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Under solar radiation the efficiency of solar cells decreases as a result of heating up by short wavelengths photons. To minimize loss of efficiency with increasing temperatures, we designed a heterostructure AlGaAs/AlGaAs/GaAs cascaded p-i-n solar cells with 30 Å wide quantum wells and 10 Å wide barriers in p and i regions. Our modeling demonstrated that quantizing high energy carriers in the superlattice prevents scattering of excessive electron energies, thus decreasing the temperature rise per unit of time by a factor of 2. The modeling based on continuity equations included integration of absorption coefficients for various wavelengths and summarizes all thermodynamic heat exchanges in the designed solar cell.

Effect of temperature on photovoltaic conversion has been a cause of much study for a long time. Rise in temperature does not significantly affect the light-generated current of the cell [^{2} [

It was established that the reason for heat build-up during cell operation is the generation of hot electrons [

In this study we demonstrate that performance of the solar cell can be improved by reducing the heat generated by hot carries. We use thermodynamic modeling in predicting the temperature rise in AlGaAs/AlGaAs/GaAs cascade p-i-n structure [

Consider a semiconductor material of band gap

Hot carrier relaxation [

Thus, power dissipated in heat due to carrier scattering in a heterostructute (multilayer) structure is given in (

This heat is utilized in increasing the temperature of the materials. From basic laws of thermodynamics, the total thermodynamic power density required to raise the temperature of a multijunction cell though

We designed a pin cascade solar cell with and without superlattices in p and i regions to address heating issues. First we consider the solar cell without superlattices (Figure _{0.43}Ga_{0.57}As/Al_{0.25}Ga_{0.75}As/GaAs, respectively. The p-i-n thicknesses were 0.1 ^{18}/cm^{3}.

Band structure of p-i-n solar cell.

The dark current for such a cell would be the reverse saturation diode current. Forward currents in p, i, and n regions were calculated by solving the continuity equation in each region [^{2}. With the open circuit voltage of 1.04 V the efficiency was 25%.

The power dissipated in heat is given by (

One-dimensional quantization of carriers can be achieved by superlattice built between high band gap and low band gap materials. The relative location of discrete energy levels from valance and conduction band edges was obtained by solving the Schrödinger wave equation for particles bounded by finite potential barriers. Finite difference method was used to convert the wave equation to a Hamiltonian matrix form. Eigenvalues of this matrix represent the energy levels, and the eigenvectors identify the wave function. The effective band gap of the region with quantum well would then be

Quantum well dimensions in a superlattice were selected to provide sufficiently high energy levels for carriers. The barrier thickness of about 10 Å was chosen to ensure good quantum transparency. Aluminum phosphide (AlP) with a band gap of 3.57 eV was used as a barrier material in p and i regions. This resulted in barriers of potential 0.954 eV in conduction band and 0.636 eV in valance band, respectively. In i region, this was 1.08 eV in conduction band and 0.72 eV in valance band. A well width of 30 Å with 10 Å barriers resulted in 4 energy levels in conduction and valance bands in p and i regions. Well period was 23 and 998, respectively, in p and i regions. Due to narrow barrier thickness, these energy levels penetrate into adjoining well. Since all the wells were identical, the energy levels were identical, resulting in resonant tunneling through the region. We feel that QWs in n-region might not be required as most of the high energy photon absorption takes place in p and i regions.

Carrier transport can be analyzed by using a particle through a potential barrier paradigm [

Tunneling probability through

The current in the QWSC was obtained by solving the continuity equation for carrier concentration in each well and barrier regions with boundary conditions

Tunneling through superlattice.

Our model also took into account the fact that there would be no generation in barrier region for photons energies less than the barrier band gap. The wave nature of the electron would enable them to tunnel through the barriers. The presence of high field in i-region eliminates recombination. The current contribution in each region (at wavelength

In the presence of QWs, the amount of heat dissipated in each region is given by (

In our modeling, absorption coefficient is not a constant but a function of wavelengths for AM1.5 solar spectrum obtained from [

Our modeling assumed that QW energy levels in p and i regions were not aligned before illumination. Under solar radiation, the built-in potential step of p-i-n junction will be eliminated, thereby aligning the energy levels in p and i regions. This ensures carrier tunneling and transport across the junction.

Temperature increase for each wavelength of incident photon was calculated using the theory presented in Section

Temperature distribution (a) without QW and (b) with QW.

Designing superlattices in a, p, and i regions of our solar cell demonstrated that high energy carriers, having an option to occupy certain energy levels provided by our design, become less harmful as far as cell heating is considered. While analyzing the effect of quantum wells on temperature rise, it was assumed that the photons of energies lying within the gaps between the discrete energy levels would excite the charge carriers to energy levels just below such a gap. Figure

Clearly, there is significant reduction in the temperature rise. The 10 Å width barriers would ensure quantum tunneling of electrons through the barrier. The wider band gap also ensured that the barriers were optically inactive.

A formalized approach has been presented to assess the heating impact of high energy carriers. Modeling of current in superlattice structures for a solar cell under illumination was also proposed. Modeling shows that heat-up per unit of time was 8.5°C/s with no quantum wells (cumulative) for a p-i-n heterostructure solar cell. As a remedy to solar cell heating, we designed superlattice structure with 30 Å wide quantum wells and 10 Å wide barriers in p and i regions. The modeling shows that the cumulative temperature rise per unit of time of operational solar cell equipped with superlattices was about 4°C/s. This implies a reduction of heating up per unit of time by a factor 2. Modeling results also indicate reduction in current with the inclusion of quantum wells. This was expected as there would be no carrier generation inside barriers by photons with longer wavelengths. However, such a reduction can be remedied by increasing the thickness of the p and i regions. Our design ensures enhanced performance of a solar cell as reduction in heat-up leads to higher efficiency.