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

## TL;DR

This paper systematically derives and evaluates conduction-band effective mass equations for semiconductor quantum dots, highlighting their limitations and the importance of including non-parabolicity and off-diagonal terms for accurate modeling.

## Contribution

It provides a hierarchical classification of effective mass equations derived from 8-band kp theory and assesses their accuracy in quantum dot spectral and spin properties.

## Key findings

- Effective mass equations have limited accuracy without non-parabolicity corrections.
- Including off-diagonal valence band terms improves modeling accuracy.
- The Roth-Lax-Zwerdling formula effectively predicts g-factors in nanostructures.

## 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 Schr\"odinger- 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.