Theoretical Comparative Study of Quantum Dot Solar Cell Behavior for Single and Multi-Intermediate Bands

In this paper, the mathematical model of the intermediate band quantum dot solar cell (IBQDSC) is investigated by using one and two intermediate bands (IBs). The IBs arise from the quantum dot (QD) semiconductor material within the barrier bandgap energy. Some factors, such as the thickness of the quantum dot ($T_{\mathrm{QD}}$) and the thickness of the barrier or inter-dot distances between quantum dots ($T_B$), are studied to show their influence on the performance of the IBQDSC. In the proposed model, the cubic shape of QDs from ${\mathrm{InAs}}_{0.9}{\mathrm{N}}_{0.1}$ and the barrier or bulk semiconductor material from ${\mathrm{GaAs}}_{0.98}{\mathrm{Sb}}_{0.02}$ are utilized. The time-independent Schrödinger equation is solved by employing the Kronig-Penney model. From the obtained results, after a homogenous range of the $T_{\mathrm{QD}}$ and $T_B$ is assigned for each one IB (1IB) and two IBs (2IBs) quantum dot solar cells (QDSCs), various comparative studies between the induced efficiency and the parameters of 1IB and 2IB QDSCs are investigated for one and maximum sun concentrations (MSCs). Consequently, reassigned ranges of the $T_{\mathrm{QD}}$ and the $T_B$, according to the type of IBs and sun concentration, are determined. The $T_{\mathrm{QD}}$ is an essential parameter for determining the number, location, and thickness of IBs into the QDSC. The small variation of $T_B$ is noticeable for each type of IBQDSC at different sun concentrations. Consequently, the induced values of the 1IB energy width ($\mathrm{\Delta }$) and the 2IBs energy widths (${\mathrm{\Delta }}_1$ and ${\mathrm{\Delta }}_2$) are determined. The value of $\mathrm{\Delta }$ is held constant, whereas the values of ${\mathrm{\Delta }}_1$ and ${\mathrm{\Delta }}_2$ are changed according to the solar cell (SC). However, the difference in the value of ${\mathrm{\Delta }}_2$ is large and noticeable. The $T_{\mathrm{QD}}$ and $T_B$ values, which achieve the optimum efficiency, are varied from 2.1 and 2.5 nm to 2.4 and 2.3 nm for the 1IB QDSC at one sun to MSC, respectively. The $T_{\mathrm{QD}}$ and $T_B$ values are also varied from 5.3 and 3 nm to 5.25 and 2.09 nm for the 2IBs QDSC at one sun to MSC, respectively. One can notice that, in the case of 2IBs, an improvement into the efficiency is achieved. The optimum efficiencies of the 1IB QDSC and 2IBs QDSC for the model under study are 42.39 and 58.01% at one sun and 66.21 and 73.55% at MSC, respectively.