www.elsevier.com/locate/optmat

Optical Materials 27 (2005) 1041–1045

Efficient silicon light emitting diodes by boronimplantation: the mechanism

J.M. Sun *, T. Dekorsy, W. Skorupa, A.Mucklich, B. Schmidt, M. Helm

Institute of Ion Beam Physics and Materials Research, Forschungszentrum Rossendorf, Dresden, Germany

Available online 8 October 2004

Abstract

Experiments and theoretical modeling are presented on the origin of efficient electroluminescence from boron implanted Si-

LEDs. At low lattice temperatures two bound exciton traps created by high dose boron implantation were observed in the most

efficient LEDs with external power efficiency above 0.12%. The temperature dependence of the correlation between the EL intensity

from free and bound excitons is analyzed by a rate equation model. This analysis reveals that the bound excitons have a unique

characteristic of a low recombination rate. The enhancement of EL from free electron-hole pairs with increasing temperature is

due to the thermal activation of carriers from bound exciton traps.

� 2004 Elsevier B.V. All rights reserved.

Keywords: Silicon pn junction; Electroluminescence; Bound excitons; Rate equations

Silicon light-emitting devices (LEDs) are important

for the realization of silicon based optoelectronics[1,2]. However, standard bulk silicon is an inefficient

light emitter due to its indirect bandgap, the radiative

recombination probability is very low with spontaneous

recombination lifetimes in the milliseconds range. Re-

cently, successful approaches for gaining light from pn

diodes have been reported with the prospect of sufficient

electroluminescence (EL) efficiency. The most promi-

nent systems are surface textured silicon diodes [3],and dislocation-rich silicon pn diodes [4,5]. Recently,

concepts for the suppression of the fast non-radiative

recombination have succeeded in obtaining efficient

EL from silicon pn diodes, e.g. by using high purity

floating-zone silicon with efficient surface passivation

[3] or carrier confinement by strain induced potentials

around dislocation loops [5]. In this paper we propose

a new approach for increasing the room-temperatureluminescence efficiency of silicon by back-transitions

0925-3467/$ - see front matter � 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.optmat.2004.08.059

* Corresponding author.

E-mail address: j.sun@fz-rossendorf.de (J.M. Sun).

from long-lived bound excitons to free excitons in silicon

at elevated temperature. Our study reveals that the fastnon-radiative recombination processes can be effectively

suppressed by introducing appropriate traps into silicon

[6], which exhibit low recombination rates. These traps

act as temporary reservoirs of excitons and contribute

to the efficient band edge EL via the thermal release of

free electrons and holes to the conduction and the

valance bands at elevated temperatures. The theoretical

calculations are consistent with the temperature depen-dences of the EL from bound excitons and free excitons

observed in our previously reported efficient silicon light

emitting diodes with a room temperature power effi-

ciency up to 0.12% [6].

The silicon pn diodes were prepared by boron

implantation into (100) oriented Sb-doped n-type

(0.1Xcm) silicon substrates at a tilt angle of 7� througha 50nm thermally grown SiO2 layer. Boron doses of4 · 1015 (A), and 2 · 1013cm�2 (B), were implanted at

an energy of 25keV. Samples were subsequently furnace

annealed at 1050 �C for 20 min and processed into 1mm

diameter diodes with metallic ring contacts on top. For

1042 J.M. Sun et al. / Optical Materials 27 (2005) 1041–1045

low-temperature EL studies, the diodes were mounted

on the cold finger of a closed-cycle cryostat with silver

paste. I–V characteristics were measured with a

sourcemeter (Keithley 2410) in a current- or voltage-

controlled mode. EL spectra were measured with a mon-

ochromator and a liquid nitrogen cooled InGaAs detec-tor. The EL intensity was simultaneously recorded with

the I–V characteristics measured in a current-controlled

mode. The absolute EL power from the diode at RT was

measured using a calibrated large-area optical power

meter placed in proximity of the diode. The external

EL power efficiency is calculated by dividing the total

EL output power from the front plus the back surface

of the diodes by the input electrical power.The theoretical model concerning the interaction be-

tween free excitons and bound exciton states are based

on solving a group of rate equations under steady-state

conditions. The rate equations of excitons at different

energy levels are based on capture, emission, and recom-

bination processes of excitons or free electron-hole

pairs. For simplification of the theoretical treatment,

we summarize all the steady state rate equations of theexcitons ( bound and free excitons) and all excitons

bound to trap states:

G�Pmi¼1

W i � ni � n0 � W 0 ¼ 0

n0 �Pm

i¼1ci0ðNi�niÞPm

i¼1Ni

�Pmi¼1

ei0 � ni �Pmi¼1

W i � ni ¼ 0;

ð1Þ

where G is the area generation rate of free excitons, m is

the number of the discrete energy levels of bound exci-

tons, n0 is the area density of free exciton states and free

excitons in the planar diodes, Ni, and ni are the area den-

sity of bound excitons states and bound excitons at the ith

trap band below the free exciton band, c0i is the capturecoefficient of a free exciton to an empty states in the ith

trap level, ei0 is the emission coefficient of a bound exciton

from a trap state into the ith free exciton level,W0 andWi

are recombination coefficients of a free exciton and a

bound exciton, respectively. From the Eq. (1) we derive

a second order equation for the free carrier density n0:

W 0n20 � ðG� b� W 0aÞn0 � Ga ¼ 0; ð2Þwhere

a ¼ ðei0 þ W iÞci0

Xmi¼1

Ni ¼Pm

i¼1niei0 þPm

i¼1niW i

� �Pmi¼1nic0i

Xmi¼1

Ni;

ð3Þand

b ¼ W i

Xmi¼1

Ni: ð4Þ

The magnitude of a denotes the area density of

bound excitons, which are subsequently released to free

excitons and annihilated through recombination. The

meaning of b is the maximum recombination rate of

the bound exciton at trap states. The valid positive root

of Eq. (2) gives the expression of the free carrier density

as a function of the generation rate:

n0 ¼G� W 0a� bþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðJ þ W 0aþ bÞ2 � 4Jb

q2W 0

: ð5Þ

Under the thermal equilibrium between bound exci-

tons and free excitons, the mean filling factor, ft, of all

excitons bound at traps states are related to the free exci-

ton density, as derived from Eq. (1):

ft ¼Pm

i¼1niPmi¼1Ni

¼ n0ðn0 þ aÞ : ð6Þ

We assume that the injected hole current equals the

electron current at the injection interface of the diode,

and—initially—all injected holes and electrons form free

electron-hole pairs which become subsequently trapped

as bound excitons. Hence the area generation rate G

of free electron-hole pairs equals the injection currentdensity J. Finally the expression of the free exciton EL

intensity can be simply written as a function of the in-

jected current density. The integrated luminescence

intensity of FETO, is proportional to the free exciton

radiative recombination rate, Wr, of free electron-hole

pairs times the area free exciton density n0, IFE= Wrn0. By setting kf = Wr/W0, a 0 = W0a, we get a sim-

ple expression for the EL intensity from the free elec-tron-hole recombination as a function of the current

density

IFE ¼ kfJ � a0 � bþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðJ þ a0 þ bÞ2 � 4Jb

q2

: ð7Þ

Two regimes of injection current can be distin-

guished, e.g. at high injection, J � a 0, the luminescence

intensity of the free electron-hole recombination shows a

linear relationship with increasing current,

IFE ¼ kfðJ � bÞ: ð8ÞSetting IFE = 0 gives the value of the maximum

recombination rate when all traps states are occupied

by excitons. At lower injection currents below the linear

regime, where n0 is comparable to a, the free exciton

luminescence can be strongly influenced by the filling

factor of the trap states if a 0 is large. By using Eq. (6)

we obtain:

IFE ¼ kfa0ft

1� ft: ð9Þ

This reveals that the luminescence of the free elec-

tron-hole recombination at low current injection isproportional to a 0, which is related to the thermal

emission, capture, and recombination coefficient of

bound excitonic traps (having a linear relationship

to b),

0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.200

50

100

150

200

250

B

A

PI

TO

PII

TO

FETO

A: B+ 4x1015 cm-2

B: B+ 2x1013 cm-2

T=12KCurrent 50 mA

EL

inte

nsity

(ar

b. u

nits

)

Photon energy (eV)

Fig. 1. (a) EL spectra at 12K from silicon pn diodes prepared by B+

implantation at 25keV with different doses of 4.0 · 1015 (A), and

2.0 · 1013 (B) cm�2 after annealing at 1050 �C for 20 min.

0.0 0.1 0.2 0.3 0.4 0.5 0.610-1

100

101

102

103

300 K 100 K 25 K 12 K Simulation

EL

inte

nsity

(ar

b. u

nits

)

Current (A)

Fig. 2. The integrated EL intensity of the FETO peak versus current of

a silicon pn diode prepared by B+ implantation at 25keV with a dose

of 4.0 · 1015cm�2 at different temperatures of 12 (hollow squares), 25

(circles), 100 (hollow up triangles) and 300K(hollow down triangles).

The solid lines are theoretical fits.

J.M. Sun et al. / Optical Materials 27 (2005) 1041–1045 1043

a0 ¼ W 0

c0i� 1þ ei0

W i

� �b ¼ W 0

c0i� 1þ

Pmi¼1niei0Pmi¼1niW i

� �b: ð10Þ

The ratio of the recombination coefficient of free elec-

tron-hole pairs divided by the capture coefficient of the

traps states, W 0=c0i, can be determined at very low tem-

peratures, where ei0 � 0, a0=b ¼ W 0=c0i. The logarithm

ofPm

i¼1niei0=Pm

i¼1niW i is expected to show several linear

regimes as a function of reciprocal temperature if differ-

ent trap bands with different activation energies exist.

Each linear regime can be fitted separately by anequation

Xmi¼1

niei0

,Xmi¼1

niW i ¼ A0 þ Ai � T32e

�EiaKT ; ð11Þ

where A0 can be regarded as the contribution of the

thermal emission by other bound exciton levels, Ai is a

constant related to the density of states in the ith bond

exiton level, K is Boltzmann constant, Eia is the activa-

tion energy of the bound excitons at the ith trap level.

The slope of each linear regime represents the activation

energy of the bound excitons.

From Eqs. (8) and (9) we see that reducing the totalrecombination rate from the trap states results in an

increase of the thermally transition probability from

bound excitons to free electron-hole pairs at elevated

temperatures. This provides a new approach for increas-

ing the luminescence efficiency from free electron-hole

recombination at room temperature if an appropriate

high density of excitonic traps is introduced in the pn

diode. The requirements for the related bound excitonsare a high capture coefficient, a low recombination

coefficient, and an appropriate value of the activation

energy for efficient thermal back-transfer from bound

excitons to free electron-hole pairs at room

temperature.

This model was successfully used for the simulation a

S-type negative differential resistance of pn diodes in-

duced by bound excitons at low temperature [7]. Moreimportant, it can describe the EL mechanisms concern-

ing the exchange of bound excitons and free excitons in

highly-efficient pn diodes. Fig. 1 shows the EL spectra at

12K from two silicon pn diodes prepared by boron

implantation at different doses of 4 · 1015 (A), and

2 · 1013cm�2 (B). At the very low boron implantation

dose of 2 · 1013cm�2, no strong luminescence from

bound excitons is observed in the EL spectrum (B). Atthe high implantation dose of 4 · 1015cm�2, the spectra

show a peak from the transverse optical (TO) phonon-

assisted free exciton recombination at 1.1eV (FETO)

and two asymmetric broad EL peaks close to 1.05eV

and 0.95eV from TO phonon-assisted recombination

of excitons bound to traps (PTOI and PTO

II , respectively).

Above an implantation dose of 5 · 1014cm�2, the

bound-exciton peaks (PTOI , PTO

II ) increase strongly withincreasing the boron doses up to 4 · 1015 cm�2.

The EL intensity of FETO peak versus the injection

current density can be very well simulated in a wide

range of device temperature from 12 to 300K for the

diodes (A) prepared by boron implantation with differ-

ent doses. The experimental data of diode (A) fit very

well with the theoretical simulation of Eq. (7) as shown

by the semi-logarithmic plot of the integrated EL inten-sity of the FETO peak in Fig. 2 at temperatures of 12, 25,

100 and 300K. At higher injection current when the

traps are nearly saturated, a linear relationship between

EL intensity and injection current is consistent with the

solution of Eq. (8); and also, the temperature depend-

ence of the FETO peak becomes weaker. At low current

injection below the linear regime, the free exciton den-

sity is comparable to the value of a, the integrated inten-sity of FETO peak shows a much stronger increase with

increasing temperatures due to the significant influence

1044 J.M. Sun et al. / Optical Materials 27 (2005) 1041–1045

of trapping and detrapping of bound excitons. The val-

ues of kf, a 0 and b can be determined at each tempera-

ture by simulating the intensity of FETO versus current

density through Eq. (7). Fig. 3(a) shows the calculated

logarithm of the ratio of a 0/b as a function of the recip-

rocal temperature of four samples implanted with dif-ferent boron doses. The samples A, which show

bound-exciton peaks PTOI and PTO

II in the EL spectra, have

an increased value of a 0/b as compared to the sample (B)

without bound-exciton peaks. Fig. 3(b) shows the loga-

rithm of the integrated EL intensity of the FETO peak

as a function of the reciprocal temperature of the same

samples. As a consequence, the EL intensity of the FETO

peak increases with a similar temperature dependence ofa 0/b in Fig. 3(a). The sample (A) implanted with a high

boron implantation dose has a larger ratio of a 0/b com-

pared to sample (B). This reveals that the increase of

the EL from FETO peak is originating from an increase

of thermally induced back transfer from bound excitons

to free electron-hole pairs. The extrapolation of the func-

tion to low temperature where ei0 ffi 0 gives the ratio of

free electron-hole recombination rate to the sum of thecapture rate of the traps W 0=c0i ¼ 0:005 in the diode

(A) implanted with a boron dose of 4 · 1015 cm�2. This

means that the trap created by boron implantation has a

very high capture rate of excitons about 200 times higher

0 200 400 600 800 100010

-5

10-3

10-1

10-4

10-2

100

102

A

B

(b)

A: B 4.0x1015 cm2

B: B 2.0x1013 cm2

EL

pow

er e

ffici

ency

(%

)

1/kT (eV-1)

B

A

(a)

FETO peak

I= 50 mA

α'/

β

Fig. 3. The calculated ratio of a 0/b (a) and the power efficiency of the

EL from the FETO peak (b) as a function of reciprocal temperature for

silicon pn diodes prepared by B+ implantation at 25keV with different

doses of 4.0 · 1015 (A) (squares), and 2.0 · 1013 (B) (up triangles).

than the recombination rate of free excitons. Fig. 4 is the

logarithm of the ratio of the emission/recombination ra-

tio,Pm

i¼1niei0=Pm

i¼1niW i, as a function of reciprocal tem-

perature for diode (A), which shows bound exciton peaks

PTOI and PTO

II in the low-temperature EL spectra. Two lin-

ear regimes in the curves clearly show thermal emissionfrom two excitonic traps levels with activation energies

of 9.5meV and 63meV by fitting with Eq. (11) in the tem-

perature ranges of 12–50K and of 60–340K. The calcu-

lated binding energies are consistent with the activation

energy of 9.5meV and 61meV, determined independ-

ently by fitting the temperature dependence of EL inten-

sity of PTOI and PTO

II [6]. The consistency of the binding

energies of bound excitons between the theoretical simu-lations and experimental results reveals that the increase

of free exciton emission is related to the thermal emission

of excitons from the two excitonic trap with emission

bands PTOI and PTO

II created by high dose boron

implantation.

In comparison to the temperature dependence of the

EL of the FETO peak in Fig. 3(b), the bound excitons

with a lower binding energy contribute to the first in-crease of the FETO peaks at low temperatures; while

the bound excitons with higher binding energy contri-

bute to the second increase of the FETO peaks at high

temperatures. Fig. 4 also shows that the excitons bound

at these traps have a thermal emission rate more than

3000 times higher than the recombination rate at

300K. This result is consistent with the spatially indirect

recombination characteristic of bound excitons observedin our diodes [8], which showed similar optical property

as the long-lived spatially indirect bound excitons in p-

type d-doped silicon layers grown by molecular beam

epitaxy [9,10], as well as GaAs d-doped superlattices [11].

In conclusion, our calculated and experimental re-

sults reveal that the thermal release from bound excitons

0 200 400 600 800 100010

-3

10-1

101

103

105

Calculated fit for P

I

TO

fit for PII

TO

emis

sion

/rec

ombi

natio

n

Ea =9.5 meV

Ea =63 m

eV

1/KT (eV-1

)

Fig. 4. Ratio of emission/recombination ratio of the bound excitons

PTOI and PTO

II versus reciprocal temperature (squares). The solid lines

are theoretical fits to the two exponential regimes using Eq. (11) for

two trap levels with activation energy of 9.5 and 63meV.

J.M. Sun et al. / Optical Materials 27 (2005) 1041–1045 1045

to free excitons is a new approach for improving the

luminescence efficiency in indirect bandgap semiconduc-

tors with a low band edge recombination probability.

This is consistent with the enormous increase of the

EL efficiency up to 0.12% at room temperature in silicon

pn diodes. The theory suggests that similar approacheswould be possible to improve luminescence of silicon

by introducing temporary source of long-lived bound

excitons with a low recombination rate and an appropri-

ate binding energy, such as isoelectronic traps or quan-

tum dots with type II band structures.

Acknowledgements

We would like to thank H. Felsmann, C. Neisser, G.

Schnabel, I. Winkler, and M. Missbach for assistance in

the sample preparation.

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