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Absorption coefficient modeling of microcrystalline silicon thin film using Maxwell-Garnett effective medium theory

Sheng-Hui Chen, Hsuan-Wen Wang, and Ting-Wei Chang

Open Access Open Access

Abstract

Considering the Mott-Davis density of state model and Rayleigh scattering effect, we present an approach to model the absorption profile of microcrystalline silicon thin films in this paper. Maxwell-Garnett effective medium theory was applied to analyze the absorption curves. To validate the model, several experimental profiles have been established and compared with those results from the model. With the assistance of the genetic algorithm, our results show that the absorption curves from the model are in good agreement with the experiments. Our findings also indicate that, as the crystal volume fraction increases, not only do the defects in amorphous silicon reduce, but the bulk scattering effect is gradually enhanced as well.

©2012 Optical Society of America

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Figures (6)
Fig. 1
Fig. 1 Flow chart of the process.

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Fig. 2
Fig. 2 Example of constructed DOS distributions of the a-Si with Nd 4 × 1017cm−3eV−1.

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Fig. 3
Fig. 3 Absorption spectrum of a-Si with mobility gap 1.8eV and Nd 4 × 1017 cm−3eV−1.

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Fig. 4
Fig. 4 Absorption spectra measured by CPM and the modeling curves fitted by the genetic algorithm for the eight samples. (a)XC = 41.2%, (B) XC = 42.5%, (c) XC = 53.4%, (d) XC = 56.7%, (e) XC = 57.4%, (f) XC = 58.5%, (g) XC = 60.8%, (h) XC = 63.4%.

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Fig. 5
Fig. 5 Correlation between amorphous defects and crystalline volume fraction.

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Fig. 6
Fig. 6 Correlation between scattering factor and crystalline volume fraction.

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Tables (1)

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Table 1 Parameters of DOS Model

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Equations (8)

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α(hυ)= K hυ ∫ N i (E)f( E ) N f (E+hυ)[ 1−f( E+hυ ) ]⋅d(E) ,
N D (E)= N d exp( | E | 2 2 W 2 ),
N D = ∫ 0 E g N D (E)dE
4 π 2 D 2 15 λ 2 ( ε+4 )( ε+2 ) ( 2ε+3 ) ≪1
ε ˜ μc MG ( E )= ε ˜ a ( E ) ε ˜ C ( E )+2⋅ ε ˜ a ( E )+2⋅Xc⋅[ ε ˜ C ( E )− ε ˜ a ( E ) ] ε ˜ C ( E )+2⋅ ε ˜ a ( E )−Xc⋅[ ε ˜ C ( E )− ε ˜ a ( E ) ] ,
ε ˜ a ( E )=[ n a−Si ( E ) 2 − κ a−Si ( E ) 2 ]+i[ 2 n a−Si ( E ) κ a−Si ( E ) ]
ε ˜ C ( E )=[ n C−Si ( E ) 2 − κ C−Si ( E ) 2 ]+i[ 2 n C−Si ( E ) κ C−Si ( E ) ]
α μc MG ( E )= 4πE hc { [ ε μc Re ( E ) 2 + ε μc Im ( E ) 2 ] 1 2 − ε μc Re ( E ) 2 } 1 2 ,
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