Band gap maps beyond the delocalization limit: correlation between optical band gaps and plasmon energies at the nanoscale

Wei Zhan,Thomas Aarholt,Øystein Prytz,Vishnukanthan Venkatachalapathy,Andrej Yu Kuznetsov

doi:10.1038/s41598-017-18949-9

Abstract

Recent progresses in nanoscale semiconductor technology have heightened the need for measurements of band gaps with high spatial resolution. Band gap mapping can be performed through a combination of probe-corrected scanning transmission electron microscopy (STEM) and monochromated electron energy-loss spectroscopy (EELS), but are rare owing to the complexity of the experiments and the data analysis. Furthermore, although this method is far superior in terms of spatial resolution to any other techniques, it is still fundamentally resolution-limited due to inelastic delocalization of the EELS signal. In this work we have established a quantitative correlation between optical band gaps and plasmon energies using the Zn1−xCdxO/ZnO system as an example, thereby side-stepping the fundamental resolution limits of band gap measurements, and providing a simple and convenient approach to achieve band gap maps with unprecedented spatial resolution.

Highlights

In the periodic table, Cd is located directly below Zn and can be considered iso-electronic
In this work, using monochromated EELS in probe-corrected STEM, we investigate the relationship between band gaps and plasmon energies, and establish a robust quantitative correlation using in the ZnO-CdO alloys as an example
Higher Cd content is associated with a drop in plasmon energy, since the valence electron density decreases as the unit cell volume expands

Summary

Introduction

Cd is located directly below Zn and can be considered iso-electronic. Where Ep,F is the free electron plasmon energy in EELS spectrum, ωp is the plasmon frequency, ħ is the reduced Planck constant, N is the number of valence electrons per unit cell, e is the elementary charge, V(x) is the Cd-concentration dependent volume of unit cell, m0 is the electron mass, and ε0 is the permittivity of free space. This free electron model assumes that the valence electrons behave as simple harmonic oscillators, which is an obvious simplification when considering real materials. Many simple metals (e.g. Be, B, Na, Al) and semiconductors (e.g. Si, Ge, GaAs) have sharp plasmon peaks near the value predicted by this model[26], and it has been shown that Equation (1) is quite successful in estimating the plasmon energy of more complex materials[21]

Methods

Results

Discussion

Conclusion