Multiband k·pk·p Riccati equation for electronic structure and transport in type-II heterostructures

An alternative method is proposed and implemented to calculate electronic structure and quantum transport properties of type-II heterojunctions. By deriving a multiband k·pk·p Riccati equation for the envelope function matrix, it is shown how to obtain the reflection matrix through a simple numerical integration of the Riccati equation. Numerical instability, which is usually associated with type-II systems due to the simultaneous presence propagating and evanescent states, is avoided by working with the logarithmic derivative of the envelope function matrix.The theory is implemented numerically for a 6-band k·pk·p matrix Hamiltonian in which the electron spin components have been decoupled. Preliminary results are presented for InAs/GaSb/InAs quantum wells. First, the calculated transmission versus energy curves are compared to those obtained from the microscopic empirical pseudo-potential calculation of Edwards and Inkson [Semicond. Sci. Technol. 9 (1994) 178]. For GaSb layer widths of 18, 55 and 152 Å, the transmission spectra agree almost exactly. Minor discrepancies are discussed. Second, the net current density is calculated at room temperature as a function of applied voltage. For a GaSb layer width of 74 Å, the self-consistently calculated net current density and peak-to-valley ratios are found to be in semi-quantitative agreement with the experiment of Yu et al. [Appl. Phys. Lett. 57 (1990) 2675].Other than its applications to electron tunneling, which can include spin-dependent tunneling (spintronics), the theory may also be applied to emerging field of multi-channel inverse scattering; in which desired transmission or reflection properties are used as input for designing heterostructure potential profiles.