Solar Energy 146 (2017) 119–124

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Solar Energy

journal homepage: www.elsevier .com/locate /solener

Two dimensional device simulation and performance optimizationof n-type silicon solar cell structure using PC2D

http://dx.doi.org/10.1016/j.solener.2017.02.0180038-092X/� 2017 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: mekemeche@live.com (A. Mekemeche).

A. Mekemeche a,⇑, M. Beghdad a, M. Belarbi b, B. Semmache c, Y. Cuminal d

a Laboratory Signal-Systems and Department of Physics, Faculty of Exact Sciences and informatics, University Abdelhamid Ibn Badis, Mostaganem, AlgeriabDepartment of Technics Sciences, Faculty of Engineering Sciences, University Abdelhamid Ibn Badis, Mostaganem, Algeriac Semco Technologies, 625 rue de la Croix Verte-Euromedicine Park, 34196 Montpellier Cedex 5, Franced Institut d’Electronique et des Systèmes (IES)-CC 05002, Campus St Priest-860 rue de St Priest-F, Université Montpellier-CNRS-UMR 5214, 34095 Montpellier Cedex 5, France

a r t i c l e i n f o a b s t r a c t

Article history:Received 6 May 2016Received in revised form 3 February 2017Accepted 9 February 2017

Keywords:Silicon solar cellsn-TypeSelective emitter (SE)PC2D

In this paper, we analyze the impact of various parameters on the performances of the n-type monocrys-talline silicon solar cell experimented by Fraunhofer Institute for Solar Energy Systems (ISE) in Germany.We studied, especially the influence of the base parameters (lifetime, resistivity and thickness), the emit-ter sheet resistance and the back surface field (BSF) sheet resistance, on the solar cell performances.To optimize this cell we have used PC2D which is a solar cell device simulator that models two-

dimensional effects entirely within a Microsoft Excel spreadsheet. With an Al2O3/SiNx front side boronemitter passivation, the metallization parameters were optimized by the authors getting efficiency of19.60%. If all the parameters have ideal values our optimization provided an efficiency of 20.05% forhomogeneous emitter with sheet resistance of 75X/h. Furthermore, the study of the emitter led to anew structure developed recently: the selective emitter of n-type solar cell achieving efficiency of20.20% with sheet resistance of 50X/h under the contacts and 100X/h, between contacts.

� 2017 Elsevier Ltd. All rights reserved.

1. Introduction

The first silicon solar cells were made on n-type substrates in1950s. This technology changed to p-type substrates because oftheir high resistance to space radiation, at a time when the onlyapplication for those cells was for space (Zhao et al., 2002).

Up to a certain period, all commercialized silicon solar cellswere realized on p-type silicon substrate because the technologyof their production was easily industrialized and accessible. Thephotovoltaic industry of silicon was therefore developed aroundthis idea and terrestrial market is still mainly supplied today bycells in p-type silicon (Wang and Wang, 2014). Another reason ofthe choice of p-type crystalline silicon is that the electrons mobility(minority carriers) is higher about three times than the holes, sothey have a big diffusion length, and then it is easy to collect them(Sze and Ng, 2007).

Nevertheless, in equivalent technology, the best results of effi-ciency are obtained with n-type crystalline silicon solar cells(20–25%) (Green et al., 2015). For example, Benick et al. (2008)obtained a maximum efficiency of 23.2% on 4 cm2 surface cells.

The main cause of this is the presence of very recombinantdefects in the p-type crystalline silicon, particularly boron-oxygen pairs which are generated under illumination and areresponsible of the loss of cells efficiency during the first monthsof operation (Light-induced degradation: LID) (Schmidt et al.,2003; Bothe et al., 2005). Cells with n-type crystalline silicondoped with phosphorus are not affected to this type of defectsand are much more stable over time (Lim et al., 2011). Further-more, the n-type wafers may offer greater immunity to the effectsof metal contaminants like iron, molybdenum, titanium and others(Macdonald and Geerligs, 2004), so these cells have a high lifetimeexceeding 1 ms (Zhao et al., 2002; Cuevas et al., 2002).

In this work, we would optimize the following layer parame-ters: base, emitter and BSF for n-type solar cells to improve theirefficiency using PC2D (Basore and Cabanas-Holmen, 2011).

2. Simulated devices

The design used is a two-busbars p+nn+ full square monocrys-talline silicon cells of real surface 139.3 cm2 (125 mm � 125 mm),homogenously boron doped front side emitter with a sheet resis-tance of 90X/h corresponding to a surface doping concentrationof 6 � 1019 cm–3 and a depth of about 0.25 lm calculated withPC1D (Clugston and Basore, 1997). The back side was doped by a

Fig. 2. Mesh of the simulated region.

120 A. Mekemeche et al. / Solar Energy 146 (2017) 119–124

phosphorous gaussian profile of 30X/h corresponding to a surfacedoping concentration of 3 � 1019 cm–3 and a depth of 2 lm thencontacted with evaporated aluminum on the whole cell area(Kalio et al., 2011; Richter et al., 2010).

The front surface was textured with alkaline (KOH) in the pur-pose to have a surface pyramid structure with angle of 54.74� anddepth of 3 lm, passivated with aluminum oxide (Al2O3) then cov-ered with silicon nitride (SiNx) antireflective coating layer (Fig. 1)(Kalio et al., 2011; Richter et al., 2010).

Using inkjet and aerosol jet printing with consequent silverelectroplating, the metallization was optimized by Kalio et al.(2011) (Fraunhofer ISE) giving a contact resistance values of3.8X cm2, series resistance of 0.64X cm2 (verified by calculation)and shunt resistance of 65 kX cm2.

The most optical parameters for all simulated solar cells aretaken from examples of Basore and Cabanas-Holmen (2014).

3. Simulation program

The simulation is done with PC2D which is relatively a newsolar device simulator (2011) that models two-dimensional effectsof solar cells with the companionship of PC1D (Basore andCabanas-Holmen, 2011).

The region simulated by PC2D is the smallest elementary part,representative of the entire cell area of 1 cm2. The solution regionis defined by X which is the width measured from the center of thecontact to the midpoint situated between the center of two succes-sive contacts, and Y which is the thickness of the cell. This region isdivided into a grid of 20 � 20 identical rectangular elements bor-dered in two perpendicular directions by a mesh of 21 � 21 nodes(Fig. 2) in which the continuity equations and minority carrierscurrent (n, p) are solved by the method of finite elements(Basore and Cabanas-Holmen, 2011):

dn=dt ¼ Gn � Rn þ divJn=q

dp=dt ¼ Gp � Rp � divJp=q

Jn ¼ q nlnE þ Dngradn� �

Jp ¼ q plpE � Dpgradp� �

The vectors Jn; Jp (in bold type) are carrier currents, Gn and Gp:rates of carrier generation, Rn and Rp: rates of carrier recombina-

Fig. 1. Parameters used of

tion, mn and mp: carrier mobilities, Dn and Dp: constants carrier dif-fusion (n for electrons and p for holes respectively), the vector E isthe whole electric field across the structure and q, the electroniccharge.

The boundary conditions at the top and bottom surfaces repre-sent the complex physics occurring in the very thin layers adjacentto each of these surfaces. The boundary conditions at the left andright side boundaries of the solution region can be either reflectingor repeating, according to the user’s specification (Basore andCabanas-Holmen, 2011).

The user defines the solar cell that he wishes to model in the‘‘Device” and ‘‘Recombination” sheets with it solution region, typ-ically selected to extend from the middle of a gridline to the mid-point between gridlines. In the ‘‘Device” sheet, we enter thestructural, electrical and optical parameters. In ‘‘Recombination”sheet, we integrate recombination density currents J01 in dopedemitter and at metal contacted surfaces of the cell, and the recom-bination density current J02 in the space charge region. J01 and J02are determined by PC1D (Cabanas-holmen and Basore, 2012).

simulated solar cells.

Table 1Results of the two solar cells real/simulated.

Cell Jsc (mA/cm2) Voc (mV) FF (%) g (%)

Real 38.00 651.6 79.00 19.60This work 37.46 649.5 80.92 19.68

Fig. 3. Simulated J–V curve.

A. Mekemeche et al. / Solar Energy 146 (2017) 119–124 121

There are no material files in PC2D as there are in PC1D; everythingis in the spreadsheet itself. Once the solar cell is defined, we initi-ate the simulation in the ‘‘Excitation” sheet and can view theresults and the graphs in the same sheet (Basore and Cabanas-Holmen, 2011; Cabanas-holmen and Basore, 2012).

The simulation with our parameters gives the following resultspresented in Table 1. The results found (short-circuit density cur-rent Jsc, open-circuit voltage Voc, fill factor FF and efficiency g)are approximately the same as those of experience results of thesolar cell (Kalio et al., 2011) (see Fig. 3).

We note that the short-circuit density current value is slightlysmaller than the experimental one (about 0.5 mA/cm2), same thingfor the value of the open-circuit voltage (about 0.2 mV). The fill fac-tor is weakly higher than the experimental one (less than 2%)(Table 1).

This good accordance with experience permits us to use thisprogram to study our cell and then optimize it by varying differentparameters.

4. Results and discussions

Now, as we found approximately the same results (betweenreal cell and the simulated one), we can optimize the parametersof this cell (base, emitter and BSF layer).

Fig. 4. Effect of lifetime on the paramet

The most important parameters of the base are lifetime, resis-tivity and thickness. These parameters have a very important rolein the collection of the charge carriers and influence significantlyon density current of the solar cell and therefore on its efficiency(Goetzberger et al., 1998).

The sheet resistance of the emitter has a big effect on recombi-nation density currents, so consequently on the open-circuit volt-age (Goetzberger et al., 1998).

The back surface field layer has an important effect on the per-formance of the solar cells; it creates a potential barrier tending toconfine minority carriers (holes) in the more lightly doped regionand helps to drive them toward the front improving the efficiency.

4.1. Effect of base parameters

4.1.1. Effect of the lifetimeBy varying the lifetime of the base minority carrier from 100 ms

to 2.5 ms, all the graphs have the same allure, noting that allparameters of the cell increase quickly up to about 1 ms corre-sponding to: 649.5 mV of Voc, 37.46 mA/cm2 of Jsc, 80.92% of FFand 19.68% of Ƞ.

The increase becomes slow beyond this value (Fig. 4). Thisresult is expected since the increase in lifetime leads to a bettercollection of carriers.

4.1.2. Effect of the resistivityWhen varying the base resistivity from 1 to 10X cm (Fig. 5), it

is found that the short-circuit density current increases up to37.89 mA/cm2 corresponding to 6X cm base resistivity, beyondthis value the improvement is not too significant. This improve-ment is due to the decrease of recombination current due to reduc-ing of the base doping (Sze and Ng, 2007).

On the contrary, the open-circuit voltage decreases slightly withthe base resistivity (variation of 1.5 mV in the range of 1–5X cm),then it becomes almost invariable (Fig. 5). Theoretically, this resultis expected because the reduction of base doping increases the sat-uration current which reduces the open-circuit voltage, thisdecrease is low because this voltage is also function of short-circuit density current, exactly it is proportional to logarithm ofrate of short-circuit density current to saturation density currentas it indicates by the following equation (Goetzberger et al., 1998):

Voc � ðkT=qÞlnðJsc=j0ÞLikewise, the fill factor decreases with the resistivity due to the

decrease of base resistance. Consequently, the result is an opti-mization of the efficiency (19.71%) shown on the graph in therange of 1.5–2X cm (Fig. 5).

ers of solar cell (Jsc, Voc, Ƞ and FF).

122 A. Mekemeche et al. / Solar Energy 146 (2017) 119–124

4.1.3. Effect of the thicknessIt is clear that the increase in thickness of the substrate is an

advantage to absorb more photons, but if the diffusion length L(L ¼ ffiffiffiffiffiffiffi

Dsp

, D is the constant carrier diffusion and s is the lifetime)falls below the value of the base thickness, then the photocurrentwill drop sharply (Goetzberger et al., 1998). So, for the short-circuit density current and the efficiency there are some optimiza-tion of 37.86 mA/cm2 and 19.89% respectively around 400 lm(Fig. 6).

The fill factor decreases from 80.98% at 100 lm to 80.64% at600 lm because of the increase in base resistance. Note that a verylarge thickness substrate increases its cost.

Fig. 5. Effect of base resistivity on the para

Fig. 6. Effect of base thickness on the para

Fig. 7. Effect of emitter sheet resistance on the

4.2. Effect of emitter sheet resistance

We remark that the short-circuit density current and the open-circuit voltage increase with the emitter sheet resistance (Fig. 7),since the reduction of emitter doping decreases recombinationdensity current in the emitter from 143.53 fA/cm2 for 50X/h to44.3 fA/cm2 for 100X/h (calculated with PC1D) (Cabanas-holmen and Basore, 2012). Contrarily, the fill factor decreasesbecause of the increase of the emitter resistance. Therefore, weremark an optimization of the efficiency at 75X/h (average ofthe little range of 70–80X/h) giving values of 19.70%, this isbecause high sheet resistance causes a low recombination density

meters of solar cell (Jsc, Voc, Ƞ and FF).

meters of solar cell (Jsc, Voc, Ƞ and FF).

parameters of solar cell (Jsc, Voc, Ƞ and FF).

Table 2Results of optimized solar cells (HE and example of SE).

Cell Jsc (mA/cm2) Voc (mV) FF (%) g (%)

Optimized 75X/h (HE) 38.07 651.50 80.86 20.05Example 50–100X/h (SE) 38.14 654.56 80.90 20.20

A. Mekemeche et al. / Solar Energy 146 (2017) 119–124 123

current. Beyond this range the efficiency decreases because theseries resistance becomes predominant.

Hence the choice of the selective emitter structure of n-typesubstrate (Poulain et al., 2012) which reduces the sheet resistancein the contacts to reduce the series resistance and increases itbetween the contacts to decrease recombination density current(Fig. 8) (Rahman, 2012).

4.3. Effect of the back surface field (BSF)

The graphs show that the four parameters decrease with theincrease of BSF sheet resistance (Fig. 9). In other words, theincrease of BSF doping causes an improvement of the intensityback surface field in the high-low junction n+/n creating a potentialbarrier which tends to confine minority carriers (holes) in the morelightly doped region and helps to drive them toward the front.Therefore, the short-circuit current density will increase, theopen-circuit voltage also will increase due to increased short-circuit current. Consequently, the efficiency and the fill factor willnoticeably increase. For example, the efficiency increases from19.06% for the solar cell without BSF layer to 19.68% with 30X/h of BSF sheet resistance (real cell), improved to 19.82% with20X/h of BSF.

5. Performance of the optimized solar cell

The optimized values: thick, resistivity, lifetime of substrate andBSF are respectively 250 mm, 1.75X cm (average of 1.5–2X cm),1.5 ms and 20X/h. With these parameters, the results of this opti-mization are shown in the following Table 2:

Fig. 8. Part of selective emitter (SE) structure.

Fig. 9. Effect of the back surface field on the p

The optimization of Kalio’s cell (HE90) leads to two structures:homogeneous emitter cell of 75X/h (HE75) with an absolute gainof 0.37% in efficiency and selective emitter cell of 50X/h under thecontacts and 100X/h between contacts (SE50-100) as example(Fig. 8) with an absolute gain of 0.52% in efficiency.

This improvement is shown clearly on the graph of externalquantum efficiency (EQE) in the infrared wavelength range dueto the good collection of the charge carriers in the base of the opti-mized solar cells (optimization of the base and BSF parameters)(Fig. 10).

We can also view the improvement of 0.15% in efficiency of(SE50-100) compared to (HE75) due to the selective emitter(Fig. 11).

It is found that this structure permits an improvement of quan-tum efficiency in the ultra-violet wavelength range, due to adecrease in recombination density current from 73 fA/cm2 to44.3 fA /cm2 (Section 4.2), resulting from a lower rate of differentrecombinations, mainly Auger type, due the highest sheet resis-tance of the emitter (between contacts). On the contrary, at highestwavelengths, the two cells give identical results, confirming thatthe structure of (SE) does not influence much the volume or therear surface of these cells but the absorption is more superficial.This result can be improved by making a detailed study on thisstructure.

arameters of solar cell (Jsc, Voc, Ƞ and FF).

EQE

(nm)

SE50-100

HE75

HE90

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

300 400 500 600 700 800 900 1000 1100 1200

Fig. 10. Comparison of external quantum efficiency of SE50-100, HE75 and HE90.

55%

60%

65%

70%

75%

80%

85%

90%

95%

300 350 400 450 500

EQE SE50-100

HE75

(nm)

Fig. 11. Comparison of external quantum efficiency of SE50-100 and HE75.

124 A. Mekemeche et al. / Solar Energy 146 (2017) 119–124

6. Conclusion

Using PC2D simulation, we have optimized the most importantparameters: base, emitter and BSF of n-type homogeneous solarcells experimented by Kalio et al.

For the base parameters, we have noted that all parameters ofthe cell increase quickly up to 1 ms of lifetime, this increasebecomes slow beyond this value. Likewise, the efficiency increaseswith the base thickness up to 400 lm then it decreases due to theincrease of the resistance. The optimized base resistivity value is1.75X cm for a maximum efficiency.

The analysis of the emitter solar cell shows that the efficiencyincreases up to the value of 75X/h because high sheet resistancecauses a low recombination density current. Beyond this value, theefficiency decreases because series resistance becomes predomi-nant. Hence the choice of the selective emitter structure whichreduces the sheet resistance in the contacts to reduce the seriesresistance and increases it between the contacts to decreaserecombination density currents. The introduction of the BSFimproved enormously the efficiency; with 20X/h of BSF weobtained an improvement of 0.14% in relation to 30X/h of BSF(experimental solar cell).

Our optimization gives us an efficiency of 20.05% with sheetresistance of 75X/h homogeneous emitter. This efficiency isimproved to 20.20% with selective emitter of 50–100X/h takenas example. A detailed study of this structure can give us higherefficiencies.

Conflict of interest

None declared.

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