2-1 Motivation
There are several advantages of thin film solar cells. Solar cell with flexible substrate is the forerunner of the photovoltaic energy. Costs for this technology are dropping quickly and with the investment in research and development, these costs will continue to fall. The biggest advantages with thin film solar cells are their various application options. Unlike traditional panels, flexible panels can be applied to a wide variety of surfaces. In addition to the traditional roof mounted design, these cells can be placed in the transportation vehicles, in the building surfaces, and even in the daily goods. Under low-light condition (such as cloudy sky, bright moon light, etc.), thin film solar cell is better than the crystalline silicon cell. Thin film solar cells do not require the glass and aluminum casings of traditional cells because the materials within them are flexible and ductile. This means they will likely take more abuse and last longer.[14]
Why do we chose amorphous silicon? Because silicon is the second most abundant material on earth, and its light absorption layer thickness can be thin and still be effective. Also it is more mature in manufacturing process. Therefore, amorphous silicon is still one of the prominent candidates for thin film solar cell technology.
Amorphous silicon material used in the thin film solar cell has two unique features, the first is the band tail. Due to its disordered lattice points and extra defects in the material, amorphous silicon has a tail of density of states extended into forbidden gap region. The second is interfacial roughness. This comes from the thin film cell
fabrication processes, and will optically benefit the light absorption. So these two
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topics need to be considered for modeling.
Finally, our goal is to create a platform which includes the following characteristics, easily accessible, accuracy in electrical and optical properties, .and possible future improvement for device.
2-2 Theory
In our simulation calculation, several aspects of the amorphous silicon solar cell needs to be covered. They are basic carrier drift-diffusion model of amorphous silicon alloy p-i-n solar cells, tunnel junction, haze, and band tail models. We will discuss these topics as follows.
2-2-1 Physics of amorphous silicon alloy p-i-n solar cells
Many efforts have been done to properly model the amorphous silicon p-i-n structure [15]. We will follow the model from ref. 15 closely in the next few sections.
Our simulation is based on the solution of the electron and hole continuity equations:
)
where G is the generation rate and R is the recombination rate. Poisson’s equation is
(x) dx
d (2-3)
, where is the electric field inside the device. The electron and hole conduction current densities are
)
12 sample temperature, and ε the dielectric constant of amorphous silicon.
We can then calculate the recombination rate R(x) and charge density ρ(x) by considering the electron and hole concentrations and the distribution of localized states g(E) in the mobility gap.
where EA and ED are the characteristic energy slopes of exponential distributions of acceptor- and donor-type localized states and Emc is the energy difference between the minimum in the density of states and the conduction band edge.
And then we assumed the densities of states to be the same as for crystalline silicon of their conduction band and valence band. In particular, there is experimental
evidence that the existence of defect band associated with dangling bonds is at around 1eV below the conduction band edge.[20] Discussed in Ref [21], it affects values of undoped samples, for gmin=1016cm-3eV-1.We assume
We can model the effect of dopants on the density of states spectrum as it is well known that small quantities of dopants introduce new states into the gap.[16]
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Some experimental evidence shows that the dopant-created defect density is proportional to the square root of the dopant density [17] and the density of states:
)
where N=total dopant concentration, K a suitable constant, and gmin(N=0)=1016
cm-3eV-1. Using the model [18] which is a detailed analysis of amorphous silicon under the steady-state photoconductivity phenomenon, and for the K value, we use an appropriate value of K tobe equal 3×1016 cm-3eV-1.5.
The space-charge density ρ (x) described as
)
Here pt(x) and nt(x) are the concentrations of trapped holes and electrons, respectively, ND+
(x) and NA
-(x) are the ion concentrations of shallow donors and acceptors.
The concentrations of Pt and Nt is defined as the electron and hole trap quasi-Fermi levels positions.[19]
For acceptor-like states these are given by
)
and for donor-like states
14
Where NC and NV are the density of states in the conduction band and valence band, and EC and EV are the energy corresponding to the conduction band bottom and the top of the valence band, and
N
We use the zero-temperature distribution function to calculate the density of trapped electrons and holes. The results underestimate the trapped electron density, but it has not manifest error, provided the characteristic energy density of the slope of EA and ED is greater than KT.
In this approximation donor-like trap probability occupied by electron is
d
and for acceptor-like traps it is
a
The concentrations of trapped carriers nt and pt are demonstrated as
15
And then, we use the Shockley-Read recombination model to find the carrier recombination and the rate R(x) is
where ni is the intrinsic carrier concentration, ν is the thermal velocity, and (np-ni2
) is driving force of recombination. [22]
In the simplest condition, the generation rate G is e x
G x
G( ) 0
(
) () (2-23) where G0 is the incident photon flux of wavelength λ, α(λ) is the absorptioncoefficient, and x is the distance from the top of the cell. Then, we consider the more realistic model of generation rate including the actual back reflection in amorphous silicon solar cells.
) where P is a transmission factor for light traveling twice through the cell.
Equations (2-1~2-24) are our considered model.