1100

Influence m

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 39, NO. 5, MAY 1992

of Surface Texturization on the Light 'l'rapping and Spectral Response

of Silicon Solar Cells Hiranmay Saha, Swapan K . Datta, Kanak Mukhopadhyay, S. Banerjee,

and Manish K. Mukherjee, Senior Member, IEEE

Abstract-A quantitative model is presented to explain the spectral response, internal quantum efficiency, total short-cir- cuit current, open-circuit voltage, and efficiency of high-effi- ciency solar cells with textured front surface and Lambertian back-surface reflector. A comparison of the textured cell char- acteristics is made with those of planar cells and the separate roles of the front surface reflection coefficient and internal quantum efficiency in enhancing the short-circuit current have been investigated. it is shown that in case of large diffusion lengths, almost all the contribution towards the increase of spectral response on texturization is due to the reduced reflec- tion coefficient while for small diffusion length, there is a sig- nificant increase in internal quantum efficiency on texturiza- tion, specially in the region of higher wavelengths. However, there is a small decrease in open-circuit voltage for large dif- fusion lengths whereas no significant change is observed for small diffusion lengths on texturization. Nevertheless, there is a net gain in power conversion efficiency which is larger for smaller diffusion lengths.

I. INTRODUCTION IGH EFFICIENCY in a solar cell is achieved by H maximizing light-generated current and minimizing

losses in the bulk base and emitter, within the collecting junction and the surfaces.

Texturization of the front surface has been successfully employed to improve the short-circuit current for crystal- line silicon solar cells [ 11-[5] through the absorption of light effectively closer to the junction, reduction of front- surface reflection losses by multiple incidence, and the trapping of weakly absorbed photon within the cell.

A theoretical analysis of the effect of light trapping through texturization of the front surface was reported by Green et al. [l] . However, the analysis is applicable to only weakly absorbing light. The enhancement of the short-circuit current and changes in open-circuit voltage and efficiency due to the reduction in reflection coefficient

Manuscript received September 7, 1990; revised April 19, 1991. The review of this paper was arranged by Associate Editor S. J . Fonash.

H. Saha, K. Mukhopadhyay, and M . K. Mukherjee are with the De- partment of Electronics and Telecommunication Engineering, Jadavpur University, Calcutta-700 032, India.

S. K. Datta is with the Department of Physics, Rabindra Mahavidyalaya, Champadanga-712 401, West Bengal, India.

S. Banerjee is with the Department of Physics, Bangobasi College, Cal- cutta, India.

IEEE Log Number 9105898.

alone of a texturized surface has been considered theoret- ically for 111-V solar cells which is also applicable to sil- icon cells [6]. Recently, numerical modeling of textured silicon solar cells by using quasi-one-dimensional finite- element program on a personal computer has been re- ported [7]. However, the comparative analysis of the role of the various parameters on the increase of internal quan- tum efficiency, open-circuit voltage, and efficiency of a texturized silicon solar cell relative to that of a planar cell has not been carried out.

In this paper, the effect of top surface texturization of silicon solar cells on the spectral response and related characteristics has been studied by a simple two-dimen- sional analytical approach. Section I1 describes the effect of surface texturization and back-surface reflection on the effective path length resulting in an effective absorption coefficient which adequately describes the photogenera- tion profile for light of both short and long wavelengths. Section I11 describes the relevant photodiffusion equations and analytical expressions are obtained for spectral re- sponse, internal quantum efficiency, total short-circuit current, and open-circuit voltage which clearly reveal the individual effect of the geometry of texturized surface on the material parameters and the reflection coefficient on the cell characteristics in comparison to the planar solar cells. Section IV describes the results and its discussions includes a comparison with those reported by other au- thors.

11. CELL GEOMETRY, LIGHT TRAPPING, AND EFFECTIVE ABSORPTION COEFFICIENT WITH PYRAMIDAL FRONT

SURFACE AND LAMBERTIAN REAR REFLECTOR Fig. l(a) and (b) illustrates the model used to represent

top surface texturization and the path of the light rays leading to light trapping. The texturized solar cell has py- ramidal top surface produced by anisotropic etching of (100) oriented Si surface [ 5 ] . Sides of these pyramids are the intersection of (1 1 1) crystallographic planes. Unlike flat surfaces, light incident on the sides of a pyramid will be reflected onto another pyramid instead of being lost due to which the reflectivity of the textured surface is less than that for a planar surface [8]. The face angle which is sometimes called the apex angle [5] (i.e., the angle be-

0018-9383/92$03.00 0 1992 IEEE

SAHA et al.: INFLUENCE OF SURFACE TEXTURlZATlON ON SILICON SOLAR CELLS I101

RADlAllON i v iNc'DEN'

50 (I-R)e-'D

(b) Fig. 1 . (a) Schematic diagram of top surface texturized silicon (n'-on-p) solar cell. (b) Light trapping by Lambertian rear surface through pyramidal top surface.

tween the intersecting (1 11) planes on the texturized sur- face as shown in Fig. l(a) and l(b)) is 70.53" [ 5 ] , [9].

The texturization is generally deeper than the emitter diffusion, but extremely thin compared to the base thick- ness [7].

Light incident in a direction normal to the base of the solar cell enters the cell material through refraction at the front pyramidal surface. The path angle (p ) which the light trajectory makes with the normal to the base (Fig. l(b)) is determined by the face angle (28) and the wavelength of incident light. Some fraction of the photons, after com- pleting their first pass by traversing a path length D (= d/cos p) through the cell thickness d, reach the back surface of the cell and undergoes diffuse reflection from the Lambertian reflector at the back (of reflectivity R). The photons are assumed to leave the back surface with random path angles represented by an average path length of 2d through the cell [ 11.

The photon that complete the first round trip back to the front surface undergoes further reflection at the front surface. While a fraction of light f (= 1 / p 2 , p being the refractive index of the cell material) will leak out of the front surface at each impact, a major fraction is trapped inside the cell due to total internal reflection. However, due to the possibility of double (for grooves) or triple (pyramids) bounces on the front surface enhancing the

probability of escape, fmay also turn out to be larger than

The trapped electrons are reflected back into the cell with random orientation again represented by an average path length "2d" and the process of randomized reflec- tions from back and front surfaces continues which leads to the phenomena known as light trapping. However, it is to be noted that the amplitudes of the fields associated with the waves and hence their intensity are attenuated as the light progresses through the lossy cell material.

Because of the nonperpendicular trajectory of the light and repetitive reflections from rear and top surfaces, there is an increase in the effective path length and therefore the photogeneration rate can be effectively described by an increased "effective" absorption coefficient such that it adequately describes the absorbed light energy in one pass.

If Z0 is the incident light intensity and a and a* are the true and effective absorption coefficients, then referring to Fig. l(b) we can write

ZO(l - = ZO(l - e-aD) + Z0 Re-&

1 / P 2 .

. [(I - e-2ad) ( 1 + (1 - f )e -2ad}] (1) 1 - ~ ( 1 - f)e-4"d

which leads to

where is determined by Snell's law and is given by cos 0 ,-

CL = cos (0 + p) '

p is a function of wavelength of light through the depen- dence of p on wavelength.

The effective absorption coefficient is therefore a mul- tiple (C) of the true absorption coefficient (a) where C is given by

Equation (4) is applicable for the cases of both highly ab- sorbed and weakly absorbed light. It is evident from (4) that for highly absorbed light ( a h @ ) , the second term will be negligible and C will be determined by the oblique tra- jectory of light, influencing the value of the first term. For weakly absorbed light (asmall) however, the second term will be much higher indicating that light trapping will pre- dominantly determine the value of C.

Due to the dependence of 0, f, and a on the wavelength of incident light, the values of C would depend on the spectral wavelength according to (4) and the effective photogeneration rate can now be represented by modify- ing the absorption coefficient (a) to a new value (a* = Ca) so that it becomes

( 5 ) g(z) = ~*(X)N~(X) [I - RF(X)]e-"*'A)z

1102 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 39, NO. 5 , MAY 1992

( r 2 + h 2 ) ' / 2 I qD,V(An) 1 where 2 is the depth from the front surface, No is the in-

coefficient of the cell. r x = h y / r cident photon flux, and RF is the front-surface reflection JSCT ==

111. PHOTODIFFUSION EQUATIONS Light is incident on the n-type emitter layer along the

x direction perpendicular to the base and photogenerated carriers, primarily the minority carriers in the p-base re- gion of silicon cells, diffuse along the x and y directions towards the p-n junctions (Fig. l(b)) generating the pho- tocurrent. For the sake of simplicity, the top surface roughness profile is taken to be periodic in the Y direction and independent of the third coordinate so that one has to carry out two-dimensional analysis in the p-base region. The excess electron density ( A n ) in the steady-state con- dition can be obtained by solving the diffusion equation given by

(6) where L, and r, are the diffusion length and lifetime of electrons in the p-base region and tan 8 = r / h (Fig. l(b)).

A number of mathematical techniques exist by which (6) can be solved but we have used a trial solution, sat- isfying boundary conditions for the equations. The boundary conditions are

i) A n = 0 at the junction surface represented by x =

ii) An = 0 at x = d assuming an ohmic contact at the

- A n = 0 (0 I x I d, 0 I y I r)

hY / r

back surface.

- -

C2a2Li (1 + ;) - 1

Equation (8) expresses the short-circuit current density JsCT as a function of incident wavelength A determining the spectral response characteristics of the cell.

The total short-circuit current density for the cell under AM 1.5 solar spectral irradiance will be given by

JT = T JSCT (9)

where the summation extends over all wavelengths from 400 to 1100 nm in the solar spectrum.

The short-circuit current for the solar cell with nontex- turized flat surface can be computed by putting h / r = 0 and C = CNT in (8) where CNT can be obtained from (4) by putting /3 = 0 so that

The short-circuit current density as a function of wave- length of incident light is then given by

Further, assuming d >> h, the trial solution is given 4No(1 - R F N ) C N T ~ L ~ 1 I cNTa - by JSCNT = CiTa2Li - 1

+ B sinh [ k (x - F)] where

1 k2' L'( l +;)

L

(7)

where R F N expresses the front surface reflection coeffi- cient for a solar cell with flat nontexturized cell. The total short-circuit current density of the nontexturized solar cell under AM 1.5 solar spectral irradiance is then expressed as

JNT = J S C N ~ (12)

B. Internal Quantum Eficiency A(e-kd - e-a*d)

sinh kd '

The internal quantum efficiency (IQE) is intended to represent the fraction of the photogenerated minority car- riers in the cell that can be collected under short-circuit conditions. It is computed by dividing the short-circuit current density as a function of wavelength by 4NO (1 - R F ) or qNo (1 - R F N ) as the case may be.

For the texturized cell, the IQE can be expressed as

B = -

A . Short-circuit Current Density

will be given by The short-circuit current density per unit planar area

n

SAHA et al.: INFLUENCE OF SURFACE TEXTURIZATION ON SILICON SOLAR CELLS 1103

C. Open-Circuit Voltage

be written as The open-circuit voltage of the texturized solar cell can

(20) 4

( 1 3 ) where JOT is the saturation current density. An expression for JOT can be obtained by solving the

diffusion equation (6) satisfying the same boundary con- ditions and by putting the photogeneration term equal to

sinh kd

and for the nontexturized cell, the IQE is given by

JSCNT - c N T d i 1 zero and can be written as - = qNO(1 - RFN) C iTa2L; - 1

qD,npo ( 1 + ;) ' I2

(21)

where D, and ny0 represents, respectively, the diffusion coefficient and minority -carrier concentration in the p-base

Ln tanh (kd) JOT =

(14)

Since the interpretation of IQE data is better obtained from a plot of (1QE)-' versus a-' [ 7 ] , analytical expres- sions for (1QE)-' are obtained here for both cases from (13) and (14) . It is of significance to obtain expressions in the two limits of large a and small a.

For large a and ad >> 1, one obtains after suitable simplifications

and 1 1 d

QNTI = - = 1 + -, for- >> 1 (15) QNT aLn Ln

region. The open-circuit voltage of a nontexturized solar cell

can be obtained by replacing JT and JOT by JNT and JONT, respectively, where JoNT represents the saturation current density for the nontexturized cell which can be obtained from (21) by putting h / r = 0.

The ideal fill factor (FF) of the texturized cell can be calculated by the empirical expression [ 101

KBT

The (FF)NT in the case of planar cell can also be calculated as well as by replacing ( Vac), by (Vac),, in the above equation.

cos p QTI = 1 + - ad IV. RESULTS

A . Spectral Response 1 d The effect of texturization on the short-circuit current

QNT1 = 1 + - for- << 1. (16) has been elaborated by numerical calculations of (JSCTIJSCNT) as a function of the wavelength (A) of inci- dent light (AM 1.5 global spectrum) with the following parameters: back-surface reflectance (R) = 0.9 [ 4 ] , and base thickness (d) = 300 pm.

Fig. 2(a) and (b) shows the plots of ( J S C T I J ~ C N T ) versus h for different values of the diffusion length of minority carriers in the base region (L,). It can be observed that

and

ad' Ln Similarly, for small a and ad << 1 , one gets after sim-

plification for d/L, >> 1 (assumingf << 1 )

(17) d

QTI =

1 - R

and for nontexturized cells the ratio (JscT/JscNT) increases with increase in the wave- length (A) for a particular value of L,. On the other hand,

d

L,, In 1 + - 4R ad)' ( 1 - R

In those cases, where d/L,, << 1 , we obtain

f o r a particular ialue of h, the ratio is found to increase with the decrease in value of L, indicating that for low values of L, texturization is more effective. One observes that JscT/JscNT is a product of two factors:

a) Factor F, [= ( 1 - R F ) / ( l - RFN)] by which the intensity of light in the texturized cell increases compared to a nontexturized one due to multiple incidence in tex- turized cell.

b) Factor F2 (= QT/QNT) depicting the ratio of internal

QNTI = ( 1 8 )

(19) 2

In 1 + - 4R ad)' QTI = QNTI =

( 1 - R

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 39, NO. 5 , MAY 1992

WAVE LENGTH IN MICRON d (a)

< I I

'-* t 1.11 I

WAVE LENGTH IN MICRON - (b)

Fig. 2. (a) Ratio of spectral response (curve 1). front-surface reflectance factor (curve 2) , and ratio of internal quantum efficiencies (curve 3) of a texturized and a nontexturized cell as a function of wavelength of incident light for L, = 5 pm and d = 300 pm. (b) Ratio of spectral response (curve l ) , front-surface reflectance factor (curve 2), and ratio of internal quantum efficiencies (curve 3) of a texturized and a nontexturized cell as a function of wavelength of incident light for L, = 500 pm and d = 300 pm.

quantum efficiencies of a texturized and nontexturized cell which indicates how the minority-carrier collection effi- ciency under short-circuit conditions is improved on tex- turizing the front surface.

Also shown in Fig. 2(a) and (b) are FI and F2 as a func- tion of A. It is seen that F2 increases with the increase in wavelength for a particular value of L, while for a partic- ular wavelength, F2 decreases with the increase in L,. It is also seen that the contribution F2 towards JscT/JsCNT decreases with the decrease in wavelength and increase in L, and at high values of L,, almost all the contribution towards JscT/JscNT comes from the reflectance factor F, . Only for low values of L,, it is found that in the higher wavelength ranges (0.75-1.1 pm), the contribution of F, is comparable to or even larger than that of F2.

It can be shown that in the region of high a and low h

1 1 I-

for d/L, >> 1 (i.e., small L,) and

1 1 + -

ad cos p

1 + - ad

F2 =

for d/L, << 1 (i.e., large L,). It is found from the above equations that the back-re-

flection coefficient (R) has no effect on F2. For low L, values, F2 is determined by both the oblique trajectory of the li ht and the modification of L, by a factor [l + ( h 2 / r ) ] ' I 2 due to texturization. For high values of L,, F2 is controlled only by the factor cos f l due to the oblique light trajectory and does not show any dependence on L,. For very low values of L, such that aL, < 1 is satisfied, the effect of texturization becomes more prominent as is seen from (23). This is due to the fact that two-dimen- sional effects come into picture so that the photogenerated carriers originated at a particular depth greater than 1 / L , "sees" the texturized surface at a smaller distance which is [ l + ( h 2 / r 2 ) 3 - ' I 2 times the depth and are more effec- tively collected by the junction at the texturized surface. But in the case of high L,, the photogenerated carriers "sees" no difference between a texturized and nontextur- ized surface because almost all photogenerated carriers lie within a depth of 1/a << L, and since ad >> 1, F2 = 1 which indicates that texturization has almost no effect in the region of high a and high L,.

In the region of low a and high X such that a*d << 1, we have C = CNT and F2 = [ l + ( h 2 / r 2 ) ] 1 / 2 for d/L, >> 1.

In the range of L, for which d / L , << 1, F2 can be expressed as

4

1 ; Cad

It is now obvious from (23)-(25) that as long as L, has such large values that aL, >> 1, texturization has little effect on F2 throughout the entire range of solar spectrum considered here and the entire contribution towards JsCT/JSCNT will come from the factor FI due to reflection coefficient. But for small L, values such that d/L, >> 1, F2 contributes significantly towards (JSCT/JSCNT) , the largest contribution occurring when both ad >> 1 and aL, << 1 holds good so that F2 becomes

due to which a peak occurs in the plot of F2 versus h, since for higher h and low a, F2 saturates to a value of [ I + ( h 2 / r 2 ) ] 1 / 2 as shown in Fig. 2(a).

SAHA et al . : INFLUENCE OF SURFACE TEXTURIZATION ON SILICON SOLAR CELLS I105

1 6 0 -

1.55 - 1 1.50-

\ 145- 7

0.3 0 5 0.7 0 9 1 1

WAVE LENGTH IN MICRON-->

Fig. 3 . Internal quantum efficiency of a texturized cell as a function wave- length of incident light for d = 300 pm and different values of L,.

~ , . 2 0 p m

L, = 50pm

B. Internal Quantum Eficiency In Fig. 3 the IQE of texturized solar cells calculated

using (13) is plotted as function of A. It is seen that for large values of L,, IQE is significantly affected by changes in L, throughout the whole spectrum. It is also observed that in this range of values of L, while optical degradation (i.e., lowering of the values of base reflection coefficient R) does not affect in any way the IQE at large a (small A), it affects IQE at longer wavelengths (small a). These observations are in qualitative agreement with those re- ported by Basore [7].

To have further insight into the dependence of IQE on the effect of texturization and light trapping, our analysis of (IQE)-l (= Q,,) as a function of a shows that the plot of Q , versus 1 /a has two linear ranges for small absorp- tion length (large a) and for large absorption length (small a) provided that values of R lie in a range such that (4R/ 1 - R ) ad << 1 in the region of a satisfying ad << 1 [see (17)]. A plot of Q,, as a function of 1 / a for different values of L, is shown in Fig. 4. The same observations are made by Basore [7], however, without indicating the necessary limiting conditions.

1.35

C. Total Short-circuit Curreni The ratio of the total short-circuit currents for the tex-

turized and nontexturized cell has been calculated as a function of base thickness for different values of L, and the variation is shown in Fig. 5 . It is observed that the ratio remains approximately constant throughout the range of base thicknesses but increases from 1.35 to 1.70 as the diffusion length increases from 5 to 900 pm.

Ln 'q" -P

D. Open-circuit Voltage The effect of texturization on the open-circuit voltage

and efficiency for different values of minority-carrier dif- fusion length, lifetime, and carrier concentrations [8], [ 111 is shown in Table I.

It is observed that the ratio of open-circuit voltage of a texturized and nontexturized solar cell lies in the range of

INVERSE OF ABXY)PTCN COEFFKIENT Own->

Fig. 4. Variation of inverse of internal quantum efficiency of texturized cell with the inverse of absorption coefficient ford = 300 p n and different values of L,,.

175

1.70 - L,= 5pm

1'65 1

0.97-1.00. The ratio increases from 0.97 towards unity as the values of L,, T,, and npo decreases. The small de- crease of V,, due to the reduction of the reflection coef- ficient alone on etching the surface anisotropically has also been reported in the case of 111-V solar cells [6]. This is due to the fact that for higher values of the parameters (L,, r,, npo), the reverse saturation current density in- creases due to texturization by a larger factor than the ra- tio of total short-circuit current density while for low val- ues of these parameters, Jo,/JoN, and J T / J N T are almost the same.

It is found that there is always a net gain in overall efficiency on texturization. The efficiency is observed to increase by 32% for higher values of material parameters which is due solely to the reduction in the reflection coef- ficient. Incidentally, it may be noted that a similar in- crease in efficiency of 111-V solar cells, due to reduction in front-surface reflection coefficient alone on texturiza- tion, has been reported [6]. It increases by about 70% for lower values of the lifetime and diffusion length of mi- nority carriers, the additional contribution coming from the increase in internal quantum efficiency.

1106 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 39, NO. 5 , MAY 1992

TABLE I

(Base thickness D = 300 pm.) EFFECT OF TEXTURIZATION ON SILICON SOLAR CELL PARAMETERS

Si Wafer Parameters

Minority- Percentage Gain in Efficiency on Minority- Carrier Minority-

Carrier Diffusion Carrier Ratio of Reverse Ratio of Total Short- Ratio of Open- Ratio of Solar Texturization Concentration Length Lifetime Saturation Current Circuit Current Circuit Voltage Cell Efficiencies ( (qT - q N T ) / ? ) N T )

( ~ m - ~ ) (cLm) (PS) ( J o T / J o N T ) ( J T / J N T ) [( v O C ) T / ( VOC)NTl ( q T / q N T ) x l o o ( % ) ~~~ ~~~ ~~

2.56 X IO4 280 30 2.48 1.36 0.973 1.32 32 2.56 x io3 90 4 1.73 1.41 0.989 1.40 40 2.56 x IO2 20 0.4 1.73 1.53 0.995 1.52 52 25.6 5 0.04 1.73 1.71 0.999 I .70 70

V. CONCLUSIONS The separate roles of the front-surface reflectance and

internal quantum efficiency in enhancing the short-circuit current on texturization of silicon solar cells have been studied and a comparative analysis with that of planar cells has been made. The major contribution is seen to come from the reduction of the front surface reflection coeffi- cient on texturization when the minority-carrier diffusion length is much larger than the base thickness. Significant contribution of internal quantum efficiency through an “effective” increase in absorption coefficient and diffu- sion length is made for smaller diffusion lengths than the base thickness. The open-circuit voltage, however, de- creases slightly on texturization for large diffusion length but it does not change significantly for small diffusion lengths. The efficiency is always found to increase on tex- turing. The gain in efficiency is observed to be as high as 70% for silicon wafers having lower values of minority- carrier concentration, diffusion length, and lifetime due to the combined effect of reduced reflection coefficient and enhanced quantum efficiency. This implies the important role which texturization can play in case of low-purity silicon wafers that are necessary for cost reduction of sil- icon solar cells.

REFERENCES [I] M. A. Green and P. Campbell, “Light trapping properties of pyra-

midally textured and grooved surfaces,” in Proc. 19th IEEE Photo- voltaic Specialist Conf. (New Orleans, LA, May 4-8), 1987, pp. 912- 917.

[2] F. F. Ho, P. A. Iles, and C. Cheng, “High efficiency silicon solar cell,” in Proc. 17th IEEE Photovoltaic Specialist Conf., 1984, pp.

[3] A. M. Barnett and J . S. Culik, “New solar cell design options,” in Proc. 19th IEEE Photovoltaic Specialist Conf. (New Orleans, LA, May 4-8), 1987, pp. 931-936.

[4] M. A. Green, A. W. Blakers, S. R. Wenham, S. Narayanan, M. R. Willison, M. Tauok, and T. Szpitalak, “Improvements in silicon so- lar cell efficiency,” in Proc. 18th IEEE Photovcoltaic Specialisfs Conf., Oct 1985.

[5] A. W. Blakers and M. A. Green, “20% efficiency silicon solarcells,” Appl. Phys. Lett., vol. 48, pp. 215-217, 1986.

[6] R. J. Roedel and P. M. Holm, “The design of anisotropically etched 111-V solar cells,” Solar Cells, vol. 1 I , pp. 221-239, 1984.

[7] P. A. Basore, “Numerical modeling of textured silicon solar cells

591-595.

using PC-ID,” IEEE Trans. Electron Devices, vol. 37, pp. 337-343, Feb. 1990.

[8] S. M. Sze, Physics ofSemiconductor Devices, 2nd ed. New Delhi, India: Wiley-Eastern Ltd., 1981.

[9] A. L. Fahrenbmch and R. H. Bube, Fundamentals of Solar Cells- Photovoltaic Energy Conversion. New York: Academic Press, 1983.

[IO] M. A. Green, Solar Cells. Englewood Cliffs, NJ: Prentice-Hall, 1982.

[ l l ] P. A. Basore and R. M. Swanson, “Crystalline silicon cell model- ing,” in Proc. 19th IEEE Photovoltaic Specialisfs Conf. (New Or- leans, LA, May 4-8), 1987.

Hiranmay Saha was born in 1946. He received the Master’s degree in radio physics and electron- ics from Calcutta University, Calcutta, India, and the doctoral degree in physics from the University of Kalyani, West Bengal.

He is currently Professor in the Department of Electronics and Telecommunication Engineering Department, Jadavpur University, Calcutta. Prior to this he was Professor of Physics in the Univer- sity of Kalyani. His primary fields of interest in research are solar cells and systems, thin-film

transistors, and optoelectronic sensors. Dr. Saha is the council member of the Indian Physical Society, the Solar

Energy Society of India, and the Institute of Electronics and Telecommu- nication Engineers.

Swapan K. Datta was born in West Bengal, In- dia, in 1950. He received the Ph.D degree in physics in 1987 from the Jadavpur University.

He worked in the field of photoconductivity of polycrystalline semiconductor films and prepara- tion of low-cost silicon from rice husk in the I.I.T., Kharagpur, and the Jadavpur University during 1974-1987. He worked as a Lecturer in the Rabindra Mahavidyalaya, West Bengal, during 1981-1991, and at present is a Senior Lecturer in the Department of Physics, City College, Cal-

cutta. His present research interests include solar cells and optoelectronic devices.

Dr. Datta is a member of Solar Energy Society of India.

SAHA et al . : INFLUENCE OF SURFACE TEXTURIZATION ON SILICON SOLAR CELLS 1107

Kanak Mukhopadhyay was born in West Ben- gal, India, in 1951. He received the M.Sc. and Ph.D. degrees in physics from the University of Kalyani, India, in 1976 and 1981, respectively. The subject of his Ph.D. dissertation was Cu,S/CdS solar cell.

He worked as a Lecturer in the University of Nigeria, Nsukka, Nigeria, during 1983-1986 and as an Assistant Professor in the Bright Star Uni- versity of Technology, Libya, during 1986-1989. At present he is a Research Associate in the Ja-

Manish K. Mukherjee (M’64-M’77-SM’82) was born on December 4, 1936. He received the B.Te1.E. and M.Te1.E. degrees in 1961 and 1963, respectively, and the Ph.D. degree in engineering from the Jadavpur University, Calcutta, India.

He joined the Jadavpur University where he is now a Professor in the Department of Electronics and Telecommunication Engineering. He has ac- tive interest in solar cells, both single-crystal and thin-film. Further, he is working with other de- vices such as TFT with amorphous silicon layer.

davpur University, India. H‘is interests focus on solar cells, photovoltaic systems, and optoelectronic devices.

He has worked for more than a year in the Institut fur Physikalische Eiek- tronik, Stuttgart, Germany, on solar cells with the support of the Alexander Von Humboldt Foundation.

S. Banerjee, photograph and biography not available at the time of pub- lication.