The electron effective mass $m_e^{*}$ can be calculated from the Kramers-Kronig transformation of electron energy loss spectra (EELS) for III-V semiconductor materials. The mapping capabilities of a scanning transmission electron microscope, equipped with a ${\text{Gatan Enfina}}^{™}$ EELS system are exploited to produce maps showing the variation of $m_e^{*}$ with nanometer scale resolution for a range of semiconductors. The analysis was carried out on three material systems: a GaInNAs quantum well in a GaAs matrix; InAs quantum dots in a GaAs matrix, and bulk wurzitic GaN. Values of $m_e^{*}$ were measured as $\sim 0.07m_0$ for GaAs and $0.183m_0$ for GaN, both in excellent agreement with the literature. It has also been shown that the high frequency dielectric constant can be calculated using the Kramers-Kronig methodology. When the high frequency dielectric constant is incorporated into the calculations a much more accurate visual representation of $m_e^{*}$ is displayed in the maps.

• Received 7 October 2005

DOI:https://doi.org/10.1103/PhysRevB.73.035312