Limited accuracy of conduction band effective mass equations for semiconductor quantum dots

Abstract

Effective mass equations are the simplest models of carrier states in a semiconductor structures that reduce the complexity of a solid-state system to Schrödinger- or Pauli-like equations resempling those well known from quantum mechanics textbooks. Here we present a systematic derivation of a conduction-band effective mass equation for a self-assembled semiconductor quantum dot in a magnetic field from the 8-band kp theory. The derivation allows us to classify various forms of the effective mass equations in terms of a hierarchy of approximations. We assess the accuracy of the approximations in calculating selected spectral and spin-related characteristics. We indicate the importance of preserving the off-diagonal terms of the valence band Hamiltonian and argue that an effective mass theory cannot reach satisfactory accuracy without self-consistently including non-parabolicity corrections and renormalization of kp parameters. Quantitative comparison with the 8-band kp results supports the phenomenological Roth-Lax-Zwerdling formula for the g-factor in a nanostructure.

arXiv commentFinal version

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Cited by in corpus (5)

• Spin-orbit coupling and magnetic field dependence of carriers states in a self-assembled quantum dot
• Dominant role of the shear strain induced admixture in spin-flip processes in self-assembled quantum dots
• Invariant expansion of the 30-band k.p model and its parameters for III-V compounds
• Tunneling-related electron spin relaxation in self-assembled quantum-dot molecules
• Electron ground state $g$ factor in embedded InGaAs quantum dots: An atomistic study