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Nano Energy (2015) 14, 382–391

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Piezoelectric field enhancement in III–Vcore–shell nanowires

Hanan Y.S. Al-Zahrania, Joydeep Pala,n, Max A. Miglioratoa,Geoffrey Tseb, Dapeng Yub

aSchool of Electrical and Electronic Engineering, University of Manchester, M13 9PL, United KingdombState Key Laboratory of Mesoscopic Physics and Department of Physics, Peking University, Beijing 100871,PR China

Received 14 October 2014; received in revised form 17 November 2014; accepted 18 November 2014Available online 2 December 2014

KEYWORDSIII–V Semiconductors;Core shell nanowires;Piezoelectricity;Nanogenerators

0.1016/j.nanoen.2he Authors. Publismons.org/licenses

thor. Tel.: +44 16oydeep.pal@manc

AbstractLinear and quadratic piezoelectric coefficients of wurtzite III–V (GaP, InP, GaAs and InAs)semiconductors are calculated using ab-initio density functional theory. We show that thepredicted magnitude of such coefficients is much larger than previously reported and of thesame order of magnitude as those of III-N semiconductors. In order to show the applicability ofwurtzite III–V semiconductors as piezoelectric materials, we model the bending distortioncreated on a nanowire by an atomic force microscope tip. We calculate the dependence of thepiezoelectric properties of both homogeneous and core shell wurtzite III–V semiconductorstructures on the induced deflection. We show that a number of combinations of III–V materialsfor the core and the shell of the nanowires can favor much increased voltage generation. Weobserve the largest core voltages in core/shell combinations of InAs/GaP, InP/GaP, GaP/InAsand GaP/InP which are predicted to be 3 orders of magnitude larger than the typical values of73 V in homogeneous nanowires. Also considering properties such as voltage generation,bandgap discontinuity and mobility, III–V wurtzite core–shell nanowires are candidates for highperformance components in piezotronics and nanogeneration.& 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BYlicense (http://creativecommons.org/licenses/by/3.0/).

Introduction

Piezoelectricity in III–V and II–VI semiconductors is a well-known phenomenon that has recently gained strong interestin the field of Piezotronics [1]. The fundamental paradigm

014.11.046hed by Elsevier Ltd. This is an op/by/3.0/).

13064724.hester.ac.uk (J. Pal).

of this recent field of research is the exploitation of straininduced piezoelectric (PZ) polarization in semiconductornanostructures to develop unique electronic devices inoptoelectronics [2], mechanical sensing [3], piezoelectrictransducers [4], transparent conductors [5] and energyharvesting nanogenerators (NGs) [6].

As piezoelectricity is a deformation induced process, theneed for highly flexible devices requires nanostructured mate-rials. The most commonly used nanostructure in piezotronic

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383PZ field enhancement in CSNWs

devices is the nanowire (NW) [1]. To date most of theaforementioned applications have been realized using ZnONWs. However there are many other PZ semiconductors thatcould be utilized as piezotronic materials.

III–V Nanowires

NWs made from III–V semiconductors [7], with excellent controlover dimensions and compositions, can be now routinely grownby metal organic chemical vapor deposition MOCVD [8] ormolecular beam epitaxy (MBE) using a vapor� liquid�solidmethod with gold as catalyst, allowing for NWs containingmany variations and combinations of different materials. NWsin this case are vertically grown, epitaxially on a latticemismatched semiconductor substrate. Depending on the sub-strate orientation both zincblende (ZB) and wurtzite (WZ)crystal structures are possible.

Moreover, NWs can be grown on other substrates such asglass, metals and polymers [9]. Glass substrates are a veryattractive alternative to semiconductor substrates, becauseof availability, transparency and cost. On the other hand,the amorphous state of the substrate and the presence ofimpurities cause limitations to growth on a glass surface.Nevertheless defect free ZB GaAs NWs grown on glasssubstrates by using a horizontal MOVPE process involvingtrimethylgallium and tertiarybutylarsine at growth tem-peratures of 410–580 1C have been found to exhibit brightphotoluminescence emission which implies good crystalquality [9].

The stability of crystals varies notably when overalldimensions approach the nanometer scale. In fact, withsmaller sizes, the energy present on the nanostructure'ssurface takes greater significance in assessing the overallfree energy change in the crystal formation [10]. Previousresearch indicates that lower surface energy is seen in WZcrystals as compared to the ZB lattice [11]. From this, it canbe postulated that once the surface area of the WZnanostructures reaches a particular proportion in relationto volume, thermodynamic conditions may become favor-able. In support of this view, a number of experimentalworks [12–17], using epitaxy or catalysis driven vapor–liquid–solid growth, has resulted in WZ single-crystal NWs. Thenanostructures created show optoelectronic parametersdifferent to those usually seen in the equivalent ZB bulklattices [18–20]. As an example of this, NWs consisting ofGaP in the WZ phase shows direct bandgap as opposed to theindirect bandgap typical of the ZB phase [13]. Based onimprovements in terms of creating suitable alloys, there ispotential for WZ NWs being used even in the silicon systemas effective and ecological emitters [10]. This is with theprovision that surface-based non-radiative recombination isavoided as far as possible by means of appropriate passiva-tion of the surface or with a sufficiently large NW diameter.A limitation exists however in the maximum diameter thatensures crystal stability in the WZ phase. Instability leads tothe development of the nanostructure into mixed hexagonaland cubic lattices [11,21,22] (also known as polymorphism)which create discontinuities in the band profile and henceplaces restrictions in terms of electro-optical performance.

Work conducted with III-As and III-P shows that only if thematerial is synthesized as NWs, a defect free WZ phase can

be obtained [23]. Crystalline structural alteration accom-panies electronic structural change. Previous hypothesessuggested that the ZB phase would align as a type II bandwith the WZ phase when utilized in III–V semiconductors[24]. In more recent studies, there is evidence of type-IIband alignment for InP NWs [25,26] giving rise to crystal-phase quantum-dot formation [27]. A broad variation ofband edges, from 1.43 eV to 1.54 eV is observed whenmeasuring luminescence of GaAs NWs with a predominantWZ phase [28–30,12,27,31] showing how the interplaybetween the ZB and WZ sections affects the homogeneityof the band edges, occasionally forming quantum confinedregions due to the different line-ups of the two crystalphases.

Core shell nanowires

MBE or MOCVD has enabled the preparation of NWs combin-ing two or more compounds, leading to the formation ofheterostructures. Such NWs fall into two main categories:radial and axial, based on the chosen growth method of thecompound [32].

While axial NWs [33–35] are easily synthesized by chan-ging the growth conditions and material supply during theirformation (e.g. through one-dimensional modulation of theNW composition [34–36] and doping [33]), radial NWs,commonly referred to as core–shell NWs (CSNWs) [32],require a two-step process involving the synthesis of thecore first followed by coating with the shell material. Thisprocess can be repeated several times to obtain multi-shellstructures.

CSNWs have a range of potential applications and are notrestricted to III–V semiconductors. Those based on e.g.Group IV [37–42] are motivated by the predicted enhancedperformance of nanophotonic and nanoelectronic devices[43], while II–VI compounds like CdSe and ZnTe [44] are idealfor achieving high optical performance together with energyharvesting ability. Finally III–V semiconductor based CSNWs[45–49] have been explored as enhanced light-emitting andlaser diodes [50,51] photovoltaics [52] and high-currentbattery electrodes [53].

The WZ CSNW system with an epitaxial interface providese.g. an attractive way to explore the effect of piezo-phototronic in energy harvesting system, GaN/InGaN CSNWsLEDs have rivaled planar InGaN single quantum-well LEDs[54]. The composition and thickness of InGaN in planardevices [54] can be limited by the lattice mismatch strain.However, a NW structure provides pathways to lateral strainrelaxation that often preserve coherence and preventsdefect formation. A core/multishell NW was reported byQian et al. [55,56] where both electron and hole carrierswere confined into the InGaN shell permitting an externalquantum efficiency of 5.8% at 440 nm and 3.9% at 540 nmand a tunable emission in the range of 365–600 nm.

In general, CSNW systems offer many advantages whencompared to their homogeneous NW counterparts. Themore notable advantages include; firstly, the ability toregulate surface impurities and surface states, which arenormally found in the vast majority of nanoscale structures[38,41]. Secondly, the semiconducting NW core can beisolated from the substrate inhomogeneity [33]. Lastly and

H.Y.S. Al-Zahrani et al.384

mostly notably, the realizations of quantum confinement ofcarriers within the core by cladding with a larger bandgapshell [37,38].

The rationale for using the shell material to significantlyimprove the optical and electrical properties of the nanos-tructure through passivation of the free core surface, hasbeen verified in ZB GaAs/AlGaAs CSNWs [57] and wide bandgap InP shells on InAs cores [58–60]. Furthermore enhancedcarrier mobility is observed in InAs NWs when covered withInP shells [58]. In CSNWs strain effects are different fromconventional 2D heterostructured semiconductors. Niquet[61,62] studied the electronic properties of InAs NWsembedded in a GaAs shell, showing that the strain relaxa-tion of the InAs layers are limited by the GaAs shell yet thehydrostatic strain distribution is homogenized. Conse-quently, the formation of strain-induced surface well inthe conduction band is prevented and the electron wavefunctions are more confined to the core material.

Piezoelectricity in III–Vs

While the NWs described so far have several applications asoptoelectronic devices, not all material systems and crystalstructures are strongly PZ and exploitable in Piezotronicdevices. Generally III–V semiconductors in the WZ phase(e.g. III-N) have a larger PZ response compared to ZBcrystals (e.g. III-As). Furthermore the polar axis of WZcrystals is typically parallel to the growth direction, unlikethe [111] polar axis of ZB materials [63].

All WZ III–V semiconductors, under strain, would lead tothe generation of electric dipoles and a resultant PZ fieldalong the polar axis [0001] of the crystal. One would assumethat all III–V semiconductors, if synthesis as stable WZcrystals rather than ZB was possible, would result in largePZ coefficients. This was reported not to be true byBernardini et al. [64] who found e.g. WZ InP, GaP, InAsand GaAs to have PZ coefficients one order of magnitude ormore smaller than those of the III-N materials.

The question that we intend to answer in this work iswhether such WZ NWs, in addition to favorable opticalproperties, also possess electrical properties and a PZresponse that would be sufficiently large to allow the useof these materials in piezotronic devices and NGs.

Table 1 Calculated and measured physical parameters for WZour calculated values and other calculated/experimental ones a

Parameters GaP InP

a (Å) 3.789 (3.759 [84])exp. 4.115 (4.054[8c (Å) 6.253 (6.174[84])exp 6.753 (6.625[8u 0.371 (0.374[84]) 0.374 (0.375[8C33 (GPa) 1.722[87] 1.438[87]C13 (GPa) 0.468[87] 0.386[87]Psp (C/m

2) 0.004 (0.003[78])th 0.001 (�0.001e33 (C/m

2) 0.48 (�0.07[64])th 0.59 (0.04[64])e31 (C/m

2) �0.26 (0.03[64])th �0.24 (�0.02e311 (C/m

2) 1.64453 1.64704e333 (C/m

2) �2.89973 �2.64647e313 (C/m

2) 1.08261 0.83724

Piezoelectricity in semiconductors has long been treatedas a linear effect in the strain. Non-linearity has insteadbeen recognized to have a significant magnitude in ZB III–V[65–67] WZ III-N [68,69] and ZnO [70] semiconductors.However, in the WZ crystal phase, for some III–V semicon-ductors, second-order PZCs have not yet been reported,making it difficult to assess the influence of non-linearpiezoelectricity in NWs and CSNWs.

To resolve the issue of calculating the spontaneous andstrain-induced PZ effect in WZ structures, we report thequadratic piezoelectric coefficients (PZCs) of four III–Vsemiconductors, namely GaP, InP, GaAs and InAs, and showthe magnitude of such coefficients is vital and non-negligible in any calculation of the polarization field. Wealso performed calculations on the properties of III–V CSNWsgrown in (0001) direction.

Evaluation of linear and non-linearpiezoelectric coefficients

In order to evaluate the linear and non-linear piezoelectriccoefficients (LPZCs and NLPZCs) we use the same method[71] that was proved accurate when calculating the NLPZCsof ZnO [72], III-N [68,69] and III-As [65,66]semiconductors.The method, based on Harrison's formalism [72] involves asemi-empirical approach where PZ charges are the sum of abond and a direct dipole contribution. In the model,Harrison's effective charge is always determined such thatwhen the bond polarity and the elastic deformation arecomputed within small strain limits, the PZCs tend towardsknown experimental values [71].

Model data was used in the evaluation of the PZCs andobtained via plane-wave pseudopotential (the Troullier–Martin approach [73] was used for pseudopotential), withdensity functional theory with local density approximation(DFT–LDA) [74] and density functional perturbation theory(DFPT) via the Hamann approach [75] in the CASTEP code[76]. The Berry phase approach [77], applying a finiteelectric field perturbation within periodic boundary condi-tions, was also used. DFT calculated equilibrium values aregiven in Table 1 for WZ III-P and WZ III-As along with thevalues of the effective charge (Zn), the resulting bond

III-P and III-As used in the calculations. Comparisons betweenre given in brackets.

GaAs InAs

5])th 3.928 (3.912[86])th 4.248 (4.192[85])th5])th 6.482 (6.440[86])th 6.969 (6.844[85])th5]) 0.3712 (0.374[86]) 0.374 (0.376 [85])

1.602[87] 1.209[87]0.334[87] 0.321[87]

[78])th 0.002 (0.002[78])th 0.001 (0.001[78])thth 0.32 (�0.12[64])th 0.51 (�0.03[64])th[64])th �0.17 (0.06[64])th �0.26 (0.01[64])th

0.87939 1.83548�1.61433 �2.758580.5155 0.9449

385PZ field enhancement in CSNWs

polarity (αp) and the much smaller Harrison's effectivecharge (ZnH).

The linear and quadratic parameters e33, e31, e311, e333and e313 are obtained when the DFT data for the strainedcrystal is fitted to the following equation:

PTot ¼ Pspþe33ε? þ2e31ε==þe311ε2==þe311ε2? þe313ε==ε? ð1Þ

For all four materials listed, the values of ZnH were fittedto experimentally known linear parameter of the ZB phase,as no experimental values can be found for the WZ phase.The NLPZCs that we obtained are listed in Table 1. The firstnotable prediction contained in the model data is thatsmaller values of the spontaneous polarization (Psp) arepredicted compared to those of other WZ semiconductors[71]. However, for the same materials, such reduced valuesare instead well matched to calculated values [78] using theBerry phase (electrostatic) approach of polymorphic struc-tures with mixture of WZ and ZB [78]. Furthermore Psp ispositive for the case of III-P and III-As, in both the calcula-tions of Belabbes et al. [78] and in our work (with the onlyexception of InP which has an opposite sign though is verysmall in magnitude). The similarity between the values ofPsp obtained through independent methods by Belabbeset al. [78] and us, provides further confidence in Harrison'smethod. Very recent experimental work on WZ GaAs NWs byBauer et al. [79] reported the Psp value to be in the samerange (0.002770.0006 C/m2) as our predicted value(0.002 C/m2). Since in our method the framework toevaluate Psp and the PZCs is consistent, we can also drawconfidence in the validity of our predictions for e31 and e33.The second notable prediction is that the coefficients e33and e31 (Table 1), which were originally predicted to benegligible [64] are instead sizeable and not very dissimilarto those of the III-N systems (e.g. in GaN e31=�0.55 C/m2,e33=1.05 C/m

2) [68], albeit slightly smaller (roughly half).It is also worth noting here that these results appear toalways differ in sign from the published values by Bernardiniand Fiorentini [64], which is most likely due to having used adifferent convention for the [0001] crystal direction.

The most notable conclusion is that contrary to what wascommonly believed WZ III-As and III-P semiconductorsappear to possess linear PZ properties that are comparablewith WZ III-N semiconductors and that hence can too be

Figure 1 AFM Tip Lateral Deflection of nanowire where (R), is thdiameter of the NW and the deflection caused by the AFM tip is (d)NW, (Hþ ) and (H� ) lengths of the NW on the tensile and compress

exploited as materials for piezotronics and NGs. In the nextsection we will show that the flexibility in alloying, elec-trical and electronic properties and compatibility of the III-Pwith III-As materials can offer properties that can evensurpass those of III-N semiconductors.

Modeling AFM tip lateral deflection

An atomic force microscope (AFM) tip is often used to bothprovide deflection to a NW and measure its electricalproperties. Tensile and compressive strains on either sideof a single NW are a result of the tip induced mechanicalforce applied. By modeling the AFM tip induced deflectionand predicting the resulting piezoelectric polarization wecan quantify the effect of the LPZCs and NLPZCs on the PZfield and voltage. We show the polarization on a crosssection of the NW, making the approximation that subject-ing the NW to a bending force deforms the cylindrical shapeinto an arch with constant curvature (Figure 1).

The quantities that are needed as input are the radius ofcurvature (R), the length of the NW (H), the diameter of theNW (D) and the deflection caused by the AFM tip (d). If weassume that θ is the angle that subtends the arch formed bythe deformed NW, then its undeformed length (H) is given by

H¼ Rθ ð2Þwhile the increased (Hþ ) and decreased (H� ) lengths of theNW on the tensile and compressed ends would be given by

H7 ¼ R7ΔRð Þθ ð3Þwhere ΔR is exactly equal to the radius of the nanowire (D/2).With reference to Figure 1, and since θ is typically small (limitof small deflection), we can expand the expression for thedeflection (d) to O N3

� �, resulting in

d ¼ R�R cos θ¼ R 1� cos θð ÞffiR 1�1þ θ2

2

� �¼ R θ

2

2¼ H

θ

θ2

2¼ Hθ

2

ð4Þfrom which

θffi 2dH

ð5Þ

e radius of curvature, (H) is the length of the NW, (D) is the. θ is the angle that subtends the arch formed by the deformeded.

Figure 2 Comparison of the total polarization in WZ homogeneous and core–shell nanowires (CSNWs) when deflected by AFM tip.The first row resembles the homogeneous III-As and III-P nanowires having 1 mm length and 0.5 mm diameter in dimensions with anAFM tip deflection range of 0–360 nm. While the second, third and fourth row are the different combinations of CSNWs. Typical CSNWdimensions are of 1 mm length and core/shell diameter of 0.25 mm/0.5 mm with a 360 nm deflection.

H.Y.S. Al-Zahrani et al.386

which when used in combination with Eq. (2), gives:

Rffi H2

2dð6Þ

Eqs. (5) and (6), in conjunction with Eq. (3), give theexpressions for the tensile and compressive strain deformedlengths of the NW:

H7ffi H2

2d7

D2

!2dH

¼ H7dDH

� �ð7Þ

Eq. (7) depends solely on the diameter (D) and length (H) ofthe Nanowire and the applied AFM tip deflection (d). The

strain along the NW, in the direction [0001] is easily calculatedusing Eq. (7):

e? ¼H7�H

Hffi 7dD

H2

� �ð8Þ

While the in-plane component (assuming that the unit cellpreserves the volume elastically), is given by

e J ¼ �e?C332C13

ð9Þ

where C33 and C13 are the elastic constants of the material,given in Table 1.

387PZ field enhancement in CSNWs

Homogeneous and core shell nanowires

We have performed AFM tip deflection calculations for III-Asand III-P homogeneous NWs using the method describedabove. The NWs with dimensions of 1 mm length and 0.5 mmdiameter are subjected to an AFM tip deflection range of 0–360 nm. The effect of varying deflection on the polarizationof a cross section of a NW or CSNW is shown in Figure 2. Weassume that the polarization varies when moving from thecompressive (bottom of each graph) to the tensile side (topof each graph), but not in the orthogonal direction, so that a1D line of data is fully representative of the polarization overthe 2D cross section. As expected, for all four cases ofhomogeneous III-As and III-P NWs shown, the PZ polarizationis enhanced with increasing deflection, as illustrated in thefirst row of Figure 2. For the largest deflection of 360 nm, thepredicted maximum polarization values for all combinationsof GaAs, InAs, InP and GaP CSNWs range from �0.23 C/m2 atthe compressed end of the section, to +0.33 C/m2 at thetensile end and are in the same order but smaller than thoseof III-N NWs of equivalent dimensions and for similar deflec-tions. As an example, when a homogeneous GaN nanowireundergoes a deflection of 360 nm, polarization values of�0.27 C/m2 (compressed region) and +0.81C/m2 (tensile

Table 2 Calculated values of the total polarization (C/m2)in different WZ homogeneous nanowires comprising GaAs,InAs, GaP and InP in comparison with GaN nanowire whensubjected to an AFM lateral tip deflection of 360 nm.

Material system Total polarization (C/m2)

Tensile Compressed

InP 0.32 �0.22GaP 0.28 �0.23InAs 0.33 �0.20GaAs 0.28 �0.13GaN 0.81 �0.27

Table 3 Total polarization and their difference (in %) using Wcompared with homogeneous NWs at 360 nm deflection at both

Material system(core|shell)

Tensile end

CSNWpolarization(C/m2)

Homogeneouspolarization(C/m2)

Diff(in

GaP|InAs 0.13 0.33 �60GaP|InP 0.17 0.32 �45GaAs|InAs 0.19 0.33 �44GaAs|InP 0.24 0.32 �25GaP|GaAs 0.21 0.28 �23GaAs|GaP 0.22 0.28 �23InP|InAs 0.26 0.33 �20InAs|InP 0.38 0.32 21InP|GaAs 0.36 0.28 29InP|GaP 0.42 0.28 49InAs|GaAs 0.44 0.28 61InAs|GaP 0.48 0.28 68

regions) are predicted. In Table 2, we show the comparisonbetween all the strain induced polarizations in different III-Asand III-P NWs when deflected by 360 nm.

All possible combinations of GaAs, InAs, InP and GaPCSNWs, using typical NWs dimensions (1 mm in length and acore/shell diameter ratio of 0.25 mm/0.5 mm), are sub-jected to the same deflections of 0–360 nm as the homo-geneous NWs. The predicted strain induced polarizationsare shown in the second, third and fourth row of Figure 2.

Considering the case of an InP/GaAs CSNW, a hypotheticalsituation since very few defect free monolayers can betypically grown due to strain, in the absence of any deflection,then the tensile perpendicular strain would be around 4% witha typical compressive parallel strain of around 10%. Then theinherent strain due to the heterostructured growth of theCSNWs produces a much stronger polarization compared to thecase where the whole NW was made homogeneously of theshell material. As an example, for a deflection of 360 nm, thetotal polarization of an InP/GaAs CSNW is increased by 29% atthe tensile end of the shell and reduced by 13% (making it lessnegative) at the compressed end of the shell. In Table 3, wehave compared the strain induced polarization and theirdifference compared to the case where the whole NW wasmade homogeneously of the shell material (in %), for all thedifferent combinations of GaAs, InAs, InP and GaP CSNWs

It is obvious that there are a number of combinationswhere there is an advantage in using a CSNW structure,namely core/shell combinations of InAs/GaAs, InP/GaAs, InP/GaP, InAs/InP and InAs/GaP where the total polarization isincreased by 20–68% at the tensile end and reduced by 13–60%(making it less negative) at the compressed end of the shell.The rest of the core/shell combinations (GaP/InAs, GaP/InP,GaAs/InAs, GaAs/InP, GaP/GaAs, GaAs/GaP, InP/InAs) canprovide even more negative polarization by 20–60% at thetensile end and 7–30% at the compressed end. However not allare possible under experimental conditions due to very highlattice mismatch/strain making it extremely challenging togrow such structures. Alloy combinations in the shell arepotentially more favorable as they would allow for much

Z CSNWs for all combinations of GaAs, InAs, GaP and InPtensile and compressive ends.

Compressed end

erence%)

CSNWpolarization(C/m2)

Homogeneouspolarization(C/m2)

Difference(in %)

�0.26 �0.20 29�0.28 �0.22 28�0.25 �0.20 22�0.25 �0.22 16�0.14 �0.13 7�0.28 �0.23 20�0.23 �0.20 11�0.19 �0.22 �15�0.11 �0.13 �13�0.13 �0.23 �43�0.09 �0.13 �32�0.09 �0.23 �60

Figure 3 Comparison of calculated output piezoelectric voltage from WZ core–shell nanowires (CSNWs) when laterally deflected4 nm by AFM tip. Typical CSNW dimensions are of 1 mm length and core/shell diameter of 0.25 mm/0.5 mm.

H.Y.S. Al-Zahrani et al.388

reduced strain during growth. Experimentally a typical alloycomposition of 4–45% [80–82] for InGaAs/GaAs CSNW isreported in literature, whose crystal quality is demonstratedby high optical performance.

We also calculated the piezoelectric voltage, which is theimportant quantity for piezotronics applications, and com-pared all combinations of GaAs, InAs, InP and GaP CSNWs (withdimensions, 1 mm in length and a core/shell diameter ratio of0.25 mm/0.5 mm), at 4 nm deflection (Figure 3). The largestcore voltages are predicted for the core/shell combinationsInAs/GaP (�1725 V), InP/GaP (�1246 V), GaP/InAs (+1034 V)and GaP/InP (+912 V), which are much larger than the valuesfor typical homogeneous NWs (73 V). While we observe strongnegative voltages (�1725 V to �420 V) in InAs/GaP, InP/GaP,InAs/GaAs, GaAs/GaP, InP/GaAs and InAs/InP, swapping thecore and shell materials yields strong positive voltages(+335 V to +1034 V) in InP/InAs, GaP/GaAs, GaAs/InP,GaAs/InAs, GaP/InP and GaP/InAs CSNW combinations.

However the absolute values of the voltage in the core orshell are not necessarily the important quantity when con-sidering NWs as the power source in a NG. In fact what isimportant is the aptitude to change such voltage whendeformed. In Table 4 we show both the core and shell voltages(in V) at a typical deflection of d=4 nm, at the tensile andcompressed ends. We also show the differences in voltage for4 nm and 0 deflection. The largest differences, which canrelated to voltage generation in NGs, are in the order of 73 Vfor InAs/GaP, InP/GaP and GaAs/GaP. The last four columnsprovide comparison between the shell voltage of the core–shell structure and a homogenous nanowire of the samedimensions (1 mm in length and a diameter of 0.5 mm) made

of the shell or core material only. The best improvements arefound for InAs/GaP (+40.2% compared to InAs) and GaAs/GaP(+48.3% compared to GaAs).

However, while considering CSNWs, we should also take intoaccount the electron mobility and bandgap of GaAs (8500 cm2

V�1 s�1, 1.42 eV), InAs (40,000 cm2 V�1 s�1, 0.35 eV), GaP(250 cm2 V�1 s�1, 2.26 eV) and InP (5400 cm2 V�1 s�1,1.34 eV). All the values of electron mobility and bandgaps aregiven for the ZB crystal phase as the WZ phase properties are notavailable [83]. Materials with higher electron mobility and lowerbandgap should be preferred in the core compared to the shellmaterial as they provide unique benefits of higher conductivityalong with electron confinement within the core. All the sixcore/shell combinations of InAs/GaP, InP/GaP, InAs/GaAs, GaAs/GaP, InP/GaAs and InAs/InP conform to the above criteria foroptimal CSNW structures while if switching the core and shellmaterial in such combinations can be beneficial for applicationsseeking higher resistivity. The combinations InAs/GaP and GaAs/GaP have both increased voltage generation, high conductivity inthe core and confinement between shell and core.

Conclusions

In conclusion we have discussed the importance of piezo-electricity in III–V semiconductors nanowires for applicationsin piezotronics and nanogeneration devices. Piezoelectricwurtzite III-V semiconductors, including laterally hetero-structured semiconductors, as in core shell nanowires, arenow routinely grown using catalyst enabled MBE growth.

Table 4 Core and shell voltages (in V) at d=4 nm deflection, at the tensile and compressed ends. Differences are also givenbetween voltages at 4 nm and 0 deflection. The last four columns provide comparison between the shell voltage of the core–shell structure and a homogenous nanowire of the same dimensions (1 mm in length and a diameter of 0.5 mm) made of theshell or core material only.

Materialsystem

Core Shell Voltage difference between shell andhomogeneous NW

At deflection d=4 nm VoltageDifferencefrom(d=0 nm)

At deflection d=4 nm Voltagedifferencefrom(d=0 nm)

Compressedend

Tensileend

Compressedend

Tensileend

InAs GaAs InP GaP

Core/shellInAs/GaP �1724.45 �1722.17 1.15 �3.21 3.20 3.21 0.92

(40.2 %)0.31(10.7%)

InP/GaP �1245.85 �1243.17 1.34 �3.12 3.11 3.12 0.44(16.4%)

0.22(7.6%)

InAs/GaAs

�959.65 �957.37 1.15 �2.67 2.67 2.67 0.38(16.6 %)

0.64(31.5%)

InP/GaAs �452.51 �452.25 1.34 �2.36 2.35 2.36 0.33(16.3%)

�0.32(�11.9%)

InAs/InP �420.29 �418.01 1.15 �2.85 2.84 2.85 0.56(24.5%)

0.17(6.3%)

GaAs/GaP

�619.16 �617.12 1.02 �3.01 3.01 3.01 0.98(48.3%)

0.11(3.8%)

GaP/GaAs

399.61 402.51 1.45 �1.72 1.72 1.72 �0.31(�5.3%)

�1.18(�40.7%)

GaAs/InAs

741.06 743.09 1.02 �1.87 1.86 1.87 �0.42(�18.3%)

�0.16(�7.9%)

GaP/InAs 1031.17 1034.07 1.45 �1.68 1.68 1.68 �0.61(�26.6%)

�1.22(�42.1%)

InP/InAs 331.91 334.59 1.34 �2.11 2.10 2.11 �0.18(�7.9%)

�0.57(�21.3%)

GaAs/InP 526.57 528.60 1.02 �2.47 2.46 2.47 0.44(21.7%)

�0.21(�7.8%)

GaP/InP 908.94 911.83 1.45 �2.31 2.30 2.31 �0.37(�13.8%)

�0.59(�20.3%)

HomogeneousInAs �2.29 2.29 2.29GaAs �2.03 2.03 2.03InP �2.68 2.68 2.68GaP �2.90 2.90 2.90

389PZ field enhancement in CSNWs

In order to assess the piezoelectric properties of coreshell nanowires made of wurtzite III-Vs we reported valuesof the linear and quadratic piezoelectric coefficients ofwurtzite GaP, InP, GaAs and InAs and show the magnitude ofsuch coefficients is much larger than previously reportedand comparable with those of III-N semiconductors.

In order to evaluate the piezoelectric properties of wurtziteIII–Vs core shell nanowires we developed a model of the bendingdistortion created on a nanowire by an atomic force microscopetip induced deflection. We then analyzed a series of crosssections of the NW, with increasing tip induced deflection,assuming that subjecting to a bending force deforms thecylindrical shape into an arch with constant curvature.

For the core shell nanowires we show that a number ofcombinations of III–V semiconductors are favorable for much

increased voltage in the nanowire. The largest core voltagesfor a 4 nm deflection are predicted for the core/shellcombinations InAs/GaP (-1725 V), InP/GaP (-1246 V), GaP/InAs (+1034 V) and GaP/InP (+912 V), which are much largerthan the values for a typical homogeneous nanowires (73 V).

Since materials with higher electron mobility and lowerbandgap would increase the nanowire conductivity in the coreregion, the six core/shell combinations of InAs/GaP, InP/GaP,InAs/GaAs, GaAs/GaP, InP/GaAs and InAs/InP satisfy thesecriteria. Of these, also considering which ones are predictedto have the largest voltage generation ability, InAs/GaP (anincrease of 40.2% compared to InAs) and GaAs/GaP (an increaseof 48.3% compared to GaAs) are predicted to be optimalcandidates for highly conductive piezotronics and nanogenera-tion elements.

H.Y.S. Al-Zahrani et al.390

Acknowledgments

This work was supported by the Royal Embassy of SaudiArabia, cultural Bureau in London (UKSACB) and the Ministryof Higher Education Kingdom of Saudi Arabia. The authorsalso like to thank the UK Engineering and Physical SciencesResearch Council (EPSRC) for Doctoral Prize Fellowship. Alsothe authors thank the National Natural Science Foundationof China (NSFC), P.R China grant No. 91433102.

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Hanan Yahya Saeed Al-Zahrani obtained herB.Sc. in Physics in 2008 from King Abdul AzizUniversity in Jeddah, Kingdom of Saudi Arabia.In 2010 she joined the University of Manche-ster where she obtained an M.Sc. in Nanoelec-tronics (2011). She is currently pursuing herPh.D. at University of Manchester. Hanan'sresearch area is atomistic modeling using abinitio Density Functional Theory applied toGroup III–V and II–VI semiconductors and their

non linear piezoelectric properties.

Joydeep Pal received his Bachelor of Tech-nology in Electronics and CommunicationEngineering with First Class at the HeritageInstitute of Technology, West Bengal Uni-versity of Technology (WBUT), India in 2007.He then obtained his Master of Science inNanoelectronics with Distinction at the Uni-versity of Manchester in 2010. He thenobtained his Ph.D. in Electrical and Electro-nic Engineering at the University of Man-

chester in 2013. In October 2013, he was

awarded a prestigious EPSRC Doctoral Prize Fellowship at Manche-ster. His research interests include modeling and exploitation of nonlinear piezoelectric properties in III-Nitrides, III–Vs and II–VI semi-conductor and nanostructured devices.

Max A. Migliorato (Laurea in Physics, 1999,University of Rome “La Sapienza”, Italy, andPh.D., 2003, University of Sheffield, UK). In2004 he was awarded a Royal Academy ofEngineering – EPSRC Research Fellowship atthe University of Sheffield. In 2007 he wasalso awarded an RCUK Fellowship at theUniversity of Manchester. His work hasalways concentrated on atomistic modelingof semiconductor nanostructures and he has

pioneered the study of non linear polariza-

tion effects in III–V and II–VI semiconductors. He is currently the Co-Chairman of the international conference on Theory, Modeling andComputational methods for Semiconductors (TMCS).

Geoffrey Tse studied at UCL, obtained an M.Eng in Electronic and Electrical Engineering(first class honours) in 2007. He then obtainedEPSRC DTA studentship, investigated non-linear piezoelectricity in strained III-As zinc-blende semiconductors and completed hisPhD from The University of Manchester, UKin August 2012. In October 2013, he joinedPeking University, China as a Postdoc, inparticular investigating the electronic and

optical properties of non-linear induced-

strain gradient across the bending of ZnO nanowire with quantumespresso. Since April 2014, he is a visiting scientist at the University ofManchester with Dr Migliorato's atomistic modeling research group.

Dapeng Yu is a Chang Kung professorship inPhysics in School of Physics, Peking Univer-sity. He received his Ph.D. Degree (1993) inLaboratoire de Physicque des Solides, Uni-versité Paris-sud, Orsay, France, and thenjoined Department of Physics, Peking Uni-versity in 1995. His current interests are 1-Dsemiconductor nanowires, transport in low-Dmaterials, and single DNA detection/sequen-cing via solid state nanopore microscope.

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Piezoelectric field enhancement in III–V core–shell nanowiresIntroductionIII–V NanowiresCore shell nanowiresPiezoelectricity in III–Vs

Evaluation of linear and non-linear piezoelectric coefficientsModeling AFM tip lateral deflection

Homogeneous and core shell nanowiresConclusionsAcknowledgmentsReferences