Energy-dependent conduction band mass of SiO2 determined by ballistic electron emission microscopy

Quantum interference oscillations in ballistic electron emission microscopy (BEEM) spectra were observed for metal–oxide–semiconductor structures with 23 and 30 Å ${\mathrm{SiO}}_{\mathrm{2}}$ interlayers. Maxima in the transmission coefficients, obtained from solutions of the one-dimensional Schrödinger equation that included image force corrections, could be matched to the spectral maxima provided that the effective electron mass $m_{\mathrm{ox}},$ an adjustable parameter, was increased at each of the consecutive higher energy maxima. The resulting energy dependence or dispersion of $m_{\mathrm{ox}}\mathrm{(E)}$ showed a dependence on the oxide thickness. The 23 and 30 Å oxides exhibit initial (zero kinetic energy) $m_{\mathrm{ox}}$ values of 0.52 $m_0$ and 0.45 $m_0,$ respectively, that disperse upward with energy by ≈0.3 $m_0$ over a 0–2.5 eV range in kinetic energies. The range of $m_{\mathrm{ox}}$ values observed is substantially lower than the average $m_{\mathrm{ox}}$ values deduced from quantum interference in Fowler–Nordheim tunneling experiments. The origin of these differences are discussed, and it is argued that BEEM is an inherently simpler and less error prone technique to evaluate $m_{\mathrm{ox}}.$