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Analytical solution for haze values of aluminium-induced texture (AIT) glass superstrates for a-Si:H solar cells

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Abstract

Light scattering at randomly textured interfaces is essential to improve the absorption of thin-film silicon solar cells. Aluminium-induced texture (AIT) glass provides suitable scattering for amorphous silicon (a-Si:H) solar cells. The scattering properties of textured surfaces are usually characterised by two properties: the angularly resolved intensity distribution and the haze. However, we find that the commonly used haze equations cannot accurately describe the experimentally observed spectral dependence of the haze of AIT glass. This is particularly the case for surface morphologies with a large rms roughness and small lateral feature sizes. In this paper we present an improved method for haze calculation, based on the power spectral density (PSD) function of the randomly textured surface. To better reproduce the measured haze characteristics, we suggest two improvements: i) inclusion of the average lateral feature size of the textured surface into the haze calculation, and ii) considering the opening angle of the haze measurement. We show that with these two improvements an accurate prediction of the haze of AIT glass is possible. Furthermore, we use the new equation to define optimum morphology parameters for AIT glass to be used for a-Si:H solar cell applications. The autocorrelation length is identified as the critical parameter. For the investigated a-Si:H solar cells, the optimum autocorrelation length is shown to be 320 nm.

© 2013 Optical Society of America

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Figures (9)

Fig. 1
Fig. 1 Schematic drawing illustrating a haze measurement setup with an integrating sphere. The opening angle of the haze measurement is 2Δθ. The coherently transmitted light and parts of the incoherently transmitted light fall within the cone of the opening angle and thus escape from the integrating sphere.
Fig. 2
Fig. 2 AFM images of the four investigated AIT samples. The rms roughness ( σ r m s ) of each sample was calculated based on the height distribution and is shown in the image. Note that samples AIT-3 and AIT-4 have the same σ r m s but different morphology.
Fig. 3
Fig. 3 ARS of the transmitted light for the samples shown in Fig. 1, at λ = 620 nm.
Fig. 4
Fig. 4 Simulated haze in transmission for four AIT samples. The symbols show the measured haze, while the lines show the simulated haze using the calculated ARS of the samples. a) Samples AIT-1 and AIT2 with different σrms ; b) Samples AIT-3 and AIT-4 with the same σrms.
Fig. 5
Fig. 5 Haze in transmission for the four AIT samples of Fig. 2. The symbols show the measured data, while the lines show the haze calculated from Eq. (3).
Fig. 6
Fig. 6 Measured power spectral density (symbols) of the four investigated AIT samples and, as a reference, of a textured AZO sample. The lines are fitted PSD functions using Eq. 10(a).
Fig. 7
Fig. 7 a) Calculated fit factor C(λ) using Eqs. (7) and (12) b) Relevant roughness values σ r e l ( λ ) , using Eq. (13).
Fig. 8
Fig. 8 Haze calculated using Eq. (14). Here, both the incoherent light scattered inside the opening angle of the haze measurement as well as the relevant roughness for the scattered wavelength are considered.
Fig. 9
Fig. 9 Calculated haze values at λ = 650 nm as a function of intrinsic roughness σint and autocorrelation length. Graphs show the transmission haze value of a) glass (n1 = 1.5) into air (n2 = 1), and b) AZO (n1 = 2) into a-Si:H (n2 = 4).

Tables (2)

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Table 1 Sample preparation conditions

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Table 2 Surface characteristics of the samples shown in Fig. 2

Equations (16)

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H T = 1 T c o h e r e m t T t o t a l
H T1 = 1 T total 2π Δθ π 2 ARS( θ )Sinθdθ
H T2 =1exp[ ( 2π σ rms ( n 1 n 2 ) λ ) 2 ]
H T3 =1exp[ ( 2π σ rms C( λ )( n 1 n 2 ) λ ) m ]
H T4 =1exp[ 4 π 2 ε 1 ( σ rms λ ) 2 × { ε 2 ε 1 1 } 2 ×{ 12 ε 2 G( l ) λ SinΔθ } ]
G( l )= 1 2Δq Δq Δq PS D 1D ( q )dq
C( λ )= 12 n 2 G( l ) λ SinΔθ
σ rel 2 ( λ )=2π f=0 1 λ PSD( f )fdf
PSD( f )= A [ 1+ ( Bf ) 2 ] ( C+1 ) 2
PS D 2D ( f )= 2π σ int 2 l 2 [ 1+ ( 2πlf ) 2 ] 3 2
PS D 1D ( f x )= 4 σ int 2 l 1+ ( 2πl f x ) 2
ACV( τ )= σ int 2 exp( τ /l )
σ int 2 =2π f=0 PS D 2D ( f )fdf
G( l )= 2 Δq tan 1 ( lΔq )
σ rel = σ int 1 1 1+ 4 π 2 l 2 λ 2
H T4 =1exp[ 4 π 2 ε 1 ( σ int λ ) 2 ×{ 11/ 1+ 4 π 2 l 2 λ 2 }× { ε 2 ε 1 1 } 2 ×{ 12 ε 2 G( l ) λ SinΔθ } ]
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