Near vacuum-ultraviolet aperiodic oscillation emission of AlN films

Abstract

An accurate measurement of the refractive index is necessary for the optical design of both deep ultraviolet laser diodes and light-emitting diodes. Generally, the refractive indices along different crystallographic axes of anisotropic thin films are measured using variable angle spectroscopic ellipsometry. However, there are still some limitations concerning this method. Here we proposed a potential method to measure the band edge refractive index of wide bandgap semiconductor. An aperiodic oscillation emission phenomenon due to the Fabry-Perot effect was observed in the fluorescence spectrum of an AlN film with a thickness of 1500 nm. Based on the characteristics of the fluorescence spectrum and the definition of Fabry-Perot effect, we obtained the ordinary refractive index of the AlN thin film near the band edge directly. This refractive index measurement method is a supplement to the variable angle ellipsometry, and it is a more direct and effective method for transferred film and thinner samples to measure the fluorescence spectrum.

Introduction

Refractive index and extinction coefficient are optical constants closely related to each other which have significant impacts on the extraction efficiency of light-emitting diodes (LEDs) and laser diodes (LDs), the photoelectric conversion efficiency of solar cells, and the quantum efficiency of photodetectors [1], [2], [3], [4], [5], [6]. Therefore, the accurate measurement of these optical constants is important in the field of optoelectronics. Theoretically, the refractive index can be derived from the extinction coefficient based on the Kramers-Kronig transformation relationship [7], [8]. Experimentally, the optical constants of thin films and bulk materials are usually obtained through spectroscopic ellipsometry and the optical waveguide technique [9], [10], [11], [12], [13], [14], [15].

Hexagonal AlN, a semiconductor with an ultrawide direct bandgap (~6 eV) and a wurtzite structure [16], [17], [18], [19], has a potential use in deep ultraviolet (DUV) emitters and detectors [20], [21], [22], [23], [24], [25], and its optical constants can be measured using an spectroscopic ellipsometer. When incident light is perpendicular to the c-plane of an AlN thin film, the refractive index only depends on the ordinary part ${\epsilon }_{\mathrm{o}}$ of the dielectric function; when incident light is oblique, the refractive index depends not only on ${\epsilon }_{\mathrm{o}}$, but also on the extraordinary part ${\epsilon }_{\mathrm{e}}$ of the dielectric function. Therefore, the refractive index of an AlN thin film measured by a single-angle spectroscopic ellipsometer is called the “apparent” refractive index, of which the ordinary and extraordinary refractive indices ($n_{\mathrm{o}}$ and $n_{\mathrm{e}}$) are usually coupled with each other, limiting the measured object of a single-angle spectroscopic ellipsometer. According to the electronic transition selection rule, the large negative splitting of the lattice field at the valence band maximum (VBM) of AlN determines the strong anisotropy of ordinary and extraordinary extinction coefficients ($k_{\mathrm{o}}$ and $k_{\mathrm{e}}$) [26], which leads to a large measurement error for $n_{\mathrm{o}}$ and $n_{\mathrm{e}}$. To solve this issue and accurately measure the $n_{\mathrm{o}}$ and $n_{\mathrm{e}}$ of anisotropic thin films, variable angle spectroscopic ellipsometry (VASE) has been used [27], [28], [29]. For instance, Shokhovets et al. [30] have obtained accurate values of $n_{\mathrm{o}}$ and $n_{\mathrm{e}}$ for AlN and GaN films in the transparent waveband. With the development of theory and coating technology, VASE has also been used to measure optical constants near the absorption waveband. Jiang et al. [31] successfully obtained $n_{\mathrm{o}}$ and $n_{\mathrm{e}}$ near the band edge of an AlN thin film using VASE. However, this method still has some limitations in terms of the measurement of the optical constants of a transformed film and has strict requirement for the thickness of the film to obtain effective elliptical parameters $\Psi$ and $\mathrm{\Delta }$, which reflect the change in the polarization states of reflected or transmitted light. However, the measured $\Psi$ and $\mathrm{\Delta }$ cannot determine the optical constants directly.

We propose a new method to both accurately and directly measure $n_{\mathrm{o}}$ and $n_{\mathrm{e}}$ of an AlN thin film near the band edge. For the first time, we observed an aperiodic oscillation emission phenomenon in the near vacuum ultraviolet (VUV) fluorescence spectrum of the c-plane of an AlN epitaxial thin film with a certain thickness, which can be explained through the Fabry-Perot model. Thus, the $n_{\mathrm{o}}$ near the band edge of the AlN thin film was derived accurately and directly, suggesting that the aperiodic oscillation fluorescence spectrum is of great engineering significance, specifically for designing DUV LEDs and LDs.