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Accurate Data Extraction Approach for Absorption Coefficient Calculation in
Solar Cell Application
Conference Paper · May 2018
DOI: 10.1109/ICOEI.2018.8553698
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Proceedings of the 2nd International Conference on Inventive Computation Technologies ( ICICT 2017)
IEEE Xplore Compliant - Part Number:CFP17K52-ART, ISBN:978-1-5090-6697-1
Accurate Data Extraction Approach for
Absorption Coefficient Calculation in Solar Cell
Application
Somnath Biswas1, * and Somenath Chatterjee2
1
2
Wells Fargo India Solutions, Embassy tech village, Devarabisanahalli, Bellandur, Bengaluru, Karnataka, India
Center for Material Science and Nanotechnology, Sikkim Manipal Institute of Technology, Sikkim Manipal University,
Sikkim, India
*corresponding Author: som.biswas09@gmail.com
Abstract
Incident of light energy generates an electron-hole
pair in a solar cell. One of the parameters that affect
the generation of the electron-hole pair is absorption
coefficient. The absorption coefficient values
corresponding to the wavelength for different
materials are different. For theoretical analysis of
solar cell modeling, these values are very crucial;
however, the model equations are not sufficient for
extraction of absorption coefficient values for
different materials. In this paper, using
interpolation technique (Newton forward, Newton
backward and Lagrangian interpolation), a model is
proposed for generating absorption coefficient
1. Introduction:
The energy of a photon is integrated within a material,
usually by electronic polarization or by an electron
excitation event. Absorption of a photon may excite an
electron from the highest level of occupied valence band,
to move across the band gap, and place the electron into the
lowest empty state in the conduction band, which in turn
produces the electron-hole (e-h) pair. In a solar cell, the
interactions of semiconductor with light radiation (due to
the opacity of material) are significant phenomena for
generating the e-h pair. However, the efficiency is still
lower than optical absorption in the active layer because of
recombination losses [1]. When a monochromatic light is
incident on the surface (p-i-n structure) of a solar cell, a
certain fraction of incident energy will be reflected from
the surface and rest is transmitted inside the solar cell. The
intensity of the transmitted light energy decreases as it
passes through the same; the fraction of incident radiant
energy absorbed per unit mass or thickness of an absorber,
is defined as absorption coefficient [2]. To design a thin
film based solar cell using any solar cell based simulator,
values with the corresponding wavelength for solar
radiation. Accordingly, an absorption coefficient
calculator (ACC) is developed which provides
absorption coefficient values for a given wavelength.
One can use ACC to obtain absorption coefficient
values for a wide range of wavelength of solar
radiation. ACC can be used for materials like
crystalline, microcrystalline, nano-crystalline and
amorphous based Silicon materials and compound
semiconductors, like Gallium Arsenide, Copper
Indium Gallium Selenide, and Cadmium Telluride.
Keywords: Absorption coefficient calculator, solar
cell Modeling, Silicon thin film absorption
coefficient.
absorption coefficient values are very essential [3]. Photon
flux decreases exponentially with a travel distance of x and
can be written as [4]
 x   0 e  .x - - - - - (1)
Photon
absorption through intrinsic layer and consequently carrier
generation per unit volume is
G x  
- dΦx 
 α Φ0 e  α.x  α.Φx  - - - - - (2)
dx
the inverse of
average photon penetration depth. Several researchers
proposed different numerical model based interpretation for
different absorber layer of the solar cell [5-7]. However, the
inconsistency of the experimental results with the proposed
is stimulated for the current
interest. In this paper, A calculator is designed for finding
to a particular wavelength for
crystalline silicon (C:Si), amorphous silicon (A:Si),
microcrystalline silicon (µc:Si), nanocrystalline silicon
(Nc:Si), copper indium gallium selenide (CIGS), Cadmium
978-1-5090-6697-1/17/$31.00 ©2017 IEEE
689
Proceedings of the 2nd International Conference on Inventive Computation Technologies ( ICICT 2017)
IEEE Xplore Compliant - Part Number:CFP17K52-ART, ISBN:978-1-5090-6697-1
Telluride (CdTe) and gallium arsenide (GaAs). For this
purpose, we are using Newton forward interpolation,
Newton backward interpolation as well as Lagrangian
interpolation technique and generating the stream of data
based on experimental data points. To best of our
knowledge, the attempt to design an absorption coefficient
calculator with the accuracy of above- mentioned materials
is the first time.
2.
 (h )  h - E g  2  h - E g  2
Calculation of absorption coefficient:
In general abs
transmission and reflection measurements using the
following formula [8],
 
1 
T
ln 
d  (1  R) 2



 (3)
Where d, T, and R are the penetration depth, transmission
and reflection coefficients, respectively. The concept of
free carrier absorption is the presence of free electrons and
holes due to doping as well as fundamental absorption of
photons [9,10]. For those working with a simulation model,
various empirical equations have been suggested for
calculation of absorption coefficient for a different range of
spectrum. An empirical model for free carrier absorption in
silicon was suggested by Schroder. This model is valid
only for large wavelength, λ greater than 5000 nm [6]
  1 10
24
n  2.7  10
3
24
p - (4)
2
For solar cell application, one can consider the wavelength
of solar radiation which is near to the energy bandgap of the
materials used in solar cell. For this wavelength range it was
found Green’s model was better .Green’s model is given as
[6]:-
  2.6  10 18 n3  2.7 10 18 p2 - -(5)
is free carrier absorption coefficient in cm-1
n and p in cm-3.
Santbergen at al. [11] has used equation (5) with proper
values of n and p to show the absorber layer thickness
dependence dominancy for free-carrier absorption values.
There is not a single equation which can define both direct
band (GaAs) and indirect band gap (C-Si) semiconductors.
For direct band gap materials,
square root of the energy difference between the absorbed
photon and material bandgap [12]
 (h )  h  Eg 2 for h  Eg
1
Where,
is the energy of incident photon and E g is the
energy gap of the direct transition material. When incident
photon energy increases above Eg, photons are absorbed in a
thin layer surface of the material. However, for indirect
transition material, electron is transferred from valence to
conduction band (not align in the same wave vector k-space)
through absorption of a photon and emission/absorption of a
phonon following the energy and momentum conservation
laws [13]
 (6)
for h  Eg  (7)
The ħΩ is phonon energy of the material. Again Eqn. (7)
can be written in the following expression with the concept
of the Bose–Einstein statistics, a constant (A) and the
product of the density of states of initial and final state from
the initial to the final energy [13, 14].
First term of the expression is due to absorption and second
term corresponds to emission in semiconductors due to the
incident radiation.

Ah - E g   

e KT  1
2

Ah - E g   

2

1  e KT
for h  E g  (8)
All the above empirical equations suggest absorption
coefficient ( ) only for Silicon. However a better approach
is to collect the experimental data, which contains discrete
values and generate a continuous string of data using the
interpolation techniques. A computer program has been
written for the calculation of absorption coefficient for
different material including Silicon with the spectrum of
wavelength for solar cell radiation. In this program,
interpolation technique has been implemented for the
calculation of absorption coefficient ( ) for a particular
wavelength. The schematic diagram of detailed flowchart is
shown in fig. 1. Experimental data for different material was
obtained from different reported journals and those data
were used in interpolation method to find absorption
coefficient at any particular wavelength. In this aspect our
proposed method is showing best fit with experimental
curves. Different calculator based techniques are available
to find absorption coefficient with corresponding
wavelength. But their values are based on discrete values of
experimental data points as available in their database,
which becomes a problem for the user, who is working with
modelling for photovoltaic devices. Different generalised
equations have been proposed for the calculation for
absorption coefficient ( ). But they also either fail to
produce correct data or they do not cover the wide range of
spectrum.
978-1-5090-6697-1/17/$31.00 ©2017 IEEE
690
Proceedings of the 2nd International Conference on Inventive Computation Technologies ( ICICT 2017)
IEEE Xplore Compliant - Part Number:CFP17K52-ART, ISBN:978-1-5090-6697-1
3. Basic layout of Absorption Coefficient Calculator
Fig 2 shows the layout of the Absorption Coefficient
Calculator. Select the required material for which intrinsic
layer, absorption coefficient is required. There is an option
to select materials with defined wavelength range; one can
choose the absorber layer materials, as shown in fig. 2 (a).
Then enter the wavelength within the range specified and
the calculator will give the result for the corresponding
energy and absorption coefficient. The data is automatically
stored in data file, which is associated with the calculator. If
the wavelength entered is outside the range specified than it
will give its corresponding energy and for absorption
coefficient it will show “value beyond range” in the
calculator interface.
wavelength corresponding to solar radiation range is shown
in fig. 3. The plotted data are obtained using mentioned
equations (6) and (8), as well as experimental data Ref. [15]
with the data from ACC. One can notice that the result that
is being generated by our proposed calculator is much more
efficient/accurate than other model equations. We have
done the error calculation of our obtained ACC results with
the experimental data and 4.12% is observed.
4. Results and discussion
It is very much necessary to validate the result that is being
produced by the Absorption Coefficient Calculator (ACC).
The validation for this calculator is done by comparing the
result that is generated by the calculator and the
experimentally obtained data. This comparison is done by
plotting the graph for both the data against wavelength.
Figure 2: Absorption coefficient calculator (a)
Option/selection of intrinsic material (b) Calculation of
Absorption Coefficient for selected material within specified
spectral range.
4.2 ACC for Amorphous, Microcrystalline and Nanocrystalline Silicon intrinsic layer
ollected
from experimentally obtained graph from ref. [16] and [17].
Figure 4 is an evidence of validity of ACC with obtained
data for amorphous, microcrystalline and nanocrystalline
Silicon materials. It can be observed that the curve obtained
by ACC is similar to that of experimental curve, and in
proper range of wavelength. From figures 4 (a), (b) and (c),
one can noticed that microcrystalline and nanocrystalline
silicon films have lower optical absorption compared to the
amorphous silicon. Thus, light trapping is necessary to
extract photon energy efficiently in the earlier case.
Figure 1: Flow-chart used for applying the interpolation
technique of experimental obtained absorption coefficient
data with wavelength.
4.1 Validation of ACC for Crystalline silicon absorber
layer
978-1-5090-6697-1/17/$31.00 ©2017 IEEE
691
Proceedings of the 2nd International Conference on Inventive Computation Technologies ( ICICT 2017)
IEEE Xplore Compliant - Part Number:CFP17K52-ART, ISBN:978-1-5090-6697-1
data collected from mentioned references and our ACC
obtained
Figure 3: Comparison of obtained Absorption coefficient
values: experimental values from ref. [15], data from ACC,
applying model Eqns. (6) and (8).
Figure 5: Absorption coefficient spectra, obtained from
experimental data collected from references and data from
ACC for (a) CIGS, (b) CdTe, and (c) GaAs compound
semiconductor materials.
results for CIGS, CdTe and GaAs compound semiconductors,
respectively, as shown in figure 5. The ACC obtained data
are well-matched with the reported experimental data
considering from ref. [17,18], for CIGS, CdTe and GaAs
compound semiconductors.
Figure 4: Absorption coefficient (
from experimental data collected from references and data
from ACC for (a) Amorphous, (b) Microcrystalline, and (c)
Nano-crystalline phase of Silicon materials.
4.3 Validation of ACC for CIGS, CdTe and GaAs
intrinsic layer
Absorption coefficient values corresponding to the
wavelength have been plotted for experimentally obtained
5. Conclusions
Absorption coefficient plays an important role in case of
thin film solar cell. To do the modelling of solar cell, proper
material properties and the absorption coefficient values are
required. Interpolation technique is used to find the
absorption coefficient values based on the experimental data
of the same for the silicon based material (i.e. a-Si, C-Si, Si, n-Si) as well as CdTe, GaAs, CIGS based compound
semiconductors, which are mostly used for fabrication of
solar cell. Validation of the Absorption coefficient values
978-1-5090-6697-1/17/$31.00 ©2017 IEEE
692
Proceedings of the 2nd International Conference on Inventive Computation Technologies ( ICICT 2017)
IEEE Xplore Compliant - Part Number:CFP17K52-ART, ISBN:978-1-5090-6697-1
calculated from Absorption Coefficient Calculator with
experimental data is discussed for the materials. The wellmatched behaviour of the absorption coefficient values from
our proposed calculator with experimental data is the proof
of usefulness of our proposed calculator than any other
methods so far used for extracting the absorption coefficient
values corresponding to the wavelength of solar radiation.
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