponta-neous polarisation. Therefore, a complete description of polarisation e�ectsin GaN needs to include both the spontaneous and piezoelectric contribu-tion, that is additional polarisation induced by variations of strain. Thewurtzite crystal structure has the hexagonal 6mm symmetry, and, conse-quently, the piezoelectric tensor of wurtzite crystals dij has three di�erentnonzero components (piezoelectric strain coeÆcients): d33; d31(= d32), andd15(= d24) [178]. The �rst two are relevant for extensional strain and thethird component for shear strain. We have recently determined their valuesusing interferometric methods [179{181]. Sometimes the piezoelectric stresscoeÆcients eij are used, these are related to dij through a tensor relationship[182]:

eip = �qdiqcE

qp; (4.1)

65

66PART 4. PIEZOELECTRICEFFECT IN GAN AND ITS INFLUENCEON EMISSION

where cEqp is the elastic sti�ness tensor at constant electric �eld. d15 for GaNhas been measured to be 3.1 �0.2 pmV�1 [183]. The values of d31 and d33are given in Table 4.1, other coeÆcients are given in Table 4.2.

The GaN �lms have two faces: a Ga face and a N face. They correspond topolarities where the bonds along the c direction are from Ga cations to Nanions and N anions to Ga cations, respectively (see Figure 4.1). Most GaNstructures are grown along c or (0001) direction, which is also the directionof spontaneous polarisation Peq. The piezoelectric polarisation along the caxis is expressed through the piezoelectric coeÆcients as:

Ppiezo = e33�3 + e31 (�1 + �2) : (4.2)

Here, �3 is the strain along the c-axis, �3 = (c�c0)=c0 and the in-plane strain�1 = �2 = (a� a0)=a0 is assumed to be isotropic. Spontaneous polarisationhas only recently been understood [184{186]. In general, spontaneous po-larisation manifests itself as polarisation charge at hetero-interfaces and itcan be observed in unstrained structures [187]. While the consensus on themagnitude and the relevance of spontaneous polarisation has not yet beenreached, certain optical e�ects such as large red spectral shifts in otherwiseunstrained GaN quantum well structures have been attributed to sponta-neous polarisation e�ects [187]. It is quite likely, although not yet proven,that the magnitude of spontaneous polarisation can be controlled by appro-priate growth procedures.

The spontaneous polarisation and piezoelectric coeÆcients were recently cal-culated by Bernardini et al [186] using the Berry phase approach and therelevant values are given in Table 4.3. For comparison, the same authorsshow the piezoelectric constants for a number of III-V and II-VI compounds,also including those crystallising in a cubic structure. It is known that inpolytypical materials the values of the piezoelectric constants agree to withina few percent. Interestingly, the values in all three nitrides appear to be closeto those in II-VI oxides. The absolute value of the piezoelectric constants e33and e31 are about ten times larger than in the III-V and II-VI compounds,and only about three times smaller than in ferroelectric perovskites. Thespontaneous polarisation, that is the polarisation at zero strain is also verylarge, and that of AlN is only 3-5 times smaller to that in ferroelectric per-ovskites.

The values given in Table 4.3 allow us to evaluate the importance of spon-taneous polarisation compared to the piezoelectric polarisation [177]. For abiaxially strained layer the e�ective piezoelectric polarisation is given by:

Ppiezo = [e31 � (c31=c33) e33] (�1 + �2) ; (4.3)

4.2. FILM SURFACE POLARITY 67

where the last term in brackets is the in-plane strain, c31 and c33 are the elas-tic constants. As an example, in the AlxGa1�xN �lm deposited on GaN [177]the values of Ppiezo=-4.26 x 10�2 C/m2 and the spontaneous polarisation,Pequ =-5.2 x 10�2 C/m2 are calculated. The piezoelectric and spontaneouspolarisation contributions are thus comparable in size. This observation wascon�rmed in recent PL kinetics studies of unstrained GaN quantum wellsin GaN/AlGaN heterostructures [187]. The piezoelectric and spontaneouspolarisation in �lms with Ga polarity and tensile strain in the alloy havethe same sign and point in the [000�1] direction. The sign of polarisationis such that it produces a potential energy of electrons decreasing from theGa face towards the N face (see Figure 4.2). An important consequenceof this feature of spontaneous polarisation is that the relative direction ofthe two polarisation components depends on growth conditions [188]. Thestructures grown directly on sapphire GaN �lm have N-phase polarity, butif an AlGaN bu�er is grown on sapphire prior to GaN deposition, then theGaN �lm has Ga-face polarity. In the latter case, and for �lms under tensilestress, both polarisations are directed towards the substrate. However, inconditions of a compressive stress, the two �elds point in the opposite direc-tions. Further consequences of this e�ect on GaN device behaviour and onmaterial parameters are discussed below. The two contributions can also beeasily evaluated in structures, such as InGaN/GaN, where the piezoelectriccontribution is opposite in direction to the spontaneous contribution, buteven larger in absolute magnitude [177].

4.2 Film surface polarity

The epitaxial growth of nitrides takes place along a the polar axis of thematerial and thus the surface can be expected to have a certain polarity.However so far this aspect of the �lms, diÆcult to determine experimentallyhas been mostly overlooked (for a comprehensive review of experimentalmethods see Hellman [189]). Two relatively simple methods include mea-surements of the sign of the piezoelectric e�ect - diÆcult due to high conduc-tivity, but feasible in interferometric measurements [179, 190] and chemicalstudies through etching in KOH and NaOH, where it was found that smooth�lms etch more slowly. More advanced techniques used include coaxial im-pact collision ion scattering spectroscopy used by Sumiya et al [191]. Whilethe problem has not been conclusively resolved, Hellman has presented a"standard framework" to describe the polar faces of GaN. Selected charac-teristics include surface morphology of the �lms with the smooth side of theas-grown GaN being identi�ed as the N face and the rough side as the Gaface. The �lms with hexagonal pyramidal morphology grown on sapphireare considered to have the top N face, and in the smooth �lms grown byMOCVD the top surface is thought to have Ga face. The Ga face of GaN


is chemically more stable than the N face. KOH and NaOH solutions willetch the N face but not the Ga face. At the same time, methods of growthof single face GaN �lms have been explored. For example Bridger et al [192]report growth of Ga-polar GaN �lms by radio-frequency plasma assistedMBE on AlN bu�ers, while N-polar �lms were nucleated using GaN bu�erlayers by the same technique. These di�erent polarities a�ect the relativeorientation of piezoelectric and spontaneous polarisation components.

4.3 Piezoelectric phenomena in real structures

Theoretical predictions of a signi�cant magnitude of piezoelectric e�ects inGaN and related heterostructures is often poorly supported by experimen-tal results. Many factors in real heterostructures conspire to reduce theirrelative signi�cance. For example, in partially relaxed heterostructures withmis�t dislocations, the piezoelectric e�ect is reduced, but the spontaneouspolarisation should remain unchanged. This e�ect is manifested throughhigh internal electric �eld as recently reported in unstrained GaN QWs[187]. In �lms grown with domains of inverted polarity, the overall polarisa-tion e�ects may even be e�ectively eliminated, as shown in Ref. [193, 194].This prompted many groups to pursue growth strategies that would lead tosingle domain GaN �lms. Single-domain growth is additionally importantbecause �lms with di�erent polarities respond di�erently to various chemicalprocedures, such as wet or dry etching. Any intermixing of the interfacesbetween the two types of domains would reduce the e�ect of di�erencesin spontaneous polarisation, as the charge would be e�ectively distributedover a certain volume. Therefore, in order to fully exploit all the potential ofthe piezoelectric e�ects in GaN and related structures, growth technologiesare being developed to yield good domain control and, ultimately, singledomain �lms. The calculations presented in the preceding section (Equa-tion 4.3) indicate that the e�ect of spontaneous polarisation is signi�cant,and therefore intense electric �elds should apear and band edge energies bestrongly a�ected. However, it needs to be noted that the overall magni-tude of the e�ect depends on screening of the internal electric �elds in thebulk and at heterointerfaces and on the extent of strain relaxation. Im-provements in structural quality of GaN (AlGaN) epilayers are not relatedto the magnitude of spontaneous polarisation in a straightforward way. Toillustrate this e�ect in Figure 4.3 we compare the PL emissions from twoGaN/AlGaN multiple QW structures grown by MBE on sapphire with athick MOCVD-grown GaN bu�er layer. Two MBE growth methods wereused: one sample was grown by MBE using the electron cyclotron reso-nance (ECR-MBE) nitrogen plasma cell, and the other was grown using anew generation radio frequency (rf-MBE) nitrogen plasma cell. The �rststructure has poor structural quality and relatively high surface roughness,

4.3. PIEZOELECTRIC PHENOMENA IN REAL STRUCTURES 69

with granular �lm morphology as shown in Figure 4.4. The comparison ofthe PL spectra indicates large di�erences in optical properties of the twostructures. The relatively weak PL emission from the 8 nm wide QWs inthe ECR sample partially overlaps with the PL emission from the underly-ing MOCVD �lm, whereas the emission from the 6 nm wide QWs in the rf- MBE sample is strong and its spectral position strongly red-shifted com-pared to predictions based on quantum con�nement e�ects. In this samplethe PL from the underlying GaN MOCVD �lm is practically not observed.The observed red-shift of the PL in the 6 nm QW is due to strong built-inelectric �elds in GaN QWs, as further supported by the time-resolved PLmeasurements. Due to a strong built-in electric �eld in GaN QWs in therf - MBE structures, the PL decay time is signi�cantly larger compared toabout 100 ps observed for free excitons in the ECR-MBE sample and inMOCVD-grown epilayers. The decay times of excitons in wider QWs areup to 1000 times longer [187]. The e�ect is clearly seen in Figure 4.6 in 4nm and 6 nm wide QWs , where we compare the PL decay times in thesetwo QWs with those in 2 nm wide QW and in the MOCVD-grown GaNbu�er layer. The built-in electric �eld in the 2 nm QW can not signi�cantlyseparate the recombining e-h pairs and does not change the potential acrossthe QW. In consequence, the oscillator strength of the PL transition is nota�ected and the PL recombination energy is unchanged.

In equilibrium, that is without external e�ects such as strain and also heat ow, the charge responsible for spontaneous polarisation is usually com-pensated by either ambient charges or internal charges forming an equaland opposite dipole moment [195]. Large densities of surface and interfacestates provide an additional mechanism for the reduction of interface electric�elds due to spontaneous polarisation. The phenomenon is well documentedin ferroelectrics, where no traces of an internal electric �eld have been re-ported so far. Similar interface states have been identi�ed in AlGaN/GaNheterostructures [196, 197], and on the surface of GaN �lms [192]. In thelatter report the surface state density has been directly measured to be 9.4� 0.5 � 1010 cm �2 using the electric �eld force microscopy. The same tech-nique is capable of imaging planar distribution of the domains. While theconsensus on the magnitude and relevance of spontaneous polarisation hasnot yet been reached, certain optical e�ects such as large red spectral shiftsin otherwise unstrained GaN quantum well structures have been attributedto spontaneous polarisation e�ects [187]. We believe that the data shownin Figure 4.3 demonstrate that spontaneous polarisation may be a�ected bygrowth conditions.


4.4 Implications of piezoelectric e�ects for devices

Strong lattice polarisation e�ects identi�ed in GaN provide unique opportu-nities for GaN and related materials to be used in high temperature piezo-electric sensors and in pyroelectric detectors. Most signi�cant applicationswere found, however, in devices based on two-dimensional transport, suchas HEMTs. It needs to be emphasised that, independently of piezoelectricproperties, GaN possesses a suite of transport properties desirable from thepoint of view of high frequency/high current density electronic devices, andtheir combined e�ect leads to a vastly improved power handling capability(for details see for example Ref.[177]). However, piezoelectric e�ects intro-duce additional, bene�cial features. It was found, that piezoelectric e�ectsa�ect the concentration of 2D electrons (2DEG) con�ned in the triangularpotential well at the AlGaN/GaN heterointerface. The AlGaN layers grownon GaN are under strain, and the piezoelectric e�ect induces an electric�eld. Consequently, charge accumulation (or depletion) takes place at theheterointerfaces, depending on the polarity of the top surface (see Figure4.2 ). If the top surface has Ga polarity, then the resulting electric �eldwill drive any available electrons, for example from the ohmic contacts, to-wards the 2DEG. At some point, a balance is reached as the Fermi level,constant throughout the structure, sets the values of band bending. Thise�ect was recently illustrated by Ramvall et al [198]. We underline herethat the present mechanism makes it possible for charge carriers to be in-troduced from very remote sources, so that donor centres causing additionalscattering are not introduced. This phenomenon has thus been termed the"piezoelectric doping". The values of the sheet carrier concentration in Al-GaN/GaN heterostructure �eld e�ect transistors (HFETs) were found to beof the order of 1012�1013 cm�2 [199{201]. For such a high sheet carrierconcentration, the internal electric �eld can be partly or even fully screened,which may help maintain the rectangular shape of GaN QWs [186]. Accu-rate control of the doping level is thus crucial for the size of the observedpiezoelectric e�ects.

The second, important aspect of piezoelectric phenomena arises from thein uence of polarisation charge on the properties of heterointerfaces. It wasfound that the static potential at the GaN/AlN interface is di�erent fromthat at the AlN/GaN interface, and this e�ect was attributed to spontaneouspolarisation di�erences in GaN and in AlN. As a result, band gap discon-tinuities could not be conclusively established. This e�ect has its usefulimplications for devices, as it may allow to vary the Schottky barrier heightand to signi�cantly reduce the operating voltage of the nitride �eld emitters.

The third e�ect is related to optical properties of quantum well structures.It was found that the observed transition energies in nitride quantum wells

4.4. IMPLICATIONSOF PIEZOELECTRICEFFECTS FOR DEVICES71

generally show large red shifts compared to simple calculations (see Figure4.3 and Figure 4.5). This red shift is attributed to electric �elds due topiezoelectric e�ects [68, 187, 202, 203]. We wmphaisie that a careful analysismay be necessary to elliminate red-shifted transitions that are simply defect-related and not intrinsic. Such identi�cation can be done using two-photonspectroscopy. The electric �eld in an alternating sequence of wells Fwell andbarriers Fbarrier can be calculated as:

Fwell =�4�Lbarrier (Pwell � Pbarrier)

Lwell�barrier + Lbarrier�well; (4.4)

Fbarrier =�4�Lwell (Pbarrier � Pwell)

Lbarrier�well + Lwell�barrier: (4.5)

Here, L and � and P are widths, dielectric constants and polarisations inwells and barriers, respectively. Using these expressions, the values of elec-tric �eld in the range of 1 -3 �106 V/cm were found. Such high values leadto a signi�cant red shift through a quadratic Stark e�ect.

The magnitude of the PL red shift can be directly determined experimentallyin time-resolved experiments under intense excitation [68, 202, 203]. Imme-diately after an intense laser pulse the free carrier concentration can be largeenough to screen an internal electric �eld. Figure 4.5 shows that at an earlystage after the excitation pulse, the PL is blue-shifted from its �nal spectralposition. At longer delay times after the excitation pulse, the PL red shifts,with a time scale characteristic of the decay of free carriers population.

A range of related consequences of piezoelectric e�ects have also been ob-served, such as for example the increased exciton lifetimes observed in time-resolved spectroscopy in GaN quantum wells, as presented in Figure 4.6. Thee�ect is due to reduction of the oscillator strength in GaN/AlGaN quantumwells [68, 187, 202, 203] because of an increased separation of electrons andholes in a quantum well subjected to piezoelectric �elds.

The recent studies of piezoelectric e�ects in the nitrides have considerablyadvanced our knowledge, but many issues have not been conclusively re-solved yet. For example, the e�ects of domain inversion on the currenttransport in FET structures have not been established. It is anticipatedthat the domains might cause the electric �eld to vary, causing variationsin the sheet carrier concentration. These nonuniformities should have asigni�cant e�ect on the carrier scattering and on device performance.


Table 4.1: Values of extensional piezoelectric coeÆcients in wurtzite GaN.d33 [pmV

�1] d13 [pmV�1] e33 [Cm

�2] e31 [Cm�2]

GaN 0.73a -0.49a

bulk 3.7b -1.9b 1.12b -0.55b

clamped single crystal 2.8� 0.1b -1.4 � 0.1 b 0.85b -0.41 b

clamped polycrystalline 2.0� 0.1b;c -1.0 � 0.1b;c 0.60 b -0.30 b

a Reference [186]b Reference [190]


Table 4.2: Values of the extensional piezoelectric coeÆcients in cubic GaNobtained in [190].

d14 [pmV�1] e14 [Cm

�2]GaN, bulk 6.4 � 0.2 0.61

Table 4.3: Calculated spontaneous polarization and piezoelectric constantsin units of C=m2.

Peq e33 e31GaN �0:029 0:73 �0:49AlN �0:081 1:46 �0:6InN �0:032 0:97 �0:57


Figure 4.1: The wurtzite crystal structure of GaN. The size of spheres indi-cates the ionic radii (Ga is smaller than N). After Ref. [189].


heterostructure FET

Ga-face surface

single quantum wellp-n double heterostructure

compressioncompressiontensioncompression

Figure 4.2: Band diagrams for standard framework Ga face heterostructures.The charge accumulation (or depletion) takes place at the heterointerfaces,depending on the polarity of the top surface. After Ref. [189].


3.2 3.3 3.4 3.5 3.6

rf-MBE GaNMQW 10x6nm

ECR-MBE GaNMQW 11x8nm

MOCVD GaN

PL

Inte

nsity

(ar

b. u

nits

)

Photon Energy (eV)

Figure 4.3: PL emission of two multiple quantum well structures grownby ECR-MBE and rf-MBE. The samples were grown on sapphire substratecovered with 1.5 �m thick MOCVD-grown GaN epilayer. The PL fromthe 6 nm QW in the structure grown with radio frequency (rf) nitrogenplasma cell is strong and considerably red-shifted from its expected spectralposition. The PL from the 8 nm QWs in the sample grown with electroncyclotron resonance (ECR) nitrogen plasma cell is weak and overlaps witha strong PL emission from the MOCVD-grown bu�er layer.


Figure 4.4: Surface morphology of GaN epilayers grown by MBE studiedwith atomic force microscopy.


3.1 3.2 3.3 3.4 3.5 3.6

6 nm QW4 nm QW

2 nm QW

335 nm exc.cw-mode PL

266 nm exc.10 ns pulse

Photon Energy (eV)

PL

Inte

nsity

(ar

b. u

nits

)

Figure 4.5: Comparison of cw and pulsed PL spectra measured in an MBE-grown GaN/AlGaN QW structure with three (2nm, 4nm and 6nm wide)GaN QWs. The top spectrum was recorded with a high intensity 10 nsexciting laser pulse. A dramatic modi�cation of the PL emission is observedwith PL spectra from wider QWs signi�cantly blue-shifted compared to theircw spectral positions.


0 500 1000 1500 20001xe

0

1xe1

1xe2

1xe3

1xe4

6nm QW

4nm QW

2nm QW

MOCVD GaN

ln P

L In

tens

ity (

arb.

uni

ts)

Time (ps)

Figure 4.6: The PL decay spectra measured under 2 ps pulse excitation at2 K. The PL kinetics of free excitons is shown in the underlying MOCVD-grown GaN bu�er layer and in three (2nm, 4nm and 6nm wide) GaN QWsgrown by rf-MBE.

Part 5

Dislocations and their e�ects

on emission

Most GaN epilayers are grown on lattice mismatched substrates. This facthas important consequences as lattice mismatch results in strained epilayersand leads to generation of high concentration of dislocations. Both thesee�ects are important for optical and electrical properties of GaN. The val-ues the lattice mismatch are given in the Table 5.1 which shows that bothtensile and compressive (consile) stress is possible in GaN �lms grown ondi�erent substrates. In the latter case stress can induce changes of the se-quence of hole states, where light hole states can be shifted in energy belowthe heavy hole states. In strained epilayers the position of PL peaks can bered- or blue-shifted from their expected positions in unstrained layers [204].The shift should be directly related to the strength and character (tensile orconsile strain) of the stress. However, the experimentally documented situ-ation is not so simple. Shifts of the PL spectra often do not follow changesin the lattice constants, and, likewise, di�erences in the thermal expansioncoeÆcient, growth temperature, cooling rate etc. can be equally important.

The large lattice mismatch between GaN �lms and substrate materials andbetween GaN, InN and AlN leads to generation of a large density of disloca-tions in the epilayers. In a good quality optoelectronic material designed towork as a light emitter the density of dislocations should be below 105 cm�2

[205]. In this context, bright light emission from GaN-based light emittingdiodes, with dislocation density as high as 1010 cm�2 was very surprising.This observation prompted a continuing discussion on the role of disloca-tions in radiative and nonradiative recombination processes in GaN and inInGaN. Overall, the quantum eÆciency in many nitride devices is surpris-ingly high, about 12 % in blue and green LEDs, and 5 % in amber LEDs,and thus comparable to 11 % in high quality lattice matched AlInGaP-basedLEDs [206].

81

82 PART 5. DISLOCATIONS AND THEIR EFFECTS ON EMISSION

We discuss several works clearly showing that dislocations are centres ofnonradiative recombination in GaN and InGaN. If so, a dramatic reduc-tion of dislocation density in a new generation of InGaN-based structuresusing the concept of epitaxial layer overgrowth (ELOG) [207{209]) shouldresult in a large increase of eÆciency of light emission. However, despite thedecrease of dislocation density by about 4 orders in magnitude, the quan-tum eÆciency of the emission from ELOG structures remained nearly thesame [210, 211]. The reason for this surprising observation is still discussed.ELOG grown InGaN-based LEDs show quite homogeneous light emission,while cathodoluminescence (CL) emission from ELOG-grown InGaN andGaN �lms is strongly a�ected by dislocations [212]. Such results suggestthat dislocations act as centres of nonradiative recombination in InGaNand GaN and that an alternative explanation is required of a relatively lowimpact of dislocations on light emission processes in InGaN-based optoelec-tronic devices.

Nakamura [205] and Chichibu et al [211] proposed that nonradiative re-combination of excitons at dislocations does not contradict high quantumeÆciency of InGaN-based devices, which can be explained by strong localisa-tion e�ects in the InGaN QW plane. These localisation e�ects are caused by uctuations of In fraction in InGaN QW plane and not by high dislocationdensity in these �lms [211]. Such large composition uctuations in a QWplane lead to carrier/exciton localisation and to uncommonly large Stokesshift values between the PL and PL excitation peaks, often as large as 600meV in green LEDs, 200 meV in blue LEDs and 100 meV in laser diodes[213], or respectively 70 meV, 200 meV and 450 meV for x=0.13, 0.35 and0.45 in InxGa(1�x)N [214].

Concluding, it is believed now that dislocations are eÆcient centres of non-radiative recombination in InGaN and that localisation e�ects are crucial toexplain high quantum eÆciency of InGaN-based LEDs. This explanation ofthe link between the sample morphology or In composition uctuations andits optical properties has one weak point. A very homogeneous emission isobserved in InGaN-based LED devices, where In uctuations in a QW planeare rather random. A possible explanation of this contradiction was recentlyproposed by Bellaiche et al [215]. These authors postulate that alloying ofGaN with In leads to strong localisation of the hole states near the valenceband edge. If so, strong localisation can also occur in InGaN epilayers withthe homogeneous In composition. Recently Narukawa et al [216] proposedthat their PL kinetics studies at temperatures above 70 K can be explainedby recombination of delocalised excitons. An important role of localisatione�ects in InGaN QWs was also questioned by Kollmer et al [217]. Theseauthors explained the properties of excitons by strong built-in electric �eld

5.1. SPATIALLY-RESOLVED STUDIES 83

in strained InGaN QWs and not by strong localisation e�ect. If con�rmed,these observations would call for another explanation of the low recombi-nation rate at dislocations and the origin of large inhomogeneous PL linewidths, commonly attributed to localisation of excitons.

5.1 Spatially-resolved studies

The relationship between the density of dislocations, PL emission intensity,spectral shape of emission bands, and the rate of radiative recombinationwas recently explored by Domen et al [218] and Holst et al [219]. The�rst authors show that the etch pits density (or the density of dislocations)correlates well with density of dark spots observed in the CL mapping inves-tigations and con�rm that dislocations are centres of nonradiative recombi-nation in InGaN epilayers. They also show that their emission shares somecommon features with the emission of quantum dots. This e�ect resultsfrom a combined e�ect of granular structure of the �lms and from large Incomposition uctuations. Using the spot mode option available in the CLtechnique they were able to excite the emission from grain centres and fromgrain boundaries and compare the properties of these two emissions. Theradiation decay time from bright spots is relatively long, of about 2 ns, theCL decay time observed from the from the dark spots in the sample is tentimes smaller. Similar results are reported by Holst et al [219]. These au-thors show that the PL kinetics is strongly nonexponential, a typical featureof the PL emission in strongly disordered systems.

These observations con�rm eÆcient nonradiative recombination at dislo-cations. The carrier/exciton di�usion length in InGaN �lms can also beestimated in the CL investigations to be about 0.3 �m [218], but other au-thors report much smaller values in both InGaN and GaN [220]. In othersemiconducting materials a short di�usion length is due to enhanced nonra-diative recombination of excitons at defect sites and eÆcient carrier trappingby defects. In InGaN another mechanism appears to be responsible for theobserved short di�usion length. The photogenerated carriers/excitons movein the QW plane and can either approach the region of an increased In com-position and be trapped or approach a dislocation and decay nonradiatively.The latter process is clearly less probable, since highly eÆcient light emissionis observed. Short di�usion lengths, smaller than a typical distance betweendislocations [220]) in InGaN can be thus attributed to numerous regionswith an increased In composition rather than to carrier/exciton trapping byimpurities and/or extended defects.


Similar scanning CL and electron microscopy (SEM) studies were performedby the present authors in a range of GaN epilayers [91]. We have performeddetailed AFM, CL and SEM investigations to establish the link between thestrength of the edge and yellow emissions and morphological quality of thesamples studied. These investigations were done at room temperature, inconditions relevant for the operation of GaN-based devices. We have studieda range of di�erent GaN epilayers grown by MBE, MOCVD or CVD meth-ods. In Figures 5.2, 5.3 and 5.4 we show the results of these investigations.The AFM pro�les of our samples show relatively rough surfaces with granu-lar structure, similar to those shown in Figure 5.1. The granular structure isalso well resolved in the SEM images (see Figure 5.2). The grains are typi-cally of about 0.5 �m size or less. Having established the surface topographyof GaN epilayers we took monochromatic, spatially-resolved CL images withthe detection set either at the edge emission or at the yellow emission. Agranular structure of the samples is re ected in large uctuations of the edgeCL intensity (see Figure 5.3). The CL is relatively bright at the grain centresand weak at the boundaries, i.e., in the region of increased dislocation den-sity. We infer that excitons generated at the grain centres tend to recombinethere and do not migrate to grain boundaries. This observation thus sug-gests that strong site localisation of excitons occurs also in GaN epilayers,in analogy to the InGaN �lms. Similar conclusion was also drawn by Rosneret al [221]. We anticipate the mechanism of the localisation to be di�erentthan in InGaN layers. Localisation in this material was explained by large uctuations in In composition in the �lm. In GaN samples we relate theobserved localisation of excitons to large potential uctuations in GaN �lmsresulting from their granular structure [222]. Localisation results in creationof quasi zero-dimensional excitons which can recombine practically at thelocation where they have been created. Thus, their recombination rate isnot a�ected by a large concentration of dislocations, provided that the exci-ton wavefunction does not penetrate to the region of grain boundaries. Theabove tentative explanation has one weak point, as one should expect quitedi�erent localisation strength in InGaN and in GaN �lms. However, thisis not observed. Rosner and co-workers [221] reported that di�usion lengthof minority carriers is very similar in both materials, despite the fact thatdi�erent localisation mechanisms were proposed. This problem remains un-solved and the mechanism of strong localisation in GaN epilayers is far frombeing understood.

We expected that large intensity uctuations, observed for the GaN edgeemission, should also be noticeable in the YL emission. Surprisingly, theyellow CL (see Figure 5.4) is only very weakly position-dependent. In con-sequence, the intensity ratio of edge to yellow CL strongly uctuates in the�lm plane. We have collected the CL images at varying scan times and atdi�erent excitation densities. From these investigation we conclude that the

5.1. SPATIALLY-RESOLVED STUDIES 85

observed in-plane homogeneity of the yellow CL could not be explained bysignal averaging or by intensity saturation in the CL experiment. We alsoused the spot mode option of the CL system and measured the CL spectraexcited at di�erent positions. The results of this experiment are shown inFigure 5.5. The spot mode CL spectra con�rm a homogeneous spatial dis-tribution of the yellow PL intensity. whereas, the edge PL varies in intensityby about 250 %.

We have already mentioned that strong potential uctuations in the GaNplane can be attributed to strain inhomogeneities, resulting from the gran-ular structure of GaN �lms [111]. If so, the peak energies of the emissionsshould vary across the sample, since the PL energy depends on the mag-nitude of the built-in strain. Such shift of the PL energy was reported byDomen et al [218] in InGaN and by Hacke et al [223] in GaN epilayers. Ap-parently the shift is not a common property of all GaN layers studied. InFigure 5.5 we show the CL spectra measured at room temperature at fourdi�erent positions in the sample. The peak of the edge PL in GaN is notshifted when taken at grain centres and at grain boundaries. The spectralshift of the edge emission is thus either very small, and smaller than theaccuracy of our experiment, or nonexistent. We thus conclude that the ob-served localisation of excitons and also large uctuations of intensity of theedge emission are not always related to pronounced strain e�ects.

Several other groups studied the relationship of intensity of the yellow andedge emissions and the sample morphology. Christiansen et al. [90, 224]explained the homogenous distribution of the yellow PL by a uniform dis-tribution of screw dislocations. If this explanation is correct, the YL shouldbe directly or indirectly related to the presence of dislocations in the �lm,and should be enhanced at grain boundaries. The latter conclusion wasbased on the assumption that dislocations or defects decorating dislocationsparticipate in the yellow DAP emission [225].

The spatial uniformity of the yellow emission was also examined by Ponceet al. [226]. They examined undoped GaN MOCVD �lms grown on a bu�erlayer. Spatial distribution of the band edge emission and of the yellow bandin MOCVD-grown GaN on sapphire showed signi�cant nonuniformity [226].The observed emission nonuniformities were found for both edge (�=364nm) and for the yellow (�=559 nm) emissions. Their spatial variation wascorrelated with the columnar structure (low-angle grain size) measured bytransmission electron microscopy. Such columns are typically observed inwurtzite GaN �lms with diameters in the order of 200-500 nm. Extendeddefects seem to be absent from the interior of these columns and thus thedefect distribution is spatially nonuniform. The authors hypothesise thatthe sources of YL were either dislocations at low angle grain boundaries in


the material or point defects, which nucleate at the dislocations. The sameauthors suggest that the states responsible for the YL either arise directlyfrom the atomic structure of the dislocations or are associated with cluster-ing of native point defects in their proximity.

The nature of YL in undoped GaN on sapphire and in laterally overgrownGaN was investigated by Li et al. [227]. They have suggested that the statesresponsible for the YL are associated with extended defects. Importantly,they found that the YL could be reduced or eliminated by simply increasingthe growth temperature of the bu�er layer. This enlarges the hexagonalcrystallites and reduces the density of extended defects. Furthermore, inlaterally overgrown GaN with a very small density of extended defects, theYL intensity can be suppressed even further. Interestingly, at the same timethe authors were also able to suppress the donor-acceptor emission at about3.2-3.3 eV, which exhibited a clear correlation with YL.

Recently Li and Coleman [228] reported that the intensity ratio of the edgeto yellow PL depends on the thickness of the examined epilayer, and thatthe ratio is smaller in regions closer to the sample/substrate interface, wherethe density of dislocations is the largest. This observation was questionedby Knobloch et al [59], who underlined an important role of light reabsorp-tion e�ects. Light reabsorption a�ects more strongly the intensity of theedge emission, since this emission overlaps with the spectral region of strongabsorption. While the edge PL is strongly reabsorbed upon the passagethrough the GaN �lm, the YL band do not overlap with spectral regions ofstrong absorption, and thus the YL can freely pass through thick �lms.

The presented results combine into a rather confusing picture. All groupsconsistently report that the granular structure of GaN �lms is re ected inlarge intensity uctuations of the edge emission. Information on the prop-erties of the YL is, in turn, rather inconsistent. Recently [229] we haveproposed that signi�cant di�erences between the reported properties of theYL can be understood if we assume that several PL emissions are observedin the same spectral region and contribute to the YL.

We veri�ed the possibility that variations of the edge to yellow intensityratio depend on the sample thickness and location of the point where theemission is excited. This was possible through depth-pro�ling CL investiga-tions. In this study we used the fact that penetration depth of an electronbeam depends on beam energy [91, 137]. In Figure 5.6 we show the resultsof the depth pro�le CL study of an MOCVD �lm. We show the CL spectrataken at two accelerating voltages at constant electrical power conditions.The study was performed using a 2.5 �m thick MOCVD epilayer. At a beamenergy of 5 keV the observed CL comes from the near surface region of the

5.2. RECOMBINATION AT DISLOCATIONS 87

sample. At 20 keV and higher beam energies, the CL is excited close tothe GaN/sapphire interface. These excitation conditions were directly con-�rmed experimentally by observing the infrared substrate-related emission(not shown in the �gure) under appropriate conditions. Figure 5.7 con�rmsthe observation of Li and Coleman [228] and the recent results of Fleischeret al [137] that the yellow CL becomes stronger in the interface region. Wealso observed that the intensity of the edge PL is reduced in the same region.

The mechanism of the observed enhancement of the yellow emission re-mains unclear. It can not be simply explained by an increased dislocationdensity in the interface region, since we do not observe an intense yellowCL coming from grain boundary regions, where the dislocation density ishigh. The most likely explanation relates an increased intensity of the YLto accumulation of defects in the interface region, as suggested earlier inRefs. [230, 231]. To clarify this point we performed depth-pro�ling inves-tigations in a range of other samples, including quasi-epitaxial GaN MBE�lms grown on sapphire substrate covered with thick MOCVD-grown GaN.In all the samples studied we have observed an enhancement of the YL whenexcited near the interface region (see Figure 5.7). The YL also red-shifts andshows an asymmetric shape, as shown in Figure 5.8. We also note that theedge emission can be enhanced in the interface region, as seen in Figure 5.7.If the bound excitons dominate the edge emission, the latter observation canalso be explained by an enhanced accumulation of defects in the interfaceregion. We must however conclude that the in-plane and in-depth propertiesof GaN emission are still not fully understood.

The problem of dislocations is apparently more severe in laser diodes withcarrier densities larger than those in LEDs by a factor in excess of ten.At increased carrier densities the uctuating potential and built-in electric�elds are screened and the observed Stokes shifts are small [232]. In conse-quence, the eÆciency of light output from laser diodes varies with changesin current density, as was recently reported by Nakamura [205]. Loweringof the threshold current in GaN-based laser diodes may be of advantage, asit not only helps to reduce heat dissipation but also reduces the screeningeÆciency and consequently the rate of nonradiative recombination at dislo-cations.

5.2 Recombination at dislocations

It is not fully clear what is the mechanism of carrier recombination re-lated to the dislocations. Dislocations can a�ect the PL emissions in GaN


and InGaN by introducing competing paths for carrier trapping. They canalso introduce short-range potentials and trap excitons by the mechanismknown to form excitons at neutral centres. There is also a long list of otherpossible mechanisms of the PL deactivation, related to carrier trapping bydislocations. When dislocations trap carriers they become then chargedand introduce large uctuations of electric �eld in the samples. This uc-tuating electric �eld can a�ect the rate of exciton formation and thus thePL eÆciency. Another possible nonradiative recombination process is alsodue to carrier trapping at dislocations, namely the intensity of the edge PLcan be quenched by an Auger-type energy transfer from excitons to carrierstrapped at vacancy-related deep centres. Then, the excitons recombine non-radiatively, whereas carriers at dislocations are ionised by an energy transferprocess. Concluding, these processes relate to either carrier trapping by dis-locations or creation of uctuations in the �lms. The latter process was infact observed experimentally [233] where it was demonstrated that disloca-tions give rise to a spatially varying surface potential. Moreover, in edgedislocations, the polarisation charge density and electric �elds are gener-ated, but only near the interfaces. Recently, Shi et al pointed out that thesee�ects have a rather minimal in uence on electrical and optical propertiesof the material [234]. The most crucial issue is thus the possibility of carriertrapping by dislocations and the role of these e�ects on the PL emissionprocesses.

Most of the recent studies suggest that dislocations can trap carriers, i.e.,introduce deep trap centres in GaN lattice and lead to local uctuatingelectric �elds [221, 223, 235]. Hacke et al [223] demonstrated that the PL in-tensity decreases with increasing etch pit density (dislocation density) andalso that the di�usion length of minority carriers directly follows changes indislocation density. The latter e�ect can be understood if we consider carriertrapping by dislocations leading to the highly inhomogeneous in-plane strainand large in-plane variation of the edge PL. Similar conclusion were drawnby Rosner et al [221] from their CL mapping investigations in ELOG GaNand InGaN epilayers. They demonstrate that the ELOG procedure, whichreduces the concentration of dislocations in overgrowth regions also lowersthe density of electrically active centres. They report a rather surprisingresult that the upper limit of less than 200 nm for minority carrier di�usionis the same in InGaN and in GaN epilayers. This value is smaller than atypical inter-dislocation separation, which is signi�cant for explanation of arelatively high light emission eÆciency from GaN and InGaN �lms.

Several groups suggested that carrier trapping can lead to the PL emis-sion. We already discussed the relation between the dislocation density andthe YL intensity. Presently, most of the results rule out the dislocations asthe microscopic centre responsible for the YL. However, few other PL tran-

5.2. RECOMBINATION AT DISLOCATIONS 89

sitions were tentatively related to dislocations. Radiative recombination atdislocations was considered by Shreter and Rebane [236], who attributed thePL emission at 3.404 eV to recombination of bound excitons at the c-axisscrew dislocations. In turn, the 3.41 eV emission was tentatively assignedto radiative recombination of excitons bound at charged dislocations [236].This assignment was not con�rmed by later investigations of Fischer et al[237]. From the scanning CL investigations they have not observed any cor-relation between these two and the density of screw dislocations in GaNsamples.


Table 5.1: Lattice mismatch for thin GaN epilayers grown on various sub-strates.

%AlN +2.5� -SiC +3.5ZnO 1.9

sapphire +14.8Si(111) -16.9GaAs -20.2

References 91

Figure 5.1: Surface morphology of GaN epilayer grown by MBE studiedwith atomic force microscopy.


Figure 5.2: Scanning electron microscopy image of 5 by 5 �m region ofMBE-grown GaN epilayer. Granular structure of the �lm is well resolved.

References 93

Figure 5.3: Scanning monochromatic CL image of 5 by 5 �m region ofMBE-grown GaN epilayer. Granular structure of the �lm is well resolvedas observed in large intensity uctuations of the excitonic edge emission ofGaN.


Figure 5.4: Scanning monochromatic CL image of 5 by 5 �m region of MBE-grown GaN epilayer. The granular structure of the �lm, resolved in SEMimage, has no e�ect on the intensity of yellow emission of GaN.

References 95

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Figure 5.5: The CL spectra measured at four di�erent spots of MBE-grownGaN epilayer of granular structure.


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Figure 5.6: The CL spectra of MOCVD-grown GaN measured at roomtemperature and 5 keV and 20 keV electron beam energy. For 20 keV CLcomes from deeper regions of the sample, close to sapphire/GaN interface.

References 97

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Figure 5.7: The CL spectra of MBE-grown GaN structure measured at roomtemperature and 10 keV and 25 keV electron beam energy. At 25 keV theCL comes from deeper regions of the sample, close to the sapphire/GaN in-terface, as con�rmed by the appearance of sharp sapphire-related CL peaks.


��

�

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��

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Figure 5.8: The yellow CL observed in MBE-grown GaN epilayer grown onGaN (MOCVD)/sapphire substrate. The YL collected from the interfaceregion (at 25 keV) is asymmetric and due to two overlapping emissions.

References

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Transitions in Solids. Pergamon Press, Oxford, 1975.

[2] R. Dingle, D.D. Sell, S.E. Stokowski, and M. Ilegems. Phys. Rev. B,4:1211, 1971.

[3] B. Monemar. Phys. Rev. B, 10:676, 1974.

[4] R.L. Aulombard B. Gil, O. Briot. Phys. Rev. B, 52:17028, 1995.

[5] K. P. Korona, A. Wysmolek, K. Pakula, R. Stepniewski, J.M. Bara-nowski, I. Grzegory, B. Lucznik, M. Wroblewski, and S. Porowski.Appl. Phys. Lett., 69:788, 1996.

[6] M. Godlewski, A. Wysmolek, K. Pakula, J.M. Baranowski, I. Grze-gory, J. Jun, S. Porowski, J.P. Bergman, and B. Monemar. InProc. International Symposium on Blue Laser and Light Emitting

Diodes, Chiba, Japan, March 5-7 1996, eds: A.Yoshikawa, K.Kishino,M.Kobayashi, T.Yasuda (Omsha, Ltd., Tokyo), page 356, 1996.

[7] K. Pakula, A. Wysmolek, K.P. Korona, J.M. Baranowski, R. Step-niewski, I. Grzegory, M. Bockowski, J. Jun, S. Krukowski, M. Wrob-lewski, and S. Porowski. Solid State Commun., 97:919, 1996.

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