Antireflection Coating influences on the Quantum Efficiency and the Reflectivity of a GaAs / GaAS Solar Cell within the Visible Spectrum

A theoretical investigation of the change in reflectance of silicon carbide (SiC) as a function of the particle size was the main focus of the current research. In addition, a single layer of anti-reflection coating of a quarter the wavelength is designed and doped in gallium arsenide (GaAs/GaAs) solar cell. The efficiency of the cell is investigated in the range of (400-700 nm) using the Brus model and the theory of characteristic matrix in the case of vertical and 45° ray to the plane of the incidence. The max efficiency for the designed cell (Air/Nano SiC/(GaAs/GaAs) was (% 96.81) of the wavelength of 550 nm in the case of vertical incidence. While in the case of an incident ray of 45° to the plane of the incidence, the efficiency was (%92.99) for the perpendicular polarisation (S) and (%97.23) in the case of horizontal polarization (P). the thickness of the coating was (Ps=2.2 nm).


Introduction
The new global has experience rapid and continuous developing in technology and its potential applications. However, the solar cells are low carbon energy source of the renewable to keep the increase of the atmospheric temperature below 2 °C [1,2]. A solar cell is considered the best application on the solar energy which their operation principle depends on the photovoltaic effect [3,4]. Increasing the efficiency of the solar cell was under high concerning by the researchers via adopting a variety of materials. Recently, the adopting the nanotechnology in the fabrication of the solar cells such as the incorporation of quantum dots (QDs) in solar cell manufacturing enhanced their efficiency in order to develop the physical and the structural properties of the solar cell materials [5][6][7]. However, reducing the loss in the quantum efficiency of the solar cell which is related to many factors, depended in the interaction between the light and the material of the cell. Where most semiconductors have  [8]. The technique is depending on the phenomena of interference in the thin films where the reflected wave experience changes in their optical path and phase.

Quantitative efficiency
The quantitative efficiency (QE), which can be defined as a number of generated electronhole pairs by a photon, can be calculated from the following equation: Where R is the reflectance coefficient, α is the absorption coefficient, L P the length of diffusion in the region P for the minority of charges' mobility and w is the depletion region's width.
The diffusion length of the minority of charges' mobility at region P can be determined [9]: D p and τ p are the fixed deployment and relaxation time for region P, respectively.
The width of depletion region (W) can be calculated as below [10], and are the width of the depletion at region N and P, respectively. and are the negative and positive ion concentration, respectively. ϵ 0, K s, and q are constants. While V bi is the inward voltage.

The reflectance as a function to the incident angle
The change in the reflectance of GaAs and SiC has been investigated as a function to the angle of the incident (0°-90°) and the external reflectance ( n°< n sub ), where the air is the media of the incident ray (see increases with the increase in the angle of the incident in contrast to the values of the horizontal reflectance (R P ) which decrease and reach the minimum value at an angle called polarization angle or Brewster's angle (θ B ). While, when the angle of incidence is higher than Brewster's angle, the value of R p and R s increased to be 100%.

The reflectance of GaAs and SiC as a function to the particle size
The reflectance of SiC has been investigated as a function to the particle size (Ps) which gives the quantum dots from the following equation = 2 where is the radius of the particle [11,12]. The calculation of the reflectance is carried out at incident angles of (θ°= 0°) and (θ°= 45°). Most semiconductors have a similar optical behaviour when their particle size is lower than the bulk size. Furthermore, it is associated with an increase in their energy gap and a decrease of the refractive index. That change becomes very small where the radius of the particle becomes equal or smaller than Bohr radius (α°) for the exciton. At that point, a dramatic change in the properties occurred with the decrease in the particle size because of the increase of the effect of quantum confinement. The decrease of the refractive index leads to a change in the value of the other optical properties.   Fig 1. 3. The reflectance change of SiC with the particle size in the case of vertical incidence. noticed that the reflectance becomes (R ≈11%) when the particle size of the coating is (Ps=40-12 nm). While it decreased due to the effect of the quantum confinement and the highest quantum efficiency obtained when the particle size (Ps=2.2 nm).  Fig 1. 6. The change in the reflective of the (Air/ Nano SiC/(GaAs/GaAs) designed anticoating with the particle size in the case of the vertical incidence, at the wavelength of (λo = 550 nm) and (L = 0.25 λo) .   Fig 1. 7. The quantum efficiency of (Air/ Nano SiC/(GaAs/GaAs) designed anti-coating with the particle size in the case of the vertical incidence, at the wavelength of (λo = 550 nm) and (L = 0.25 λo).
It has been observed that the designated (Air/ Nano SiC /(GaAs/GaAs) achieved the lowest value of the reflectance (R=0.74%) in the case of vertical incidence at the designated wavelength. In addition, the highest quantum efficiency for the coating was 96.81% at a particle size of 2.2 nm which can be suggested as a proper particle size for that designated coating.    Fig 1. 11. The quantum efficiency of (Air/ Nano SiC/(GaAs/GaAs) designed anti-coating with the particle size when the angle of incidence θ o = 45 o .

Conclusion
The quantum efficiency of the solar cell is related to the reflectance of the surface of the incidence to the electromagnetic waves. The maximum quantum efficiency of the designated (Air/Nano SiC/(GaAs/GaAs) solar cell was 96.81% at the wavelength of (λ°= 550 nm) in the case of vertical incidence. While in the case of incidence at the angle of 45 o , the efficiency was 92.99% at the perpendicular polarization (S) and 97.23% at the horizontal polarization when the particle size is 2.2 nm.