Comparing the Luttinger–Kohn–Pikus–Bir and the Empiric K·P Hamiltonians in quantum dot intermediate band solar cells manufactured in zincblende semiconductors

Abstract

The calculation of the energy spectrum and absorption coefficients of quantum dot nanostructured intermediate band solar cells using the Empiric K • P Hamiltonian method and its agreement with experimental data are summarized. The well established Luttinger Kohn Hamiltonian modified by Pikus and Bir for strained material, such as quantum dot arrays, is presented using a simplified strain field that allows for square band offsets. The energy spectrum and absorption coefficients are calculated with this new Hamiltonian. With the approximations made the energy spectrum results to be exactly the same but the absorption coefficient fits experiments less accurately. The computer time using the latter Hamiltonian is much longer than the former one.

The effect of band offsets in quantum dots

“…This analysis is based on a model of the QD based on the Empiric KP Hamiltonian [9,10] (EKPH). In contrast to the ab initio calculations this model, although less accurate, can be used with modest calculation equipment (a laptop) and is relatively fast; details may be found in reference [11], a method summary is described in reference [12].…”

Four-band Hamiltonian for fast calculations in intermediate-band solar cells

“…Size and potential offsets are those used for the energy spectrum calculations of Figure 2. Figure 4 shows the internal quantum efficiency (IQE) calculated from the preceding absorption coefficients (red dashed curve) together with the measured one (green solid) and those calculated with the EKP Hamiltonian [20] (blue dot-dashed curve) and the 8-band LKPB (H) [16] (black dotted curve). It is assumed that all generated electron-hole pairs are collected at the solar cell terminals.…”

“…We think that in practice the 4B LKPB Hamiltonian can be considered as fast as the EKP Hamiltonian. On the other hand, the calculation time for the 8B LKPB Hamiltonian has been estimated as 111 times more [16] than for the EKP Hamiltonian.…”

“…[14,15]. It has been found [16] that the LKPB Hamiltonian is about 100 times more time consuming than the EKP Hamiltonian for typical problem sizes and parameters…”

“…Details of the calculation of the strain tensor terms are in reference. [16] In reality, the host lattice constant is also modified and strong shear stresses appear on the edges. Not all the potential is squared; it has peaks on the edges and extends outside the QD.…”