research article calculations in cds/cdte thin films solar ...internationaljournalofphotoenergy...

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2013 Article ID 513217 4 pageshttpdxdoiorg1011552013513217

Research Article119862-119881 Calculations in CdSCdTe Thin Films Solar Cells witha CdS

119909Te

1minus119909Interlayer

A Gonzalez-Cisneros F L Castillo-Alvarado J Ortiz-Lopez and G Contreras-Puente

Escuela Superior de Fısica y Matematicas-IPN Edificio 9 UPALM 07738 Mexico DF Mexico

Correspondence should be addressed to A Gonzalez-Cisneros omeyotlgmailcom

Received 3 June 2013 Accepted 9 August 2013

Academic Editor Francesco Bonaccorso

Copyright copy 2013 A Gonzalez-Cisneros et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

In CdSCdTe solar cells chemical interdiffusion at the interface gives rise to the formation of an interlayer of the ternarycompound CdS

119909CdTe

1minus119909 In this work we evaluate the effects of this interlayer in CdSCdTe photovoltaic cells in order to improve

theoretical results describing experimental 119862-119881 (capacitance versus voltage) characteristics We extended our previous theoreticalmethodology developed on the basis of three cardinal equations (Castillo-Alvarado et al 2010)The present results provide a betterfit to experimental data obtained fromCdSCdTe solar cells grown in our laboratory by the chemical bath deposition (for CdS film)and the close-spaced vapor transport (for CdTe film) techniques

1 Introduction

Polycrystalline solar cells based on the thin films technol-ogy are outstanding candidates for an aggressive expansionof the photovoltaic industry During the past few yearsdespite the world economic recession the photovoltaicmarket has continued to grow In Europe and Asia themarket has expanded from the Mega Watt (MW) to theGiga Watt (GW) scale PV installations grew to 73GWin 2009 which represents 20 from the previous yearThe various forecast scenarios predict an increase in thedemand from 154 to 37GW in 2014 more than five timesthe size of the 2009 market [1 2] Today there is muchinterest and research activity concerning second generationsolar cells based on polycrystalline cadmium telluride CdTethin films and cadmium sulfide CdS as ldquowindowrdquo layerCapacitance versus voltage is one of the most importanttechniques for the device characterization In this workwe extend the theoretical model used in a previous paper[3] in order to take into account the formation of a layerof the ternary compound CdS

119909Te1minus119909

(119909 the concentra-tion) at the CdSCdTe interface generated by interdiffu-sion processes [4] During manufacturing of these solarcells the CdTeCdS interface is subjected to relatively high

temperatures giving rise to atomic interdiffusion and theformation of an interfacial region of composition Cd

119909Te1minus119909

The understanding of this ternary CdS

119909Te1minus119909

interlayer willhelp to conceive improvements in the efficiency of thephotovoltaic cell In this work we use a 119862-119881 theoreticalmethod for the determination of the interface charge density120590 in the CdSternaryCdTe heterojunction and the banddiscontinuity Δ119864V simultaneously The methodology is basedon three cardinal equations as discussed in the theory belowFor comparison with our calculations we used solar cellsof maximum efficiency (124) fabricated in our group[5]

2 Theoretical Method

We present the methodology for the simultaneous calcu-lations of the valence band offset Δ119864V and the interfacecharge density 120590 It is assumed that these two quantities areindependent of the bias voltage This assumption is justifiedbecause we are interested in heterojunctions with fixed defectdensities

The clue for obtaining the energy bands at both sides ofthe interfaces are (a) the two interfacial potentials (120593

1199041 1205931199042

2 International Journal of Photoenergy

which give the band bending at each side of the interface)(b) the energy increment of the valence band and (c) theinterface charge density In addition to these three cardinalequations originating from the displacement of the band line-up equation charge neutrality and the total capacitance ofthe interface are necessary This method makes no use of anyapproximations and provides simultaneous determination ofthe discontinuities of the valence band and the interfacialcharge density

Assuming that the heterojunction is like a parallel platecapacitor the capacitance-voltage characteristics for low biasvoltages 119881

119886are given by

119862 = [

11990212057611987811205761198782119873119889119873119886

2(1205761198781119873119886+ 1205761198782119873119889)

]

12

lowast (119881119889minus 119881119886)minus12

(1)

where 119881119889is the potential well in the heterojunction 119881

119886is

the bias voltage 119902 is the electron charge 119873119886is the

acceptor concentration 119873119889is the donor concentration

and 1205761198781

and 1205761198782

are the dielectric constants of n-type andp-type semiconductor [6] Therefore in our case we havea linear dependence of 1119862

2 versus 119881119886close to 119881

119886= 0

We solve numerically the band energy in any site ofthe heterojunction using the interface according to theexperimental data [7] the spectral response of championCdSCdTe solar cells has an increase in a photon energyclose to the band gap CdS Thus we have assumed inour equations that the physical properties of the ternarycompound are closer to those of CdS for each part of theternary compound which are the total bending on each sideof the two heterojunction (CdTeCdS

119909Te1minus119909

)We note that the total band curvature at each side of the

interface depends on the bias voltage 119881119886 that is 120593

1198781(119881119886) and

1205931198782(119881119886) We assume that the discontinuities of the valence

band and the charge density at the interface are independentof the applied voltage which is a usual assumption for lowvoltages Validity of this assumption is validated by a goodagreement with experiment

Because there are a fixed equal number of separatedpositive and negative charges at the interface between differ-ent materials we consider that the region of spatial chargebehaves like a parallel plate capacitor

21 Cardinal Equations for the CdTeCdS119909Te1minus119909

Interface(119862-119881 Matching Method) The band line-up equation in thiscase is (Figure 1)

1198641198651198811

minus 1198641198651198812

minus Δ119864119881(ternary) minus 119902119881

119886= 119902 [120593

1198782(119881119886) minus 1205931198781

(119881119886)]

(2)

where ldquo119909rdquo is the ternary concentration and1198641198651198811

and1198641198651198812

arethe differences between the quasi-Fermi energy levels withsubscripts 1 and 2 corresponding to CdTe and CdS

119909Te1minus119909

Ternary

Ef1205931 lt 0

1205931 lt 0 1205932 gt 0

1205932 gt 0Ef

Va

CdTe

Ec1

Ec2

Ei1

E1

ΔE = E2 minus E1

ΔEc = Ec2 minus Ec1

E2

Ei2

Figure 1 Energy band (band lineup) diagram of two n-p hetero-junctions under reversible bias The reference level for the potentialof each semiconductor is at the intrinsic energy level We assumethat the ternary behaves like an n-type semiconductor for unionwith CdTe

respectively The valence band offset Δ119864119881(ternary) and the

respective bulk valence band levels are given by

1198641198651198811

= 1198641198651198991

minus 1198641198811

=

1198641198921

2

+

3

4

119896119879 ln(

119898lowast

ℎ1

119898lowast

1198901

) minus 1199021205931198651

1198641198651198812

= 1198641198651199012

minus 1198641198812

=

1198641198922

2

+

3

4

119896119879 ln(

119898lowast

ℎ2

119898lowast

1198902

) minus 1199021205931198652

(3)

The separation between the quasi-Fermi energy levels isdetermined for the bias voltage

1198641198651198991

= 1198641198651199012

+ 119902119881119886 (4)

where 119881119886is the bias voltage in the p-n junction

The charge neutrality equation under nonequilibrium isgiven by

1198761[1205931198781

(119881119886)] + 119876

2[1205931198782

(119881119886)] + 119902120590 = 0 (5)

where the expressions for the semiconductor charge undernonequilibrium 119876

1and 119876

2 are the half semiconductor

charges (per unit area) which are given by [8]

1198761= sign [120593

1198781(119881119886)] sdot

radic212057601205761198781

1205731198711198631

sdot 119890Δ11990612

times 1205931198781

(119881119886) sdot sinh (119906

lowast

1) + cosh [119906

lowast

1minus 1199061198781

(119881119886)]

minus cosh (119906lowast

1)12

1198762= sign [120593

1198782(119881119886)] sdot

radic212057601205761198782

1205731198711198632

sdot 119890Δ11990622

times 1205931198782

(119881119886) sdot sinh (119906

lowast

2) + cosh [119906

lowast

2minus 1199061198782

(119881119886)]


2)12

(6)

where

sign =

+1 119906 lt 0

minus1 119906 gt 0

(7)

Here 119906lowast = 120573((1205931198651

+ 1205931198652

)2) and 120573 = 119902119896119879

International Journal of Photoenergy 3

The third cardinal equation is obtained from the expres-sion of the half capacitance per unit area of the device

1

119862CdTeminuster=

1

1198621[1205931198781

(119881119886)]

+

1

1198622[1205931198782

(119881119886)]

(8)

where

1198621=

(12057601205761198781)2

1205731198712

1198631sdot 1198761

sdot 11989099877911990612

sdot sinh (119906lowast

1) minus sinh [119906

lowast

1minus 1199061198781

(119881119886)]

=

11990212057601205761198781

1198761

1198731+ 21198991198941

sdot 11989099877911990612

sdot sinh [119906lowast

1minus 1199061198781

(119881119886)]

1198622=

(12057601205761198782)2

1205731198712

1198632sdot 1198762

sdot 11989099877911990622



lowast

2minus 1199061198782

(119881119886)]

=

11990212057601205761198782

1198762

1198732+ 21198991198942

sdot 11989099877911990622


2minus 1199061198782

(119881119886)]

(9)

1

119862Totalasymp

1

119862CdTeminuster (10)

It is important to note that the energy gap of the ternary is nota simple linear combination but a more complex function of119909 [9]

119864119892(119909) = (1 minus 119909) 119864

119892(CdS) + 119909119864

119892(CdTe) minus 119887119909 (1 minus 119909) (11)

where 119887 is the ldquooptical bowing coefficientrdquo given by 169 eVand the valence band offset Δ119864

119881

3 Results

We find the ternary concentration value of 075 with the bestfitting of the curve which is in good agreement with theresults described by Cediel et al [10] The various quantitiesor constants in the cardinal equations were taken from theprevious paper [3] We show the result of the 119862-119881 fittingmethod in Figure 2 for a voltage range from0 to 05VAmuchbetter fit is obtained by assuming the formation of a ternarycompound at the CdTeCdS interface

In addition we have also obtained the values of thevalence band offset and the interface charge density simul-taneously namely

Δ119864119881

= 099 eV

120590 = 1 times 1013 cmminus2

(12)

which are in good agreement with the reported values [9 1112]

4 Conclusions

In summary we have calculated the capacitance versusapplied voltage of CdSCdTe thin film solar cells considering

00 01 02 03 04 05

ExperimentalNo ternary

Ternary

Capa

cita

nce p

er ar

ea (F

cm

2)

Applied bias (V)

000000

000002

000004

000006

000008

000010

000012

000014

Figure 2 Calculated 119862-119881 characteristics of a CdTeCdS PV cellassuming the formation of a ternary compound at the CdTeCdSinterface Comparison is made with 119862-119881 measurements of a 124efficient PV cell [5] and with calculated results within a modelwithout the assumption of the ternary compound at the interface[3]

the formation of a CdS119909Te1minus119909

interlayer using the 119862-119881matching method Our results are in better agreement withexperimental data than our previous theoretical results thatdid not assume the presence of the CdS

119909Te1minus119909

interlayer Wemay also say that the ternary layer acquires the properties ofCdS and behaves like the type n semiconductor instead of theCdS itself This could be taken as evidence of the existence ofa ternary compound that plays an important role in solar celldevices This can be taken as evidence of the existence of theternary interlayer which plays an important role in the solarcell

Acknowledgments

F L Castillo-Alvarado J Ortiz-Lopez and G Contreras-Puente gratefully acknowledge fellowships granted byCOFAA-IPN EDI-IPN and EDD-IPN This work waspartially supported by CONACyT (Mexico)

References

[1] Manufacturing cost per watt at First Solar falls to US$076centsModule Faults Hit Earnings 2011 httpwwwpv-techorgnews

[2] M Osborne First Solar First to 1GW Annual ProductionPhotovoltaics 2009 httpwwwpv-techorg

[3] F L Castillo-Alvarado J A Inoue-Chavez O Vigil-Galan ESanchez-Meza E Lopez-Chavez and G Contreras-Puente ldquoC-V calculations in CdSCdTe thin films solar cellsrdquo Thin SolidFilms vol 518 no 7 pp 1796ndash1798 2010

[4] M M Aliyu S Hossain M A Islam et al ldquoEvaluation of theeffects and impacts of the CdSTe interlayer in CdSCdTe solarcells through modeling and simulationsrdquo in Proceedings of the


2nd International Conference on the Developments in RenewableEnergy Technology (ICDRET rsquo12) pp 248ndash251 January 2012

[5] O Vigil-Galan A Arias-Carbajal and R Mendoza-PerezldquoImproving the efficiency of CdSCdTe solar cells by varying thethioureaCdCl

2ratio in the CdS chemical bathrdquo Semiconductor

Science and Technology vol 20 no 8 p 819 2005[6] B L Sharma and R K Purohit Semiconductor Heterojunctions

Pergamon Press[7] First Solar New Releases 2011 httpwwwfirstsolarcom[8] R S C Cobbolt Theory and Applications of Field Effect

Transistors Willey London UK 1970[9] S-HWei S B Zhang and A Zunger ldquoFirst-principles calcula-

tion of band offsets optical bowings and defects in CdS CdSeCdTe and their alloysrdquo Journal of Applied Physics vol 87 no 3pp 1304ndash1311 2000

[10] G Cediel F Rojas H L Infante and G Gordillo ldquoDetermi-nacion de constantes opticas y simulacion teorica del espectrode transmitancia de peloculas delgadas deCdSCdTe yCd(STe)depositadas por evaporacionrdquo Revista Colombiana de Fisicavol 34 no 1 2002

[11] A Balcioglu F Hasoon D Levi and R K Ahceukiel ldquoInves-tigation of deep impurity levels in CdTeCdS solar cells (2000)(NCPV) program review meetingrdquo in N Spu Program ReviewMeeting Proceeding p 279 2006

[12] S Vatana I Caraman G Rasu V Fedorov and P Gasin ldquoThestudy of the nonequilibrium charge carrier transport mech-anism through the interface of CdSCdTe heterojunctionsrdquoChalcogenide Letters vol 13 p 9 2006

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which give the band bending at each side of the interface)(b) the energy increment of the valence band and (c) theinterface charge density In addition to these three cardinalequations originating from the displacement of the band line-up equation charge neutrality and the total capacitance ofthe interface are necessary This method makes no use of anyapproximations and provides simultaneous determination ofthe discontinuities of the valence band and the interfacialcharge density

Assuming that the heterojunction is like a parallel platecapacitor the capacitance-voltage characteristics for low biasvoltages 119881

119886are given by

119862 = [

11990212057611987811205761198782119873119889119873119886

2(1205761198781119873119886+ 1205761198782119873119889)

]

12

lowast (119881119889minus 119881119886)minus12

(1)

where 119881119889is the potential well in the heterojunction 119881

119886is

the bias voltage 119902 is the electron charge 119873119886is the

acceptor concentration 119873119889is the donor concentration

and 1205761198781

and 1205761198782

are the dielectric constants of n-type andp-type semiconductor [6] Therefore in our case we havea linear dependence of 1119862

2 versus 119881119886close to 119881

119886= 0

We solve numerically the band energy in any site ofthe heterojunction using the interface according to theexperimental data [7] the spectral response of championCdSCdTe solar cells has an increase in a photon energyclose to the band gap CdS Thus we have assumed inour equations that the physical properties of the ternarycompound are closer to those of CdS for each part of theternary compound which are the total bending on each sideof the two heterojunction (CdTeCdS

119909Te1minus119909

)We note that the total band curvature at each side of the

interface depends on the bias voltage 119881119886 that is 120593

1198781(119881119886) and

1205931198782(119881119886) We assume that the discontinuities of the valence

band and the charge density at the interface are independentof the applied voltage which is a usual assumption for lowvoltages Validity of this assumption is validated by a goodagreement with experiment

Because there are a fixed equal number of separatedpositive and negative charges at the interface between differ-ent materials we consider that the region of spatial chargebehaves like a parallel plate capacitor

21 Cardinal Equations for the CdTeCdS119909Te1minus119909

Interface(119862-119881 Matching Method) The band line-up equation in thiscase is (Figure 1)

1198641198651198811

minus 1198641198651198812

minus Δ119864119881(ternary) minus 119902119881

119886= 119902 [120593

1198782(119881119886) minus 1205931198781

(119881119886)]

(2)

where ldquo119909rdquo is the ternary concentration and1198641198651198811

and1198641198651198812

arethe differences between the quasi-Fermi energy levels withsubscripts 1 and 2 corresponding to CdTe and CdS

119909Te1minus119909

Ternary

Ef1205931 lt 0

1205931 lt 0 1205932 gt 0

1205932 gt 0Ef

Va

CdTe

Ec1

Ec2

Ei1

E1

ΔE = E2 minus E1

ΔEc = Ec2 minus Ec1

E2

Ei2

Figure 1 Energy band (band lineup) diagram of two n-p hetero-junctions under reversible bias The reference level for the potentialof each semiconductor is at the intrinsic energy level We assumethat the ternary behaves like an n-type semiconductor for unionwith CdTe

respectively The valence band offset Δ119864119881(ternary) and the

respective bulk valence band levels are given by

1198641198651198811

= 1198641198651198991

minus 1198641198811

=

1198641198921

2

+

3

4

119896119879 ln(

119898lowast

ℎ1

119898lowast

1198901

) minus 1199021205931198651

1198641198651198812

= 1198641198651199012

minus 1198641198812

=

1198641198922

2

+

3

4

119896119879 ln(

119898lowast

ℎ2

119898lowast

1198902

) minus 1199021205931198652

(3)

The separation between the quasi-Fermi energy levels isdetermined for the bias voltage

1198641198651198991

= 1198641198651199012

+ 119902119881119886 (4)

where 119881119886is the bias voltage in the p-n junction

The charge neutrality equation under nonequilibrium isgiven by

1198761[1205931198781

(119881119886)] + 119876

2[1205931198782

(119881119886)] + 119902120590 = 0 (5)

where the expressions for the semiconductor charge undernonequilibrium 119876

1and 119876

2 are the half semiconductor

charges (per unit area) which are given by [8]

1198761= sign [120593

1198781(119881119886)] sdot

radic212057601205761198781

1205731198711198631

sdot 119890Δ11990612

times 1205931198781

(119881119886) sdot sinh (119906

lowast

1) + cosh [119906

lowast

1minus 1199061198781

(119881119886)]


1)12

1198762= sign [120593

1198782(119881119886)] sdot

radic212057601205761198782

1205731198711198632

sdot 119890Δ11990622

times 1205931198782

(119881119886) sdot sinh (119906

lowast

2) + cosh [119906

lowast

2minus 1199061198782

(119881119886)]


2)12

(6)

where

sign =

+1 119906 lt 0

minus1 119906 gt 0

(7)

Here 119906lowast = 120573((1205931198651

+ 1205931198652

)2) and 120573 = 119902119896119879



1

119862CdTeminuster=

1

1198621[1205931198781

(119881119886)]

+

1

1198622[1205931198782

(119881119886)]

(8)

where

1198621=

(12057601205761198781)2

1205731198712

1198631sdot 1198761

sdot 11989099877911990612



lowast

1minus 1199061198781

(119881119886)]

=

11990212057601205761198781

1198761

1198731+ 21198991198941

sdot 11989099877911990612


1minus 1199061198781

(119881119886)]

1198622=

(12057601205761198782)2

1205731198712

1198632sdot 1198762

sdot 11989099877911990622



lowast

2minus 1199061198782

(119881119886)]

=

11990212057601205761198782

1198762

1198732+ 21198991198942

sdot 11989099877911990622


2minus 1199061198782

(119881119886)]

(9)

1

119862Totalasymp

1



119864119892(119909) = (1 minus 119909) 119864

119892(CdS) + 119909119864

119892(CdTe) minus 119887119909 (1 minus 119909) (11)


119881

3 Results



Δ119864119881

= 099 eV


(12)


4 Conclusions


00 01 02 03 04 05


Ternary

Capa

cita

nce p

er ar

ea (F

cm

2)

Applied bias (V)

000000

000002

000004

000006

000008

000010

000012

000014




119909Te1minus119909


Acknowledgments


References

























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



1

119862CdTeminuster=

1

1198621[1205931198781

(119881119886)]

+

1

1198622[1205931198782

(119881119886)]

(8)

where

1198621=

(12057601205761198781)2

1205731198712

1198631sdot 1198761

sdot 11989099877911990612



lowast

1minus 1199061198781

(119881119886)]

=

11990212057601205761198781

1198761

1198731+ 21198991198941

sdot 11989099877911990612


1minus 1199061198781

(119881119886)]

1198622=

(12057601205761198782)2

1205731198712

1198632sdot 1198762

sdot 11989099877911990622



lowast

2minus 1199061198782

(119881119886)]

=

11990212057601205761198782

1198762

1198732+ 21198991198942

sdot 11989099877911990622


2minus 1199061198782

(119881119886)]

(9)

1

119862Totalasymp

1



119864119892(119909) = (1 minus 119909) 119864

119892(CdS) + 119909119864

119892(CdTe) minus 119887119909 (1 minus 119909) (11)


119881

3 Results



Δ119864119881

= 099 eV


(12)


4 Conclusions


00 01 02 03 04 05


Ternary

Capa

cita

nce p

er ar

ea (F

cm

2)

Applied bias (V)

000000

000002

000004

000006

000008

000010

000012

000014




119909Te1minus119909


Acknowledgments


References

























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 calculations in cds/cdte thin films solar ...internationaljournalofphotoenergy...

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