al-omar_1998_solar-energy-materials-and-solar-cells.pdf

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* Corresponding author. Tel.: #965 4811188, xtn 5850; fax: #965 4817451; e-mail: alomar@

cairo.eng.kuniv.edu.kw.

Solar Energy Materials and Solar Cells 52 (1998) 107 124

Optimum two-dimensional short circuit collectionefficiency in thin multicrystalline silicon solar cells

with optical confinement

A.S. Al-Omar*, M.Y. Ghannam

Department of Electrical and Computer Engineering, Kuwait University, P.O. Box 5969, 13060 Safat, Kuwait

Received 21 January 1997; received in revised form 7 October 1997

Abstract

The two-dimensional short-circuit AM1.5 collection efficiency is studied in thin multicrystal-

line silicon solar cells with optical confinement. The collection efficiency is calculated by linking

an optical analytical generation profile with the two-dimensional collection probability in pn

junction solar cells. The calculations are carried out for variable grain boundary recombination

velocity, cell thickness, grain width, diffusion length, and back surface recombination velocity.

The role of optical confinement leading to a strong dependence of the collection efficiency on

the cell thickness in very thin cells is confirmed. The optimum cell thickness for maximum

collection efficiency increases in cells with low back reflection or poor back surface passivation.

Also, the optimum thickness in very thin cells increases significantly with increasing the

diffusion length. It is also found that the effect of grain boundary recombination is predominantif the cell thickness is larger than the diffusion length and if the diffusion length is larger than

half the grain width, especially, in cells with unpassivated grain boundaries. On the other hand,

back surface recombination dominates the response in cells with unpassivated back surface if

the thickness is smaller than or comparable to the diffusion length. 1998 Elsevier Science

B.V. All rights reserved.

Keywords: Short circuit collection; Efficiency; Silicon solar cells

0927-0248/98/$19.00 1998 Elsevier Science B.V. All rights reserved

PII S 0 9 2 7 - 0 2 4 8 ( 9 7 ) 0 0 2 7 5 - 4


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1. Introduction

There has been a growing commercial interest in thin multicrystalline Si solar cells

[1]. Solar cell thickness affects the following energy conversion efficiency-loss mecha-

nisms: (1) voltage factor, (2) fill factor (FF), and (3) collection efficiency. The voltagefactor increases in thinner cells due to increased open-circuit voltage from reduced

Auger recombination [2]. Degraded collection efficiency and light trapping in thin

solar cells result in smaller short-circuit current (J

), which reduces its overall

efficiency. Recombination at grain boundaries produces further reduction in the

collection efficiency of thin multicrystalline solar cells. In these cells, higher efficiencies

are achieved through effective light-trapping [3], bulk passivation, grain boundary

passivation, and both back and front surface passivation. With the exception of light

trapping; all previous passivation techniques are affiliated with the enhancement of

carrier collection produced by reduced bulk recombination or surface recombination.

The magnitude of the last recombination mechanisms have a profound effect on the

collection efficiency in thin multicrystalline solar cells; especially, grain boundary and

surface recombination.

Recently, it has been shown that the collection probability, f(x, y), defined as the

fraction of those carriers generated at a point (x, y) that are collected in the external

circuit [410] is governed by the same equations governing the excess dark minority

carriers. The two-dimensional collection efficiency has been calculated from the

collection probability and used to study the impact of the grain size and of grainboundary recombination on the short-circuit performance of thick polycrystalline

silicon (poly-Si) pn junction solar cells [9].

In the present paper, a similar procedure is carried out for thin poly-Si pn-junction

solar cells with optical confinement. The spectral response, the AM1.5 collection

efficiency, and the short-circuit current are determined from spatial numerical integra-

tion of the collection probability f(x, y) over rate of carrier photogeneration g(x)

throughout the cell. The advantage of the method used here is twofold: (1) solar-cell

characteristics are determined by numerical integration, which is more accurate than

numerical differentiation of finite-difference calculation as usually done for the deter-

mination of the current, and (2) calculation of collection probability density is

decoupled from position dependent carrier generation rate g(x), which removes short

wavelength convergence problems. Optical confinement obtained by light trapping is

essential in thin cells to maintain a relatively high efficiency [11,12]. Light trapping,

usually studied with ray tracing methods [1315], is a computationally intensive task.

The analytical approximation for the optical generation rate introduced by Basore

[16] and extended by Brendel [12] to account for the absorption in the emitter and

for light trapping is adopted in this work. This model applies to a cell having a frontsurface covered with infinitesimally small grooves and a diffused back reflector and is

introduced in the present analysis through a back surface reflectivity (R

) and

a surface roughness parameter ().

108 A.S. Al-Omar, M.Y. Ghannam/Solar Energy Materials and Solar Cells 52 (1998) 107124


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Fig. 1. Schematic representation of a perfectly columnar grain PN junction poly-crystalline silicon solar

cell. In the blowup an isolated single grain cell is sketched. Due to the symmetry around the central axis

only half of the cell is analyzed.

2. Summary of methodology

2.1. Transport model

The model detailed in Ref. [9] is summarized here for convenience. Thetwo dimensional carrier collection probability density f

(x, y) is to be determined

at any point (x, y) inside an ideal pn junction solar cell at low-level injection

[17] which is adequate for one sun illumination. As shown in Fig. 1, the cell is

divided into three regions: (1) an active (neutral) n> emitter region, (2) a depletion

region, and (3) an active (neutral) p base region. Light generates minority carriers in

the three regions. In the depletion region a 100% collection probability is attained.

Therefore,

f"1 for x

)x)x

and !

2)y)

2, (1)

where x

is the edge of the depletion region in the active n> emitter region and x

is

the edge of the depletion region in the active p base region. The two-dimensional

partial differential equation for the collection probability in the n> emitter region is

given by

f"f

, (2a)

A.S. Al-Omar, M.Y. Ghannam/Solar Energy Materials and Solar Cells 52 (1998) 107124 109


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where

is the minority carrier (hole) diffusion length. The solution of Eq. (2a) is

subject to the boundary conditions

f"1 at x"x

,

jf

jx"

S

D

f

at x"0 and 0(y)

2

,

jf

jy"!

S

D

f

at y"

2

,

jf

jy"0 at y"0,

(2b)

where S

is the recombination velocity at the front surface, S

is the recombination

velocity at the vertical edge boundaries, and D

is the minority hole diffusion

coefficient in the emitter region. Note that Eqs. (2a) and (2b) for the collection

probability is similar to the steady-state continuity equation of excess minority carrier

concentration in Refs. [710]. The collection probability is unity at the depletion

region edge, and follows the same boundary conditions as that for excess minority

carriers at other boundaries. The analysis is made simpler by assuming constant

effective surface recombination velocities, S [18,19], which is assumed to be identical

at dark and under illumination. The boundary condition at y"0 results from thesymmetry around the central vertical axis.

Similarly, the two-dimensional partial differential equation of the collection prob-

ability in the p base region is given by

f"

f

, (3a)

where

is the minority carrier (electron) diffusion length. In this case, the boundary

conditions are

f"1 at x"x

,

jf

jx"!

S

D

f

at x"H,

jf

jy"!

S

D

f

at y"

2

,

jf

*y"0 at y"0,

(3b)

where S

is the recombination velocity at the back surface and D

is the minority

electron diffusion coefficient in the base. The boundary condition at y"0 results from

the symmetry around the central vertical axis.



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The collection probability in the entire solar cell is determined by combining

condition, (1) with the separate numerical solutions of the sets of Eq. (2a) and Eq. (3b).

Such numerical solutions are carried out using the finite-difference approximation

on uniform rectangular grids [20,21] in each region. As a result of symmetry

around the central vertical axis, the calculations are performed for only one-half ofthe cell.

2.2. Optical model

The optical generation model used here follows a carrier generation profile g(x, )given by [12]

g(x, )"g(x)#R()

cos

exp

!

()(H!x)cos

#RR

;()

cos L

exp(!()x/cos L)#

LR

Lexp(![()(H!x)]/cos

L)

1!RL

RLL

,

(8)

where

g

(x, )"

(1!R)

()

cos exp

!

()x

cos

, 0)x)x

()cos

exp!()x

cos

!()(x!x

)

cos

, x) x)H,where x

is the edge of the depletion region on the base side, H is the total cell

thickness, R

is the front surface reflectance, is the angle at which light is transmitted

through the emitter,

is the angle at which light is transmitted through the base for

the first pass, for the second pass,

L for the nth pass, R is the back surfacereflectance for the first pass, R

Lfor the nth pass, R

is the first internal front surface

reflection, RL

is the nth internal front surface reflection. The transmittance of the first

pass

is given by

"exp

!x

cos !

(H!x

)

cos

, (9)and the nth pass diffuse light transmittance factor

Lis given by

L"exp

!Hcos

L"2

sin cos exp!H

cos d. (10)The second pass transmittance factor

is given by

"exp

!Hcos

"L#(1!), (11)



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where is the surface roughness parameter.

represents an average of the diffuse

transmittance and the specularly reflected light transmittance

given by

"exp

!H

cos

(12)

2.3. Internal spectral response and collection efficiency

The averaged internal spectral response [5,6], (), corresponding to a photo-generation rate g(x, ) (that may take light confinement into account) is given by

()"2

5

&

f(x, y)g(x, ) dx dy, (13)

where the front and back surfaces define the integration limits along the x-axis. The

collection probability density f(x, y) at point (x, y) calculated earlier is used to carry

out the integration in Eq. (13) along the y-axis leading to the averaged response over

the illuminated region.

The average short-circuit collection efficiency, G, defined as the ratio of the total

collected carrier density to the total generated carrier density in the cell assuming

a unity quantum yield under short circuit condition, is determined from

G"1()2+"H+

H

(

)F+

(

) d

H+H

F+

() d , (14)

where F+

() is the AM1.5 radiation spectrum, the wavelength +

is set to 1103 nm

which corresponds to the energy band gap of Si, and

is 325 nm. No effect of front

contact shadowing was accounted for. The numerator of Eq. (14) represents the

AM1.5 photo-generated (short-circuit) current density per unit electronic charge, J*

,

while the denominator denotes the AM1.5 photon flux absorbable in Si. Thus, the

short-circuit current is related to the averaged collection efficiency G

by

J*"q

GH+

H

F+

() d"58.6G

mA/cm. (15)

3. Results

The collection efficiency at AM1.5 in thin poly-Si cells with optical confinement is

investigated. Optical model parameters are fixed at R"20%, R

"60%, "0.5,

R"92.8%, R"62%, which are typical for highly efficient light confinement ofRef. [12]. The grain width

and the surface recombination velocity at the grain

boundary S

are the main variables shaping grain boundary recombination in poly-Si

solar cells. Other parameters such as the cell thickness H, the minority electron

diffusion length in the base

, and the back surface recombination velocity S

are also

considered. The minority hole diffusion length in the emitter

and the front surface

recombination velocity S

shape carrier collection in the emitter. The latter has



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a weaker dependence on grain boundary recombination than the collection in the

base [9]. Therefore, the last two parameters are assumed to be secondary and are fixed

at "5 m and S

"100 cm/s which are typical values for n> emitters of silicon

solar cells with high- quality oxide-passivated surface. Grain boundary recombination

velocities of 100 and 10 cm/s are assumed for well-passivated and unpassivated grainboundaries, respectively. Back surface recombination velocity of 500 and 10 cm/s are

assumed for well passivated (e.g. back surface field contact) and metal back contact,

respectively.

3.1. Dependence of collection efficiency on substrate thickness and grain width

The AM1.5 collection efficiency is calculated according to the model described by

Eq. (13), which includes the combined effect of collection probability and optical

generation, as a function of substrate thickness (H) and grain width (). The

collection efficiency is evaluated for cells with different passivation conditions.

3.1.1. Cells with grain boundary passivation and back surface passivation

The AM1.5 collection efficiency (G) contours in cells with grain boundary passiva-

tion and back surface passivation are plotted in Fig. 2a for an optical back reflection

of 60% and Fig. 2b for a zero back reflection as a function of substrate thickness (H)

and grain width (). In these plots, the electron diffusion length (

) was fixed at

50 m.Fig. 2a shows that the collection efficiency contours are almost vertical for films

thinner than 10 m. Vertical contours indicate that the collection efficiency is inde-

pendent of the grain width but is very sensitive to the film thickness. Thickness

dependence of the collection efficiency mainly occurs through high sensitivity to

optical generation or to back surface recombination. In the present case, the back

surface is well passivated and the pronounced efficiency degradation for film thickness

below 10 m is mainly due to the highly reduced optical generation resulting from the

highly attenuated light intensity crossing the cell beyond the second reflection.

At a grain width of 100 m (twice the diffusion length), the collection efficiency

exhibits a peak value slightly larger than 66% at an optimum thickness slightly larger

than 30 m. At this point the collection probability density f

is close to unity because

S

is small and the thickness is shorter than the diffusion length. As the cell thickness

exceeds this optimum thickness, the collection efficiency decreases very slowly with

cell thickness and almost saturates once the thickness reaches 100 m. In such

relatively thick cells optical confinement has a marginal role, and the behavior of the

collection efficiency versus cell thickness is divided into two streams. First, if the cell

thickness is smaller than or comparable to the diffusion length, the collection efficien-cy is mainly controlled by back surface recombination. In the case under study, S

is

small which explains the very weak degradation observed in the collection efficiency

as the cell thickness exceeds the optimum thickness. Second, in cells much thicker than

the diffusion length, the carriers photogenerated at the back surface cannot be

collected which leads to a thickness-independent behavior as observed in cells thicker

than 100 m. For such cells, the role of grain boundary recombination takes over



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Fig. 2. (a) The internal AM1.5 collection efficiency contours as a function of cell thickness (H) and grain

width () for

"50 m, passivated grain boundary (S

"100 cm/s), and passivated back surface (S

"500 cm/s) with highly efficient light confinement: R

"20%, R

"60%, "0.5, R

L"92.8%, and

R"62%. (b) The internal AM1.5 collection efficiency contours as a function of cell thickness (H) and

grain width () for


"100 cm/s), and passivated back surface

(S"500 cm/s) with no light confinement: R

"20%, R

"0%.

leading to horizontal efficiency contours. Note that the efficiency degradation due to

grain boundary recombination is relatively weak, especially in the range 'because of the small grain boundary recombination velocity assumed in the case

under study (S"100 cm/s).

In cells without optical confinement (R"0), the position of the peak collection

efficiency is shifted towards larger thickness as depicted in Fig. 2b. The peak efficiency

occurs in this case at a film thickness of 50 m and its value at a grain width of 100 m

is slightly greater than 63%. The collection efficiency contours displayed in Fig. 2b



9/18

Fig. 3. The internal AM1.5 collection efficiency contours as a function of cell thickness (H) and grain width

() for

"50 m, unpassivated grain boundary (S

"10 cm/s), and passivated back surface

(S"500 cm/s) with highly efficient light confinement: R

"20%, R

"60%, "0.5, R

L"92.8%, and

R"62%.

exhibit an abrupt transition from a thickness-dependent behavior (vertical contours)

to a grain-size-dependent behavior (horizontal contours). This indicates that the peak,

if any, is very marginal, which is in agreement with previously reported one-dimen-

sional results for cells with very small back surface recombination velocity [5]. For

a film thickness of 10 m, the collection efficiency for a cell with 60% back reflection is61% compared to 55% for a cell without back reflection.

3.1.2. Cells with unpassivated grain boundaries but with back surface passivation

The collection efficiency contours for cells with unpassivated grain boundaries and

well-passivated back surface are displayed in Fig. 3 as a function of cell thickness and

grain width. These contours can be identically obtained by vertically shifting the

contours of Fig. 2a upwards. Below a certain critical grain size given by approximately

twice the diffusion length, the role of grain boundary recombination is very dominant.

For larger aspect ratios (ratio of grain size to thickness), the collection efficiency

becomes mainly dependent on the cell thickness primarily due to the significant role of

optical generation since in the present case back surface recombination is negligible.

The optimum film thickness corresponding to the peak collection efficiency is 30 m

like in the result of Section 3.1.1 also dealing with cells with back surface recombina-

tion. The value of the peak collection efficiency at the critical grain size of 100 m,

however, is only 62.5% compared to 66% for cells with passivated grain boundaries.

3.1.3. Cells with grain boundary passivation and unpassivated back surfaceThe collection efficiency contours for cells with grain boundary passivation and

unpassivated back surface are displayed in Fig. 4 as a function of cell thickness and

grain width. The vertical contours highly dominating the plot for cells thinner than



10/18


() for


"100 cm/s), and unpassivated back surface


"20%, R

"60%, "0.5, R

L"92.8%, and

R"62%.

30 m indicate a strong dependence of the collection efficiency on the optical genera-

tion. The corresponding value of the collection efficiency is significantly degraded dueto the very high back surface recombination velocity. This result demonstrates the

importance of back surface passivation for maintaining a relatively high efficiency in

thin cells with relatively high-quality bulk material. As the cell thickness exceeds one

diffusion length, the influence of optical confinement and back surface recombination

is weakened out leading to a collection efficiency almost solely dependent on the grain

width. Due to high back surface recombination, the maximum collection efficiency at

the critical grain size of 100 m is smaller than in cells with passivated back surface

(less than 63% compared to 66%), and the optimum cell thickness is shifted towards

larger values exceeding 100 m.

3.1.4. Cells with unpassivated grain boundary and unpassivated back surface

The collection efficiency contours for cells with unpassivated grain boundaries and

unpassivated back surface are displayed in Fig. 5 as a function of cell thickness and

grain width. These contours can be understood based on the detailed discussions

presented above and need no more elaboration. Actually, these contours can be

generated by shifting those of Fig. 2a diagonally upwards to the right. At the critical

grain size, the peak collection efficiency in the high recombination scheme studied inthis section slightly exceeds 59%.

3.2. Optimum cell thickness and maximum collection efficiency

The optimum cell thickness (H

) corresponding to the maximum collection effi-

ciency G

is plotted in Fig. 6a together with G

as a function of grain width () for



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() for

"50 m, unpassivated grain boundary (S

"10 cm/s), and unpassivated back surface


"20%, R

"60%, "0.5, R

L"92.8%, and

R"62%.

a cell with grain boundary passivation and back surface passivation having a

base diffusion length

of 50 m, taking the back reflection factor R

as an in-

dependent parameter. The curves for R"0.6 correspond to the results displayed

in Fig. 2a. Larger back reflection leads to a more efficient optical confinement,

a shallower generation profile and an enhanced absorption in thin substrates.

Such a reasoning is confirmed in Fig. 6a showing a higher maximum collection

efficiency at a smaller cell thickness when the back reflection factor is increased. In

general, Fig. 6a indicates that the optimum cell thickness is inversely proportional to

the back reflection ratio R

while the maximum collection efficiency is directly

proportional to R. In practice, plots like those displayed in Fig. 6a can be used to

determine the optimum film thickness for specific passivation and back reflection

schemes assuming that the grain width and bulk diffusion length of the resulting films

are reproducible.

The behaviors displayed in Fig. 6a of the optimum thickness and of the maximum

efficiency with respect to the grain width can be divided into two distinct regions. For

wide grains ('2

) grain boundary recombination is less influential; especially, in

cells with efficient grain boundary passivation. In such a case, the optimum cellthickness and the maximum collection efficiency are almost independent of the grain

width, and the solar cell behaves practically as single crystalline cell. On the other

hand, for narrow grains ()2

), the optimum cell thickness and the maximum

collection efficiency are proportional to the grain width . This result can also be

visualized by following the trajectory of the bottoms of the contours in Fig. 2a as the

grain width is reduced below 100 m (2

). Since the efficiency dependence on grain



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width is caused by grain boundary recombination, grain boundary recombination

continues to affect the maximum collection efficiency and the optimum thickness in

cells with unpassivated grain boundaries even if the grain width exceeds the 2

limit

described above, which is illustrated in Fig. 6b.



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Fig. 6. (a) Optimum cell thickness versus grain width

for cells with "50 m, passivated grain

boundary (S"100 cm/s), passivated back surface (S

"500 cm/s) and different back reflections ratio R

.

The right y-axis is the value of maximum internal AM1.5 collection efficiency at the optimum thickness. Theoptical model parameters are: R

"20%,"0.5, R

L"92.8%, and R

"62%. (b) Optimum cell thickness

versus grain width

for cells with "50 m, R

"60%, and different passivation schemes: (A) grain

boundary only (S"100 cm/s and S

"10 cm/s), (B) neither (S

"10 cm/s and S

"10 cm/s), (C) grain

boundary and back surface (S"100 cm/s and S

"500 cm/s), (D) back surface only (S

"10 cm/s and

S"500 cm/s). The right y-axis is the value of maximum internal AM1.5 collection efficiency at the

optimum thickness. The optical model parameters are: R"20%, R

"60%, "0.5, R

L"92.8%, and

R"62%.

3.3. Dependence of optimum cell thickness on diffusion length

3.3.1. Very wide grain (monocrystalline silicon) cells

The optimum cell thickness (H

) and the maximum collection efficiency G

of very

wide grain cells with grain boundary passivation simulating monocrystalline siliconwith back surface passivation are plotted in Fig. 7a as a function of the base diffusion

length (

) for different back reflection ratios R

. The results show that the maximum

collection efficiency and the optimum thickness increase with increasing diffusion

length. For

exceeding 100 m, the maximum collection efficiency tends to converge

to an asymptote with weakly dependence on both R

and

. The calculated values

represent a very good estimate for H

and

in most practical cases for films with

a diffusion length lying in the range 10100 m. In such cases, the calculated optimum

thickness lies between 5 and 60 m which are typical values for silicon film techno-

logy.

The theoretical dependencies ofH

and G

on the diffusion length are generated forR

"60% for cells without back surface passivation and plotted in Fig. 7b together

with the results of Fig. 7a for cells with back surface passivation. As expected,

enhanced back surface recombination leads to degradation of the maximum collec-

tion efficiency and to a strong increase in the optimum thickness of the cell. Note that

the continuous influence of back surface recombination even at very small values of

is due to the dependence of the optimum cell thickness on

.

3.3.2. Polycrystalline silicon cells with equal grain width and cell thickness

The maximum collection efficiency is determined for cells with equal grain width

and film thickness from the two-dimensional contour tangent to the line representing

the condition "H

. Such a condition is reasonable for thin multicrystalline

silicon films, where grain widths are similar to thickness. From Fig. 2a, the highest

collection efficiency that can be obtained when"H

lies between 65% and 66%

and occurs approximately at"H

"30 m. Such values are checked and con-

firmed at "50 m in Fig. 8 displaying the calculated optimum cell thickness

H

(with H") and its corresponding maximum collection efficiency as a function

of the diffusion length

for polycrystalline silicon cells with grain boundary and

back surface passivation. The results of Fig. 8 are very close to those of Fig. 7a, since



14/18

cells with grain boundary passivation behave very similarly to very wide grain cells.

However, at long diffusion lengths, the effect of grain boundary recombination is not

totally negligible leading to a smaller maximum collection efficiency than that of very

wide grain cells. Furthermore, the optimum cell thickness (H

) disappears as

exceeds a certain critical value above 100 m. In the last situation, increasing



15/18

Fig. 7. (a) Optimum cell thickness versus base diffusion length

for very wide grain cells "1 cm

(practically perfect grain boundary passivation or single crystalline cell) with passivated back surface(S

"500 cm/s) and different back reflections ratio R

. The right y-axis is the value of maximum internal

AM1.5 collection efficiency at the optimum thickness. The optical model parameters are: R"20%,

"0.5, RL"92.8%, and R

"62%. (b) Optimum cell thickness versus base diffusion length

for very

wide grain cells "1 cm (practically perfect grain boundary passivation or single crystalline cell) with

(S"500 cm/s) or without (S

"10 cm/s) back surface passivation, and R

"60%. The right y-axis is the

value of maximum internal AM1.5 collection efficiency at the optimum thickness. The optical model

parameters are: R"20%, "0.5, R

L"92.8%, and R

"62%.

Fig. 8. Optimum grain dimension of equal thickness and width ("H) versus base diffusion length

for passivated grain boundary (S"100 cm/s), passivated back surface (S

"500 cm/s), and different

back reflections ratio R

. The right y-axis is the value of maximum internal AM1.5 collection efficiency at

the optimum dimension. The optical model parameters are: R"20%, "0.5, R

L"92.8%, and

R"62%.

above this critical value does not produce a curve with maximum G

at a finite

thickness; maximum efficiency occurs at the largest possible cell thickness H. It should

be noticed that collection efficiency enhancement through reduction of grain size is

similar with what is observed with porous photochemical cells [22]. There, the effect

of bulk recombination on the collection efficiency is minimized in nanostructure

semiconductor with structural units equal to or smaller than twice the diffusion length

given that surface recombination is reduced, which is achieved by the aqueous

electrolyte solution interface.



16/18

Fig. 9. Optimum cell thickness versus back surface recombination velocity S

for very wide grain cells

"1 cm (practically perfect grain boundary passivation or single crystalline cell) with

"50 m,

Sb"500 cm/s and different back reflections ratio R

. The right y-axis is the value of maximum internal

AM1.5 collection efficiency at the optimum thickness. The optical model parameters are: R"20%,

"0.5, RL"92.8%, and R

"62%.

3.4. Dependence of optimum cell thickness and maximum collection efficiency on back

surface recombination

The optimum cell thickness and the maximum collection efficiency are plotted as

a function of back surface recombination velocity in Fig. 9 for very wide grain(monocrystalline) cells and in Fig. 10 for grain boundary passivated polycrystalline

cells for which the grain width is equal to the thickness. Cells in both figures had

"50 m. Cells with grain boundary passivation are treated in order to emphasize

the effect of back surface recombination. As long as S

is smaller than 1000 cm/s its

effect is marginal. On the other hand, when S

exceeds 1000 cm/s H

increases

drastically with S

and saturates for S

larger than 10 cm/s. The opposite behavior is

observed for G

which exhibits a strong decrease in the range 1000(S(10 cm/s

and saturates for larger S@

values. Such behaviors can be explained by a reduced

collection probability f

at large S

values with skewed distribution that requires

a much thicker substrate to obtain the maximum collection efficiency. The differences

between the values of the maximum collection efficiency for different values of R

are

strongly reduced at large S

values because the optimum thickness becomes large

enough to minimize the influence of optical confinement.

Although the difference between the maximum collection efficiency and the opti-

mum thickness of monocrystalline cells and of polycrystalline cells is reduced at large



17/18

Fig. 10. Optimum grain dimension of equal thickness and width ("H) versus back surface recombina-

tion velocity S

for L"50 m, passivated grain boundary (S

"100 cm/s), and different back reflections

ratio R

. The right y-axis is the value of maximum internal AM1.5 collection efficiency at the optimum

dimension. The optical model parameters are: R"20%, "0.5, R

L"92.8%, and R

"62%.

values ofS, a smaller maximum collection efficiency and a larger optimum thickness,

resulting from the two-dimensional distribution of the collection probability, charac-

terize the polycrystalline cells (even with grain boundary passivation), as deduced by

comparing Figs. 9 and 10. It should be noted that since the thickness is varying in cells

of both figures, relative significance of back surface recombination should be nor-

malized to D

/H. The last statement was transparent in both figures, where large

surface recombination velocity effects occurred for S'D

/H.

4. Conclusions

For thin poly-Si solar cells with effective back surface passivation and optical

confinement the optimum cell thickness is strongly dependent on the back reflection,diffusion length, and back surface recombination velocity. Higher back reflectionR

results in smaller optimum thickness and larger collection efficiencies

G. The

maximum collection efficiency and the optimum thickness increase with increasing

the diffusion length. The former saturates for

above 100 m while the latter has to

be determined from its value at the border value of"100 m. Small back surface

recombination velocity below 1000 cm/s practically has no effect on optimum cell



18/18

thickness and on the maximum collection efficiency. Larger back surface recombina-

tion velocities ('D

/H) significantly increase the optimum thickness and reduce the

maximum collection efficiency. An optimum grain size of one diffusion length is

recommended for cells with passivated grain boundaries and a size larger than twice

the diffusion length is necessary if the grain boundaries are not passivated.

Acknowledgements

This work was supported by Kuwait University research Grants EE-048 and

EE-079.

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