Band-gap measurements of direct and indirect semiconductors using monochromated electrons

With the development of monochromators for transmission electron microscopes, valence electron-energy-loss spectroscopy (VEELS) has become a powerful technique to study the band structure of materials with high spatial resolution. However, artifacts such as Cerenkov radiation pose a limit for interpretation of the low-loss spectra. In order to reveal the exact band-gap onset using the VEELS method, semiconductors with direct and indirect band-gap transitions have to be treated differently. For direct semiconductors, spectra acquired at thin regions can efficiently minimize the Cerenkov effects. Examples of hexagonal GaN $\left(h\text{−}\mathrm{Ga}\mathrm{N}\right)$ spectra acquired at different thickness showed that a correct band-gap onset value can be obtained for sample thicknesses up to 0.5 $t∕\lambda$. In addition, $\omega \text{−}q$ maps acquired at different specimen thicknesses confirm the thickness dependency of Cerenkov losses. For indirect semiconductors, the correct band-gap onset can be obtained in the dark-field mode when the required momentum transfer for indirect transition is satisfied. Dark-field VEEL spectroscopy using a star-shaped entrance aperture provides a way of removing Cerenkov effects in diffraction mode. Examples of Si spectra acquired by displacing the objective aperture revealed the exact indirect transition gap $E_g$ of $1.1\mathrm{eV}$.

Figure 1

Low-loss EELS spectra of $h\text{−}\mathrm{Ga}\mathrm{N}$: (a) raw spectrum and (b) zero-loss deconvoluted spectrum showing the band-gap onset and interband transitions. Peaks originate from critical points in the band structure.

Figure 2

(Color) (a) $h\text{−}\mathrm{Ga}\mathrm{N}$ VEEL spectra measured at different specimen thicknesses; (b) systematic shift of the apparent band gap to lower energies with increasing sample thickness; and (c) plot of apparent band gap versus sample thickness showing the true band-gap value below 0.5 $t∕\lambda$.

Figure 3

(Color) (a) $\omega \text{−}q$ map of $h\text{−}\mathrm{Ga}\mathrm{N}$ at a thick region with strong Cerenkov losses and (b) line profiles extracted at different $q$ values with a linewidth of about $5\mu \mathrm{rad}$. The energy loss of Cerenkov radiation has a narrow angular distribution.

Figure 4

$\omega \text{−}q$ maps of $h\text{−}\mathrm{Ga}\mathrm{N}$ acquired at different thicknesses. Cerenkov losses are less pronounced at thin regions.

Figure 5

Star-shaped filter-entrance aperture used for dark-field VEEL spectroscopy: (a) Image of the aperture in diffraction mode and (b) spectrum obtained by using this aperture.

Figure 6

(Color) Low-loss diamond spectra acquired with different collection angles showing the blocking of Cerenkov losses.

Figure 7

$\omega \text{−}q$ map of Si showing Cerenkov losses across the band-gap region.

Figure 8

Dark-field VEEL spectrum of Si showing the band-gap onset at $1.1\mathrm{eV}$.