Internal quantum efficiency improvement of polysilicon solar cells with porous silicon emitter

Renewable Energy 50 (2013) 441e448

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Internal quantum efficiency improvement of polysilicon solar cells with porous silicon emitter Abdessalem Trabelsi Laboratory of Applied Physics, Faculty of Sciences of Sfax, University of Sfax, B. P. 1171, Sfax 3000, Tunisia

a r t i c l e i n f o

a b s t r a c t

Article history: Received 2 February 2012 Accepted 30 June 2012 Available online 9 August 2012

The present study aimed to develop a simple analytical model to investigate the potential use and implications of porous silicon (PS) as an antireflective coating in thin polysilicon solar cells. It analytically solved the complete set of equations necessary to determine the contribution that this material has on the internal quantum efficiency (IQE) of the cell when acting as an antireflective coating agent. The increase in the IQE, the contribution of the different regions of the cell, and the effects of the physical parameters of each region were derived and investigated in comparison with conventional solar cells. The findings revealed that the internal quantum efficiency of the solar cell with PS emitter is higher than that of the conventional one particularly for short-wavelengths (l < 0.6 mm). Furthermore, for photons with higher energy, the emitter contribution in the IQE is more significant than the base and depletion regions. For photons with smaller energy, on the other hand, the absorption coefficients are also smaller, which leads to a higher generation rate in the base region and, hence, to a more pronounced contribution from this region to IQE. Last but not least, the improvement of IQE is observed to increase 20 3 with decreased PS thickness and with heavily doped PS emitter (Nþþ d ¼ 10 cm ). Ó 2012 Elsevier Ltd. All rights reserved.

Keywords: Polysilicon solar cells Porous silicon Antireflective coating Internal quantum efficiency

1. Introduction Polycrystalline silicon is a basic material with promising applications for the production of inexpensive and efficient solar cells in the terrestrial photovoltaic industry. In fact, while sharing many of the desirable physical and chemical properties of the single-crystal silicon, this material has often been reported to be more costeffective [1e6]. Nevertheless, polysilicon is often reported to induce a number of undesirable defects that considerably affect the electrical properties of semiconductor material [4]. Since polycrystalline silicon constitutes a primary component in the production of solar cells, recent research has paid special attention to the search for novel appropriate techniques to enhance its efficiency. In fact, the constructive search for the optimization of polysilicon solar cells efficiency entails the reconsideration of current modeling paradigms in light of the recent data in the field. Carrier recombination, to start with, is one of the major limiting factors to the conversion efficiency of polysilicon solar cells. Several studies indicate that reducing the cell thickness, particularly of thin film silicon, would lead to an increased efficiency provided that the cell surfaces are very well passivated and that the optical absorption is enhanced [7e9]. This can be achieved by incorporating

E-mail address: [email protected]. 0960-1481/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.renene.2012.06.063

surface texturing to reduce optical reflection. Another advantage of thin film cells is the promising opportunities they can offer with regards to reducing the cost of the component and to meeting the current high demand for silicon feed stock. More pertinent to the aims of the present study, recent studies have indicated that the reduction of optical reflectivity and enhancement of absorption are of special importance to the performance of polycrystalline solar cells. The fulfillment of these goals can be achieved through the implementation of special structures, such as the introduction of antireflective coatings. In fact, several materials have been used as antireflective coatings [10,11]. Most of these materials have, however, been reported to suffer from fundamental limitations pertaining to categorical moves and properties. Of particular relevance to this issue, a number of recent studies have reported that porous silicon has a number of promising optical properties (namely, direct gap, low reflectivity, variable refractive index, red photoluminescence, randomized morphological structure, and possibility of band-gap engineering) that make it a potential strong candidate for photovoltaic applications [8,10e12], particularly as an antireflective coating [13,14]. In fact, depending on the distinctive dimensions of the pores, the PS layer would prove different optical behavior. More importantly, PS can be used as a single or multilayer antireflective coating for solar cells [14]. The problems associated with the use of PS layer in contact with the crystalline silicon have been extensively investigated. Reports

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A. Trabelsi / Renewable Energy 50 (2013) 441e448

Nomenclature q UT ni0 Ln ðLþ nÞ

electron charge thermal voltage intrinsic carrier density diffusion length of minority carriers in the base (back) region Dn ðDþ n Þ diffusion constant of minority carriers in the base (back) region Na ðNaþ Þ doping level in the base (back) region þþ Lþ p ðLp Þ diffusion length of minority carriers in the polysilicon (PS) emitter Ndþ ðNdþþ Þ doping level in the polysilicon (PS) emitter a(l) (a*(l)) absorption coefficient in the polysilicon (PS) at a wavelength l f(l) incident photon flux reflection coefficient at the front surface. R(l) indicate that, due to the intrinsic properties of the PS, several factors have to be considered before its ultimate application in commercial photovoltaic technology [13]. Most of these limitations are, in fact, attributed to the high resistivity of porous silicon (a metallic contact on its surface is expected to have a poor electrical behavior) and its fragility in the high-temperature processes characteristic of the fabrication of silicon solar cells. From a qualitative perspective, voids might be unsupportive for carrier mobility whose lifetime might be reduced by the highly doped wafers used for its formation. Besides, small voids may not bring about significant reductions in terms of carrier mobility [12]. In this respect, several experimental studies have opted for the use of porous silicon (PS) as an antireflective coating of thin monoand polysilicon solar cells to effectively enhance the optical absorption of crystalline silicon [13,14]. Given the paucity and limitation of the currently available data, further analytical studies are deemed necessary to fully understand the potential and promising utilities of this material (PS) as an antireflective coating in thin polysilicon solar cells and, more specifically, to explain the ensuing phenomena associated with its application. Accordingly, the present study aims to present a simple analytical solution for the contribution that this material might have on the internal quantum efficiency (IQE) of the cell when acting as an antireflective coating. In order to achieve a better understanding of the key issues involved in the process, the study considers an elementary nþþ/nþ/p/pþ polysilicon solar cell with a thin film PS at the front side. The increase in the IQE, the contribution of the different regions of the cell, and the effects of the physical parameters of each region were derived and investigated in comparison with conventional solar cells.

Wb(WBSF)base (BSF) thickness We(WPS) polysilicon (PS) emitter thickness H total cell thickness d grain width recombination velocity at the back (front) contact Sn(Sp) Seff,nþþnþ(Seff,nþnþþ) effective recombination velocity at z ¼ B (z ¼ C) effective recombination velocity at z ¼ F Seff,ppþ Dn excess electron density in the base region Dpþ(Dpþþ) excess hole density in the polysilicon (PS) emitter nþ ðJ nþþ Þ polysilicon (PS) emitter light-generated current JphE phE density JphB(JphD) light-generated current density in the base (the depletion region) þ þþ IQEnE ðIQEnE Þ contribution of the polysilicon (PS) emitter to the IQE IQEB(IQED) contribution of the base (the depletion region) to the IQE

a metallic plate which was, together with a counter platinum wire electrode, connected to a potentiostat. The electrolyte was 25% hydro-fluoric acid (HF) in aqueous solution. The PS layer was obtained under a constant current density of 50 mA cm2 applied during 3.5 s which corresponds to a transferred charge of 0.175 C cm2. From results published elsewhere, the thickness of the PS layer is expected to be smaller than 100 nm. The analytical model presented in the current study takes the different heavily doped regions into account. Accordingly, the effective carrier concentration nie is related to both band-gap narrowing (BGN) and degeneracy by [7]:




n2ie ¼ n2i0 exp

DEg UT



(1)

2. Theory As illustrated in Fig. 1, the present study considers an nþþ/nþ/p/pþ solar cell that consists of a thin film polycrystalline silicon (nþ, p and pþ regions) having a porous silicon emitter (nþþ). Accordingly, the emitter consists of a porous silicon layer (AB) and a polysilicon layer (CD). The grain boundaries in the polysilicon regions, which were taken perpendicular to the nþ/p junction solar cell, with a depth equal to the thickness of the grains, were characterized by a recombination velocity Vg. The physical and structural parameters are presented in Fig. 1. The PS layer can be performed following the experimental procedure described by Strehlke et al. [13], using a two-electrode arrangement. The back of the Si wafer was strongly held to

Fig. 1. Three-dimensional schematic model for an elementary polysilicon solar cell with PS emitter.

A. Trabelsi / Renewable Energy 50 (2013) 441e448

where ni0 is the intrinsic silicon carrier concentration and DEg is the apparent BGN [15,16]. The values of the physical parameter used are shown in Table 1. The total internal quantum efficiency of an elementary cell under illumination can be presented as the sum of contributions made by the different regions of the cell. 2.1. Modeling of the porous silicon emitter

443

þþ

n J0Eðat CÞ ¼ qSeff;nþ nþþ

Ndþ Dþþ p

Seff ;nþ nþþ ¼

Ndþþ Lþþ p

Dþþ   p Fnþþ Sp ¼ Sp Lþþ p Dþþ p

(2)

where Dp refer to the excess hole density at the dark and the hole diffusion length [18]. The boundary conditions in the z-direction are:


  n2ie V1 1 þþ exp U Nd T

 Sp dDpþþ  ¼ þþ Dpþþ ðz ¼ 0Þ dz z¼0 Dp

Lþþ p

ðat z ¼ BÞ

ðat z ¼ AÞ

to

Seff ;nþþ nþ ¼ (3)

(4)

The injected current density in the PS emitter is given by: þþ

¼ qDþþ p

 dDpþþ  dz z¼WPS

þþ

n J0Eðat CÞ ¼

Sp Lþþ p 6 þþ þþ D qDp 6 p 6 6 6Sp Lþþ Lþþ p p 4 Dþþ p



WPS Lþþ p

! !

(9)


  n2ie V1 exp  1 UT Ndþþ

(10)

WPS þ sin h Lþþ p ! WPS þ cos h sin h þþ Lp cos h

!3

Ndþ Lþ p

! ¼

Ndþþ Dþ p Ndþ Lþ p

 Fnþ ðNÞ

(11)

IQEnE

nþ

þþ

þ

ðaÞ ¼ IQEnE ðaÞ þ IQEnE ðaÞ

þþ IQEnE ðaÞ

and

þ IQEnE ðaÞ

(12)

can be written as:

þþ

þþ

IQEnE ðaÞ ¼

n JphE

(13)

qð1  RÞf þ

WPS 7 7 Lþþ p !7 7 WPS 7 5 Lþþ p

þ

IQEnE ðaÞ ¼

(6)


  n2ie V1 exp  1 UT Ndþþ

We  cot h þ Lp

The contribution of the emitter to the IQE of the cell with porous þþ þ silicon IQEnE n ðaÞ consists of two contributions from the PS and the polysilicon regions. It can be written at z ¼ W1 ¼ We þ WPS (at z ¼ D) as:

where

!

Ndþþ Dþ p

2.2. Contribution of the emitter to the IQE

þþ

(5)

The solution of the current continuity equation (Eq. (2)) subject to the above boundary condition is given at C by:

2

WPS Lþþ p

So, Seff,nþþnþ is easily obtained as:

þþ

n J0E

(8)

The continuity equation in the nþ-type region at the dark should be used to determinate the ERV at z ¼ B, Seff,nþþnþ. Note that the injected current density in the polycrystalline emitter can be written as: þ

Dpþþ ðz ¼ WPS Þ ¼

   Fnþþ Sp

! WPS cos h þþ þ sin h Lp ! WPS sin h þþ þ cos h Lp

Sp Lþþ p

n J0Eðat BÞ ¼ qSeff;nþþ nþ

d2 Dpþþ Dpþþ  þþ2 ¼ 0 dz2 Lp

(7)

By combining Eqs. (6) and (7), Seff,nþnþþ can be simply obtained as:

where:

The (PS) layer has a thickness WPS and is terminated by a metal contact. Recombination at the metal contact can be characterized by a recombination velocity Sp. The nþ/nþþ contact can be described by effective recombination velocities (EVR) Seff,nþþnþ and Seff,nþnþþ at z ¼ B and z ¼ C, respectively [17]. The ERV Seff,nþnþþ is calculated by solving the continuity equation and the current transport equation in the nþþ-type region. The minority-carrier continuity equation in this region is given by the following expression:


  n2ie V1 1 þ exp U Nd T

þþ

n The depletion region (BC) is neglected, so J0Eðat CÞ can be also written as:

Table 1 Physical parameter values. Parameter

Value

Ref.

We WPS Wb Na Nþ d Ndþþ Sn Sp Vg d

0.3 mm 0.1 mm 50 mm 5  1016 cm3 1018 cm3 5  1019 cm3 106 cm s1 106 cm s1 104 cm s1 50 mm

[8] [12] [8] [8]

[8] [8] [16] [8]

n JphE

(14)

qð1  RÞf

2.2.1. Porous silicon emitter light-generated current density Under illumination, the continuity equation for minority carriers (hole) in the nþþ-type region is given by the following expression:

d2 Dpþþ ðz; lÞ Dpþþ ðz; lÞ 1  ¼  þþ gPS ðz; lÞ þþ2 D dz2 Lp p

(15)

where Dpþþ refers to the light-generated excess hole concentration and Lþþ p to the hole diffusion in the PS region. The term gPS(z,l) is the generation rate of minority carriers (hole) in this region, given by:

gPS ðz; lÞ ¼ ½1  RðlÞfðlÞa* ðlÞ exp



 a* ðlÞ  z



(16)

where a*(l) is the effective absorption coefficient of the PS layer given at [8]. The boundary conditions in the z-direction are given by:

 Sp dDpþþ  ¼ þþ Dpþþ ðz ¼ 0Þ dz z¼0 Dp

ðat z ¼ AÞ

(17)

444

A. Trabelsi / Renewable Energy 50 (2013) 441e448

Dpþþ ðz ¼ WPS Þ ¼ Dpþþ ðat BÞ ðat z ¼ BÞ

(18)

where Dpþþ represents the light-generated excess hole concenðat BÞ tration at z ¼ B. The light-generated current density in the PS emitter is given by: þþ

n þþ JphEðat BÞ ¼ qDp

 dDpþþ  dz z¼WPS

(19)

The solution of the current continuity equation (Eq. (15)) subject to the above boundary condition is given, at B, by:

Therefore, a general equation for light current collected at the nþþ reduced PS-Poly junction is expressed simply as the current JphE;0 by FPS-Poly. The expression (Eq. (24)) is similar to the one established by Dai et al. for the light current collected by the high-low nþen junction front-surface field (FSF) solar cell [19], and to the one established by Zouari et al. for the light current collected at the polysiliconeoxide interface for a polysilicon emitter solar cell [17]. The expression (Eq. (25)) shows that the porous-poly factor, FPSPoly is a function of device parameters and easy to determinate once the parameters are provided. The recombination at depletion region (BC) is neglected, so the hole light-generated current density collected at z ¼ C is similar to that collected at z ¼ B:

2

Sp Lþþ p 6 þ a* Lþþ p * þþ qð1RÞa fLp 6 Dþþ p 6 nþþ ! JphEðat BÞ ¼ 6 2 þþ a* Lþþ 1 6 p 4Sp Lp sinh WPS þcosh þþ Dp Lþþ p

! WPS Lþþ p

2 3" 3 2 ! !# 2

Sp Lþþ a* Lþþ Dþþ 1  Dpþþ p p WPS WPS ðat BÞ p * 4 5 7 þexp a WPS cosh þþ þsinh þþ 2 Dþþ Lp Lp

7 ð1RÞfa* Lþþ p 7 p * þþ * ! !   a Lp exp a WPS 7 7 þþ Sp L p 7 WPS WPS 5 þþ sinh þþ þcosh þþ Dp Lp Lp

Eq. (20) can be written as: þþ

þþ

n n JphEðat BÞ ¼ JphE;0  þþ

n ¼ JphE;0 

þþ

  qDþþ p Fnþþ Sp Lþþ p

þþ

n n JphEðat CÞ ¼ JphEðat BÞ

 Dpþþ ðat BÞ

  qNdþþ Seff;nþ nþþ Sp Ndþ

 Dpþþ ðat BÞ

(21)

þþ

n þþ JphEðat BÞ ¼ qSeff;nþþ nþ Dpðat BÞ

(22)

Substituting Eq. (22) into Eq. (21) gives: þþ

" Dpþþ ðat BÞ ¼ q

n JphE;0

Ndþþ Ndþ

#

(23)

Seff;nþ nþþ þ Seff;nþþ nþ þþ

n By combining Eqs. (22) and (23), we can rewrite JphEðat in BÞ a more explicit form as:

(26)

Finally, we should consider the recombination loss in the poly nþþ collected at the depletion region z ¼ D emitter. The hole current JphE is easily derived as [20]

þþ

n where JphE;0 refers to the hole light-generated current density in the ¼ 0, and Seff,nþnþþ to the PS region collected at z ¼ B when Dpþþ ðat BÞ nþþ can be obtained if Dpþþ ERV given by Eq. (8). The value of JphEðat ðat BÞ BÞ is known. For the boundary condition at z ¼ B, we also have:

(20)

nþþ JphE

¼ FPSPoly

! We nþþ sin h þ JphE;0 Lp

(27)

Eq. (27) gives the final expression of the contribution of lightgenerated holes current in the PS region. 2.2.2. Polysilicon emitter light-generated current density The current continuity equation for minority carriers, generated by a monochromatic light in polysilicon emitter region (nþ), is given as follows:

d2 Dpþ ðz; lÞ Dpþ ðz; lÞ 1  ¼  þ gðz; lÞ þ2 D dz2 Lp p

(28)

þþ

n JphE;0

þþ

n JphEðat BÞ ¼

1þ

þþ

Ndþþ Seff;nþ nþþ

n ! ¼ FPSPoly  JphE;0

(24)

Ndþ Seff ;nþþ nþ

where FPS-Poly is the porous-poly factor given by:

FPSPoly ¼

1þ

Ndþþ Seff;nþ nþþ Ndþ Seff ;nþþ nþ

!1 (25)

where Dpþ is the light-generated excess hole concentration. Lþ p and Dþ p represent the hole diffusion length and coefficient in the polysilicon emitter, respectively. The term g(z,l) is the generation rate of minority carriers (hole) in this region, given by:

gðz; lÞ ¼ ½1  RðlÞfðlÞaðlÞ exp



 a* ðlÞWPS

 exp ½  aðlÞ ðz  WPS Þ

(29)

A. Trabelsi / Renewable Energy 50 (2013) 441e448

Using the following boundary conditions:

The light-generated electron current density in the base region is given by:

Dpþ ðz ¼ W1 Þ ¼ 0 ðat z ¼ DÞ

(30)

dDpþ ¼ Seff;nþ nþþ Dpþ Dþ p dz

(31)

ðat z ¼ CÞ

JphB ¼

Zd=2

qDn d2

nþþ JphEðat BÞ

¼

qð1  RÞafLþ p

aLþ p 1 2

6

6 6 * exp a WPS 6 6 4

Seff;nþ nþþ Lþ p Dþ p

! þ

aLþ p

Zd=2

d=2 d=2

the solution of the current continuity equation (Eq. (28)) is given by:

2

445

"

 dDn dx dy dz z¼W2

Seff;nþ nþþ Lþ p

We  exp ðaWe Þ cos h þ Dþ Lp p ! ! Seff;nþ nþþ Lþ We We p sin h þ þ cos h þ Dþ Lp Lp p 3

!

We þ sin h þ Lp

(41)

!#

7

7 7 * a exp  W  aLþ PS 7 p 7 5

(32)

2.3. Contribution of the base to the IQE

The solution of the three-dimensional current continuity equation with respect to the above boundary conditions can be written as follows:

The contribution of the base to the IQE of the cell with porous silicon IQEB(a) can be written as:

JphB ¼

IQEB ðaÞ ¼

JphB qð1  RÞf

(33)

where JphB is the light-generated electron current density in the base region obtained from solving the continuity equation for minority carriers (electron) in the p-type region, given by the following expression [8]:

6 þ 6 4aLp exp½ aðWe þWÞ

d2 Dnðx; y; z; lÞ d2 Dnðx; y; z; lÞ d2 Dnðx; y; z; lÞ Dnðx; y; z; lÞ þ þ  dx2 dy2 dz2 L2n 1 ¼  gðz; lÞ ð34Þ Dn




 Seff;ppþ Ln  aLn exp½ aðW3 WPS Þ Dn þ 

Seff;ppþ Ln Wb Wb þcosh sinh Dn Ln Ln 
3 
Seff;ppþ Ln Wb Wb þsinh exp½ aðWe þWÞ cosh 7 Dn Ln Ln 7  

5 Seff;ppþ Ln Wb Wb þcosh sinh Dn Ln Ln

The boundary conditions in the z-direction are given by:

Dnðx; y; z ¼ W2 Þ ¼ 0 ðat z ¼ EÞ  Seff;ppþ dDn Dnðx; y; z ¼ HÞ ¼ dz z¼H Dn

(35) ðat z ¼ FÞ

qð1RÞfaLn

exp a* WPS d2 a2 L2n 1 " #"   # 8sin2 Cj d=2 8sin2 ðCk d=2Þ    2 Ck dþCk sinðCk dÞ Cj2 dþCj sin Cj d 2

(36)

where the EVR Seff,ppþ is given by [20]:

Seff;ppþ

Na Dþ ¼ þ nþ  Fpþ ðSn Þ Na Ln

(42) (37)

where:

! ! Sn Lþ WBSF WBSF n þ sin h cos h Dþ Lþ Lþ n n n ! ! Fpþ ðSn Þ ¼ Sn Lþ W W BSF BSF n þ cos h sin h Dþ Lþ Lþ n n n

(38)

The boundary conditions in the x and y directions are given by:


 Vg dDn d Dn u ¼ ; z ¼   2Dn du u¼ d 2

ðu ¼ x or yÞ

(39)

2


 Vg dDn d D ¼ n u ¼  ; z 2Dn du u¼d 2 2

ðu ¼ x or yÞ

(40)

with Ck and Cj being the eigenvalues for the eigenfunction used for the x and y directions, respectively. These coefficients are the solutions of transcendent equation:

tan


 Vg Cl d ¼ 2Cl Dn 2

ðl ¼ j or kÞ

(43)

2.4. Contribution of the depletion region to the IQE The contribution of the depletion region to the IQE of the cell with porous silicon IQED(a) can be written as:

IQED ðaÞ ¼

JphD qð1  RÞf

(44)

446

A. Trabelsi / Renewable Energy 50 (2013) 441e448

where JphD is the light-generated current density in the depletion region. It is obtained, assuming that all carriers generated within this region are collected, and given by:



*

JphD ¼ qð1RÞf exp a W1 expðaWe Þ½1exp ðaWÞ

Without PS layer

Internal Quantum Efficiency



0.8

(45)

3. Results and discussion 3.1. Effect of the grain boundaries recombination on internal quantum efficiency

With PS layer 0.6

IQE B IQE E

0.4

0.2

The recombination velocity at the grain boundaries and grain widths are two important parameters that can affect the internal quantum efficiency of polysilicon solar cells. The impacts exerted by the recombination velocity at the grain boundaries and grain width on IQE are illustrated in Fig. 2(a) and Fig. 2(b), respectively. The findings reveal that, for the recombination velocity at same the grain boundaries (Fig. 2(a)) and the same grain width (Fig. 2(b)), the internal quantum efficiency of the solar cell with PS emitter is higher than that of conventional one, particularly for shortwavelengths (l < 0.6 mm). This is due to the PS layer that allows for the conversion (with certain efficiency) of ultraviolet (UV) and blue light into longer absorbable wavelengths (in the red region). This may generate an additional photocurrent, in the UV and blue part of the solar spectrum, which may improve the internal quantum efficiency in this spectral region. In fact, when the reduction of recombination velocity at the grain boundaries and the rise of the grain width increase the photocurrent density, the IQE will be improved. Furthermore, the theoretical results obtained through our model (when Vg ¼ 102 cm s1) shown in Fig. 2(a) are noted to be in good agreement with the experimental results previously reported by Strehlke et al. [13], which provides further support for the validity of the approach presented in our work.

energy, on the other hand, the absorption coefficients are also smaller, which leads to a higher generation rate in the base and, hence, to a higher contribution from this region to the IQE (IQEB > IQEE and IQEB > IQED). These findings are in consistency with the ones previously reported in theoretical results of Yang et al. [21]. Furthermore, while the use of the PS layer is noted to affect the contribution of the emitter IQEE, particularly for l < 0.6 mm, it exerted no effect on the contribution of the base IQEB and depletion IQED regions. The improvement of the total internal quantum efficiency is, therefore, attributed to the contribution of the emitter, which is increased by the use of a PS layer.

3.2. Contribution of different regions of the cell to the IQE

3.3. Effect of the polysilicon emitter on the IQE

Fig. 3 shows the contribution of different regions to the IQE for both cells, with and without the PS layer. It can be noted that, for photons with higher energy (l < 0.4 mm), the contribution of the emitter to the IQE is higher than those of the base and the depletion regions (IQEE > IQEB and IQEE > IQED). This contribution is attributed to a greater absorption for those photons, which leads to a higher generation rate in the region. For photons with smaller

Fig. 4(a) and (b) show the effect of the thickness and the doping level of the polysilicon emitter on the IQE, respectively. Fig. 4(a) clearly demonstrates that the IQEs of both cells, with and without PS layer, decrease in the short-wavelength range when the polysilicon emitter thickness increases. This can be attributed to the significant decrease in the contribution of the base compared to the increase in the contribution of the emitter to the IQE. Fig. 4(b), on

0.0 0.4

0 .8

0 .6

Experiment 2

-

Theorie: V = 10 cms

Théorie: V = 104 cms-

0 .4

Without PS layer With PS layer

0 .2

0 .0 0 .4

0 .5

0 .6

0 .7

0 .8

Wavelengths (µm)

0 .9

1 .0

1 .1

0.6

0.7

0.8

0.9

1.0

1.1

Fig. 3. Contribution of different regions to the IQE for both cells, with and without PS emitter.

b

1 .0

0.5

Wavelengths (µm)

Internal Quantum Efficiency

Internal Quantum Efficiency

a

IQE D

1.0

0.8

d = 250 µm

0.6

d = 150 µm d = 50 µm

0.4

Without PS layer 0.2

With PS layer

0.0 0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Wavelengths (µm)

Fig. 2. (a) Effect of recombination velocity at the grain boundaries on the IQE for both cells, with and without PS emitter. (b) Effect of grain width on the IQE for both cells, with and without PS emitter.

A. Trabelsi / Renewable Energy 50 (2013) 441e448

a

b

1.0

447

1.0

With PS layer

Internal Quantum Efficiency

0.8

Internal Quantum Efficiency

With PS layer Without PS layer

0.6

0.4

We = 0.3 µm We = 0.4 µm

0.2

We = 0.5 µm

0.6

0.4

Nd+ = 1018 cm-3 Nd+ = 5.1018 cm-3 0.2

0.0

0.0 0.4

0.5

0.6

0.7

0.8

0.9

1.0

Without PS layer

0.8

1.1

Nd+ = 1019 cm-3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Wavelengths (µm)

Wavelengths (µm)

Fig. 4. (a) Effect of polysilicon emitter thickness on the IQE for both cells, with and without PS emitter. (b) Effect of doping level of the polysilicon emitter on the IQE for both cells, with and without PS emitter.

b

1 .0 With PS layer

0 .8

Internal Quantum Efficiency

Internal Quantum Efficiency

a

Without PS layer

0 .6

0 .4 Without PS layer WPS = 0.05 µm

0 .2

WPS = 0.1 µm

1 .0

0 .8

0 .6

0 .4

Without PS layer Nd++ = 1019 cm-3 Nd++ = 5.1019 cm-3

0 .2

Nd++ = 1020 cm-3

WPS = 0.15 µm

0 .0

0 .0 0 .4

0 .5

0 .6

0 .7

0 .8

0 .9

1 .0

1 .1

0 .4

0 .5

0 .6

0 .7

0 .8

0 .9

1 .0

1 .1

Wavelengths (µm)

Wavelengths (µm)

Fig. 5. (a) Effect of PS emitter thickness on the IQE for both cells, with and without PS emitter. (b) Effect of doping level of the PS emitter on the IQE for both cells, with and without PS emitter.

the other hand, shows that the IQE has improved considerably by reducing the doping level of the polysilicon emitter, especially for a cell with PS layer. 3.4. Effect of the PS emitter on the IQE Fig. 5(a) and (b) show the effect of the thickness and the doping level of the PS emitter on the IQE, respectively. They also illustrate the IQE of a cell without PS layer. It can be noted from Fig. 5(a) that the improvement of the IQE decreases with the increase of the PS thickness from 0.05 mm to 0.15 mm due to the absorption of the short-wavelength light in the PS front region. Fig. 5(b) illustrates the impact of the PS emitter doping level on the IQE. Contrary to the effect of the PS thickness, IQE can be noted to undergo a significant 20 3 improvement when a heavily doped PS emitter (Nþþ d ¼ 10 cm ) is used.

of equations for the internal quantum efficiency of the cell under the effect of the PS emitter is solved analytically. The findings demonstrate that the use of the PS layer as an antireflective coating enhances the IQE of the cell as compared to the conventional solar cell. Moreover, for photons with higher energy, most of the contribution is noted to come from the emitter. For photons with smaller energy, however, this contribution is observed to come from the base. Moreover, IQE of the cell is noted to increase with decreased PS thickness and with heavily doped PS emitter. Acknowledgments The author wish to express his gratitude to Mr. Anouar Smaoui from the English Section at the Sfax Faculty of Science for carefully proofreading the manuscript of the current paper. References

4. Conclusion The present paper provides an analytical model that has been developed to simulate the potential of porous silicon used as an antireflective coating in thin polysilicon solar cells. A complete set

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