CN100538327C - A kind of measure coating glass film optical parameters method - Google Patents

Abstract

The present invention relates to a kind of measure coating glass film optical parameters method, comprise the steps: to set up the funtcional relationship of film thickness h, refractive index n, extinction coefficient k and film transmissivity, reflectivity, constitute the curve fit problem with visible transmission, the reflectance spectrum simultaneous of actual measurement coated glass, the two-step approach of utilizing simulated annealing, Newton iteration method to combine is found the solution this curve fit problem, thereby obtains the measurement result of Film Optics parameter.The present invention compares with existing relevant art, is more suitable for the measurement of coated glass film, has measurement effect fast and accurately, and measurement result is stable, and method is simple, and is with low cost.

Description

A kind of measure coating glass film optical parameters method

Technical field

The present invention relates to a kind of measure coating glass film optical parameters method, relate in particular to and utilize visible transmission, reflectance spectrum to fit the method that obtains the Film Optics parameter, belong to Materials Processing Engineering parameter measurement field.

Background technology

Coated glass is in one or more layers metal of glass surface coating, metal oxide or other inorganic material, to change the optical property of glass, satisfies some particular requirement.Therefore measure the optical parametric of coated glass film, be thickness, refractive index and extinction coefficient, for detecting the coated glass quality, improve the plated film CONTROL PROCESS, improving the coated glass performance, the robotization control of realization film performance and technological parameter interaction and rete and optimization in Properties design all have important practical significance.

There is several different methods can be used for the optical parametric of MEASUREMENTS OF THIN, the most general with optical means especially, for example interferometric method, ellipsometry, reflectance spectrum and transmission spectrum method.Interferometric method can utilize a plurality of peak-to-valley values that occur on the curve of spectrum to estimate the thickness and the refractive index of film comparatively easily, but film thickness generally a plurality of interference peak valleys will just can occur more than the hundreds of nanometer, therefore be generally coated glass about 100 nanometers for thicknesses of layers, as sunlight controlling coated glass, then inapplicable.The measurement result of ellipsometry quick and precisely, but the measurement means complexity, the requirement for experiment condition harshness, cost is higher.

Summary of the invention

The purpose of this invention is to provide a kind of simplely, applied widely, be subjected to the little measure coating glass film optical parameters method of ectocine.

To achieve these goals, the thinking of the technology of the present invention solution is: set up the mathematical relation of Film Optics parameter and coated glass transmission, reflectance spectrum, obtain the mathematical model of problem, obtain optical parameter of film on coated glass by finding the solution mathematical model.

Concrete steps are as follows:

Measure transmission and the reflectance spectrum of coated glass under visible light vertical incidence state, be designated as T respectively _m, R _m, utilize matrix method to obtain film transmission under the vertical incidence state and reflectance spectrum about the parameter type of n, k and film thickness h, be designated as T _c(n, k, h), R _c(n, k h), and with the function that n and k expand into lambda1-wavelength λ, set up T _c(n, k, h), R _c(n, k, h) and T _m, R _mLeast squares formalism fit parameter type, as the formula (1),

$f(n,k,h)=\underset{\mathrm{\λ}}{\mathrm{\Σ}}[{(T_c(n,k,h)-T_m)}^2+{(R_c(n,k,h)-R_m)}^2]---\left(1\right)$

Find the solution formula (1), (n, k h) are one group of parameter n of minimum value, and k and h are exactly to measure the optical parameter of film on coated glass that obtains to obtain making f.

Find the solution formula (1), can adopt traditional alternative manner.Relate to a large amount of non-linear units because Film Optics calculates, in order to find the solution formula (1) fast and accurately, be solved to the two-step approach that adopts simulated annealing and Newton iteration method to combine, concrete steps are as follows:

1) uses simulated annealing under than the weak convergence condition, to find the solution formula (1), obtain one group of parameter n, the value of k and h;

2) n that obtains with step 1), k and h find the solution formula (1) once more as the calculating initial value of Newton iteration method;

3) repeating step 1), 2) M time, M=1,2 ... positive integer in obtaining M result, is obtained and is made f (n, k, h) a group of minimum parameter n, k and h of value.

The present invention uses and measures transmission, the reflectance spectrum that obtains under the vertical incidence condition, and measurement result is subjected to ectocine little, and measured value is stable.Modelling is simple and reliable, and method of testing is with low cost, is a kind of means of effective MEASUREMENTS OF THIN optical parametric.

Description of drawings

Fig. 1 is the coated glass structural representation;

Fig. 2 is the coated glass visible transmission T under the vertical incidence state _mWith reflectance spectrum R _mCurve and the T that fits _cAnd R _cCurve;

Fig. 3 is to use the sample refractive index n of the method for the invention acquisition and the curve of extinction coefficient k.

Embodiment

Below in conjunction with accompanying drawing and example the present invention is described in further details.

With online sunlight controlling coated glass is example, and rete 1 is a silicon based thin film, and substrate 2 is the common white glass, and as shown in Figure 1, I is an incident light among the figure, and R is a reflected light, and T is a transmitted light.Measure the visible transmission T under the coated glass vertical incidence state _mWith reflectance spectrum R _mAs shown in Figure 2, round dot and square point are represented T respectively _mAnd R _mMatrix method is calculated the transmissivity T that impinges perpendicularly on film surface light _cWith reflectivity R _cFollowing formula:

$T_c\left(\mathrm{\λ}\right)=\frac{{4n}_s{n}_0}{{|n_0(\cos \left(\frac{2\mathrm{\πhn}\′}{\mathrm{\λ}}\right)+i\frac{n_s}{n\′}\sin \left(\frac{2\mathrm{\πhn}\′}{\mathrm{\λ}}\right))+n_s\cos \left(\frac{2\mathrm{\πhn}\′}{\mathrm{\λ}}\right)+\mathrm{in}\′\sin \left(\frac{2\mathrm{\πhn}\′}{\mathrm{\λ}}\right)|}^2}---\left(2\right)$

$R_c\left(\mathrm{\λ}\right)=\frac{{|n_0(\cos \left(\frac{2\mathrm{\πhn}\′}{\mathrm{\λ}}\right)+i\frac{n_s}{n\′}\sin \left(\frac{2\mathrm{\πhn}\′}{\mathrm{\λ}}\right))-n_s\cos \left(\frac{2\mathrm{\πhn}\′}{\mathrm{\λ}}\right)+\mathrm{in}\′\sin \left(\frac{2\mathrm{\πhn}\′}{\mathrm{\λ}}\right)|}^2}{{|n_0(\cos \left(\frac{2\mathrm{\πhn}\′}{\mathrm{\λ}}\right)+i\frac{n_s}{n\′}\sin \left(\frac{2\mathrm{\πhn}\′}{\mathrm{\λ}}\right))+n_s\cos \left(\frac{2\mathrm{\πhn}\′}{\mathrm{\λ}}\right)+\mathrm{in}\′\sin \left(\frac{2\mathrm{\πhn}\′}{\mathrm{\λ}}\right)|}^2}---\left(3\right)$

Air refraction n wherein ₀With glass refraction n _s, n ' is a film plural form refractive index, i.e. n '=n-ik, and h is a film thickness.Adopt the Forouhi-Bloomer model n and k to be expanded into the function of incident photon energy E to silicon based thin film:

$n_{\left(E\right)}=n_{(\∞)}+\frac{B_{0}E+C_0}{E^2-\mathrm{BE}+C}$ (4)

$k_{\left(E\right)}=\frac{A{(E-E_G)}^2}{E^2-\mathrm{BE}+C}$

Wherein

$B_0=\frac{A}{Q}[-\frac{1}{2}{B}^2+E_{G}B-{\mathrm{<figure-callout\; id="2"\; label="E\; G"\; filenames="C200610053955E00061.png"\; state="\{\{state\}\}">E</figure-callout>}}_G^{}+C]$

$C_0=\frac{A}{Q}[\frac{1}{2}B({\mathrm{<figure-callout\; id="2"\; label="E\; G"\; filenames="C200610053955E00061.png"\; state="\{\{state\}\}">E</figure-callout>}}_G^{}+C)-{2E}_{G}C]$ (5)

$Q=\frac{1}{2}{(4C-B^2)}^{1/2}$

A, B, C, E in the formula _GBe constant, and 4C-B ²0.E is an incident photon energy, and E=2 π q/ λ is arranged, and q is a Planck's constant.Refractive index when n (∞) is the E infinity.

Make up T with least squares formalism _c, R _cAnd T _m, R _mThe curve fitting parameter formula, as the formula (1),

$f(n,k,h)=\underset{\mathrm{\&lambda;}}{\mathrm{\&Sigma;}}[{(T_c(n,k,h)-T_m)}^2+{(R_c(n,k,h)-R_m)}^2]---\left(1\right)$

With formula (2-5) and T _mAnd R _mSubstitution formula (1) just obtains the mathematical form of complete curve fit problem, wherein constant A, B, C, E _G, n (∞), h be undetermined parameter.

In the simulated annealing, the initial value of undetermined parameter is chosen arbitrarily, as gets A=0, B=2, C=2, E _G=0, n (∞)=1.5, h=100 with the disturbance that random sampling produces the undetermined parameter value, carries out global optimization computation under than the weak convergence condition, do not obtain more preferential treatment as continuous 100 random samplings and decide parameter value and then finish calculating.The undetermined parameter value that simulated annealing is obtained is used Newton iteration method to carry out local optimum at the curve fit problem of formula (1) and is calculated as initial value, obtains more excellent undetermined parameter value.Repeat aforementioned calculation process 24 times, (h) one group of parameter of value minimum obtains A=4.30, B=2.49, C=38.02, E as final fitted results for n, k therefrom to select to make f _G=0.68, n (∞)=2.43, h=126.92nm, corresponding transmission, reflectance spectrum fit curve shown in solid line among Fig. 2.With A, B, C, E _G, n parameter substitution formula (4) such as (∞), obtain the refractive index n and the extinction coefficient k of film, as shown in Figure 3.This sample uses its thickness of ellipsometer measurement to be 118.28nm, with measured value deviation 6.8% of the present invention.

Claims (2)

1, a kind of measure coating glass film optical parameters method is characterized in that step is as follows:

Measure transmission and the reflectance spectrum of coated glass under visible light vertical incidence state, be designated as T respectively _m, R _m, utilize matrix method to obtain film transmission under the vertical incidence state and reflectance spectrum about the parameter type of n, k and film thickness h, be designated as T _c(n, k, h), R _c(n, k h), and with the function that n and k expand into lambda1-wavelength λ, set up T _c(n, k, h), R _c(n, k, h) and T _m, R _mLeast squares formalism fit parameter type, as the formula (1),

$f(n,k,h)=\underset{\mathrm{\&lambda;}}{\mathrm{\&Sigma;}}[{(T_c(n,k,h)-T_m)}^2+{(R_c(n,k,h)-R_m)}^2]---\left(1\right)$

Find the solution formula (1), (n, k h) are one group of parameter n of minimum value, and k and h are exactly to measure the optical parameter of film on coated glass that obtains to obtain making f.

2, measure coating glass film optical parameters method according to claim 1 is characterized in that the two-step approach that the formula of finding the solution (1) adopts simulated annealing and Newton iteration method to combine finds the solution, and concrete steps are as follows:

1) uses simulated annealing under than the weak convergence condition, to find the solution formula (1), obtain one group of parameter n, the value of k and h;

2) n that obtains with step 1), k and h find the solution formula (1) once more as the calculating initial value of Newton iteration method;

3) repeating step 1), 2) M time, M=1,2 ... positive integer in obtaining M result, is obtained and is made f (h) value is one group of parameter n, k and the h of minimum for n, k.

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