Application of coordinate transformation and finite differences method in numerical modeling of quantum dash band structure

Application of Finite Difference Method in Modeling Quantum Dot Superlattice Silicon Tandem Solar Cell

“…In comparison to the wafer-based first-generation photovoltaic technologies and second-generation thin-film approaches, the third-generation photovoltaic approaches arouse the extensive attention from world-wide researchers due to the advanced electronic and optical properties and the novelty [1,2]. They aim to tackle the two major power losses in standard single-bandgap cells, which are the inability to absorb photons with energy less than the bandgap and thermalisation of photon energy exceeding the bandgap.As of these issues, there have been proposed three families of approaches: (a)increasing the number of energy levels; (b) capturing hot carriers before thermalisation; and (c)multiple electron-hole pair generation per high energy photon or generation of one higher energy-carrier pair with more than one low energy photon.…”

Asymmetric double quantum wells with smoothed interfaces

“…It is well known that exact analytical solutions to such problems are only available for simple structures such as a square or parabolic well [28], and even in these structures, in general, in the presence of perturbations such as external fields, disorder effects [29], etc., the problem cannot be solved exactly. There have been various numerical methods used to calculate the band profiles in QWs: the matrix approach (MA) [30,31], the transfer matrix (TM) method [32,33], the finite difference method (FDM) [34,35], the "shooting method" (SM) [34,36], the finite element (FE) technique [37,38], discreet variable representation (DVR) approach [39], envelope function (EF) method [40], Wentzel-Kramers-Brillouin (WKB) approximation [41], variational method (VM) [42], and Monte Carlo (MC) simulations [43]. Among them, the WKB and EF methods adopt approximations, thus giving unreliable results; the VM only works well at simple QWs and weak fields; the MC and FE methods are highly computerorientated approaches; the MA usually require wave function to be well behaved; the SM's speed comes at the cost of stability.…”

Asymmetric Double Quantum Wells with Smoothed Interfaces

“…There have been various numerical methods used to calculate the band profiles in QWs: the matrix approach (MA) [13], the transfer matrix (TM) method [14,15], the finite difference method (FDM) [16,17], the finite element (FE) technique [18,19], discreet variable representation (DVR) approach [20], envelope function (EF) method [21], Wentzel-Kramers-Brillouin (WKB) approximation [22], variational method (VM) [23], and Monte Carlo (MC) simulations [24]. Among them, the WKB and EF methods adopt approximations, thus give the results unreliable; the VM only works well at simple QWs and weak fields; the MC and FE methods are highly computer-orientated approaches; the MA usually require wave function to be well behaved.…”