Analysis of the dielectric constants of the Ag₂O film by spectroscopic ellipsometry and single-oscillator model

Abstract

Ag₂O film was prepared on glass substrate by direct current reactive magnetron sputtering under a careful control of the preparation parameters. The analysis of the dielectric constants of the Ag₂O film related to the optical properties was conducted by spectroscopic ellipsometry (SE) and single-oscillator model. The dielectric constants were fitted in terms of general oscillator model (a model combined with three Tauc–Lorentz oscillator models) by using the measured SE data. Refractive-index dispersion data below the interband absorption edge of the Ag₂O film were analyzed using a single oscillator fit of the form $n^2-1=E_d{E}_0/(E_0^2-{\mathit{\hslash }}^2{\omega }^2)$ proposed by Wemple and DiDomenico, where ℏω is the photon energy, E₀ is the single oscillator energy, and E_d is the dispersion energy. The optical energy gap of approximately 2.32 eV was fitted by single oscillator model, which was in good agreement with that in terms of Tauc relation. The fitted dispersion energy E_d of approximately 20.28 eV determined the parameter β of approximately 0.32 by a simple empirical relationship E_d=βN_cZ_aN_e, which indicated that Ag₂O film falls into covalent class. Additionally, the band gap parameter E_a and plasma frequency ℏω_p fitted were 1.16 and 4.85 eV, respectively.

Introduction

The reported forms of silver oxide include the AgO, Ag₂O, Ag₃O₄, Ag₄O₃ and Ag₂O₃ phases, of which Ag₂O is most thermodynamically stable [1]. The Ag₂O phase possesses a simple cubic structure with a lattice parameter of 0.4728 nm at room temperature [2], whereas AgO usually crystallizes with a monoclinic structure containing the both Ag⁺ and Ag³⁺ [2]. Silver oxide with a wide energy band gap range can be deposited using magnetron sputtering [1], [3], [4], [5], chemical bath deposition [6] and ECR oxygen plasma assisted e-beam evaporation of Ag [7], [8], etc. The wide energy band gap ranging from 1.2 to 3.4 eV is due to different stoichiometries, crystalline phases and properties arising from different deposition techniques. Rivers et al. [7] reported a direct band gap of 3.29 eV for Ag_2−xO mixed film including Ag₂O phase with 〈1 1 1〉 and 〈0 0 2〉 orientation and AgO phase with 〈1 1 1〉 and 〈0 0 2〉 orientation. Fortin et al. [9] deduced a 1.2 eV gap of Ag₂O power by spectrophotometry and photoconductivity. Pierson et al. [3] used RF-reactive magnetron sputtering to grow Ag₂O film with a 2.23 eV band gap. Varkey et al. [6] grow AgO using chemical bath deposition and form Ag₂O with a band gap of 2.25 eV by subsequent air annealing.

The promising application of silver oxide films in many fields is being paid more attention due to its unique properties [10], [11], [12]. In particular, due to the thermal instability, silver oxide may be applied in optical and magneto-optical storage disk. Fuji et al. [13] pointed out that silver oxide film could be used as a readout layer in a new type of optical disk by producing a metallic probe as a non-transparent aperture. Kim et al. [14] reported that silver oxide film could also act as a mask layer in a new magneto-optical disk to strongly enhance the magneto-optical signal. However, the high threshold of thermal decomposition temperature (TTDT) over 400 °C [15], [16] for silver oxide films has being a bottleneck of application in optical and magneto-optical storage. This may originate from the coexistence of AgO and Ag₂O phases in the silver oxide film. Application of Ag₂O film may be an effective method to sharply slow down the TTDT. However, Ag₂O film is difficult to prepare on glass substrate by reactive magnetron sputtering.

For semiconductor materials, the real part of dielectric constants in the transparent region below the gap is related to optical absorption above the gap by

$${\epsilon }_1(\omega )=n^2(\omega )=1+\frac{2}{\pi }P{\int }_{{\omega }_t}^{\infty }\frac{{\omega }^{\prime }·{\epsilon }_2({\omega }^{\prime })}{{\omega }^{\prime 2}-{\omega }^2}·d{\omega }^{\prime },\omega <{\omega }_t$$

where ω_t is the threshold frequency of absorption spectrum, ω is assumed to lie above all lattice vibration modes, i.e. only electronic excitation is considered, while ε₂(ω) calculations require integration over the full Brillouin zone as well as all frequencies, which is sometimes impossible due to the limited data. As well known, spectroscopic ellipsometry is an effective method to measure the dielectric constants based on appropriate system model. However, some meaningfully physical parameters related to structural and optical properties are hidden and obscure. It is difficult to establish the relationship between dielectric constants and structural, and optical properties. So it is useful, therefore to define some meaningfully physical parameters depending on the particular approximation made of the general theoretical expressions for ε₁(ω). Philips and Van Vechten [17], for example, defined an ‘average energy gap’ E_g in terms of the Penn model description of the static dielectric constant, whereas Wemple and DiDomenico [18] used a single oscillator description of the frequency-dependent dielectric constant to define a ‘dispersion-energy’ parameter E_d. These parameters are very useful to describe the influence of crystal structure and ionicity on the refractive index behavior. As proved by Wemple and DiDomenico [18], E_d is related to the charge distribution within each unit cell and chemical bonding. The observed simple dependence on coordination number and chemical valency suggests further that nearest-neighbor atomic-like quantities strongly influence the optical properties of materials.

In the present article, our purpose is to prepare Ag₂O film by reactive magnetron sputtering and analyze the relationship between the dielectric constants and structural and optical properties by some meaningfully physical parameters (E_d, E₀, E_a, ℏω_p) fitted in terms of single-oscillator model.