Electronic structure and optical absorption of ionized donor molecules in a magnetic field: A finite-element approach

A three-dimensional finite-element scheme is used to calculate the electronic structure of ${\mathrm{H}}_2^{+}$ in magnetic fields of arbitrary directions. The result is used to obtain the magnetoabsorption spectrum of ionized donor molecules ${\mathit{D}}_2^{+}$ in high-purity n-type semiconductors in the effective-mass approximation. The absorption peak energy as a function of the magnetic field, expressed in nondimensional units, is found to be universal, i.e., independent of the effective mass, donor concentration, compensation, etc. The calculation provides a clear characteristic feature of ${\mathit{D}}_2^{+}$. Also, the usefulness and versatility of the finite-element method in electronic-structure calculations are demonstrated.