research article density functional theory simulations of...

Research ArticleDensity Functional Theory Simulations of Semiconductorsfor Photovoltaic Applications Hybrid Organic-InorganicPerovskites and IIIV Heterostructures

Jacky Even1 Laurent Pedesseau1 Eric Tea12 Samy Almosni1

Alain Rolland1 Ceacutedric Robert1 Jean-Marc Jancu1 Charles Cornet1

Claudine Katan3 Jean-Franccedilois Guillemoles2 and Olivier Durand1

1 Universite Europeenne de Bretagne INSA FOTON UMR CNRS 6082 20 avenue des Buttes de Coesmes35708 Rennes France

2 Institute of RampD on Photovoltaic Energy UMR 7174 EDF-CNRS-Chimie ParisTech 6 quai Watier BP 4978401 Chatou Cedex France

3 CNRS Institut des Sciences Chimiques de Rennes UMR 6226 35042 Rennes France

Correspondence should be addressed to Jacky Even jackyeveninsa-rennesfr

Received 5 November 2013 Accepted 7 February 2014 Published 2 June 2014

Academic Editor Patrick Meyrueis

Copyright copy 2014 Jacky Even et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Potentialities of density functional theory (DFT) based methodologies are explored for photovoltaic materials through themodeling of the structural and optoelectronic properties of semiconductor hybrid organic-inorganic perovskites and GaAsGaPheterostructures They show how the properties of these bulk materials as well as atomistic relaxations interfaces and electronicband-lineups in small heterostructures can be thoroughly investigated Some limitations of available standard DFT codes arediscussed Recent improvements able to treat many-body effects or based on density-functional perturbation theory are alsoreviewed in the context of issues relevant to photovoltaic technologies

1 Introduction

Photovoltaic (PV) solar electricity is one of the key tech-nologies of the 21st century to reduce the worldrsquos reliance onfossil fuels for energy generation Reduced costs and higherconversion efficiencies are of crucial importance to makePV-based technologies economically more competitive Thequest for quality and improved performances for futuresolar cells has attracted a tremendous research effort overthe last decade towards the semiconductor heterostructuresnanostructuredmaterials and thin films Various approachesare used ranging from high-costhigh-performance III-Vtechnology multiple junctions and concentrator systems tothe low-cost thin films [1] Obviously the design of novelandor efficient PV devices requires a deep understanding ofunderlying materialrsquos properties including chemical compo-sition mechanical electrical and optical properties whichcould be achieved from state-of-the-art ab initio approaches

Such knowledge is also desirable to reach low-cost PVcells composed of earth-abundant elements based materialscapable of full recycling

Among the large panel of available theoretical approach-es the density-functional theory (DFT) has become over-whelmingly popular This success greatly relies on the factthat no input adjustable parameters are needed and thatefficient numerical codes exist and a strong versatility espe-cially in the description of the ground state properties ofsemiconductors and metals Increase in computing powerhas afforded further capabilities in systemrsquos size that DFTmethods can handle However the current limit does notyet reach the window 10000ndash10 million atoms involved inthe active device region of PV cells Indeed modern semi-conductor optoelectronic devices have a feature size of fewnanometers including nanostructures like quantumwells [2]or quantum dots [3] Such systems consist of involved two-

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2014 Article ID 649408 11 pageshttpdxdoiorg1011552014649408

2 International Journal of Photoenergy

(2D) andor three- (3D) dimensional geometries composedof multiple materials andor alloys Nevertheless DFT meth-ods are useful to get insight into physical phenomena of eachcomponent part of the device that is separate materials orsmall heterostructures For example a quantitative design ofPV requires a reliable prediction of the electronic band-gapsband-lineups and effective masses

It is well known that DFT based on the local densityapproximation (LDA) [4] or generalized gradient approx-imation (GGA) [5] does not reproduce accurately theexcited states of compounds Conversely hybrid methodsthat include a fraction of Hartree-Fock exchange may cir-cumvent the band-gap problem but their performancesstrongly depend on the material of interest Interestinglythe HSE06 hybrid functional proposed by Heyd et al [6]is a good alternative to compute band-gaps band offsetsor alloys properties [7 8] even so it fails to reproduce thedirect-indirect crossover in GaAsP alloys [8] Alternativelyreliable results can be obtained frommany-body perturbationtheory (MBPT) especially within the GW approach (GWwhere G stands for Greenrsquos function and W for the screenedpotential) that may be used in a perturbative scheme [9ndash11] or self-consistently [12 13] For charge separation keyquantities are the ionization potential and electron affinityrespectively of the donor and acceptor materials as theycontrol the relative alignment of electron and hole levels Thedrop of the interfacersquos potential in heterostructures can beestimated by DFT within a superlattice (SL) approximationwhich consequently offers a nice estimate of the band-lineupFor a complex stack a GW treatment is beyond reach butthe DFT potential drop at the interface can be efficientlycorrected by the GW eigenvalues obtained for the bulkvalence band states [11 14 15] A good estimation of alloyselectronic properties is also a difficult task inDFT simulationIndeed semiconductors even conventional ones undergoa significant bowing of the band-gap that is the band-gapenergy follows 119864119892(119909) = 119864119892(119909) minus 119887 sdot 119909 sdot (1 minus 119909) where119887 is a bowing parameter Supercell approaches for statisti-cally random alloys are more adequate than virtual crystalapproximations For special alloy compositions equivalentresults can be obtained from DFT with special quasirandomstructures (SQS) (small supercells) that reproduce mixingenthalpies and atomic correlations of very large supercells [8]Noteworthily SQS models include chemical mixing strainand atomic relaxation effects

In addition semiempirical methods for mechanical orelectronic properties studies as the valence force field (VFF)and the tight binding approximation [16] or elasticity and thekp method [17] require accurate electronic parameters asinput They can be derived from DFT calculations or experi-ment For example quantitative estimates of electromechan-ical tensors of bulk materials are achieved from density-functional perturbation theory (DFPT) [18ndash20] An efficientuse of the ldquo2119899+1rdquo theorem where only by-products of a first-order perturbation calculation are required provides second-and third-order derivatives of the total energy providedthat atomic-displacement variables have been eliminated Forsecond-order derivatives various physical responses of insu-lating crystals can be obtained including elastic constants

linear piezoelectric tensors and linear dielectric susceptibil-ity as well as tensor properties related to internal atomicdisplacements like Born charges and phonons [20 21] Forthird-order components related to physical properties suchas nonlinear electrical susceptibilities nonlinear elasticityor photoelastic and electrostrictive effects finite differencetechniques and symmetry analysis must be associated withthe DFPT method [22] Finally excitonic and transportproperties can also be studied by DFT methods but they arebeyond the scope of the present paper

This paper aims at illustrating with two examples someof the DFTrsquos potentialities for PV technologies First we willfocus on hybrid organicinorganic perovskites (HOP) thatopen new routes for solar cells (Section 31) In particular adirect optical transition and isotropic activity are predictedfor a model 3D system Secondly the investigation of struc-tural elastic and electronic properties will be illustratedon III-V semiconductor heterostructures for GaPSi pseudo-substrates (Section 32) Computational details are given inSection 2

2 Computational Details

Total energy DFT calculations were carried out using theABINIT code [20] within LDA or GGA A plane-wave basisset with an energy cut-off of 340 and 680 eV for compoundsinvestigated respectively in Sections 31 and 32 was used toexpand the electronic wave-functions The reciprocal spaceintegration was performed over Monkhorst-Pack grids [23]The energy was computed from the linear response methodand convergence is accurately reached with tolerance onthe residual potential which stems from differences betweenthe input and output potentials Pseudopotentials were con-structed either from the Fritz Haber Institute (FHI) for-mat [24] or using the Hartwigsen-Goedecker-Hutter (HGH)scheme [25] The dielectric properties were studied from thedensity-functional perturbation theory (DFPT) based on thelinear response theory implemented in SIESTA code [26] Allmany-body GW calculations were performed at the G0W0level [9] The quasiparticles energies were converged withrespect to the energy cut-offs the number of k-points inthe Brillouin Zone (BZ) and the number of bands usedto compute the dielectric function and the self-energy Theplasmon-pole model was used to describe the dynamicdependence of the screening function [20]

3 Results

31 Optoelectronic Properties of HybridOrganicInorganic Per-ovskites for High Efficiency and Low-Cost Solar Cells Hybridorganicinorganicmaterials have attracted increasing interestover the past decade due to their potential applications Inparticular hybrid nanomaterials are expected to offer a waytowards enhanced performances of optoelectronic devices[27] The versatility of the organic part affords the possibilityof fine tuning materialrsquos optoelectronic properties [28] Forexample it has been shown that the optical spectra of HOPcan be easily tailored by varying the organic cation whichimproves optical efficiencies and the tuning of the emission

International Journal of Photoenergy 3

b

c

a

Pb

I

H

C

N

(a)

a

b

c

(b)

Figure 1 (a) Overview of the low-temperature crystal structure of CH3NH3PbI3projected into the (bc) plane Atom labels are given (b)

Overview of the low-temperature crystal structure of CH3NH3PbI3projected into the (ab) plane

wavelength Among them self-assembled layered (2D) HOPhave recently shown enhanced nonlinear optical propertiesin microcavities [29] Moreover following pioneering recentworks [30ndash32] 3D HOP based on relatively small organiccations have also been shown to drastically improve thephotonic conversion in dye sensitized solar cells (DSSC) [33ndash38] and expected to afford efficiencies up to 20 in the nearfuture [39] It is even predicted to open ldquoa new era and a newavenue of research and development for low-cost solar cells likely to push the absolute power conversion efficiencytoward that of CIGS (20) and then toward and beyondthat of crystalline silicon (25)rdquo [40] Our theoretical workon this rapidly evolving topic shows that these compoundscan be considered now as a new class of semiconductors[41] Indeed compared to alternative strategies based oninorganic semiconductor quantum dots (QDs) or extremelythin absorbers coated upon the internal surface of a meso-porous TiO2 electrode 3D HOP offer different benefitsAmong those one can note the ease and low temperature ofsynthesis the tailoring of electronic properties by chemicalsubstitution hole transport their high stability in dry air andthe formation of pn-like heterojunctions on TiO2

DFT calculations on prototypes 3D or 2DHOP combinedwith symmetry analysis of the band edge Bloch states showthat the ordering of the band edge states is found reversedcompared to tetrahedrally bonded semiconductor structures[28 41] Moreover from the computation of Kanersquos energyparameters we have explained the underlying mechanism ofthe transverse electric (TE) optical activity of 2DHOP result-ing from a subtle interplay between the electronic structureand exciton binding energies [28] Interestingly it has alsobeen shown that the spin-orbit coupling (SOC) induces alarge splitting of the conduction bands in comparison withthose of the valence bands of cubic semiconductors Theimportance of SOC was also put forward for 3D HOP [41]To illustrate this point and the understanding gained fromDFT methodologies for hybrid compounds we considerone of the 3D HOP proposed for PV devices It belongsto the CH3NH3PbX3 family (where X is a halogen atom)

and exhibits a disordered average cubic phase (space groupPm3m) at room temperature Structural disorder is associ-ated with both the rotation of ammonium cations and tilt ofthe lead halide octaedra CH3NH3PbI3 presents an orderedstructure at low temperature which is orthorhombic (spacegroup Pnma) with a cell doubling when compared to theroom temperature phase [41 45] (Figure 1) The electronicdegeneracy lifting is associated with the low temperaturesymmetry breaking and strain into the unit cell 119886 = 86885gt119887 = 123775gt and 119888 = 86384gt [45] The low temperaturecell strain is larger along the 119887-axis The theoretical study of3DHOP predicts an isotropic absorption at high temperaturefor these materials used in the active zone of solar cells [41]The triply degenerate CB without SOC of 3D HOP states isindeed associated with the vectorial representation of a cubicsimple group For the low temperature orthorhombic Pnmaphase of the 3D CH3NH3PbI3HOP the number of CB statesis doubled (Figure 2(a)) The fundamental electronic transi-tions for the CH3NH3PbI3compound with and without SOCare found at the DFT-LDA level equal to 04 (Figure 2(b))and 14 eV (Figure 2(a)) respectively These values are a littlebit smaller than the values computed at the DFT-GGA level[41] Even though the fundamental transitions calculatedwithout SOC for the low temperature Pnma structure (14 eV)compare nicely with the values obtained experimentally(15 eV [30]) the agreement is fortuitous and stems fromlarge error cancellations SOC effect indeed strongly reducesthe band-gap (Figure 2) without modifying the main char-acter of the optical transitions [41] At the same time it isknown that a DFT ground state computation systematicallyunderestimates the excited states This deficiency can besolved with the inclusion of many-body effects namelythe GW self-energy correction for the band-gap and thesubsequent resolution of Bethe Salpeterrsquos equation to accountfor the excitonic features However such calculations are farbeyond available computational resources for large systemsIn the corresponding double group including spinors theCB of the high temperature cubic phase is split by SOC intotwofold degenerate states and fourfold degenerate states [41]


05

1

15

2

25

minus08

minus06

minus04

minus02

0

Ener

gy (e

V)

MAPbI3

U998400ΓΓU Y

VBM1-2gt|

CBM1-6gt|

(a)

MAPbI3

U998400ΓΓU Y

(b)

Figure 2 Electronic band structures of CH3NH3PbI3without (a) and with (b) SOC calculated at the LDA level The origin of the energy

scale is taken at the top of the VB

a

b

c

(a)

c

a

b

(b)

Figure 3 (a) Overview of the monoclinic crystal structure of (C18H37NH3)2PbI4projected in the (119887 119888) plane (b) Overview of the low-

temperature crystal structure of (C18H37NH3)2PbI4projected into the (119886 119887) plane

A similar effect is predicted for the low-temperature phase(Figure 2(b)) The SOC splitting (on the order of 10 eV) ismuch larger than the one usually encountered in the valenceband (VB) of cubic conventional semiconductors The CBminimum is associated with the twofold degenerate and oddspin-orbit split-off (SO) states leading for symmetry reasonsto a strong and isotropic optical transition with the even VBstates [41]

These findings differ from those derived for analogue 2DHOP with larger organic cations In fact the 2D densities ofstates obtained from 4F-PEPI ((C5H11NH3)2PbI4) [28] and

that obtained from (C18H37NH3)2PbI4 whose structure isshown in Figure 3 [46] show quite different features Theband-gap remains located at the Γ-point are direct and asso-ciated with only three active Bloch states a nondegeneratelevel for the valence-band maximum (VBM) and two nearlydoubly degenerate levels for the conduction-band minimum(CBM1-2) ( Figure 4 [28])Moreover due to the 2D characterof these layered compounds no energy dispersion occursalong the Γ-X direction (characterizing the stacking axis inreal space) illustrating the Pb-I-Pb bond breaking and thedielectric mismatch between inorganic and organic sheets


minus1

0

1

2

3

Band

ener

gy (e

V)

Z XY

|CBM1gt

|CBM2gt

ΓΓ

gt|VBM

Figure 4 Electronic band structure of monoclinic crystal structureof (C18H37NH3)2PbI4calculated by DFT without SOC The energy

levels are referenced to the valence band maximum

The fundamental transition of hybrid organicinorganiclayered (2D) perovskites is indeed expected to display aTE character and it could be even further enhanced byorientational disorder introduced by the organic layer [28]Contrarily in the CH3NH3PbI3 HOP an almost isotropicoptical activity is expected from symmetry that should alsobe enhanced at room temperature with the disorder observedfor the cubic phase [41] The computation of the relativeimaginary dielectric permittivity is computationally involvedwith such large systems It is then limited in this work toa calculation without SOC for the 3D HOP and for a 2DHOP compoundwith a shorter alkyl chain (C5H11NH3)2PbI4[41 47] Relative imaginary dielectric permittivity computedat the GGA-level presented in Figure 5 for CH3NH3PbI3 (a)and (C5H11NH3)2PbI4 (b) confirms our earlier theoreticalpredictions based on symmetry analyses [28 41] The resultsare given for light polarizations along the three crystallo-graphic axes (1ndash3) or for a polycrystalline sample in thecase of CH3NH3PbI3 (a) and TE or TM polarizations for(C5H11NH3)2PbI4 (b)

32 III-V Semiconductors Heterostructures for GaPSi Pseu-dosubstrates High efficiency PV technology is based onIII-V materials growth on expensive Ge or GaAs sub-strates [1 48 49] With the combination of bulk GaInPand GaAs 30 conversion efficiencies are attained Higherconversion efficiencies than 40 can be reached usingtriple GaInPGa(In)AsGe junctions in solar cells Efficienttandem cells based on Si substrates have been recentlyproposed [50ndash52]They are based on alloyed heterostructuresGaAsP(N)GaP(N)Si double-pn-junctions The key pointconcerns a coherent growth of III-V semiconductors on a Sisubstrate An initial deposition of thin GaP layer (with a lat-tice mismatch equal to 036) and a subsequent overgrowthof the diluted-nitride GaAsPN compound lattice-matched toSi are a possible solution to obtain a 17 eV11 eV tandem cellElaborated growth strategies have however to be used in orderto overcome the problems related to extended structural

0

2

4

6

8

1 15 2 25 3

E (eV)

Polycrystal

(2)

(1)(3)

120576998400998400

(a)

0

2

4

6

8

1 15 2 25 3

E (eV)

120576998400998400

TM

TE

(b)

Figure 5 Imaginary parts of the dielectric functions com-puted without SOC at the GGA-level for CH

3NH3PbI3(a) and

(C5H11NH3)2PbI4(b) The results are given for light polarizations

along the three crystallographic axes (1ndash3) or for a polycrystallinesample in the case of CH

3NH3PbI3(a) and for TE or TM (perpen-

dicular to the stacking axis) polarizations for (C5H11NH3)2PbI4(b)

defects formation like antiphase domains and MicroTwins[50ndash52]

GaAsP(N)GaP(N) material combinations are good can-didates to reach optimal absorption at 17 eV [53 54]Accurate band structure calculations of strained Ga(NAsP)heterostructures have been performed within the frame-work of the extended-basis sp3d5slowast tight-binding model[16] DFT calculations are helpful to yield comparisons andband parameters for semiempirical approaches They are


xz

y

GaP

GaAs

az = 583 A

az = 542 A

Figure 6 Schematic representation of a short-period GaAs(4)GaP(4) [001] superlattice grown on a GaP substrate after theatomic relaxation The lattice parameters along the [100] and [010]directions are both equal to that of GaP

however limited for the simulation of ultrashort superlatticesor binary alloys Figure 6 shows the atomic positions ofGaAs(4)GaP(4) SLs grown along the [001] direction TheGaAs layer is strained onto a GaP substrate where the DFTlattice parameter is of 119886 = 542gt to be compared to theexperimental value of 544gt at119879 = 0K [55] After relaxationthe lattice constant of GaP is recovered almost everywherealong the [001] direction in the GaP layer whereas the GaAslayer is strongly strained along the [001] direction with anaverage lattice parameter 119886119911 = 583gt For GaAs bulk 119886 =563gt in our DFT simulations in very good agreement withthe experimental value of 565gt at low temperature [55]It should be noted that 119886119911 fairly corresponds to the valueestimated from the linear elasticity theory using experimentalelastic constants (11986211 = 122GPa and 11986212 = 57GPa)

DFT offers the possibility to study the structural prop-erties beyond classical elasticity especially close to theinterfaces between materials [11 15] Figure 7 represents thevariation of the atomic interlayer spacing close to the P-Ga-As interface of the relaxed stack shown in Figure 6 The samestack is simulated using the semiempiricalVFF approach [16]VFF is optimized to describe semiconductor heterostructuresat room temperatureThus theVFF atomic interlayer spacingvalues are then shifted to slightly higher values when com-pared to the DFT results Both methods show neverthelessthat bond stretching undergoes a small fluctuation close tothe interface This fluctuation only extends over roughly onemonolayer in the two layers apart from the interfaceThe layerspacing fluctuation can be interpreted by using an atomiccharge analysis Indeed the Hirshfeld population analysis[20 42] is based on the separation of the electron densityin real space close to atoms Conceptually simple it shouldbe however used with some caution [43] It was used todescribe qualitatively the variation of atomic polarizabilitiesand atomic charges in III-V semiconductor nanostructureswith heteropolar bonds [44] Figure 8 shows the variation

VFF

DFT

136

138

14

142

144

146

Atom

ic la

yer s

paci

ng (A

)

P-Ga P-Ga P-GaGa-P Ga-P Ga-As Ga-AsAs-Ga As-Ga

Figure 7 Variation of the atomic interlayer spacing close to a P-Ga-As interface simulated by theDFT (dashed line and circles) andVFFmethod (straight line and circles) for short-period GaAs(4)GaP(4)[001] superlattices

minus02

minus01

minus005

minus015

02

015

01

005

0

GaGa Ga Ga

GaGa Ga Ga

P P P P

As As As As

Hirs

hfel

d ch

arge

(fra

ctio

n of

e)

Figure 8 Atomic Hirshfeld charges for short-periodGaAs(4)GaP(4) [001] superlattice calculated form the DFTelectron density in real space

of the atomic charges in short-period GaAs(4)GaP(4) [001]SLs Atomic charges calculated for P (minus015 e) andAs (minus018 e)atoms correspond to the ones obtained in GaP and GaAsbulk respectively This also applies for Ga atoms (+015 eor +018 e) except for those located exactly at the interface(+016 e) The stretching of the P-Ga and Ga-As bondsconnected to the Ga atom at the interface can thus be relatedto their reduced polarizabilitiesThis effect is well reproducedby the VFF computations It should be stressed that advancedempirical force field models are now developed beyond


EvA

VA

EvB

VB

EcAEcB

Bulk material A Bulk material B

AB superlatticeΔV LDA

Figure 9 Schematic representation of the model solid approach to compute the valence band-lineup between compounds A and B [42ndash44]The band calculations for the bulk materials are combined with a computation of the Δ119881LDA ab initio potential drop at the AB interfacelineup The conduction band energy levels are represented schematically but not used in the valence band-lineup computation

-1

0

1

2

3

Ener

gy (e

V)

Bulk biaxially strained GaAs

M(Xxy) Γ(Xz) Z

-1

0

1

2

3

Ener

gy (e

V)

XL Γ

Bulk GaP

Figure 10 Electronic band diagrams of biaxially strained GaAsGaP(001) and unstrained GaP bulk at LDA (dark lines) and LDA + G0W0

(red lines with circles) levels

the VFF method in order to get a fine agreement with DFTresults for elastic constants and LO-TOphonon splitting [56]

The drop of the interfacersquos potential between materialsin heterostructures is a very important parameter for PVstructurersquos designModern theory of band-lineup in semicon-ductors relies on the model solid approach of van de Walleand Martin [57ndash59] The calculation of the valence band-lineup Δ119864V(BA) between two semiconductors A (GaAs) andB (GaP) is based on the construction of a superlattice withAB pseudomorphic interfaces as presented in Figures 6 and9 The Δ119881LDA = 119881B minus 119881A drop at the AB interface and theplanar averaged ab initio potential is then calculated [57]To complete the computation of valence band discontinuityΔ119864V(BA) = 119864VB minus 119864VA one has also to perform theband calculations for bulk and shift the averaged ab initiopotentials and valence band maxima Δ119864A = 119864VA minus 119881A andΔ119864B = 119864VB minus 119881B The valence band discontinuity is thencalculated by transitivity Δ119864V(BA)= Δ119881LDA +Δ119864B minusΔ119864ATheconduction band energy levels are represented schematicallyin Figure 9 but they are not used in the valence band-lineup

computationThe valence band-lineupmust also be correctedto account for strain and SOC effects [59] or for the valenceband self-energy corrections at the G0W0 level [11 15]The one-shot G0W0 self-energy correction is known toimperfectly correct the band-gap calculated at the LDA levelThe quality of the G0W0 approximation is indeed closelytied to the quality of the LDA eigenfunctions at the startingpointThe quasiparticle self-consistent GW (QSGW)method[12] results in state-of-the-art predictions of excited-stateproperties However the additional corrections associatedwith QSGW self-consistency mostly affect conduction bandlevels in conventional semiconductors [12]

We apply in the following the model solid approach forthe GaAsGaP interface and would like to point out that asimilar LDA + G0W0 study was already presented for theInAsGaP interface taking into account strain and SOC [15]The LDA + G0W0 study of unstrained bulk GaAs and GaP(Figure 10) yields as expected a direct band-gap for GaAsand an indirect band-gap for GaP A detailed inspection ofthe G0W0 corrections (Table 1) demonstrates that they are


Table 1 Electronic band-gap energies at 119879 = 0K without SOC derived from experiment [55] and calculated at the LDA and LDA + G0W0levels

Energy gap (eV) GaP (exp) GaP (LDA) GaP (G0W0) GaAs (exp) GaAs (LDA) GaAs (G0W0)119871 273 146 237 199 084 154Γ 292 161 250 163 036 122119883 237 147 211 209 133 176

CB

VBXzΓ

Γ

Γ

M

minusb(120576zz minus 120576xx)

2b(120576zz minus 120576xx)

minus1

3Ξxu(120576zz minus 120576xx)

2


Xxy Xz

Xx

Xy

Figure 11 Energy shifts and definition of deformation potentials associated with a pure biaxial strain along the [001] axis at the Γ and 119883points for zinc-blende semiconductors Splittings of electronic states at the 119883 point are also defined Folding of 119883

119911states at the Γ point is

associated with the doubling of the primitive unit cell The tetragonal primitive cell is shown in insert

required to recover the right order for the X and L band-gapsin GaP In addition the effects are more pronounced for thetwo compounds at Γ than at X This point is very importantfor GaAsP(N)GaP(N) SL [53] and (In)GaAsGaP quantumdots [60] where the observed optical transitions result froma fine competition between the Γ and X conduction bandstates The DFT simulations carried out only at the LDAlevel for superlattices are then not expected to yield accuratepredictions especially for the conduction subbands AsDFT+LDA fails to reproduce correctly the electron effective masses[12] the quantum confinement is not indeed reproducedcorrectly for small nanostructures

LDA + G0W0 studies have been recently applied directlyto very short-period SL instead of using the corrections forbulkmaterials [14 61]Major error in that case however lies inthe assumption that the self-energy in the central part of thesuperlattice can already be identified with the self-energy ofthe bulkTheGWself-energy contains indeed the huge imageeffect due to the dielectric discontinuities at the interfacesof short-period SL This can be partially corrected usinga semiempirical approach based on the dielectric constantdiscontinuity [61] In this work we present LDA + G0W0studies for bulk GaAs and GaP but taking into accountstrain effects The computed G0W0 valence band shifts areequal to minus008 eV and minus025 eV for unstrained GaAs andGaP respectively The interplay of strain and many-bodyeffects can be investigated for bulk materials LDA + G0W0calculations were performed for a biaxially strained GaAs

Table 2 Electronic band-gap energies at 119879 = 0K without SOCderived from experiment [55 63] and LDA + G0W0 simulations forunstrained and strained bulk GaAs

Energy gap(eV)

UnstrainedGaAs (G0W0)

Strained GaAs(G0W0)

Strained GaAs(exp)

Γ rarr Γ 122 139 191119883119911rarr Γ 176 192 229119883119909119910rarr 119872 176 141 184

on GaP (001) (Figure 10) In order to understand the effectof the strain state the strain tensor was decomposed intoa hydrostatic component Δ119881119881 = 120576119909119909 + 120576119910119910 + 120576119911119911 and apure biaxial component 120576119909119909 minus 120576119911119911 The energy shifts anddefinitions of deformation potentials are given in Figure 11In addition the interpretation of the electronic band diagramshown in Figure 10 must take into account the band foldingeffect associated with the doubling of the primitive cell fromthe rhombohedral system to the tetragonal one Electronicenergy band-gaps deduced for strained GaAs from LDA +G0W0 at the119883119909119910 and Γ points are almost equal Calculationsbased on experimental deformation potentials predict anindirect band-gap at 119883119909119910 point (Table 2 [53 62]) The G0W0valence band shift for GaAs is equal to minus019 eV

The planar averaged and fully averaged ab initio poten-tials are calculated independently in each crystal bulk forexample 119881GaAs and 119881GaP and for the GaAs(8)GaP(8) [001]


-18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

Pote

ntia

l (eV

)

GaP

GaAs

Figure 12 Effective lineup of the LDAplanar averaged potentials forGaP and GaAs in a short-period GaAs(8)GaP(8) [001] superlatticeThe planar averaged potentials for bulk GaP and strained GaAs arerepresented in green and red respectively The potential curve ofbulk GaP has been downshifted by minus066 eV in order to fit intothe GaP layer of the potential curve of the GaAs(8)GaP(8) SLThe potential curve of strained GaAs has been upshifted by 062 eVin order to fit into the GaAs layer of the potential curve of theGaAs(8)GaP(8) SL

SL (Figure 9 [20 64]) The shifted planar averaged poten-tials for bulk GaP and strained bulk GaAs are shown inFigure 12 respectively in green and red The potential curveof GaP has been downshifted by minus066 eV to fit into therespective part far from interface of the potential curveof the GaAs(8)GaP(8) SL The potential curve of strainedGaAs has been upshifted by 062 eV The effective lineupof the LDA averaged potentials for GaP and strained GaAscan then be deduced Δ119881(GaAsGaP) = 152 eV Taking intoaccount the energy shifts for bulk Δ119864GaAs = 1124 eV andΔ119864GaP = 1220 eV the valence band-lineup in a GaAsGaPheterostructure is finally computed at the LDA level

Δ119864V(GaAsGaP)GW = Δ119881(GaAsGaP) + Δ119864GaAs minus Δ119864GaP

= 056 eV(1)

Adding the valence band G0W0 corrections onefinally ends up with a valence band-lineup value ofΔ119864V(GaAsGaP)GW = 062 eV The GaAsGaP valence band-lineup calculated from experiment [55] including straineffects and without SOC is equal to 055 eV Another studyusing a similar method at the LDA level with a somewhatsmaller plane wave cut-off (220 eV) yields a comparativevalue of 061 eV [65] As three independent DFT calculationsare needed in the model solid approach (Figure 9) such anagreement is satisfying

Finally it is possible to calculate at the LDA level thevalence band spin-orbit splitting of GaAs and GaP usingpseudopotentials constructed from the HGH scheme [25]Theoretical results are in good agreement with experiment[55] for GaAs 035 eV (exp 034 eV) and GaP 004 eV(exp 008 eV) State-of-the-art DFT calculations have beenrecently developed in order to fully take into account SOC

in the single-particle Green function G and the screenedinteraction W of the GW approximation [66] It is possiblein such a way to correctly predict the reverse band orderingof II-VI semiconductor alloys containing Hg atoms Thesecompounds are important for the design of topologicalinsulators [67 68]

4 Conclusions

We have demonstrated that DFT simulations yield relevantinformation on PV materials Quantitative design of PVdevices is beyond the possibility of nowadays DFT codesbut greatly benefits from reliable physical predictions ofstructural and optoelectronic properties of bulk materialsStudies of small heterostructures may give also additionalinformation on atomistic relaxations interfaces and elec-tronic band-lineups DFT methods are efficiently used inconnection with atomistic simulation tools like the VFF andtight binding codes Much effort has been done recently bythe DFT community to take into account precisely many-body effects for bulk and small nanostructures or to develop adensity-functional perturbation theoryThese improvementsare also promising for the future of PV materials

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was performed using HPC resources fromGENCI CINES and IDRIS 2013 (c2013096724) It is also sup-ported by Agence Nationale pour la Recherche (PEROCAIProject ANR-2010-04 and MENHIRS Project ANR (Grantno ANR-2011-PRGE-007-01))

References

[1] A Feltrin and A Freundlich ldquoMaterial considerations forterawatt level deployment of photovoltaicsrdquo Renewable Energyvol 33 no 2 pp 180ndash185 2008

[2] M Guezo S Loualiche J Even et al ldquoUltrashort nonlinearoptical time response of Fe-doped InGaAsInP multiple quan-tum wells in 155-120583m rangerdquo Applied Physics Letters vol 82 no11 pp 1670ndash1672 2003

[3] C Cornet C Labbe H Folliot et al ldquoTime-resolved pumpprobe of 155-120583m InAsInP quantum dots under high resonantexcitationrdquo Applied Physics Letters vol 88 no 17 Article ID171502 2006

[4] J P Perdew and Y Wang ldquoAccurate and simple analyticrepresentation of the electron-gas correlation energyrdquo PhysicalReview B Condensed Matter and Materials Physics vol 45Article ID 13244 1992

[5] J P Perdew K Burke andM Ernzerhof ldquoGeneralized gradientapproximation made simplerdquo Physical Review Letters vol 77no 18 pp 3865ndash3868 1996


[6] J Heyd G E Scuseria and M Ernzerhof ldquoHybrid functionalsbased on a screened Coulomb potentialrdquo Journal of ChemicalPhysics vol 118 no 8207 Article ID 219906 2006

[7] A Wadehra J W Nicklas and J W Wilkins ldquoBand offsetsof semiconductor heterostructures a hybrid density functionalstudyrdquo Applied Physics Letters vol 97 Article ID 092119 2010

[8] J W Nicklas and J W Wilkins ldquoAccurate ab initio predictionsof III-V direct-indirect band gap crossoversrdquo Applied PhysicsLetters vol 97 Article ID 091902 13 pages 2010

[9] M P Surh SG Louie andM LCohen ldquoQuasiparticle energiesfor cubic BN BP andBAsrdquoPhysical ReviewB CondensedMatterand Materials Physics vol 43 no 11 pp 9126ndash9132 1991

[10] N Chimot J Even H Folliot and S Loualiche ldquoStructural andelectronic properties of BAs and B

119909Ga1minus119909

As BxIn1minus119909

As alloysrdquoPhysica B Condensed Matter vol 364 pp 263ndash272 2005

[11] P Prodhomme F Fontaine-Vive A V D Geest P Blaise andJ Even ldquoAb initio calculation of effective work functions for aTiNHfO

2SiO2Si transistor stackrdquo Applied Physics Letters vol

99 no 2 Article ID 022101 2011[12] M van Schilfgaarde T Kotani and S Faleev ldquoQuasiparticle

self-consistent GW theoryrdquo Physical Review Letters vol 96 no22 Article ID 226402 2006

[13] J Vidal F Trani F Bruneval M A L Marques and S BottildquoEffects of electronic and lattice polarization on the bandstructure of delafossite transparent conductive oxidesrdquo PhysicalReview Letters vol 104 no 13 Article ID 136401 2010

[14] R Shaltaf G-M Rignanese X Gonze F Giustino and APasquarello ldquoBand offsets at the SiSiO

2interface from many-

body perturbation theoryrdquo Physical Review Letters vol 100 no18 Article ID 186401 2008

[15] L Pedesseau J Even A Bondi et al ldquoTheoretical study ofhighly strained InAs material from first-principles modellingapplication to an idealQDrdquo Journal of PhysicsDApplied Physicsvol 41 no 16 Article ID 165505 2008

[16] C Robert M Perrin C Cornet J Even and J M JanculdquoAtomistic calculations of Ga(NAsP)GaP(N) quantum wellson silicon substrate band structure and optical gainrdquo AppliedPhysics Letters vol 100 no 11 Article ID 111901 2012

[17] C Cornet A Schliwa J Even et al ldquoElectronic and opticalproperties of InAsInP quantum dots on InP(100) and InP(311)B substrates theory and experimentrdquo Physical Review B Con-densed Matter and Materials Physics vol 74 no 3 Article ID035312 2006

[18] S Baroni P Gianozzi andA Testa ldquoElastic constants of crystalsfrom linear-response theoryrdquo Physical Review Letters vol 59 p2662 1987

[19] X Gonze and J-P Vigneron ldquoDensity-functional approach tononlinear-response coefficients of solidsrdquo Physical Review BCondensed Matter and Materials Physics vol 39 no 18 pp13120ndash13128 1989

[20] X Gonze B Amadon P-M Anglade et al ldquoABINIT first-principles approach to material and nanosystem propertiesrdquoComputer Physics Communications vol 180 no 12 pp 2582ndash2615 2009

[21] J Even F Dore C Cornet L Pedesseau A Schliwa and DBimberg ldquoSemianalytical evaluation of linear and nonlinearpiezoelectric potentials for quantum nanostructures with axialsymmetryrdquo Applied Physics Letters vol 91 no 12 Article ID122112 2007

[22] L Pedesseau C Katan and J Even ldquoOn the entanglementof electrostriction and non-linear piezoelectricity in non-centrosymmetricmaterialsrdquoApplied Physics Letters vol 100 no3 Article ID 031903 2012

[23] H J Monkhorst and J D Pack ldquoSpecial points for Brillouin-zone integrationsrdquo Physical Review B Condensed Matter andMaterials Physics vol 13 no 12 pp 5188ndash5192 1976

[24] M Fuchs and M Scheffler ldquoAb initio pseudopotentials forelectronic structure calculations of poly-atomic systems usingdensity-functional theoryrdquo Computer Physics Communicationsvol 119 no 1 pp 67ndash98 1999

[25] C Hartwigsen S Goedecker and J Hutter ldquoRelativistic sep-arable dual-space Gaussian pseudopotentials from H to RnrdquoPhysical Review B CondensedMatter andMaterials Physics vol58 no 7 pp 3641ndash3662 1998

[26] J M Soler E Artacho J D Gale et al ldquoThe SIESTA methodfor ab initio order-N materials simulationrdquo Journal of PhysicsCondensed Matter vol 14 no 11 p 2745 2002

[27] D B Mitzi S Wang C A Feild C A Chess and A M GuloyldquoConducting layered organic-inorganic halides containing(110)-oriented perovskite sheetsrdquo Science vol 267 no 5203 pp1473ndash1476 1995

[28] J Even L Pedesseau M-A Dupertuis J-M Jancu andC Katan ldquoElectronic model for self-assembled hybridorganicperovskite semiconductors reverse band edgeelectronic states ordering and spin-orbit couplingrdquo PhysicalReview B Condensed Matter and Materials Physics vol 86 no20 Article ID 205301 2012

[29] Y Wei J S Lauret L Galmiche P Audebert and E DeleporteldquoStrong exciton-photon coupling in microcavities contain-ing new fluorophenethylamine based perovskite compoundsrdquoOptics Express vol 20 no 9 pp 10399ndash10405 2012

[30] A Kojima K Teshima Y Shirai and T MiyasakaldquoOrganometal halide perovskites as visible-light sensitizers forphotovoltaic cellsrdquo Journal of the American Chemical Societyvol 131 no 17 pp 6050ndash6051 2009

[31] M M Lee J Teuscher T Miyasaka T N Murakami andH J Snaith ldquoEfficient hybrid solar cells based on meso-superstructured organometal halide perovskitesrdquo Science vol338 no 6107 pp 643ndash647 2012

[32] H S Kim C R Lee J H Im et al ldquoLead iodide perovskitesensitized all-solid-state submicron thin film mesoscopic solarcell with efficiency exceeding 9rdquo Scientific Reports vol 2article 591 2012

[33] J H Heo S H Im J H Noh et al ldquoEfficient inorganic-organic hybrid heterojunction solar cells containing perovskitecompound and polymeric hole conductorsrdquo Nature Photonicsvol 7 pp 487ndash492 2013

[34] J Burschka N Pellet S Moon et al ldquoSequential deposition asa route to high-performance perovskite-sensitized solar cellsrdquoNature vol 499 no 7458 pp 316ndash319 2013

[35] M Liu M B Johnston and H J Snaith ldquoEfficient planarheterojunction perovskite solar cells by vapour depositionrdquoNature vol 501 pp 395ndash398 2013

[36] J Even L Pedesseau J M Jancu and C Katan ldquoDFT andk sdot p modelling of the phase transitions of lead and tin halideperovskites for photovoltaic cellsrdquo Physica Status SolidimdashRapidResearch Letters vol 8 pp 31ndash35 2014

[37] S D Stranks G E Eperon G Grancini et al ldquoElectron-holediffusion lengths exceeding 1 micrometer in an organometaltrihalide perovskite absorberrdquo Science vol 342 no 6156 pp341ndash344 2013


[38] G Xing N Mathews S Sun et al ldquoLong-range balancedelectron- and hole-transport lengths in organic-inolong-rangebalanced electron- and hole-transport lengths in organic-inorganic CH

3NH3PbI3rdquo Science vol 342 no 6156 pp 344ndash

347 2013[39] N G Park ldquoOrganometal perovskite light absorbers toward

a 20 efficiency low-cost solid-state mesoscopic solar cellrdquoJournal of Physical Chemistry Letters vol 4 pp 2423ndash2429 2013

[40] H J Snaith ldquoPerovskites the emergence of a new era for low-cost high-efficiency solar cellsrdquo Journal of Physical ChemistryLetters vol 4 no 21 pp 3623ndash3630 2013

[41] J Even L Pedesseau J M Jancu and C Katan ldquoImportance ofspin-orbit coupling in hybrid organicinorganic perovskites forphotovoltaic applicationsrdquo Journal of Physical Chemistry Lettersvol 4 no 17 pp 2999ndash3005 2013

[42] F L Hirshfeld ldquoBonded-atom fragments for describing molec-ular charge densitiesrdquo Theoretica Chimica Acta vol 44 no 2pp 129ndash138 1977

[43] S Saha R K Roy and P W Ayers ldquoAre the Hirshfeld andMulliken population analysis schemes consistent with chemicalintuitionrdquo International Journal of Quantum Chemistry vol109 no 9 pp 1790ndash1806 2009

[44] A Krishtal P Senet and C van Alsenoy ldquoOrigin of the size-dependence of the polarizability per atom in heterogeneousclusters the case of AlP clustersrdquo Journal of Chemical Physicsvol 133 no 15 Article ID 154310 2010

[45] T Baikie Y Fang J M Kadro et al ldquoSynthesis and crystalchemistry of the hybrid perovskite (CH

3NH3)PbI3for solid-

state sensitised solar cell applicationsrdquo Journal of MaterialsChemistry A vol 1 no 18 pp 5628ndash5641 2013

[46] D G Billing and A Lemmerer ldquoSynthesis characterization andphase transitions of the inorganic-organic layered perovskite-type hybrids [(C

119899H2119899+1

NH3)2PbI4] (119899 = 12 14 16 and 18)rdquoNew

Journal of Chemistry vol 32 pp 1736ndash1746 2008[47] D G Billing and A Lemmerer ldquoSynthesis characterization and

phase transitions in the inorganic-organic layered perovskite-type hybrids [(C

119899H2119899+1

NH3)2PbI4] (119899 = 4 5 and 6rdquo Acta

Crystallographica B vol 63 pp 735ndash747 2007[48] K A Bertness S R Kurtz D J Friedman A E Kibbler C

Kramer and J M Olson ldquo295-efficient GaInPGaAs tandemsolar cellsrdquo Applied Physics Letters vol 65 no 8 pp 989ndash9911994

[49] J F Geisz and D J Friedman ldquoIII-N-V semiconductors forsolar photovoltaic applicationsrdquo Semiconductor Science andTechnology vol 17 no 8 pp 769ndash777 2002

[50] W Guo A Bondi C Cornet et al ldquoThermodynamic evolutionof antiphase boundaries in GaPSi epilayers evidenced byadvancedX-ray scatteringrdquoApplied Surface Science vol 258 no7 pp 2808ndash2815 2012

[51] T NguyenThanh C RobertW Guo et al ldquoStructural and opti-cal analyses of GaPSi and (GaAsPNGaPN)GaPSi nanolayersfor integrated photonics on siliconrdquo Journal of Applied Physicsvol 112 Article ID 053521 2012

[52] T Quinci J Kuyyalil T N Thanh et al ldquoDefects limitationin epitaxial GaP on bistepped Si surface using UHVCVD-MBEgrowth clusterrdquo Journal of Crystal Growth vol 380 pp 157ndash1622013

[53] C Robert A Bondi T N Thanh et al ldquoRoom temperatureoperation of GaAsP(N)GaP(N) quantum well based light-emitting diodes effect of the incorporation of nitrogenrdquoAppliedPhysics Letters vol 98 no 25 Article ID 251110 2011

[54] S Almosni C Robert T Nguyen Thanh et al ldquoEvaluation ofInGaPN and GaAsPNmaterials lattice-matched to Si for multi-junction solar cellsrdquo Journal of Applied Physics vol 113 ArticleID 123509 2013

[55] S L Chuang Physics of Optoelectronic Devices Wiley Inter-science New York NY USA 1995

[56] P Han and G Bester ldquoInteratomic potentials for the vibrationalproperties of III-V semiconductor nanostructuresrdquo PhysicalReview B Condensed Matter and Materials Physics vol 83Article ID 174304 2011

[57] C G van de Walle and R M Martin ldquoTheoretical study ofband offsets at semiconductor interfacesrdquo Physical Review BCondensed Matter and Materials Physics vol 35 no 15 pp8154ndash8165 1987

[58] C G van de Walle ldquoBand lineups and deformation potentialsin themodel-solid theoryrdquo Physical Review vol 39 p 1871 1989

[59] C G van de Walle and J Neugebauer ldquoUniversal alignment ofhydrogen levels in semiconductors insulators and solutionsrdquoNature vol 423 no 6940 pp 626ndash628 2003

[60] C Robert C Cornet P Turban et al ldquoElectronic optical andstructural properties of (InGa)AsGaP quantum dotsrdquo PhysicalReview B Condensed Matter and Materials Physics vol 86 no20 Article ID 205316 2012

[61] C Mitra B Lange C Freysoldt and J Neugebauer ldquoQuasi-particle band offsets of semiconductor heterojunctions froma generalized marker methodrdquo Physical Review B CondensedMatter and Materials Physics vol 84 no 19 Article ID 1933042011

[62] R G Dandrea and A Zunger ldquoFirst-principles study ofintervalley mixing ultrathin GaAsGaP superlatticesrdquo PhysicalReview B Condensed Matter and Materials Physics vol 43 no11 pp 8962ndash8989 1991

[63] O Madelung Ed Semiconductors Intrinsic Properties of GroupIV Elements and III-VII-VI and I-VII Compounds vol 22 ofLandolt-Bornstein New Series Group III part A SpringerBerlin Germany 1987

[64] A Baldereschi S Baroni and R Resta ldquoBand offsets inlattice-matched heterojunctions a model and first-principlescalculations for GaAsAlAsrdquo Physical Review Letters vol 61 p734 1988

[65] M di Ventra M Peressi and A Baldereschi ldquoChemical andstructural contributions to the valence-band offset at GaPGaAsheterojunctionsrdquo Physical Review B Condensed Matter andMaterials Physics vol 54 no 8 p 5691 1996

[66] R Sakuma C Friedrich T Miyake S Blugel and F Aryaseti-awan ldquoGW calculations including spin-orbit coupling applica-tion to Hg chalcogenidesrdquo Physical Review B CondensedMatterand Materials Physics vol 84 Article ID 085144 2011

[67] O A Pankratov S V Pakhomov and B A Volkov ldquoSupersym-metry in heterojunctions band-inverting contact on the basisof Pb

1minus119909Sn119909Te and Hg

1minus119909Cd119909Terdquo Solid State Communications

vol 61 no 2 pp 93ndash96 1987[68] C L Kane and J E Moore ldquoTopological insulatorsrdquo Physics

World vol 24 no 2 pp 32ndash36 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Carbohydrate Chemistry

International Journal of


Journal of

Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


(2D) andor three- (3D) dimensional geometries composedof multiple materials andor alloys Nevertheless DFT meth-ods are useful to get insight into physical phenomena of eachcomponent part of the device that is separate materials orsmall heterostructures For example a quantitative design ofPV requires a reliable prediction of the electronic band-gapsband-lineups and effective masses

It is well known that DFT based on the local densityapproximation (LDA) [4] or generalized gradient approx-imation (GGA) [5] does not reproduce accurately theexcited states of compounds Conversely hybrid methodsthat include a fraction of Hartree-Fock exchange may cir-cumvent the band-gap problem but their performancesstrongly depend on the material of interest Interestinglythe HSE06 hybrid functional proposed by Heyd et al [6]is a good alternative to compute band-gaps band offsetsor alloys properties [7 8] even so it fails to reproduce thedirect-indirect crossover in GaAsP alloys [8] Alternativelyreliable results can be obtained frommany-body perturbationtheory (MBPT) especially within the GW approach (GWwhere G stands for Greenrsquos function and W for the screenedpotential) that may be used in a perturbative scheme [9ndash11] or self-consistently [12 13] For charge separation keyquantities are the ionization potential and electron affinityrespectively of the donor and acceptor materials as theycontrol the relative alignment of electron and hole levels Thedrop of the interfacersquos potential in heterostructures can beestimated by DFT within a superlattice (SL) approximationwhich consequently offers a nice estimate of the band-lineupFor a complex stack a GW treatment is beyond reach butthe DFT potential drop at the interface can be efficientlycorrected by the GW eigenvalues obtained for the bulkvalence band states [11 14 15] A good estimation of alloyselectronic properties is also a difficult task inDFT simulationIndeed semiconductors even conventional ones undergoa significant bowing of the band-gap that is the band-gapenergy follows 119864119892(119909) = 119864119892(119909) minus 119887 sdot 119909 sdot (1 minus 119909) where119887 is a bowing parameter Supercell approaches for statisti-cally random alloys are more adequate than virtual crystalapproximations For special alloy compositions equivalentresults can be obtained from DFT with special quasirandomstructures (SQS) (small supercells) that reproduce mixingenthalpies and atomic correlations of very large supercells [8]Noteworthily SQS models include chemical mixing strainand atomic relaxation effects

In addition semiempirical methods for mechanical orelectronic properties studies as the valence force field (VFF)and the tight binding approximation [16] or elasticity and thekp method [17] require accurate electronic parameters asinput They can be derived from DFT calculations or experi-ment For example quantitative estimates of electromechan-ical tensors of bulk materials are achieved from density-functional perturbation theory (DFPT) [18ndash20] An efficientuse of the ldquo2119899+1rdquo theorem where only by-products of a first-order perturbation calculation are required provides second-and third-order derivatives of the total energy providedthat atomic-displacement variables have been eliminated Forsecond-order derivatives various physical responses of insu-lating crystals can be obtained including elastic constants

linear piezoelectric tensors and linear dielectric susceptibil-ity as well as tensor properties related to internal atomicdisplacements like Born charges and phonons [20 21] Forthird-order components related to physical properties suchas nonlinear electrical susceptibilities nonlinear elasticityor photoelastic and electrostrictive effects finite differencetechniques and symmetry analysis must be associated withthe DFPT method [22] Finally excitonic and transportproperties can also be studied by DFT methods but they arebeyond the scope of the present paper

This paper aims at illustrating with two examples someof the DFTrsquos potentialities for PV technologies First we willfocus on hybrid organicinorganic perovskites (HOP) thatopen new routes for solar cells (Section 31) In particular adirect optical transition and isotropic activity are predictedfor a model 3D system Secondly the investigation of struc-tural elastic and electronic properties will be illustratedon III-V semiconductor heterostructures for GaPSi pseudo-substrates (Section 32) Computational details are given inSection 2

2 Computational Details

Total energy DFT calculations were carried out using theABINIT code [20] within LDA or GGA A plane-wave basisset with an energy cut-off of 340 and 680 eV for compoundsinvestigated respectively in Sections 31 and 32 was used toexpand the electronic wave-functions The reciprocal spaceintegration was performed over Monkhorst-Pack grids [23]The energy was computed from the linear response methodand convergence is accurately reached with tolerance onthe residual potential which stems from differences betweenthe input and output potentials Pseudopotentials were con-structed either from the Fritz Haber Institute (FHI) for-mat [24] or using the Hartwigsen-Goedecker-Hutter (HGH)scheme [25] The dielectric properties were studied from thedensity-functional perturbation theory (DFPT) based on thelinear response theory implemented in SIESTA code [26] Allmany-body GW calculations were performed at the G0W0level [9] The quasiparticles energies were converged withrespect to the energy cut-offs the number of k-points inthe Brillouin Zone (BZ) and the number of bands usedto compute the dielectric function and the self-energy Theplasmon-pole model was used to describe the dynamicdependence of the screening function [20]

3 Results

31 Optoelectronic Properties of HybridOrganicInorganic Per-ovskites for High Efficiency and Low-Cost Solar Cells Hybridorganicinorganicmaterials have attracted increasing interestover the past decade due to their potential applications Inparticular hybrid nanomaterials are expected to offer a waytowards enhanced performances of optoelectronic devices[27] The versatility of the organic part affords the possibilityof fine tuning materialrsquos optoelectronic properties [28] Forexample it has been shown that the optical spectra of HOPcan be easily tailored by varying the organic cation whichimproves optical efficiencies and the tuning of the emission


b

c

a

Pb

I

H

C

N

(a)

a

b

c

(b)







05

1

15

2

25

minus08

minus06

minus04

minus02

0

Ener

gy (e

V)

MAPbI3

U998400ΓΓU Y

VBM1-2gt|

CBM1-6gt|

(a)

MAPbI3

U998400ΓΓU Y

(b)



a

b

c

(a)

c

a

b

(b)







minus1

0

1

2

3

Band

ener

gy (e

V)

Z XY

|CBM1gt

|CBM2gt

ΓΓ

gt|VBM





0

2

4

6

8

1 15 2 25 3

E (eV)

Polycrystal

(2)

(1)(3)

120576998400998400

(a)

0

2

4

6

8

1 15 2 25 3

E (eV)

120576998400998400

TM

TE

(b)


3NH3PbI3(a) and








xz

y

GaP

GaAs

az = 583 A

az = 542 A




VFF

DFT

136

138

14

142

144

146

Atom

ic la

yer s

paci

ng (A

)



minus02

minus01

minus005

minus015

02

015

01

005

0

GaGa Ga Ga

GaGa Ga Ga

P P P P

As As As As

Hirs

hfel

d ch

arge

(fra

ctio

n of

e)




EvA

VA

EvB

VB

EcAEcB




-1

0

1

2

3

Ener

gy (e

V)


M(Xxy) Γ(Xz) Z

-1

0

1

2

3

Ener

gy (e

V)

XL Γ

Bulk GaP










CB

VBXzΓ

Γ

Γ

M


2b(120576zz minus 120576xx)

minus1


2


Xxy Xz

Xx

Xy







Energy gap(eV)


Strained GaAs(G0W0)

Strained GaAs(exp)





-18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

Pote

ntia

l (eV

)

GaP

GaAs




= 056 eV(1)




4 Conclusions




Acknowledgments


References












119909Ga1minus119909

As BxIn1minus119909












































3NH3)PbI3for solid-



119899H2119899+1




119899H2119899+1




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


b

c

a

Pb

I

H

C

N

(a)

a

b

c

(b)







05

1

15

2

25

minus08

minus06

minus04

minus02

0

Ener

gy (e

V)

MAPbI3

U998400ΓΓU Y

VBM1-2gt|

CBM1-6gt|

(a)

MAPbI3

U998400ΓΓU Y

(b)



a

b

c

(a)

c

a

b

(b)







minus1

0

1

2

3

Band

ener

gy (e

V)

Z XY

|CBM1gt

|CBM2gt

ΓΓ

gt|VBM





0

2

4

6

8

1 15 2 25 3

E (eV)

Polycrystal

(2)

(1)(3)

120576998400998400

(a)

0

2

4

6

8

1 15 2 25 3

E (eV)

120576998400998400

TM

TE

(b)


3NH3PbI3(a) and








xz

y

GaP

GaAs

az = 583 A

az = 542 A




VFF

DFT

136

138

14

142

144

146

Atom

ic la

yer s

paci

ng (A

)



minus02

minus01

minus005

minus015

02

015

01

005

0

GaGa Ga Ga

GaGa Ga Ga

P P P P

As As As As

Hirs

hfel

d ch

arge

(fra

ctio

n of

e)




EvA

VA

EvB

VB

EcAEcB




-1

0

1

2

3

Ener

gy (e

V)


M(Xxy) Γ(Xz) Z

-1

0

1

2

3

Ener

gy (e

V)

XL Γ

Bulk GaP










CB

VBXzΓ

Γ

Γ

M


2b(120576zz minus 120576xx)

minus1


2


Xxy Xz

Xx

Xy







Energy gap(eV)


Strained GaAs(G0W0)

Strained GaAs(exp)





-18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

Pote

ntia

l (eV

)

GaP

GaAs




= 056 eV(1)




4 Conclusions




Acknowledgments


References












119909Ga1minus119909

As BxIn1minus119909












































3NH3)PbI3for solid-



119899H2119899+1




119899H2119899+1




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


05

1

15

2

25

minus08

minus06

minus04

minus02

0

Ener

gy (e

V)

MAPbI3

U998400ΓΓU Y

VBM1-2gt|

CBM1-6gt|

(a)

MAPbI3

U998400ΓΓU Y

(b)



a

b

c

(a)

c

a

b

(b)







minus1

0

1

2

3

Band

ener

gy (e

V)

Z XY

|CBM1gt

|CBM2gt

ΓΓ

gt|VBM





0

2

4

6

8

1 15 2 25 3

E (eV)

Polycrystal

(2)

(1)(3)

120576998400998400

(a)

0

2

4

6

8

1 15 2 25 3

E (eV)

120576998400998400

TM

TE

(b)


3NH3PbI3(a) and








xz

y

GaP

GaAs

az = 583 A

az = 542 A




VFF

DFT

136

138

14

142

144

146

Atom

ic la

yer s

paci

ng (A

)



minus02

minus01

minus005

minus015

02

015

01

005

0

GaGa Ga Ga

GaGa Ga Ga

P P P P

As As As As

Hirs

hfel

d ch

arge

(fra

ctio

n of

e)




EvA

VA

EvB

VB

EcAEcB




-1

0

1

2

3

Ener

gy (e

V)


M(Xxy) Γ(Xz) Z

-1

0

1

2

3

Ener

gy (e

V)

XL Γ

Bulk GaP










CB

VBXzΓ

Γ

Γ

M


2b(120576zz minus 120576xx)

minus1


2


Xxy Xz

Xx

Xy







Energy gap(eV)


Strained GaAs(G0W0)

Strained GaAs(exp)





-18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

Pote

ntia

l (eV

)

GaP

GaAs




= 056 eV(1)




4 Conclusions




Acknowledgments


References












119909Ga1minus119909

As BxIn1minus119909












































3NH3)PbI3for solid-



119899H2119899+1




119899H2119899+1




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


minus1

0

1

2

3

Band

ener

gy (e

V)

Z XY

|CBM1gt

|CBM2gt

ΓΓ

gt|VBM





0

2

4

6

8

1 15 2 25 3

E (eV)

Polycrystal

(2)

(1)(3)

120576998400998400

(a)

0

2

4

6

8

1 15 2 25 3

E (eV)

120576998400998400

TM

TE

(b)


3NH3PbI3(a) and








xz

y

GaP

GaAs

az = 583 A

az = 542 A




VFF

DFT

136

138

14

142

144

146

Atom

ic la

yer s

paci

ng (A

)



minus02

minus01

minus005

minus015

02

015

01

005

0

GaGa Ga Ga

GaGa Ga Ga

P P P P

As As As As

Hirs

hfel

d ch

arge

(fra

ctio

n of

e)




EvA

VA

EvB

VB

EcAEcB




-1

0

1

2

3

Ener

gy (e

V)


M(Xxy) Γ(Xz) Z

-1

0

1

2

3

Ener

gy (e

V)

XL Γ

Bulk GaP










CB

VBXzΓ

Γ

Γ

M


2b(120576zz minus 120576xx)

minus1


2


Xxy Xz

Xx

Xy







Energy gap(eV)


Strained GaAs(G0W0)

Strained GaAs(exp)





-18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

Pote

ntia

l (eV

)

GaP

GaAs




= 056 eV(1)




4 Conclusions




Acknowledgments


References












119909Ga1minus119909

As BxIn1minus119909












































3NH3)PbI3for solid-



119899H2119899+1




119899H2119899+1




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


xz

y

GaP

GaAs

az = 583 A

az = 542 A




VFF

DFT

136

138

14

142

144

146

Atom

ic la

yer s

paci

ng (A

)



minus02

minus01

minus005

minus015

02

015

01

005

0

GaGa Ga Ga

GaGa Ga Ga

P P P P

As As As As

Hirs

hfel

d ch

arge

(fra

ctio

n of

e)




EvA

VA

EvB

VB

EcAEcB




-1

0

1

2

3

Ener

gy (e

V)


M(Xxy) Γ(Xz) Z

-1

0

1

2

3

Ener

gy (e

V)

XL Γ

Bulk GaP










CB

VBXzΓ

Γ

Γ

M


2b(120576zz minus 120576xx)

minus1


2


Xxy Xz

Xx

Xy







Energy gap(eV)


Strained GaAs(G0W0)

Strained GaAs(exp)





-18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

Pote

ntia

l (eV

)

GaP

GaAs




= 056 eV(1)




4 Conclusions




Acknowledgments


References












119909Ga1minus119909

As BxIn1minus119909












































3NH3)PbI3for solid-



119899H2119899+1




119899H2119899+1




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


EvA

VA

EvB

VB

EcAEcB




-1

0

1

2

3

Ener

gy (e

V)


M(Xxy) Γ(Xz) Z

-1

0

1

2

3

Ener

gy (e

V)

XL Γ

Bulk GaP










CB

VBXzΓ

Γ

Γ

M


2b(120576zz minus 120576xx)

minus1


2


Xxy Xz

Xx

Xy







Energy gap(eV)


Strained GaAs(G0W0)

Strained GaAs(exp)





-18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

Pote

ntia

l (eV

)

GaP

GaAs




= 056 eV(1)




4 Conclusions




Acknowledgments


References












119909Ga1minus119909

As BxIn1minus119909












































3NH3)PbI3for solid-



119899H2119899+1




119899H2119899+1




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




CB

VBXzΓ

Γ

Γ

M


2b(120576zz minus 120576xx)

minus1


2


Xxy Xz

Xx

Xy







Energy gap(eV)


Strained GaAs(G0W0)

Strained GaAs(exp)





-18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

Pote

ntia

l (eV

)

GaP

GaAs




= 056 eV(1)




4 Conclusions




Acknowledgments


References












119909Ga1minus119909

As BxIn1minus119909












































3NH3)PbI3for solid-



119899H2119899+1




119899H2119899+1




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


-18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

Pote

ntia

l (eV

)

GaP

GaAs




= 056 eV(1)




4 Conclusions




Acknowledgments


References












119909Ga1minus119909

As BxIn1minus119909












































3NH3)PbI3for solid-



119899H2119899+1




119899H2119899+1




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of







119909Ga1minus119909

As BxIn1minus119909












































3NH3)PbI3for solid-



119899H2119899+1




119899H2119899+1




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of












3NH3)PbI3for solid-



119899H2119899+1




119899H2119899+1




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of










Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

research article density functional theory simulations of...

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