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Solar Energy 94 (2013) 8–18

Performance analysis of vertical multi-junction solar cellwith front surface diffusion for high concentration

Yupeng Xing ⇑, Peide Han, Shuai Wang, Yujie Fan, Peng Liang, Zhou Ye, Xinyi Li,Shaoxu Hu, Shishu Lou, Chunhua Zhao, Yanhong Mi

State Key Lab on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China

Received 8 June 2012; received in revised form 20 March 2013; accepted 29 April 2013Available online 2 June 2013

Communicated by: Associate Editor Prof. H. Upadhyaya

Abstract

The vertical multi-junction (VMJ) solar cell has good potential applications in high concentration photovoltaic. The efficiency of VMJcell reached to 19.19% under 2480 suns has been reported. Numerical calculations show that the efficiency can reach close to 30% afteroptimization. In this work, the performance of the silicon VMJ cell with front surface diffusion working under 1 sun and 1000 suns wascalculated numerically using a TCAD software. The front surface diffusion can reduce the requirement of high quality front surface pas-sivation, but increases the series resistance. The effect of the N-type emitter dopant profile, P+-type back surface field dopant profile,width, thickness, bulk doping concentration and lifetime of the sub-cell on the performance of the VMJ cell with front surface diffusionwas calculated and analyzed. The efficiency reached to 30.56% under 1000 suns after optimization.� 2013 Elsevier Ltd. All rights reserved.

Keywords: Vertical multi-junction solar cell; Numerical simulation; High concentration; Series resistance

1. Introduction

Photovoltaic is a promising clean energy source towhich more and more attention is being paid. Most ofthe solar cells on the photovoltaic markets are monocrys-talline and multicrystalline silicon solar cells. Their highcosts constrain their use. Lots of effort has been made todecrease the costs. Concentrator photovoltaic is consideredto be a promising technology (Castro et al., 2008; Kinget al., 2012; Vivar et al., 2012). The highest efficiency ofthe most widely used III-V multi-junction solar cells hasreached to 44% under 942 suns (Green et al., 2013) andmay reach to 50.91% by adding junctions (King et al.,2012). Their development is constrained by their high costs

0038-092X/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.solener.2013.04.030

⇑ Corresponding author. Tel.: +86 010 82304817; fax: +86 01082304181.

E-mail address: xingyupeng@semi.ac.cn (Y. Xing).

and complex manufacture processes. Most of the currentcommercial concentrator solar cells use the structure offront and back contacts, which have the tradeoff betweenseries resistance and shading caused by the front electrodegrids (Xing et al., 2013). So their efficiency will saturatewith concentration increasing (Daliento and Lancellotti,2010). The efficiency of the concentrator III–V multi-junc-tion cell usually reaches the highest below 1000 suns andthat of the concentrator silicon solar cell usually reachesthe highest below 100 suns (Green et al., 2013). The verticalmulti-junction (VMJ) solar cells, also called edge-illumina-tion solar cells, are proposed in the 1970s (Pozner et al.,2012). They consist of a number of non-monolithic edge-illuminated junctions connected together in parallel or inseries (Rafat, 2006), the schematic is plotted in Fig. 1.The direction of the incident light is vertical to that ofPN junction. The metal contacts are made on the lateralsides of the sub-cells. Their width is small and their height

Fig. 1. Schematic of the vertical multi-junction solar cell.

Fig. 2. Cross sections of the sub-cells of the three kinds of VMJ cells.

Y. Xing et al. / Solar Energy 94 (2013) 8–18 9

is large. So there are no shading and series resistance prob-lems. The efficiency increases with concentration increasingeven when the concentration reaches to 2000 suns (Pozneret al., 2012). The VMJ cell provides a high voltage, low cur-rent operation with a better compatibility to most powerprocessing loads (Sater and Sater, 2002). It also has goodlong wavelength spectral response (Rafat, 2006) and itsmodule has good performance under non-uniform illumi-nation (Segev and Kribus, 2013). The efficiency of theVMJ cells made by Sater et al. using simple processes hasreached to 19.19% under 2480 suns (Sater and Sater, 2002).

The “sliver” solar cell which has a similar structure tothe VMJ cell has the efficiency of 18.2% under 50 suns(Franklin et al., 2009). The difference between the two cellsis that the front and back surfaces of the “sliver” cell arealso diffused besides the lateral sides. Since the manufactur-ing processes limitation, the width of the “sliver” cell can-not be made too small. It can only be used for lowconcentration because of the series resistance losses causedby front side emitter sheet resistance, which is similar to thefront and back contact cells. Kerst et al. (2001) and Ortegaet al. (2008) have reported monolithic series-interconnec-tion solar cells. A series of sub-cells were made on thetop active silicon layer of the SOI (Silicon-On-Insulator)substrates first, and then they were connected together bymetal electrodes. These two cells have high output voltage,but their efficiencies are low due to the lack of optimiza-tions of device parameters and manufacture processes.

Lots of effort has been devoted to VMJ cells simula-tions. Catchpole et al. have done detailed analysis to the“sliver” cell using a TCAD (Technology Computer AidedDesign) software (Catchpole et al., 2003). But they onlydiscussed the width of the cell between 300 lm and1000 lm, and the concentration below 10 suns. Rafatestablished a simple analytical model to Sater et al.’s cell(Sater and Sater, 2002; Rafat, 2006) and concluded hiswork with the call for a thorough numerical analysis (Poz-ner et al., 2012). Pozner et al. did detailed numerical anal-ysis to the sub-cell of Sater et al.’s cell (Sater and Sater,2002) using a TCAD software recently (Pozner et al.,2012). They found that the efficiency would be close to30% under 1000 suns by optimizing device parameters.Whereas, the width and thickness of the optimized sub-cellare so small that Sater et al.’s method (Sater and Sater,

2002) cannot be used to fabricate it. The SOI substratesand the CMOS process can be used to realize it as Kerstet al. (2001) and Ortega et al. (2008) did. Braun et al.reported a new structure of VMJ cells recently. They addeda wide bandgap GaP VMJ cell and a narrow bandgap GeVMJ cell to the top and bottom of the Si VMJ cell, respec-tively. They simulated the cell using a TCAD software andfound that the efficiency could exceed 40% under 10,000suns by optimizing device parameters (Braun et al., 2012).

The requirement of the front surface passivation qualityof Sater et al.’s cell is high (Sater and Sater, 2002; Pozneret al., 2012). It will be reduced if the front surface of the cellis diffused, but the series resistance will increase (Catchpoleet al., 2003). If the SOI substrates and the CMOS processare used to manufacture the cells as Pozner et al. reported(Pozner et al., 2012), the width of the sub-cell can be mademuch smaller than that of “sliver” cell (Franklin et al.,2009). And the series resistance will be reduced. The struc-ture of the cell is similar to the cell made by Kerst et al.(2001). The performance of the VMJ cell with front surfacediffusion (shown in Fig. 2b) was analyzed numerically inthis work using a TCAD software, which solves the cou-pled continuity and Poisson equations under specificboundary conditions in two or three dimensions (Arm-strong and Maiti, 2007; Pozner et al., 2012) and has beenused to simulate silicon and III–V multi-junction cells suc-cessfully by many people (Aberle et al., 1994; Catchpoleet al., 2003; Jahanshah et al., 2009; Altermatt, 2011; Nawaz

10 Y. Xing et al. / Solar Energy 94 (2013) 8–18

and Ahmad, 2012; Pozner et al., 2012). First, the effect ofthe front surface recombination velocity on the perfor-mances of three different kinds of VMJ cells was calculatedand compared. The effect of the N-type emitter dopant pro-file, P+-type back surface field dopant profile, width, thick-ness, bulk doping concentration and lifetime of the sub-cellon the performance of the VMJ cell with front surface dif-fusion was calculated and analyzed after that. The mainconclusion of this work was summarized at last.

2. Structure of device and models

We assumed that the VMJ cell was made on the P-typetop active silicon layer of the SOI substrate. First, theinverted pyramids were made on the top surface. Second,the trenches were made by etching the top layer. Third,the P+-type and N-type dopants were made by diffusion.Fourth, the contacts were made by filling the trenches withmetal. Fifth, most of the bottom silicon was etched. Sixth,the buried oxide under the contacts was etched. Seventh,metal was deposited on the back surface. Last, oxide pas-sivation layer and MgF2/ZnS double antireflection filmswere deposited on the front surface. The width of the con-tacts cannot be made as thin as Sater et al. did (Sater andSater, 2002). A constant ratio (contact trench width tothickness) of 1:25 was assumed. The inactive area of thecontacts was considered. We concentrated our simulationon two dimensions, which were shown in Fig. 2, becausethe electric properties of the sub-cell on the third dimensionare almost the same for the same two dimensions (shown inFig. 2) positions. The front and lateral side N-type emitterdopant profiles of the sub-cell are set the same to simplifythe discussion, just like that the lateral side N-type emitterof the cell shown in Fig. 2a is extended to the front side.Gaussian dopant profile was used to characterize the N-type emitter and P+-type BSF dopant profiles.

The models we used were based on Altermatt’s newestreview about the models used in computer numerical sim-ulation of silicon solar cells (Altermatt, 2011) and listedin Table 1. The accuracy of the simulation was ensuredby comparing with the test results of Sater et al.’s cells(Sater and Sater, 2002). The maximum SRH lifetime inthe SRH (Shockley–Read-Hall) recombination model wasset as 1000 ls, corresponding to the state-of-the-art FloatZone (FZ) silicon substrate (Pozner et al., 2012). The life-time of the bulk corresponding to SRH recombinationhas the following relationship with the maximum SRH life-time in the SRH recombination model:

Table 1Physical models used in the numerical simulations.

Free carrier statistics Fermi–DiracIntrinsic carrier density ni = 9.65 � 109 cm�3

Band gap narrowing model SchenkAuger recombination Dziewior and SchmidSRH bulk recombination LawFree carrier mobility Klaassen

s ¼ smax

aþ b Ndope

NSRH

� �þ c Ndope

NSRH

� �d ð1Þ

where Ndope is the doping concentration, smax is the maxi-mum SRH lifetime, a = 1, b = 1, c = 0 and NSRH = 1 -� 1017 cm�3 (Law et al., 1991). The following model wasused for front surface recombination velocity (SRV)assuming that the passivation layer was a high-qualityoxide (Cuevas and Russell, 2000):

Spassivated ¼ S0NDs

N ref

� �a

cm=s ð2Þ

where a = 1, Nref = 1 � 1018 cm�3, S0 = 100 cm/s, and NDs

is the surface doping concentration. The SRV of the lateralmetal contact regions and back surface were assumed as3 � 106 cm/s (Cuevas and Russell, 2000) and 1 � 103 cm/s(Pozner et al., 2012), respectively. The volume and contactresistances of the metal contacts were ignored because oftheir large contact areas. The incident light was modeledusing ray tracing method and a standard AM1.5G spec-trum was used. The intensity of 1 sun was 1000 W/m2.The reflectivity of the front surface was assumed as 0.03(Zhao et al., 1996), but the surface texture was not consid-ered here to simplify the simulation. The reflectivity of theback surface was assumed as 0.97 according to the Si/SiO2/Metal structure (Ristow et al., 2009). The heat generated inthe sub-cell was assumed to flow laterally to the metal con-tacts, which had a higher thermal conductivity, and thenflowed to the bottom metal. And the cells were assumedto be mounted in a good heat sink to ensure that the cellsoperated at room temperature. Thus, the thermal problemswere not considered here.

3. Results

3.1. Comparison of three kinds of VMJ cells

The effect of the front surface recombination velocity onthe performances of three different kinds of VMJ cells wascalculated in this section. According to the optimizedresults of Pozner et al. (2012) and Catchpole et al. (2003),the device parameters of the sub-cell in our simulation wereas follows: the width w = 80 lm, the thickness t = 100 lm,the bulk doping concentration ND = 1 � 1017/cm�3; thesurface doping concentration of the N-type emitterNDs = 1 � 1019/cm3, the junction depth WN = 2.8 lm; thesurface doping concentration of the P+-type BSF NAs = 1 -� 1019/cm3, the junction depth WP = 1 lm. These threekinds of VMJ cells shown in Fig. 2a–c were referred toNPP+ cell, NNPP+ cell and NP cell, respectively. The Jsc,Voc, FF and efficiency of the three cells under 1 sun and1000 suns were calculated for 0 cm/s < SRV < 1 � 105 -cm/s, which were shown in Fig. 3. The Jsc, Voc, FF and effi-ciency of the NNPP+ cell were highest under 1 sun and1000 suns except the FF under 1000 suns. For the NNPP+

cell, the added front side N-type emitter enhanced the sep-

10-1 100 101 102 103 104 105

0.01

0.02

0.03

0.04

0.72

0.75

0.78

0.81

0.84

0

10

20

30

0.6

0.7

0.8

0.9

Jsc

[A/c

m2 ]

Front SRV [cm/s]

10-1 100 101 102 103 104 105

Front SRV [cm/s]

10-1 100 101 102 103 104 105

Front SRV [cm/s]

10-1 100 101 102 103 104 105

Front SRV [cm/s]

NP cell c=1 sunNP cell c=1000 suns

NPP+ cell c=1 sun

NPP+ cell c=1000 suns

NNPP+ cell c=1 sun

NNPP+ cell c=1000 suns

FF

Eff

icie

ncy

[%]

Voc

[v]

(a) (b)

(c) (d)Fig. 3. Dependence of Jsc (a), Voc (b), FF (c) and efficiency (d) on front SRV under 1 sun and 1000 suns of the three kinds of VMJ cells. (Jsc of 1000 suns isdivided by 1000 to compare with that of 1 sun).

Y. Xing et al. / Solar Energy 94 (2013) 8–18 11

aration and collection of photogenerated electrons gener-ated by short wavelength light and shielded the adverseeffect of front surface recombination, because the photo-generated electrons near the front surface did not need torun a long way to the lateral side N-type emitter like theNPP cell and could be collected through the nearer frontside N-type emitter. The Jsc, Voc, FF and efficiency of thethree cells all decreased with SRV increasing and thedecrease magnitude of the NNPP+ cell was the smallest.Thus the requirement of high quality front surface passiv-ation could be reduced if using NNPP+ cell. The differencesof above four parameters between the NPP+ and NP cellswere decreasing with SRV increasing. Thus the effect of theP+-type BSF weakened with SRV increasing for NPP+ cell.The NNPP+ cell did not have this problem. The FF hadthe following relationships with Voc, Jsc and Rs (series resis-tance) (Green, 1977, 1982):

voc ¼V oc

nkTq

ð3Þ

FF0 ¼voc � lnðvoc þ 0:72Þ

voc þ 1ð4Þ

RCH ¼V oc

J sc

ð5Þ

rs ¼Rs

RCH

ð6Þ

FF ¼ FF0ð1� rsÞ ð7Þ

where n was the ideal factor of the pn junction of the solarcell, voc was the normalized Voc, FF0 was the ideal FF, RCH

was the characteristic resistance, rs was the normalized Rs.The method of comparing two IV curves measured at twodifferent illumination intensities (Pysch et al., 2007) wasused to calculate the Rs of the three cells under 1000 suns,the results were as follows: 0.65 mX cm2 (NP),0.49 mX cm2 (NPP+), 1.1 mX cm2 (NNPP+). The 2D plotsof the electron current density (Je) distributions of the threecells under 1000 suns and short circuit were shown inFig. 4, which were corresponding to Fig. 2. It was obviousthat the Je in the front side emitter of the NNPP+ cell wasvery large, because lots of photogenerated electrons trans-ported through the front side emitter to the lateral elec-trodes. Thus, its Rs was largest. The Je distributions ofthe NPP+ and NP cells were very like to each other. Butthe Je of the NP cell was more concentrated in the upperright region. Thus, its Rs was larger. The RCH of the threecells under 1000 suns for SRV = 0 cm/s were as follows:30.79 mX cm2 (NP), 22.27 mX cm2 (NPP+), 19.96 mX�cm2

(NNPP+). Thus, the rs were as follows: 0.021(NP),

Fig. 4. 2D plots of the electron current densities of the three cells under 1000 suns and short circuit.

12 Y. Xing et al. / Solar Energy 94 (2013) 8–18

0.022(NPP+), 0.055(NNPP+), which was largest and led tothe smallest FF.

3.2. Effect of the N-type emitter and P+-type back surface

field

The N-type emitter dopant profile of the VMJ cell withfront surface diffusion (NNPP+ cell) was optimized in thissection, as shown in Fig. 5. The device parameters were thesame as that in Section 3.1. The change trends of the effi-ciency with the change of emitter dopant profile under 1sun and 1000 suns were very different except the upperright regions, where the emitter sheet resistance (RN) waslow. The best dopant parameters were as follows: NDs = 7 -� 1018/cm3, WN = 2 lm, RN = 80.83X/h (under 1 sun);NDs = 5 � 1018/cm3, WN = 5 lm, RN = 39.69X/h (under1000 suns), which was a half of that under 1 sun. Basedon the best N-type emitter dopant profile under 1000 suns,the P+-type BSF dopant profile was optimized, as shown inFig. 6. The change trends of efficiency with the change ofBSF dopant profile under 1 sun and 1000 suns were almostthe same. The best dopant parameters for 1 sun and 1000suns were as follows: NAs = 2 � 1020/cm3, WP = 1.5 lm.

The effect of the emitter junction depth under 1000 sunswas calculated by fixing NDs = 1 � 1019/cm3 and changingthe WN from 0.1 lm to 10 lm, as shown in Fig. 7a and b.RCH and the product of Jsc and Voc were also calculated toreveal the effect of the emitter sheet resistance on Rs, FFand efficiency. The Jsc increased with WN increasing untilreached to maximum at WN = 0.4 lm, and then decreased.The Voc increased with WN increasing first, then saturated,and decreased a little at last. The Rs changed little whenWN < 0.7 lm and decreased with WN increasing whenWN > 0.7 lm. The FF decreased with WN increasing first,reached to minimum at WN = 0.3 lm, and then increased.The RCH had the opposite trend to FF. The final conver-sion efficiency was determined by all above parametersand reached to maximum at WN = 3 lm. However, theproduct of Jsc and Voc reached to maximum at WN = 1 lm.The RN at WN = 1 lm was so large that the FF and effi-ciency at WN = 1 lm were lower than that at WN = 3 lm.This revealed the important effect of RN on Rs, FF and effi-ciency under high concentration.

The directions of the electron transport whenWN = 0.2 lm and 0.5 lm were plotted in Fig. 8. It wasobvious that the electrons generated by long wavelength

Fig. 5. Contour plots of conversion efficiency for the NNPP+ cell on N-type emitter dopant profiles under 1 sun (a) and 1000 suns (b).

Fig. 6. Contour plots of conversion efficiency for the NNPP+ cell on P+-type BSF dopant profiles under 1 sun (a) and 1000 suns (b).

Voc

[v]

Junction depth [μm] Junction depth [μm]

Vo Js eff Vo

occficiencoc*Jsc

cy

Jsc [A

/cm

2 ]

Eff

icie

ncy

[%]

Rs

[mΩ

.cm

2 ] RsFF

RCH FF

RC

H [m

Ω.c

m2 ]

(a) (b)Fig. 7. Dependence of Jsc, Voc, Jsc � Voc and efficiency (a), Rs, RCH and FF (b) on junction depth of the N-type emitter of the NNPP+ cell under 1000

suns.

Y. Xing et al. / Solar Energy 94 (2013) 8–18 13

light were mainly collected through the lateral side emitter,which was similar to the common VMJ cells. The electronsgenerated by short wavelength light were mainly collectedthrough the front side emitter, which was similar to the

conventional front and back contacts cells, but the emitterresistance losses of the NNPP+ cell was much lower thanthat of the front and back contacts cell because of the muchlower electron current density in the front side emitter. The

Fig. 8. 2D plots of the directions of the electron transport whenWN = 0.2 lm (a) and WN = 0.5 lm (b).

14 Y. Xing et al. / Solar Energy 94 (2013) 8–18

increase of WN was detrimental to the separation and col-lection of the photogenerated carriers generated by shortwavelength light for front side emitter (Cuevas and Russell,2000). Thus, the Jsc decreased with WN increasing whenWN > 0.4 lm. The RN decreased with WN increasing.And the Rs of the front and back contacts cell decreasedwith RN decreasing. Thus, the Rs decreased with WN

increasing when WN > 0.7 lm. However, when the currentflowed in the front side emitter in a lateral directiontowards the lateral N-type contact, it produced a lateralvoltage drop due to the emitter sheet resistance (Altermattet al., 1996). This voltage drop made the region close to theP-type contact more strongly forward-biased than theregion close to the N-type contact (Aberle et al., 1994).Thus, there was increased forward injection of electronsinto the base in the region close to the P-type contact (Alt-ermatt et al., 1996). And there were extra lateral diffusions

of electrons in the base towards N-type contact besides thecommon vertical diffusions towards the front side emitter.Thus, the path of the photogenerated electron transportbecame oblique, which could be seen obviously in theupper regions of Fig. 8, the transport length became longerand the recombination of photogenerated electronsincreased, and the Jsc was decreased by this 2D effect.The Rs was also decreased by this 2D effect, because thecurrent density in the front side emitter was significantlyreduced, leading to smaller emitter sheet resistance losses(Aberle et al., 1994). The 2D effect was enhanced withthe RN increasing (WN decreasing) (Morales-Acevedo,2009), which could be seen by comparing Fig. 8a and b.Thus, the Jsc decreased with WN decreasing whenWN < 0.4 lm, and the Rs changed little when WN < 0.7 lmalthough RN increased with WN decreasing. The increase ofWN suppressed the adverse effect of the high surface recom-bination velocity of metal contact regions and front surface(Cuevas and Russell, 2000). Thus, the saturation currentdensity decreased and the Voc increased with WN

increasing.

3.3. Effect of the width of the sub-cell

The effect of the width (w) of the sub-cell on the perfor-mance of the NNPP+ cell was discussed in this section. Thebest dopant profiles of the emitter and BSF under 1000suns were used. Jsc, Voc, FF, Rs, RCH and efficiency ofthe NNPP+ cell were calculated for 10 lm < w < 800 lm(t = 100 lm) under 1 sun and 1000 suns, which were shownin Fig. 9. The NPP+ cell of the same parameters was alsocalculated under 1000 suns to compare. The efficiencyincreased fast with width increasing first for the two cells,and reached to maximum at w = 80 lm (NNPP+ cell)and 40 lm (NPP+ cell) under 1000 suns and 500 lm(NNPP+ cell) under 1 sun, then decreased fast under1000 suns and slowly under 1 sun. The increase of efficiencyin the beginning mainly came from the increase of Jsc andVoc for the two cells. The ratio of the inactive width ofmetal contacts to the total width of the sub-cell decreasedwith width increasing. And the increase of width madethe adverse effect of the metal contact regions reduced.Thus the Jsc increased, the saturation current densitydecreased and the Voc increased. The next fast decreaseof efficiency under 1000 suns for the two cells mainly camefrom the decrease of Jsc and FF. For the NPP+ cell, theincrease of width made the average length of the photogen-erated electrons transport increased, and the recombina-tion of photogenerated electrons increased especiallythose near the front and back surfaces. For the NNPP+

cell, the 2D effect discussed in Section 3.2 was enhancedwith width and illumination density increasing (Morales-Acevedo, 2009), and the recombination of photogeneratedelectrons increased, too. Thus, the Jsc of the two cellsdecreased. Besides, the increase of Rs also led to thedecrease of Jsc for the NNPP+ cell when the Rs was largeenough (Green, 1982).

Jsc

[A/c

m2 ]

Width [μm] Width [μm]

Width [μm]

Width [μm]

Width [μm]

Width [μm]

FF

Eff

icie

ncy

[%]

NNPP+ cell c=1 sun

NNPP+ cell c=1000 suns

NPP+ cell c=1000 suns

Rs

[mΩ

.cm

2 ]

Voc

[v]

RC

H [m

Ω.c

m2 ]

(a) (b)

(c) (d)

(e) (f)Fig. 9. Dependence of Jsc (a), Voc (b), FF (c), efficiency (d), Rs (e) and RCH (f) on the width of the NPP+ cell under 1000 suns and the NNPP+ cell under 1sun and 1000 suns. (Jsc of 1000 suns is divided by 1000 to compare with that of 1 sun).

Y. Xing et al. / Solar Energy 94 (2013) 8–18 15

The fast decrease of FF under 1000 suns was caused bythe increase of Rs for the two cells. The Rs of the NNPP+

cell under 1000 suns was lower than that under 1 sun. How-ever, the RCH under 1000 suns was much lower than thatunder 1 sun. So the rs increased faster and FF decreasedfaster with width increasing under 1000 suns. The Rs ofthe NNPP+ cell was larger than that of the NPP+ cell when60 lm < w < 600 lm as discussed in Section 3.1, and was a

little smaller when w < 60 lm and w > 600 lm. The reasonsare as follows: the series resistance of the NNPP+ cellcaused by the front side emitter was few when w < 60 lm;the increased 2D effect made the Rs of the NNPP+ cell sat-urate with width increasing when w > 600 lm. The RCH ofthe NNPP+ cell was smaller than that of the NPP+ cellwhen w > 40 lm under 1000 suns. The larger Rs and smal-ler RCH made the FF of the NNPP+ cell smaller when

16 Y. Xing et al. / Solar Energy 94 (2013) 8–18

w > 80 lm. However, the best widths for the two cellsunder 1000 suns were around 60 lm, and their Rs andFF were close to each other in this range.

3.4. Effect of the thickness of the sub-cell

The effect of the thickness (t) of the sub-cell on the per-formance of the NNPP+ cell was discussed in this section.Jsc, Voc, FF and efficiency of the 80 lm wide NNPP+ cellunder 1 sun and 1000 suns were calculated for5 lm < t < 700 lm, which were shown in Fig. 10. Becausethe best width under 1 sun was much larger than thatunder1000 suns as discussed in Section 3.3, the 500 lmwide NNPP+ cell was also calculated under 1 sun to ana-lyze the effect of the thickness. The efficiency increased fast

0 150 300 450 600 750

0.025

0.030

0.035

0.040

0.045

0.5

0.6

0.7

0.8

0

4

8

12

16

Thick [μm]

0 150 300 450 600 750Thick [μm]

0 150 300 450 600 750Thick [μm]

Jsc

[A/c

m2 ]

μ

μ

μ

FFR

s [m

Ω.c

m2 ]

(a)

(c)

(e)Fig. 10. Dependence of Jsc (a), Voc (b), FF (c) and efficiency (d) on the thicknescell under 1 sun and 1000 suns and dependence of Rs (e) on the thickness of th1000 to compare with that of 1 sun).

with thickness increasing first for the two cells, the 80 lmwide cell reached maximum at t = 75 lm under 1 sun and100 lm under 1000 suns, then decreased fast; the 500 lmwide cell reached maximum at t = 200 lm under 1 sun,then decreased slowly. The increase of efficiency for thetwo cells in the beginning mainly came from the increaseof Jsc. More light was absorbed and more carriers weregenerated and collected with thickness increasing. Andthe adverse effect of high surface recombination velocityof the back surface decreased with thickness increasing.So Jsc increased first. The fast increase of FF of the80 lm wide cell under 1000 suns when t < 100 lm is alsoa major reason for the beginning increase of efficiency.The increase of FF came from the fast decrease of Rs,which was shown in Fig. 10e. This reflected the effect of

10

15

20

25

30

0 150 300 450 600 7500.65

0.70

0.75

0.80

0.85

0.90

Eff

icie

ncy

[%]

Voc

[v]

Thick [μm]

0 150 300 450 600 750Thick [μm]

(b)

(d)

s of the 500 lm wide NNPP+ cell under 1 sun and the 80 lm wide NNPP+

e 80 lm wide NNPP+ cell under 1000 suns. (Jsc of 1000 suns is divided by

1015 1016 1017

27

28

29

Eff

icie

ncy

[%]

ND [cm-3]

1015 1016 1017

ND [cm-3]

1015 1016 1017

ND [cm-3]

27

28

29

30

τmax

=10μs

τmax

=100μs

τmax

=1000μsEff

icie

ncy

[%]

22

24

26

28

Eff

icie

ncy

[%]

(a)

(c)

(b)

Fig. 11. Dependence of efficiency on bulk doping concentration (ND) and maximum SRH lifetime (smax) of the 40 lm (a), 80 lm (b) and 160 lm (c) wideNNPP+ cell.

Y. Xing et al. / Solar Energy 94 (2013) 8–18 17

the thickness on the Rs, FF and the final efficiency under1000 suns. The next fast decrease of efficiency of the80 lm wide cell under 1 sun and 1000 suns mainly camefrom the decrease of Jsc and Voc. The inactive area of thecontacts increased with thickness increasing due to the con-stant ratio of contact trench width to thickness. And theincrease of the thickness increased the adverse effect ofthe metal contact regions. Thus the Jsc decreased, the satu-ration current density increased and the Voc decreasedwhen t > 100 lm. The ratio of the width of contacts tothe total width of the 500 lm wide cell increased muchslower than that of 80 lm wide cell with the thicknessincreasing. And the increase of width can suppress theadverse effect of metal contact regions as mentioned above.Thus, the Jsc, Voc and final efficiency of the 500 lm widecell decreased slowly.

Above all, the Rs of the NNPP+ cell under 1000 sunscould be reduced to close to that of the NPP+ cell and evenlower by choosing suitable width and thickness. The effi-ciency of the NNPP+ cell under 1000 suns was higher thanthat of the NPP+ cell by optimizing the device parameters.

3.5. Effect of the bulk doping concentration and maximum

SRH lifetime

The effect of the bulk doping concentration (ND) andmaximum SRH lifetime (smax) of the sub-cells on the per-formance of the NNPP+ cell was discussed in this section.

The best device parameters got in above sections were used.The efficiencies of the 40 lm, 80 lm and 160 lm wideNNPP+ cells were calculated for 1 � 1015/cm3 < ND < 1 -� 1017/cm3 and 10 ls < smax < 1000 ls under 1000 suns,which were shown in Fig. 11. When smax = 100 ls and1000 ls, the efficiency increased with ND increasing. Andthe increase of efficiency came from the increase of FFand Voc. When smax = 10 ls, the efficiency changed littlewith ND increasing. The highest efficiency decreased0.23%, 0.41% and 0.80% for 40 lm, 80 lm and 160 lmwide cell when smax dropped from 1000 ls to 100 ls; anddecreased 1.45%, 2.38% and 3.72% when smax droppedfrom 100 ls to 10 ls, which were much larger. Thus, theeffect of lifetime decreased with width decreasing and life-time increasing. The results were similar to Catchpoleet al. (2003).

4. Conclusion

The efficiency of the VMJ cell increased after front sur-face diffusion and the requirement of high quality front sur-face passivation was reduced. The N-type emitter dopantprofile, P+-type back surface field dopant profile, width,thickness, bulk doping concentration and lifetime of thesub-cell had large effect on the performance of the VMJ cellwith front surface diffusion. The best emitter dopant profileunder 1000 suns was much different from that under 1 sunand the best BSF dopant profiles under 1 sun and 1000

18 Y. Xing et al. / Solar Energy 94 (2013) 8–18

suns were almost the same. The Rs of the NNPP+ cell couldbe reduced to close to that of NPP+ cell by choosing properthickness and width. The final best parameters for theNNPP+ cell used for 1000 suns were as follows:ND = 1 � 1017/cm3, NDs = 5 � 1018/cm3, WN = 5 lm,NAs = 2 � 1020/cm3, WP = 1.5 lm, w = 80 lm, t =100 lm, and the efficiency is 30.56%. The ranges of the bestdopant profiles of the emitter and BSF were large. Aboveparameters can be realized using current manufacture pro-cesses easily. The efficiency decreased 0.41% and 2.38%when the maximum SRH lifetime dropped from 1000 lsto 100 ls and from 100 ls to 10 ls. The maximum SRHlifetime can be kept larger than 100 ls by controlling thehigh temperature processes, keeping the manufacture envi-ronment clean and avoiding contaminations if using FZsilicon.

This work was supported by the National Natural Sci-ence Foundation of China under Grant (Nos. 61275040,60976046, 60837001, and 61021003), the National BasicResearch Program of China (973 Program) (No.2012CB934200) and by Chinese Academy of Sciences(No. Y072051002).

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