METHOD FOR MEASURING THICKNESS AND OPTICAL CONSTANTS OF DIAMOND FILM

Abstract

First, it is judged whether the diamond film is the single-crystal diamond film or the polycrystalline diamond film according to ellipsometric spectrum data and absorption spectrum data, and different calculation methods are selected to obtain the optical constants and the thickness of the diamond film according to spectral data (e.g., the ellipsometric spectrum data and the absorption spectrum data). Additionally, in the single-crystal diamond film, the optical constants and the thickness of the diamond film are obtained through calculation using the Cauchy model. In the polycrystalline diamond film, the spectral region is selected, and the optical constants and the thickness of the diamond film are obtained through calculation according to the oscillator model and the evaluation function MSE.

Claims

1. A method for measuring a thickness and optical constants of a diamond film, comprising: step 1: depositing a diamond film on a substrate; step 2: measuring ellipsometric spectrum data and absorption spectrum data of the diamond film; step 3: judging whether the diamond film is a single-crystal diamond film or a polycrystalline diamond film according to the ellipsometric spectrum data and the absorption spectrum data, executing step 41 when the diamond film is the single-crystal diamond film, and executing steps 42, 5, and 6 when the diamond film is the polycrystalline diamond film; step 41: obtaining optical constants and a thickness of the single-crystal diamond film through calculation using Cauchy model in a full spectral region, wherein the optical constants of the single-crystal diamond film at least comprise a refractive index n and an extinction coefficient k; step 42: selecting a spectral region defining a transparent section for the polycrystalline diamond film from the polycrystalline diamond film, and obtaining optical constants and a thickness d of the polycrystalline diamond film through calculation using the Cauchy model in the spectral region; step 5: adding an oscillator model for dielectric constants to the absorption spectrum data of the polycrystalline diamond film, and at least adjusting an amplitude and a width of the oscillator model of the polycrystalline diamond film according to the ellipsometric spectrum data; and step 6: evaluating a difference between an experimental value and a fitted value by an evaluation function mean square error (MSE) to determine the optical constants and the thickness d of the polycrystalline diamond film, wherein the optical constants of the polycrystalline diamond film at least comprise a refractive index n and an extinction coefficient k.

2. The method according to claim 1, wherein in the step 3, judging whether the diamond film is the single-crystal diamond film or the polycrystalline diamond film comprises judging whether the diamond film is the single-crystal diamond film or the polycrystalline diamond film according to an absorption difference of the absorption spectrum data.

3. The method according to claim 1, wherein in the step 42, a calculation formula of the Cauchy model is: $\begin{array}{cc}n=\mathrm{An}+\frac{\mathrm{Bn}}{{\lambda }^2}+\frac{\mathrm{Cn}}{{\lambda }^4}& \left(1\right)\end{array}$ $\begin{array}{cc}k\left(\lambda \right)=A_k{e}^{B_k\left(\begin{array}{cc}E& E_b\end{array}\right)}& \left(2\right)\end{array}$ wherein An, Bn and Cn are parameters of the Cauchy model, λ is wavelength, the extinction coefficient k is described by three parameters A.sub.k, B.sub.k, and E.sub.b, E.sub.b=1240/4, and E.sub.b relates to a material of the substrate.

4. The method according to claim 1, wherein: in the step 5, the oscillator model for the dielectric constants is Lorentz oscillator, and a calculation formula of the Lorentz oscillator is: $\begin{array}{cc}n=\frac{{\mathrm{AE}}_n}{E_n^2-E^2-\mathrm{iBrE}}& \left(3\right)\end{array}$ wherein A is an amplitude of parameters of the oscillator model, En is a center position of the parameters of the oscillator model, and Br is a half wave width of the parameters of the oscillator model.

5. The method according to claim 1, wherein: in the step 6, a calculation formula of the evaluation function MSE is: $\begin{array}{cc}{\mathrm{MSE}}^2=\frac{1}{2N-M}{.Math.}_{i-1}^n\left[{\left(\frac{{\phi }_i^{\mathrm{mod}}-{\phi }_i^{\exp }}{{\delta }_{\phi ,i}^{\exp }}\right)}^2+{\left(\frac{{\Delta }_i^{\mathrm{mod}}-{\Delta }_i^{\exp }}{{\delta }_{\Delta ,i}^{\exp }}\right)}^2\right]& \left(4\right)\end{array}$ wherein mod is a fitted value, exp is a measured value, 6 is a measurement error, N is a total logarithm of ψ and Δ measured by an ellipsometer at the same time, and M is a logarithm of a selected fitted parameter.

6. The method according to claim 1, wherein the substrate in the step 1 is a Si substrate, an Al.sub.2O.sub.3 substrate, or a diamond substrate.

Description

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0029] The technical solution of the present disclosure will be further described below in combination with the accompanying embodiments and drawings.

[0030] A method for measuring a thickness and optical constants of a diamond film comprises the following steps:

[0031] Step 1. A diamond film is deposited on a substrate. For example, the substrate can be a Si substrate, an Al.sub.2O.sub.3 substrate, or a diamond substrate, but the disclosure is not limited thereto. Other substrates can be selected as required;

[0032] Step 2. Ellipsometric spectrum data and absorption spectrum data of the diamond film are measured. For example, the ellipsometric spectrum data and the absorption spectrum data are obtained by an ellipsometer;

[0033] Step 3. It is judged whether the diamond film is a single-crystal diamond film or a polycrystalline diamond film according to the ellipsometric spectrum data and the absorption spectrum data obtained in step 2. When the diamond film is the single-crystal diamond film, the step 41 is executed, and when the diamond film is the polycrystalline diamond film, the steps 42, 5, and 6 are executed. For example, it is judged whether the diamond film is the single-crystal diamond film or the polycrystalline diamond film according to an absorption difference of the absorption spectrum data, such as according to a variation of absorption coefficient k. When there is no absorption, k is 0, and the diamond film is the single-crystal diamond film. When there is absorption, k is a curve, and the diamond film is the polycrystalline diamond film;

[0034] Step 41. The optical constants and the thickness d of the single-crystal diamond film are obtained through a calculation using the Cauchy model in a full spectral region. The optical constants of the single-crystal diamond film at least comprise a refractive index n and an extinction coefficient k;

[0035] Step 42. A spectral region defining a transparent section for the polycrystalline diamond film is selected from the polycrystalline diamond film, and the optical constants and a thickness d of the polycrystalline diamond film are obtained through calculation using the Cauchy model in the spectral region;

[0036] A calculation formula of the Cauchy model is:

[00007]$\begin{array}{cc}n=\mathrm{An}+\frac{\mathrm{Bn}}{{\lambda }^2}+\frac{\mathrm{Cn}}{{\lambda }^4}& \left(1\right)\end{array}$$\begin{array}{cc}k\left(\lambda \right)=A_k{e}^{B_k\left(E-E_b\right)}& \left(2\right)\end{array}$

[0037] Wherein An, Bn, and Cn are parameters of the Cauchy model, λ is wavelength, an extinction coefficient k is described by three parameters A.sub.k, B.sub.k, and E.sub.b, E.sub.b=1240/4, and E.sub.b relates to a material of the substrate;

[0038] Step 5. An oscillator model for dielectric constants is added to the absorption spectrum data of the polycrystalline diamond film, and an amplitude and a width of the oscillator model of the polycrystalline diamond film are adjusted according to the ellipsometric spectrum data;

[0039] The oscillator model for the dielectric constants is the Lorentz oscillator, and a calculation formula of the Lorentz oscillator is as follows:

[00008]$\begin{array}{cc}n=\frac{{\mathrm{AE}}_n}{E_n^2-E^2-\mathrm{iBrE}}& \left(3\right)\end{array}$

[0040] Wherein A is an amplitude of parameters of the oscillator model, En is a center position of the parameters of the oscillator model, and Br is a half wave width of the parameters of the oscillator model.

[0041] Step 6. A difference between an experimental value and a fitted value is evaluated using an evaluation function MSE to determine a refractive index n, the extinction coefficient k, the thickness d of the polycrystalline diamond film. A fitted effect is better when the evaluation function MSE is smaller.

[0042] A calculation formula of the evaluation function MSE is as follows:

[00009]$\begin{array}{cc}{\mathrm{MSE}}^2=\frac{1}{2N-M}{.Math.}_{i=1}^n\left[{\left(\frac{{\phi }_i^{\mathrm{mod}}-{\phi }_i^{\exp }}{{\delta }_{\phi ,i}^{\exp }}\right)}^2+{\left(\frac{{\Delta }_i^{\mathrm{mod}}-{\Delta }_i^{\exp }}{{\delta }_{\Delta ,i}^{\exp }}\right)}^2\right]& \left(4\right)\end{array}$

[0043] Wherein mod is the fitted value, exp is a measured value, δ is a measurement error, N is a total logarithm of ψ and Δ measured by ellipsometer at the same time, and M is a logarithm of a selected fitted parameter.

[0044] The aforementioned embodiments are merely some embodiments of the present disclosure, and the scope of the disclosure is not limited thereto. Thus, it is intended that the present disclosure cover any modifications and variations of the presently presented embodiments provided they are made without departing from the appended claims and the specification of the present disclosure.