Self-consistent 1-D Schrödinger–Poisson solver for III–V heterostructures accounting for conduction band non-parabolicity

Abstract

We present in this paper a novel method to solve self-consistently the Schrödinger and Poisson’s equations with non-parabolic conduction bands in III–V heterostructures with one dimensional material and electrostatic potential variation. Our calculation suggests ∼20% more sheet charge density ( N s ) may be expected for a representative quantum well FET structure featuring an InGaAs channel cladded with an AlGaSb barrier, compared to predictions from the parabolic band assumption; N s reaches >5 × 10 12 cm −2 at 0.8 V gate overdrive. The increase in sheet density directly results in a higher FET gate capacitance and therefore better transconductance, which stems from the different density of states (DOS) function with the non-parabolic conduction band. Calculation demonstrates that non-parabolicity results in a “tilted staircase” DOS function (as opposed to the classical “flat staircase”). This model was also extended to accommodate satellite valleys, which allows the proper FET gate bias range to be determined in order to avoid overall carrier mobility drop due to L-valley occupation.