An Investigation of The J-V Curve for N-AlGaAs/p-GaAs Heterojunction Solar Cell Due to Influence of Surface Recombination Velocity

Theoretical analysis can substantially reduce the time and costs required for developing a specific device such as solar cell, by allowing the designer to take a suitable geometry and doping profile prior to the fabrication stage. In this paper, theoretical analysis of electric field and electric potential within depletion layer of N-AlGaAS/p-GaAs has been made by solving Poisson's equation numerically using finite difference method (FDM) with Fortran program. Continuity equations of charge carriers in quasi-nature regions in N and p-layers were solved numerically to obtain the current density curve (J-V curve). Boundary conditions related to surface recombination velocity were implemented in this analysis. The effect of front and back surface recombination velocity on the excess minority carriers distribution and photocurrent have been studied. The aim of this work is to find the influence of surface recombination velocity in the output of N-AlGaAs/p-GaAs heterojunction solar cell. The analysis showed that, the low surface recombination velocity produce high efficient solar cell.


Introduction
Various heterojunctions, including Si-GaAs, Si-GaP, GaAs-Ge and other such materials have been used for making solar cells [1][2][3].Gallium arsenide (GaAs) is an excellent semiconductor for the fabrication of high efficient solar cell due to its high absorption of light and has an ideal band gap for solar photovoltaic conversion.There is strong interest in heterojunction solar cells this due to; (a) heterojunction cells can form window absorber which can be used to form structures that shield carriers from top-surface or back-surface recombination sinks.(b)heterojunction cells have a better match to the solar spectrum due to graded band gap.Thus, lot of research work, both experimental and theoretical has been carried out on the p/n heterojunction solar cells.An analysis of the photocurrent of a heterojunction solar cell has been reported [4], [5].The photocurrent density can be found by evaluating the excess minority carriers ∆ and ∆ generated by absorption of light in quasi-neutral regions of N and p layers respectively.Concentration of these carriers effected by various parameters such as surface recombination velocities at front and back layer, wavelength of incident light, absorption coefficient and energy gap of semiconductors.An analytical analysis of minority carriers concentration and spectral response from the top layer and from the base layer of p/n GaAs-Si heterojunction solar cell has been studied [6].In this paper, we use numerical analysis for evaluating the minority carriers concentration and photocurrent contribution from front and back layer of the solar cell.The generation rate (, ) of electron-hole pairs at each mesh point xi inside the solar cell is evaluated by using N(λ) photons flux of sun light (AM1) of wavelength range from   to   = ℎ   .The minority carrier equations were solved by implemented surface recombination velocities.Depletion Layer Approximation Figure 1, shows the AlGaAs/GaAs N-p heterojunction.The energy band diagram of a N-p heterojunction under thermal equilibrium is shown in Fig. 2 before and after the intimate contact [7].It is noted that the Fermi level is aligned [8,9].
Where   is dielectric of semiconductor, ϕ is the electrostatic potential, q is electric charge,   + ionized donor and   − ionized acceptor densities.The n(x) and p(x) are the free electron and hole density respectively.Neglecting a free charge n(x) and p(x), the Poisson's equation can be solved analytical given the depletion layer in each side of the junction as [10].
Where ∅  is built in potential given by [9].
Where ∆  is the offset energy at valance band,  is Boltzmann constant, T is room temperature,   and  0 are the hole concentration in p-and N-materials respectively, Nvn and Nvp are the effective density of state functions in the N-and p-materials respectively.

Finite Difference Methods
For nonhomogeneous material eq.( 1) become Where   is the intrinsic charge carrier related to semiconductor, the   (  ) are the quasi-Fermi potentials and   (  ) are so-called band parameters [11].
Using finite difference method, eq.( 5) can be written as Where   =  0   and the h is spacing between the grid points.Using these boundary conditions, equation ( 9) and ( 10) can be solved numerically using finite difference method (FDM).The photocurrent density  ℎ can be evaluated through the equation

Continuity Equation for Charge Curriers
The J-V curve for the solar cell will be Where  0 is the current density given by [10] Where  * is Richardson constant.

Result and Discussions
We solved Poisson's equation by finite difference method as a boundary value problem.The boundaries are the quasi-Fermi potentials   ,   at −  and   .First, the equation was translated into a system of equations and then solved by iteration method using Fortran program.I and Table II.The distribution of impurity charge density in abrupt N-AlGaAs/p-GaAs heterojunction is shown in Fig. 5.The distribution of free charges are very low in-order of 10 4 as seen in Fig. 6.The electrostatic potential is shown in Fig. 7.The continuity equations for minority charge carriers were solved numerically with boundary condition related to surface recombination velocity.The flowchart program is just as has been done for solving Poisson's equation but different physical quantity.Fig. 9 shows the distribution of excess charge carriers obtained which were identical to that obtained by Sayantan et.al [4] for an analytical analysis of a GaAs-Si n/p heterojunction solar cell.The corresponding current densities for these excess charge were shown in Fig. 10.The J-V characteristic curve for the simulation is shown in Fig. 11 under illumination of solar radiation AM1.The power profile for three solar cells at fixed Sn is shown in Fig. 12.The solar cell output parameters were given in Table .III.The data shows that by decreasing surface recombination velocity higher efficient solar cell can be obtained.

Fig. 2 :
Fig. 2: band energy diagram of AlGaAs/GaAs N-p heterojunction (a) before contact and (b) after the intimate contact [7].The Poisson's equation in depletion layer in N-p heterojunction is (  ) +    −(  −  −  ) (  ) +    − (  −  −  )  −    (  +  −  ) When light incident in solar cell, the generation rate G of electronhole pairs is given by(, ) = ∑ ()()[1 − ()] exp(−())Where () is absorption constant, the () is photon density, the () is reflection at front side of the solar cell, the h is the Plank constant , the c is the velocity of light, and   is the energy gap of semiconductor.Fig,3Shows light incident in N-p heterojunction solar cell.

Fig. 4 Fig. 4 :
Fig.4: Flowchart for solving Poisson's equation The material parameters used in the calculation are shown inTable I and Table II.

Fig. 9 :
Fig.9: Distribution of excess holes ∆  in n-layer and electrons ∆  in p-layer calculated with different surface recombination velocity.

Fig. 10 :
Fig.10: Distribution of excess minority current density   and   in n-layer and p-layer calculated with different surface recombination velocity.

Fig. 12 :
Fig.12: Power profile for three different solar cells