Optimal optical design of thin-film photovoltaic devices

Optimal optical design of thin-film photovoltaic devices

Solar Energy Materials and Solar Cells ELSEVIER Solar Energy Materials and Solar Cells 49 (1997) 163-169 Optimal optical design of thin-film photov...

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Solar Energy Materials and Solar Cells

ELSEVIER

Solar Energy Materials and Solar Cells 49 (1997) 163-169

Optimal optical design of thin-film photovoltaic devices Furong Zhu a'b'*, Philip Jennings a'b, John Cornish a'b, Glenn Hefter a'b, Kazimierz Luczak a'b aAm-Si Pty Ltd, 16 Emerald Terrace, West Perth, WA 6872, USA b Department of Physics and Energy Studies, Murdoch University, Murdoch WA 6150, Australia

Abstract In this paper we report the results of an effort to develop a design tool to optimise any solar cell with thin-film structure. An optical admittance analysis which takes into account the interference effects in the multilayer thin-film system is discussed. This method provides a technique for calculating the optical properties of a thin-film device with a multilayer configuration. It also allows us to explore the nature and magnitude of optical losses in p - i - n type single or multi-junction a-Si : H solar cells, and to optimise the structure of such cells to utilise enhanced interference effects to obtain the maximum possible utilisation of incident solar radiation. Keywords: Optical design; Thin films

1. Introduction Research into d e v e l o p i n g low cost, a m o r p h o u s silicon (a-Si) a n d its a p p l i c a t i o n s has e x p a n d e d rapidly. Extensive research efforts have resulted in a significant i m p r o v e m e n t in the p e r f o r m a n c e of a-Si : H solar cells. The low m a t e r i a l cost a n d ease of m a n u f a c t u r e of a - S i : H solar cells with single or m u l t i - j u n c t i o n structure m a k e t h e m ideally suited to low-cost terrestrial p h o t o v o l t a i c applications. The c u r r e n t m u l t i - j u n c t i o n p - i - n devices p r e p a r e d using m u l t i - c h a m b e r t e c h n o l o g y p r o v i d e an

* Corresponding author. 0927-0248/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PII S 0 9 2 7 - 0 2 4 8 ( 9 7 ) 0 0 19 1-8

164

F. Zhu el al. Solar EneJxv Materials am/5'olaf Cell~ 49 (1997) 163 169

opportunity to commercialise the cost-effectivc a-Si: H solar module for large-scale grid connected and remote area power supply systems. In order to achieve a better cell performance, the precise cell designs based on the knowledge of the optoelectronic properties of the material are important. The attempt to improve the conversion efficiency and the stability of the p i-n type devices has attracted considerable effort to optimise the structure of the devices. An a-Si : H solar cell can be considered generally as a thin-film system with a multilayer configuration. A number of studies of the optical properties of thin-film solar cells using different approaches have been suggested [1,2]. In this paper we report the development of a design tool to optimise solar cells with thin film structures. The procedure is based on an optical admittance analysis which takes into account the interference effects in the multilayer thin-film system. This enables calculation of the optical properties of a thin-film device with a multilayer configuration. It also allows us to optimise the structure of such cells and utilise interference effects to maximise usage of incident solar radiation.

2. Method Any thin-film solar cell can bc considered generally as a multilayer system composed of materials with different optoelectronic properties. For example, a thin-film photovoltaic device has m layers, the effective optical admittance. Ym, of this multilayer structure call be defined as y m = C/B, where B and C can be determined by solving the following characteristic matrix equation given by [3, 4]

(;):In (co,,,,

L_j= 1 \i~,'i sin 3 i

cos b i

)

(I)

/ J \ v , , , + i.

where y j and .Vm+1 are the admittance of the jth layer and substrate, respectively. I is the unit matrix, (5i is the angular phase given by 2rcN id i cos 0

6,

2

(2)

where d.i is the actual thickness o f t h e j t h layer in this m layered structure, and N j is the corresponding complex refractive index given by Nj = nj~) - ikj(),). Where nj(),) and kj{,:,) are real and imaginary parts of N j, respectively. The characteristic matrix Eq. (1) takes into account the effect of the multiple reflections in a multilayer structures. Using the value y~.- calculated from an m layered thin film system, the total reflectance, R(2), can be then obtain as [4, 5]

R(2)=

Ni))-Yets2

(3)

+ v,,ffI

where No is the refractive index of air. The reflectance thus obtained depends on the wavelength of the incident radiation. Assuming normal incidence, the total

F. Zhu et al./Solar Energy. Materials and Solar Cells 49 (1997) 163 169

165

transmittance, T(2), can be expressed as [4, 5] m

T(2) = [1 -- R(2)] 1-[ Oj,

(4)

j=l

where ~k2 is the ratio of the time average numerical magnitude of the Poynting's vector at the jth and (j - 1)th boundaries, and it is given by [4, 5] Re(Yj+ 1) . 2' ~'J = Re(Yj)lcos 6~ + Yj+ i sin 6j/NjI

(5)

where Re(Yj+I) and Re(Yj) represent the real parts of effective admittance for (j + 1)th, Yj+I, and jth, Yj, layers, respectively. The total absorbance A(2) in this m multilayer system can be calculated from the following expression I-4, 5] A(2) = 1 - T(2) - R(2).

(6)

Similarly, the net absorbance of any individual layer, for instance the absorbance in the ith layer Ai(2), in this m-layered structure can be determined by [5] i--1

Ai(2) = [1 -- R(2)] [1 -- ~h,(£)] H •j(2).

(7)

j=l

Using the flux of the incident solar radiation F(2), measured in W m - 2 gm-1, the integrated absorbance of any individual layer, Ai, and the total absorbance of an m-layered system, can be calculated as [4, 5] /1/_ fAI(2)F(2) d2 fF(2) d2

'

(8)

A~(2)F(2) d2 A-

(9)

F(~) d2 The results of the overall device design of a-Si : H solar cells are to maximise the efficiency and minimise the photo-degradation. It has been found that an effective way to improve the stability of a-Si : H solar cells is to use the multi-junction structure which consists of two or three p-i-n single junctions. This allows each p-i-n junction to respond actively to the different parts of the incident solar radiation. Thus, the thickness of the i-layer in each p-i-n junction can be produced so that a high electric field can be maintained across the i-layer. The thickness of the i-layer in the multijunction a - S i : H solar cell can be optimised through maximising the integrated absorbance of the i-layer and the total absorbance of a cell. Ai and A calculated from Eqs. (8) and (9) provide a way to optimise the thickness of the cell through maximising the integrated absorbance of the cells. An optimal structure of a thin film solar cell

166

F. Zhu et al. S o l a r EnerLg, Material.s and 5'o/at ('ells 49 (1997) 163 169

thus designed will be very useful in the fabrication of such cells with multi-junction configuration.

3. Results and discussion We have applied this a p p r o a c h to study the optical properties of typical singlejunction and dual-junction a-Si: H solar cells of the type: g l a s s / T C O / p i n / T C O / metal, and g l a s s / T C O / p i n/p-i n/metal, respectively. The silver, aluminium and T C O / m e t a l , as rear contact are analysed. The optical constants n(,;t) and k(),) used for metals, T C O , p-, i- and n- type layers of a-Si : H materials in the single-junction and multi-junction solar cells are taken from published experimental results [6, 7]. In a single-junction cell, we have calculated the spectral absorbance, A(2), of the two typical single-junction cells with the structures of g l a s s / T C O / p i n/Al and glass/ T C O / p i n/TCO/A1 as a function of wavelength, ,~.. The results are shown in Fig. 1, where A().) is plotted as a function of ), for both cells containing 0.5 btm thick i-layer. The dashed curve in Fig. 1 is calculated from a cell with an AI rear contact, and the solid curve in Fig. 1 is obtained from a cell with TCO/A1 back contact. It appears that in the short-wavelength region, for instance ), ~< 0.55 tam, the calculated A().) of the two cells are almost the same. This is because most incident photons with high energies are absorbed before reaching the back contact. In the longer-wavelength region, 2 >~ 0.6 ILtm, it is found that absorbance peaks in A().) of a cell with a T C O / A I back contact show a red shift in positions c o m p a r e d to that of a cell with only a metal contact. F r o m this analysis, it is obvious that the c o m b i n e d T C O / m e t a l as back contact will mainly affect the A(,)3 of the cell in the long-wavelength region. It is well known that the spectral absorbance in the long wavelength region is important for the i m p r o v e m e n t of photo-current. F r o m an optical point of view, we can optimise the

1

F

I

I .....

I

I

E-

\[ UomaL I

,-¢,

iii~

--

--

"i

J

i

~'t

,m

0.5

0.4

0.6

0.8

1

Wavelength (gin) Fig. 1. Spectral absorbance, A(2), as a function of wavelength, )_

F. Zhu et al. / Solar Energy Materials and Solar Cells 49 (1997) 163-169

167

interference peaks to achieve the maximum absorption by choosing an appropriate i-layer thickness and back contact to boost the internal reflection and hence enhance the spectral absobance of the cell in the long-wavelength region. In order to understand and to choose the thickness of the bottom TCO layer in a combined rear TCO/metal contact, we have also calculated the integrated absorbance of cell as a function of the thickness of the bottom TCO layer for three different cells with i-layer thickness equal to 0.4, 0.5 and 0.6 pm. The calculated results are given in Fig. 2. They show that the integrated absorbance of three different cells have similar structures in relation to the bottom TCO thickness. The relative maximum absorption peaks are located over the TCO thickness regions 0.05-0.091am and 0.25-0.28 I.tm. For a cell with an i-layer equal to 0.5 lam the results show that the bottom TCO thickness can be chosen as 0.05 I~m to enhance the A(2) in the longwavelength region. Integrated absorbance A as the function of i-layer thickness for three different cells with A1, TCO(0.05 lam)/A1 and TCO(0.25 lam)/A1 back contacts are also calculated. Results are plotted in Fig. 3. The actual TCO is also an absorbing layer, 0.25 p.m thick rear TCO layer may not increase the absorption in the i-layer effectively as a thick TCO layer will also absorb the light. From Fig. 3, it appears that a single p - i - n junction a-Si: H solar cell with TCO(0.05 I.tm)/A1 back contact has a higher i-layer absorbance in comparison with that of one with A1 or TCO(0.25 I.tm)/A1 as the contact electrode. For example, considering an i-layer thickness of 0.45 I~m, shown in Fig. 3, the integrated absorbance of a cell with an optimal bottom TCO layer thickness is about 4% higher than that of a similar cell with glass/TCO/p-i-n/A1 structure. This is due to the combined highly reflecting rear contact of TCO/A1 which boosts the internal reflection and hence enhances the effective absorbance in the active layer.

0.5~

o

0.5 z

'

I

'

t

'

I

X

'

I

'

di = 0.6~tm k

e,..o

0.52

di = 0.5~m •,

o

.""

"'-,.

.....

- .....

..,

0.50

.= 0.48

0"4601llllllllo.2

0.4

Thickness of bottom TCO layer (lam) Fig. 2. Integrated absorbance as a function of the thickness of rear TCO layer.

F. Zhu el al. ,'Solar Energy/vlaterials and Solar Cells 49 (1997) 163 l~59

168

I

I

I

I

~

I ,..°°

,"

.j"

.~-E. 0.5 o

,->,

~, 0.4

~

'( ) , ( U ~ 5 ~ t m g A I

J

0.3'

-

L 0.2

-

i

-

I~.'~)qG25mndAI

I 0.4

;

I 0.6

}

Thicknes~ of ~ layer (bun)

Fig. 3. Integrated absorbance as a function of the i-layer thickness.

1.0

I

Total

<

0.8 /

¢3

0.6

Top cell

© ,,:~C

..O

<

04

/ o d.)

0.2

c/?

/

\

Bottom cell

\,_.

/, i-

0.0 0.4

0.5

06

0.7

0.8

Wavelength (btm) Fig. 4. Spectral absorbance as function o f ) (a-Si : H /p i n (a-SiGe : HI/Ag.

lor a dual cell ~,ith the configuration of

glass/TCO/p-i

n

We have also applied the present method to a multi-junction cell with the configuration of glass/TCO/p i-n(a-Si: H)/p i-n(a-SiGe : H)/Ag. The spectral absorbence of the top and bottom cells in this structure are shown in Fig. 4. It is found that the spectral absorbance of the top cell is mainly dependent on the thickness of its active

F. Zhu et al./Solar Energy. Materials and Solar Cells 49 (1997) 163 169

169

layer and that of the b o t t o m one depends on both the thickness of the a-SiGe : H layer, the active layer of the bottom cell, and the type of back contact. This is because the highly reflecting rear contact enhances the interference effect, and thus increases the spectral absorption in the long-wavelength region. Our calculations implies that the use of a highly reflecting rear contact will improve the spectral absorbance of the dual-junction cell mainly in the long-wavelength region. In the design of multi-junction solar cells, the requirement of photo-current matching depends not only on the fitness of the combinations of optical energy gaps for the cells that may yield m a x i m u m conversion efficiencies, but also on the suitable ranges of optimal thicknesses of the cells which will give the m a x i m u m spectral absorbance. The choice of optical energy gaps and thicknesses for an optimal design of any multi-junction cell at particular solar radiation condition is very important. The optical admittance analysis developed in this paper provides a way to design any thin-film optoelectronic device with multilayer configuration in an optimal structure.

4. Conclusions An optical admittance analysis is developed to study the optical properties of any thin-film device with a multilayer configuration. This method provides a way to optimise the structure of thin-film solar cells to utilise the enhanced interference effects to obtain m a x i m u m utilisation of incident solar radiation.

References [1] R. Saeng-Udom, W. Kusian, B. Bullemer, Proc. 10th EC-PVSEC, 8-12, April, Lisbon, 1991, p. 212. [2] R.E. Rocheleau, M. Vierthaler, Proc. 1st WCPEC, 5-9 December Hawaii, 1994 p. 567. [3] R.E. MacLeod, Thin-film Optical Filters, 2nd ed. Adam Hilger, Bristol, 1986, p. 15. [4] F. Zhu, J. Singh, J. Non-Crystal Solids 152 (1993) 75. 1-5] F. Zhu, J. Singh, Sol. Energy Mater. and Sol. cells 31 (1993) 119. 1-6] American Institute of Physics Handbook, 3rd ed. McGraw-Hill, New York, 1977, p. 136. I-7] K.L. Eskenas, S.C.Miller, in: Proc. 20th IEEE Photovoltaic Specialists Conf., Las Vegas, NV, September 1988, p. 176.