Bandgap measurement of high refractive index materials by EELS

Abstract

The determination of bandgaps and optical properties using valence electron energy loss spectroscopy (VEELS) has gained attracted interest since monochromated transmission electron microscopes (TEMs) with excellent spatial resolution and high energy resolution­ have become available. However, to measure and interpret the bandgap of many semi‐conductors has turned out to be more challenging than expected – in particular the precise measurement of bandgaps of high refractive index materials, such as Si and GaAs, has proven especially difficult. The reasons for these difficulties are not related to any energy resolution constraints, but due to that relativistic losses, surface plasmons and waveguide modes dominate the spectrum signal in the low energy loss region of the bandgap [1‐3]. For such high refractive index materials the Cerenkov limit, i.e. the acceleration voltage one needs to stay below in order to avoid relativistic losses, is below the available voltage range of most TEMs. In this work, we present a set‐up in scanning transmission electron microscopy (STEM) mode where we do not allow Cerenkov losses, surface plasmons or waveguide modes to come onto the EEL spectrometer. We exploit that the relativistic losses, surface modes and bulk waveguide modes all are extremely forward scattered and exist only inside a narrow solid angle that extends out to a few tens of µradians. We have a set‐up where the semi‐convergence and –collection angles both are in the range below 200 µrad. This set‐up gives a nearly parallel electron beam which combined with off‐axis/dark field EELS allows for detection of an energy loss signal from a region of reciprocal space that is still very close to the center of the first Brillouin zone. The off‐axis conditions are such that we are outside the narrow angular range where the unwanted signals from relativistic losses etc. compromise the EEL spectra, but still close enough to the center of the first Brillouin zone to detect bandgap excitations of almost direct bandgap transitions. Furthermore, such a set‐up is not restricted to low acceleration voltages, but can be used over a very broad range of voltages. Our experiments were performed with a double corrected, monochromated Titan microscope, operated at 80 kV. In Fig. 1 we show two EEL spectra: One with an on‐axis set‐up and where the semi‐convergence and –collection angles are both in the milliradian range. From this spectrum it is more or less impossible to extract any reliable bandgap information. The other spectrum was acquired with semi‐convergence and collection angles of 200 and 50 µrad, respectively. Even though the energy resolution is “only” 230 meV, a bandgap of 1.42 eV± 0.02 is measured directly from the raw, un‐subtracted spectrum. This value is very close to the direct bandgap of 1.42 eV for GaAs. We will further show that the present off‐axis set‐up can be used to determine the bandgap of several GaAs‐based compositions in a sample with multiple layers of III‐V materials.