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Effective mass equations are the simplest models of carrier states in asemiconductor structures that reduce the complexity of a solid-state system toSchr\"odinger- or Pauli-like equations resempling those well known from quantummechanics textbooks. Here we present a systematic derivation of aconduction-band effective mass equation for a self-assembled semiconductorquantum dot in a magnetic field from the 8-band kp theory. The derivationallows us to classify various forms of the effective mass equations in terms ofa hierarchy of approximations. We assess the accuracy of the approximations incalculating selected spectral and spin-related characteristics. We indicate theimportance of preserving the off-diagonal terms of the valence band Hamiltonianand argue that an effective mass theory cannot reach satisfactory accuracywithout self-consistently including non-parabolicity corrections andrenormalization of kp parameters. Quantitative comparison with the 8-band kpresults supports the phenomenological Roth-Lax-Zwerdling formula for theg-factor in a nanostructure.

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