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Solar Energy 86 (2012) 1470–1476

Band gap optimization of p–i–n layers of a-Si:H by computeraided simulation for development of efficient solar cell

Sukhbir Singh 1, Sushil Kumar ⇑, Neeraj Dwivedi

Physics of Energy Harvesting Division, National Physical Laboratory (CSIR), Dr. K.S. Krishnan Road, New Delhi 110 012, India

Received 8 December 2011; received in revised form 8 February 2012; accepted 9 February 2012Available online 19 March 2012

Communicated by: Associate Editor Nicola Romeo

Abstract

The p-layer band gap and its thickness strongly influence the efficiency of hydrogenated amorphous silicon (a-Si:H) p–i–n solar cell,i and n-layer band gaps also play key role. In the present work, p, i and n layer band gaps as 2.1 eV (at thickness 10 nm), 1.75 eV (atthickness 400 nm) and 1.95 eV (at thickness 30 nm), respectively and acceptor and donor concentrations as 1 � 1018 cm�3and1 � 1020 cm�3, respectively, are optimized for obtaining efficient a-Si:H p–i–n solar cell by computer aided one-dimensional AFORS-HET software. It is important to mention that when p-layer thickness is changed to 5 nm, maximum efficiency is obtained at p-layerband gap of 2.2 eV. Such an optimized value would further help to prepare efficient a-Si:H p–i–n solar cells experimentally.� 2012 Elsevier Ltd. All rights reserved.

Keywords: Simulation; a-Si:H; p–i–n Solar cell; Band gap

1. Introduction

In the last three decades, hydrogenated amorphous sili-con (a-Si:H) thin films is studied extensively due to its usein solar cell fabrication (Chopra et al., 2004; Green, 2007;Tarui et al., 1996; Wronski et al., 2002). Comparing withconventional wafer based crystalline silicon solar cells, a-Si:H based thin film solar cells offers several advantagessuch as they are cost effective, can be grown on large areasubstrates including flexible substrates, require low temper-ature processing and can be efficiently operate in diffuselight conditions. However, maximum efficiency �11% isachieved till date in single junction a-Si:H thin film solarcells. There is hardly any significant improvement in thesesolar cells is reported in last ten years even involving microor nanocrystalline silicon thin layer in the structure. On the

0038-092X/$ - see front matter � 2012 Elsevier Ltd. All rights reserved.

doi:10.1016/j.solener.2012.02.007

⇑ Corresponding author. Tel.: +91 11 45608650; fax: +91 11 45609310.E-mail address: skumar@nplindia.org (S. Kumar).

1 Present address: University Institute of Engineering and Technology,MD University Rohtak, India.

other hand, other thin film based solar cells such as CIGSand CdTe have shown great improvement in their efficiencyduring last ten years (Chopra et al., 2004; Green, 2007).Moreover, organic, polymer and dye sensitized solar cellsare also exhibited great response towards improvement oftheir efficiencies. Thus, in order to involves a-Si:H incompetition with other solar cells, its efficiency must beenhanced, which is possible by optimization of processparameters prior to cell fabrication. Recently, some theo-retical studies are performed for optimizing the parametersin order to enhance the efficiency of a-Si:H p–i–n solar cells(Walsh, 2007; Kabir et al., 2010). Among various parame-ters, p, i and n layer band gaps have great influence on theefficiency of solar cells. Recently, theoretical studies foroptimization of p-layer band gap for improving the effi-ciency of a-Si:H p–i–n solar cells with hydrogenated amor-phous carbon as p-layer are also carried out by our group(Dwivedi et al., 2012, 2011).

Keeping all important points into the mind, the p, i and nlayer band gaps of a-Si:H and acceptor and donor concen-trations are optimized by one dimensional AFORS-HET

S. Singh et al. / Solar Energy 86 (2012) 1470–1476 1471

software. By applying these optimized band gaps, the exper-imental realization of efficient a-Si:H p–i–n solar cell is pos-sible. We are in the process for experimental realization ofthese simulation optimized band gaps.

1.1. a-Si:H p–i–n solar cell structure and working principle

Solar cell is a p–n or p–i–n junction diode device thatdirectly converts solar energy into electrical energy by pho-tovoltaic effect. Fig. 1 shows the schematic of a-Si:H p–i–nsolar cell. A thin layer of p-type a-Si:H is kept on ITOcoated glass substrate followed by thick layer of intrinsic(i) a-Si:H. Finally, a thin layer of n-type a-Si:H is kept overi-layer followed by metal contact normally silver (Ag). Inthe present simulation, the p-layer band gap and its thick-ness are varied from 1.75 eV to 2.3 eV and 5 nm to 10 nm,respectively, i-layer band gap is varied from 1.3 eV to1.95 eV and its thickness 400 nm is kept constant andn-layer band gap is varied from 1.75 eV to 2.7 eV and itsthickness 30 nm is kept constant. In p–i–n solar cells,p-layer acts as a window layer, i-layer acts as an absorberlayer and n-layer acts as a collector layer. The light fallon cell from p-layer side and almost all light get absorbin i-layer, resulting in generation of electron–holes (e–h)pairs. Immediately after generation, these e–h pairs are sep-arated by junction field (occur due to built in potential).Hence, holes are travel towards p-layer and electrons aremoved towards n-layer. This results in flow of photo cur-rent in the cell. In the solar cell device physics, the impor-tant parameters need to be discuss are open circuit voltage(Voc), short circuit current (Isc), fill factor (FF) and effi-ciency (g). Voc is the voltage when no current pass throughthe cell, whereas Isc is the current when no voltage isapplied. Hence, in ideal solar cell Isc should be equal toIph, where Iph is photo current. The parameter FF definesthe maximum power in solar cell by an expression.

FF ¼ V mIm

V ocIsc¼ P m

V ocIsc

where Vm and Im are the maximum voltage and maximumcurrent, respectively and Pm is the maximum power. The

Glass

ITO

p-Layer (a-Si:H)

i-Layer (a-Si:H)

n-Layer (a-Si:H)

Metal Contact (Ag)

Light

Fig. 1. Schematic of simple thin film p–i–n solar cell.

most important parameter in solar cell device is efficiency(g) that is the ratio of maximum electrical power generated(Pm) with respect to solar power incident (Pin). Hence, effi-ciency is given by

g ¼ P m

P in¼ FFV ocIsc

P in

1.2. Simulation

AFORS-HET is an important one dimensional com-puter program for modeling of multilayer homo and het-erojunction solar cells (Konagai, 2011; Stangle et al.,xxxx; Wang et al., 2011; Zhao et al., 2008, 2009). It solvesthe one dimensional semiconductors equation based on dif-ferent physical equations like Poissons equation and thetransport and continuity equations for electrons and holesunder different mode of operation. The generation of elec-tron/hole pairs (optical models of AFORS-HET) can bedescribed either by Lambert–Beer absorption includingrough surfaces and using measured reflection and transmis-sion values, or by calculating the plain surface incoherent/coherent multiple internal reflections, using the complexindices of reflection for the individual layers. Differentrecombination models can be considered within AFORS-HET. The radiation AM 1.5 with incident power densityof 100 mW/cm2 is used as illuminating source in presentsimulations.

1.3. Optimization of acceptor and donor concentrations for

p-layer band gap

The values of electrons and holes mobility, dielectric con-stant, electron affinity, electron and holes velocity, etc. for p,i and n layers of a-Si:H are given in Table 1 (Dao et al., 2010;Zhao et al., 2008, 2009). The band gap and carrier concen-trations are found to be important parameters that directlyinfluence the performance of solar cells. Hence, first accep-tor and donor concentrations are optimized and their vari-ations with p-layer band gap are shown in Fig. 2a–d.During optimization of acceptor and donor concentrationsother parameters are kept constant. It is clear from figurethat acceptor concentration as �1 � 1018 cm�3 and donorconcentration as �1 � 1020 cm�3 is optimized for obtainingefficient p–i–n solar cells. Hence, these values of acceptorand donor concentrations are used in present simulationstudy.

2. Simulation results and discussion

2.1. Effect of p-layer band gap

In this section, the effect of p-layer band gap on opencircuit voltage (Voc), short circuit current (Jsc), fill factor(FF) and efficiency (g) of a-Si:H p–i–n solar cell isdescribed. The variation of Voc, Jsc, FF and efficiency asa function of p-layer band gap is depicted in Fig. 3a–d.

Table 1Baseline input parameters used for this simulation.

Parameters a-Si:H(p)

a-Si:H(i)

a-Si:H(n)

Layer thickness (nm) 10 (or 5) 400 30Dielectric constant 11.9 11.9 11.9Electron affinity (eV) 3.9 3.9 3.9Band gap (eV) Varied Varied VariedOptical band gap (eV) 1.75 1.74 1.78Effective conduction band density

(cm�3)1 � 1020 1 � 1020 1 � 1020

Effective valence band density (cm�3) 1 � 1020 1 � 1020 1 � 1020

Electron mobility (cm2 v�1s�1) 5 5 5Hole mobility (cm2 v�1s�1) 1 1 1Doping concentration of acceptors

(cm�3)1 � 1018 0 0

Doping concentration of donators(cm�3)

0 0 1 � 1020

Thermal velocity of electrons (cm s�3) 1 � 107 1 � 107 1 � 107

Thermal velocity of hole (cm s�1) 1 � 107 1 � 107 1 � 107

Layer density (g cm�3) 2.328 2.328 2.328

1472 S. Singh et al. / Solar Energy 86 (2012) 1470–1476

Initially Voc is enhanced with the increasing p-layer bandgap from 1.75 eV to 2.0 eV, saturate in the range from2 eV to 2.2 eV and again increased beyond 2.2 eV.Obtained greater Voc at higher band gap is due to the largerquasi-Fermi energy-level splitting. In contrast, Jsc remainsconstant with the increase of p-layer band gap from1.75 eV to 2.25 eV but it is drastically decreased beyond2.25 eV. Despite of increasing p-layer band gap from1.75 eV to 2.25 eV, which leads to increased absorption

1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5

3

6

9

12

15 (a)

η (%

)

p-layer band gap (eV)

Na = 1x1017, Nd = 1x1017

Na = 1x1017, Nd = 1x1018

Na = 1x1017, Nd = 1x1019

Na = 1x1017, Nd = 1x1020

1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4

3

6

9

12

15 (c)

η (%

)

p-layer band gap (eV)

Na = 1x1019, Nd = 1x1017

Na = 1x1019, Nd = 1x1018

Na = 1x1019, Nd = 1x1019

Na = 1x1019, Nd = 1x1020

Fig. 2. (a–d) Variation of efficiency (g) with p-layer band gap for different

of photon at i-layer resulting in more e–h pair generation,the Jsc remains same that may be due to fact that most ofe–h recombine before their separation. However, decreasein Jsc with the increase of p-layer band gap beyond2.25 eV is ascribed due to the fact that excess absorptionof photons give rise to heat loss (absorption loss). Themaximum values of Voc and Jsc are found to be�1424 mV and �13 mA/cm2, respectively. FF follows thesame trend as observed in Jsc and remains constant withthe increase of p-layer band gap from 1.75 eV to 2.15 eV.However, it is drastically decreased between 2.15 eV and2.25 eV but again rise beyond p-layer band gap of2.25 eV. Increase in FF beyond 2.25 eV may be due tothe lowering of Jsc after this band gap (2.25 eV), as FF var-ies inversely proportional with Jsc. The maximum value ofFF is found to be 90.56%. With the increase of p-layerband gap, evaluated efficiency is also showed three differenttypes of behaviors. Initially efficiency is enhanced with theincrease of p-layer band gap from 1.75 eV to 2.0 eV, satu-rate in band gap from 2 eV to 2.1 eV and falls gradually inthe band gap range from 2.1 eV to 2.2 eV and drasticallybeyond 2.2 eV. Maximum efficiency as 15.8% is observedat p-layer band gap of 2.1 eV (at p-layer thickness of10 nm). Hence, p-layer band gap 2.1 eV is optimized forgetting excellent photoelectric properties. In order tounderstand behavior of efficiency with the p-layer bandgap, band diagrams of simulated solar cells are also dis-cussed. Fig. 4 shows the band diagram of simple p–i–nsolar cell. The states those lie between the conduction band

1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4

3

6

9

12

15 (b)

η (%

)

p-layer band gap (eV)

Na = 1x1018, Nd = 1x1017

Na = 1x1018, Nd = 1x1018

Na = 1x1018, Nd = 1x1019

Na = 1x1018, Nd = 1x1020

1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4

3

6

9

12

15 (d)

η (%

)

p-layer band gap (eV)

Na = 1x1020, Nd = 1x1017

Na = 1x1020, Nd = 1x1018

Na = 1x1020, Nd = 1x1019

Na = 1x1020, Nd = 1x1020

acceptor and donor concentration: carrier concentration optimization.

1.7 1.8 1.9 2.0 2.1 2.2 2.3

5

10

1530

60

904

8

12

1200

1320

1440

(d)

p-layer band gap(eV)

(c)

(b)

(a)η

(%)

FF(%

)Jsc(m

A/c

m2 )

V oc(m

V)

Fig. 3. Variation of (a) Voc, (b) Jsc, (c) FF and (d) g with the p-layer bandgap for a-Si:H p–i–n solar cells.

S. Singh et al. / Solar Energy 86 (2012) 1470–1476 1473

(CB) and the valence band (VB) is referred as forbiddenstates with maximum possibility of electrons into the VB.When light falls on absorber i-layer through p-layer, theelectrons present in VB gets excited to the CB leavingbehind vacancy (hole) into the VB. Excited electrons havetendency to relax to the ground state quickly. However,built in asymmetry restrict their relaxation and drag themto respective locations. Hence, electrons move towards n-type region and holes move towards p-type region. How-ever, at higher p-layer band gap the transport of holesbecome quite complex in a-Si:H p–i–n solar cell due tointroduction of band offset that leads to creation of barrier.This barrier becomes very strong at very high value ofp-layer band gap. It is expected that most of the holes accu-mulate near the barrier and only the holes with energy

Fig. 4. Band diagram of a-Si:H p–i–n solar cell representing bas

above the barrier cross it. Thus, holes accumulation maylowers the efficiency of a-Si:H p–i–n solar cell at higherp-layer band gap beyond 2.1 eV. The energy band diagramof a-Si:H p–i–n solar cell at p-layer band gaps of 1.75 eVand 2.3 eV, which as shown in Fig. 5a and b, respectivelyalso support the said statement i.e. the barrier getsenhanced with the increase of p-layer band gap. Finally,p-layer band gap 2.1 eV is optimized for getting efficient(efficiency 15.8%) a-Si:H p–i–n solar cells. By employingsimulation parameters in experimental work precisely,improvement in efficiency of experimental a-Si:H p–i–nsolar cell is possible.

Further, the role of p-layer thickness (at different bandgaps) on efficiency of p–i–n solar cell is investigated, whichas shown in Fig. 6. The efficiency is found to enhance withthe reducing p-layer thickness from 10 to 5 nm. Because atlow p-layer thickness not only the absorption loss on toplayer is reduced but also the maximum light is transferredto the absorber i-layer where it is absorbed and produceslarge number of e–h pairs. Moreover, with the decreasingp-layer thickness the hole transport towards respective con-tact become much easier. It is important to mention that onreducing the p-layer thickness the maxima of efficiency isshifted toward higher band gap side i.e. maximum effi-ciency at p-layer thickness of 5 nm is obtained at p-layerband gap of 2.2 eV (at p-layer thickness of 10 nm the max-imum efficiency is observed at p-layer band gap of 2.1 eV).The change in efficiency with the varying p-layer thicknessat p-layer band gap of 2.1 eV can be explained properly byenergy band diagram, which as shown in Fig. 7a–c. Thehigher p-layer band gap with higher 10 nm thickness(Fig. 7a) creates a barrier in the valence band of p-layerwhere most of activated hole are accumulated. However,the barrier width is reduced when p-layer thickness isdecreased from 10 nm to 5 nm (Fig. 7c). Under this situa-tion holes need comparatively lower energy to cross thebarrier and then easily conduct. This could be the reasonfor highest efficiency obtained at p-layer thickness of

ic mechanism involved in conduction of electrons and holes.

p

i

n

p=-layer band gap=1.75 eV(a)

p

n

i

p-layer band gap=2.3 eV(b)

Fig. 5. Band diagram of a-Si:H p–i–n solar cell with p-layer band gap (a)1.75 eV and (b) 2.3 eV.

1.7 1.8 1.9 2.0 2.1 2.2 2.3

3

6

9

12

15

18

η (%

)

p-layer band gap (eV)

p-layer thickness = 10 nmp-layer thickness = 7 nmp-layer thickness = 5 nm

Fig. 6. Variation of g of p–i–n solar cells with p-layer band gap fordifferent thicknesses of p-layer.

p

i

n

p-layer thickness=10 nm(a)

(b)p-layer thickness=7 nm

p

i

n

(c)p -layer thickness=5nm

p

i

n

Fig. 7. Band diagram of a-Si:H p–i–n solar cell with p-layer band gap andp-layer thickness (a) 10 nm, (b) 7 nm and (c) 5 nm.

1474 S. Singh et al. / Solar Energy 86 (2012) 1470–1476

5 nm. It is worth noting that at p-layer thickness of 5 nmand p-layer band gap of 2.2 eV, maximum efficiency as17.88% is obtained.

2.2. Effect of i-layer band gap

In this section, the effect of i-layer band gap on efficiencyof a-Si:H p–i–n solar cell is explored. During this investiga-tion, the p-layer and the n-layer band gaps are kept 2.1 eVand 1.78 eV, respectively. The variation of efficiency ofa-Si:H p–i–n solar cells with i-layer band gap is depictedin Fig. 8. The efficiency remains constant with the increaseof i-layer band gap from 1.3 eV to 1.5 eV but drasticallyenhanced in the band gap range from 1.5 to 1.72 eV and

1.8 2.0 2.2 2.4 2.6 2.8

15.8

16.0

16.2

16.4

16.6

16.8

η (%

)

n-layer band gap (eV)

Fig. 9. Variation of g with n-layer band gap for different a-Si:H p–i–nsolar cells.

S. Singh et al. / Solar Energy 86 (2012) 1470–1476 1475

again becomes constant in the band gap range from1.72 eV to 1.75 eV. However, efficiency is reduced beyondi-layer band gap of 1.75 eV. Maximum efficiency isobtained at i-layer band gap of �1.75 eV. Since p-layerband gap is kept as 2.1 eV, hence the light with energy les-ser than 2.1 eV of solar spectrum (normally 1 eV to 3.5 eV)should be reached in i-layer. At low i-layer band gap morephotons will be absorbed, which may leads to significantabsorption losses (resulting in heat) and hence, lower effi-ciency is realized. With the increase of i-layer band gap fro-m1.3 eV to 1.75 eV absorption losses should be reducedand hence, comparatively higher efficiency is obtained.With further increase in band gap beyond 1.75 eV, it isrealized that sufficient light do not absorb in i-layer thatleads to generation of lesser e–h pairs and therefore,decrease in efficiency is observed. In other words, efficiencyis product of Voc and Jsc but at low i-layer band gap (say1.3 eV) Voc is low, hence less efficiency is realized. On theother hand at high i-layer band gap (say 1.9 eV and above)Jsc is small, therefore, lower efficiency is obtained. Finally,i-layer band gap as 1.75 eV is optimized for getting betterefficiency. This is why the i-layer band gap is kept as1.75 eV during investigation of role of p-layer and n-layerband gaps on efficiency of a-Si:H p–i–n solar cells.

2.3. Effect of n-layer band gap

The efficiency of a-Si:H p–i–n solar cells strongly dependon p-layer band gap. However, if p, i and n layers are thini.e. for thin solar cell structure the n-layer band gap mayalso influence the efficiency of solar cell significantly.Therefore, in this section the role of n-layer band gap onefficiency of a-Si:H p–i–n solar cell is investigated. Duringthis investigation, p-layer and i-layer band gaps are kept as2.1 eV and 1.75 eV, respectively and n-layer band gap isvaried from 1.78 eV to 2.7 eV. Fig. 9 shows the variationof efficiency of a-Si:H p–i–n solar cell with n-layer bandgap. Initially efficiency is enhanced with the increase of n-layer band gap and it attains maximum value as 16.76%at 1.95 eV. However, efficiency shows oscillating behaviorin the n-layer band gap range from 1.95 eV to 2.2 eV and

1.3 1.4 1.5 1.6 1.7 1.8 1.9

4

8

12

16

η (%

)

i-layer band gap (eV)

Fig. 8. Variation of g with i-layer band gap for different a-Si:H p–i–n solarcells.

then saturates beyond 2.2 eV. It is worth noting that�1% efficiency changed is obtained when n-layer bandgap is varied from 1.78 to 2.7 eV. Since band gap of p-layeris kept as 2.1 eV, hence ideally photons with energy at andabove 2.1 eV should be absorbed with in p-layer and pho-tons with energy below 2.1 eV (up to 1 eV) should be trans-mitted to i-layer. Similarly, band gap of i-layer is kept as1.75 eV, ideally photons with energy at and above1.75 eV should be absorbed within i-layer and photonswith energy below 1.75 eV should be passed to n-layer.But besides band gap, thicknesses of layers and absorptioncoefficient also matters in absorption and transmission ofphotons. Hence, it is possible that some of photons withenergy even lower than 1.75 eV may also absorb in i-layer(due to large thickness of i-layer) and most of them shouldtransmit to n-layer. Similarly, it is not necessary that all thephotons with energy greater than i layer band gap absorbwithin i layer (because i layer thickness is 400 nm andabsorption coefficient of silicon is higher than this value)but some of them transmit to n-layer. However, n layer isquite thin, therefore all the photons with energy greaterthan n-layer band gap may not be absorbed within n-layerbut some of them will be reflected back to i-layer by strik-ing with back reflector and again they will participate ingenerating the e–h pairs in i-layer. In the same way photonswith energy lower than n layer band gap will not beabsorbed in n-layer but they will be reflected back to i-layer(after striking with back reflector) where they would beabsorbed. Finally, it thought that there may be less absorp-tion of photons in n-layer at n-layer band gap of 1.95 eVthan 1.75 eV. Hence, comparatively more efficiency isobtained at n-layer band gap of 1.95 eV.

3. Conclusions

In the present study, the role of p, i and n-layers bandgaps and p-layer thickness on the efficiency of a-Si:Hp–i–n solar cells is investigated theoretically by one dimen-sional AFORS-HET computer software. At first, theacceptor and the donor concentrations as 1018 cm�3 and1020 cm�3, respectively are optimized. Later, p-layer band

1476 S. Singh et al. / Solar Energy 86 (2012) 1470–1476

gap of 2.1 eV (at p-layer thickness 10 nm) is optimized forgetting highest efficiency as 15.8% in a-Si:H p–i–n cell. Inaddition, i-layer and n-layer band gaps as 1.75 eV and1.95 eV, respectively are also optimized for obtaininghigher efficiency in a-Si:H p–i–n solar cell. It is worth not-ing that when p-layer thickness is changed to 5 nm, maxi-mum efficiency as 17.88% is realized at p-layer band gapof 2.2 eV. Whereas at n-layer band gap of 1.95 eV, maxi-mum efficiency as 16.75% is obtained. By incorporatingthese optimized band gaps and the p-layer thickness inexperimental studies, solar cells with improved efficiencycan be realized. We are now in the process of incorporatingall these theoretically optimized parameters in experimen-tal studies of a-Si:H p–i–n solar cells.

Acknowledgments

The authors are grateful to the Director, NationalPhysical Laboratory (NPL), New Delhi (India) for his kindsupport. MNRE, Govt. of India is acknowledged for spon-soring Project (Sanction No. 31/29/2010-11/PVSE) and fortheir financial support. We gratefully acknowledge Mr.C.M.S. Rauthan and Dr. O.S. Panwar from NPL for theirhelps. Sukhbir Singh (JRF) and Neeraj Dwivedi (SRF)acknowledge UGC, Govt. of India and CSIR, Govt. ofIndia, respectively for providing fellowship. Authors alsoacknowledge Helmholtz-Zentrum Berlin for providingAFORS-HET simulation software, which can be freedownloaded from http://www.helmholtz-berlin.de/fors-chung/enma/si-pv/projekte/asicsi/afors-het/index_en.html.

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