CN106556572A - A kind of determination method of correlation between optical thin film characteristic - Google Patents

Abstract

The invention discloses between a kind of optical thin film characteristic correlation determination method, the characteristics of invention is the Correlation Analysis Technology by using statistical mathematics, it is not limited to specific thin-film technique experimental design, film characteristics test result prepared by same process is analyzed, the correlation between two kinds of characteristics of film is obtained.This method has universality for the analysis of correlation between optical thin film characteristic.

Description

A kind of determination method of correlation between optical thin film characteristic

Technical field

The invention belongs to optical film technology field, more particularly to the characterization technique of optical thin film optical characteristics, is related to A kind of determination method of correlation between optical thin film characteristic.

Background technology

Optical thin film element has important application, the such as ultra-low loss of laser gyro in optical instrument, optical system Beam splitter of optical element antireflection film, light path etc. in laser film, optical system, in some optical technical fields Become one of core technology.The preparation method of optical thin film is more, and such as thermal evaporation, electron beam evaporation, ion auxiliary, ion beam splash Penetrate, magnetron sputtering, ald, sol-gel, the method such as thermal oxide, in the preparation of strong non-equilibrium physics and chemistry Under journey, the film characteristics of different preparation methods are different.Under same preparation technology, generally require to its optics, heating power Preferred preparation technology parameter is balanced between characteristic, correlation between different qualities how is determined for instructing preparation technology Parameter it is preferred significant.

Optical thin film is in preparation process, also different according to the Different Preparation parameter of its process of preparing, such as exists In electron-beam evaporation technology, vacuum room temperature, electron gun current, sedimentation rate, working gas bias etc. are main techniques Parameter, and in ion beam sputtering technology, vacuum room temperature, ion beam voltage and electric current etc. are main technologic parameters, therefore make Standby film characteristics are the function of many variables of technological parameter.Researcher often concentrates research characteristic to advise with the change of technological parameter Rule, such as relation between preparation technology parameter and Film Stress Characteristic, microstructure characteristic and optical characteristics etc., to film characteristics it Between relation report it is less.In basic physical model of the stress with index of refraction relationship, Haruo Takashashi et al. are grinding When studying carefully infrared fileter temperature stability, thermal stress and film refractive index proposed based on elastic theory and physical thickness changes Relation, the model are only applicable to the little situation of range of temperature.If under same preparation technology, it is known that different qualities it Between relation, then under the technical need for different qualities, relatively easy is preferably then become to technological parameter, while The physical significance of film characteristics can deeply be understood, and how optical thin film skill is become to the relation research between film different qualities Important proposition in art field.

The content of the invention

(1) technical problem to be solved

The technical problem to be solved in the present invention is：A kind of determination method of correlation between optical thin film characteristic is provided, gram Defect of the prior art is taken, the correlation between optical thin film different qualities is accurately and rapidly obtained.

(2) technical scheme

In order to solve above-mentioned technical problem, the present invention provides a kind of determination method of correlation between optical thin film characteristic, Which comprises the following steps：

S1：The Sample Storehouse of optical thin film characteristic under same preparation technology is set up, optical thin film characteristic is according to different spies The numerical matrix of property；

S2：Two property samples matrixes are chosen, sample number is identical in feature matrix, and the sample of same position in a matrix This characteristic is the characteristic under preparation technology parameter of the same race, calculates the Pearson came product moment sample correlation coefficient of two matrixes；

S3：Significance test is carried out to sample correlation coefficient, the t distribution inspections proposed using Fischer check mould according to t Type calculates sample statistic；

S4：In assumed statistical inspection, P is defined as in null hypothesis H₀Make random sampling in the totality of defined, obtain big In the minimum level of signifiance equal to available sample statistic；In any given level of signifiance α, if p<α, then refuse null hypothesis H₀, illustrate that the correlation between two characteristics of film is notable；If p >=α, null hypothesis H can not be refused₀, illustrate to roll over film two No significant correlation between characteristic；

S5：Under level of significance α, the fiducial confidence ellipse of correlation between two characteristics of film is analyzed, with phase The increase of closing property, the ratio of semi-minor axis length of fiducial confidence ellipse gradually increase, the correlation between the bigger explanation film characteristics of ratio of semi-minor axis length Property is bigger；

S6：Have a case that correlation carries out linear regression analysis to film characteristics, obtain the correlation between film characteristics Property numerical function.

Wherein, in step S1, two property samples storehouses of optical thin film under same preparation technology is set up, X and Y is designated as Matrix, the size of matrix are sample number N, x_jAnd y_jFor the film characteristics under same preparation parameter, the sample matrix of characteristic is as follows Formula：

Wherein, in step S2, covariance and standard deviation are estimated based on sample, is calculated two characteristics Sample matrix correlation coefficient r_X,Y, expression formula is as follows：

Wherein, in step S3, set up hypothesis testing model：

H₀:ρ=0；H₁:ρ≠0 (3)

Wherein, in step S3, build t test statistics as follows：

Wherein, in step S4, in assumed statistical inspection, P is defined as in null hypothesis H₀Make in the totality of defined with Machine is sampled, and obtains the minimum level of signifiance more than or equal to available sample statistic, as formula (3) is two-sided test of hypothesis, can To obtain：

P=P { | t | >=α }=2P { | t | >=α } (5)

(3) beneficial effect

The determination method of correlation between the optical thin film characteristic provided by above-mentioned technical proposal, by setting up optical thin film The sample matrix of characteristic, the method analyzed using mathematical statistics carry out correlation analysis to two property samples matrixes of film, then Analyzed by the physical significance of film characteristics, clear and definite statistical significance and the physical significance between film characteristics may finally be determined； This method has universal versatility for the research of optical thin film characteristic.

Description of the drawings

The correlation fiducial confidence ellipse of Fig. 1-HfO2 film refractive indexs and stress.

The correlation linear regression curves of Fig. 2-HfO2 film refractive indexs and stress.

The correlation fiducial confidence ellipse of Fig. 3-Ta2O5 film refractive indexs and stress.

The correlation linear regression curves of Fig. 4-Ta2O5 film refractive indexs and stress.

Specific embodiment

To make the purpose of the present invention, content and advantage clearer, with reference to the accompanying drawings and examples, to the present invention's Specific embodiment is described in further detail.

Between the present embodiment optical thin film characteristic, the determination method of correlation comprises the steps：

S1：Initially set up the Sample Storehouse of film characteristics under same preparation technology, the ripe test of optical thin film characteristic Technology is tested, according to the numerical matrix of different characteristics.

S2：Two property samples matrixes are chosen, sample number should be identical in feature matrix, and same position in a matrix Sample properties need to be the characteristic under preparation technology parameter of the same race, calculate the Pearson came product moment sample phase relation of two matrixes Number；

S3：Population correlation coefficient due to obtaining sample, need to carry out significance test to sample correlation coefficient, adopt The t distribution inspections that Fischer (Fisher) is proposed, calculate statistic according to t testing models；

S4：In assumed statistical inspection, P is defined as in null hypothesis H₀Make random sampling in the totality of defined, obtain big In the minimum level of signifiance equal to available sample statistic；In any given level of signifiance α, if p<α, then refuse null hypothesis H₀, illustrate that the correlation between two characteristics of film is notable；If p >=α, null hypothesis H can not be refused₀, illustrate to roll over film two No significant correlation between characteristic；

S5：Under level of significance α, the fiducial confidence ellipse of correlation between two characteristics of film is analyzed, with phase The increase of closing property, the ratio of semi-minor axis length of fiducial confidence ellipse gradually increase, the correlation between the bigger explanation film characteristics of ratio of semi-minor axis length Property is bigger；

S6：Have a case that correlation carries out linear regression analysis to film characteristics, obtain the correlation between film characteristics Property numerical function.

By said method, the correlation between optical thin film different qualities can be fast and effectively obtained, can be fine Instruct actual production.

Wherein, in step S1, two property samples storehouses of optical thin film under same preparation technology is set up, X and Y squares are designated as Battle array, the size of matrix are sample number N, x_jAnd y_jFor the film characteristics under same preparation parameter, the sample matrix of characteristic is as follows Formula：

In step S2, covariance and standard deviation are estimated based on sample, be calculated the sample matrix of two characteristics Correlation coefficient r_X,Y, expression formula is as follows：

In step S3, hypothesis testing model is set up：

H₀:ρ=0；H₁:ρ≠0 (3)

Build t test statistics as follows：

In step S4, in assumed statistical inspection, P is defined as in null hypothesis H₀Make random sampling in the totality of defined, obtain The minimum level of signifiance of available sample statistic must be more than or equal to, as formula (3) is two-sided test of hypothesis, can be obtained：

P=P { | t | >=α }=2P { | t | >=α } (5)

The inventive method is described in further detail with specific example below.

Example 1：With ion beam sputtering HfO₂Film, investigates the correlation between the refractive index and stress of film.

(1) using ion beam sputter depositing technology, HfO is prepared on a quartz substrate₂Film, experimental process parameters are according to L₉ (3⁴) orthogonal, to HfO₂Film is respectively completed the preparation experiment of nine process conditions, tests out The stress and refractive index characteristic of film, experiment condition see attached list 1 with test result.

(2) reflect rate matrix X and stress matrix Y and be shown in Table 1；

1 HfO of table₂Film preparation condition and test result

(3) it is calculated HfO₂The coefficient correlation of film refractive index matrix X and stress matrix Y is -0.92049；

(4) it is calculated t inspection statistics value 6.23246；

(5) free degree of sample data is 7, the p value 0.0004 being calculated under t statistical values；

(6) herein, we select level of signifiance α=0.05, p value to be respectively less than the level of signifiance, illustrate the correlation of population sample Coefficient be zero probability more than 95%.

(7) may certify that by sample correlation coefficient significance test：HfO prepared by ion beam sputtering₂Film refractive index With coefficient correlation γ of stress_X,Y<0th, and | γ_n,S| there is negatively correlated linear relationship with stress in → 1, i.e. film refractive index, i.e., With the increase of thin-film refractive index, film layer compression gradually increases, in turn alternatively with the increase of film layer compression, film The refractive index of layer is also presented the trend of increase.

(8) fiducial probability is set as 95% (significance 5%), the HfO for obtaining₂Film fiducial confidence ellipse is shown in Fig. 1.

(9) HfO is analysis shows from above-mentioned correlation statistics₂There is strong linear correlation with stress in film refractive index, under Linear regression is carried out in the face of relation of the refractive index with stress, regression equation is：

Y=a+b × X (6)

Wherein X is refractive index, and Y is stress, and a is intercept, and b is slope, a=5.261, b=-16.490.HfO₂Film is rolled over The linear regression result that rate is penetrated with stress relation is shown in Fig. 2 respectively.

Example 2：With ion beam sputtering Ta₂O₅Film, investigates the correlation between the refractive index and stress of film.

(1) using ion beam sputter depositing technology, Ta is prepared on a quartz substrate₂O₅Film, experimental process parameters are according to L₉ (3⁴) orthogonal, to Ta₂O₅Film is respectively completed the preparation experiment of nine process conditions, tests out The stress and refractive index characteristic of standby film, experiment condition see attached list 2 with test result.

2 Ta of table₂O₅Film preparation condition and test result

(2) reflect rate matrix X and stress matrix Y and be shown in Table 2；

(3) it is calculated Ta₂O₅The coefficient correlation of film refractive index matrix X and stress matrix Y is -0.78884；

(4) it is calculated t inspection statistics value 3.39585；

(5) free degree of sample data is 7, the p value 0.0115 being calculated under t statistical values；

(6) herein, we select level of signifiance α=0.05, p value to be respectively less than the level of signifiance, illustrate the correlation of population sample Coefficient be zero probability more than 95%.

(7) may certify that by sample correlation coefficient significance test：Ta prepared by ion beam sputtering₂O₅Film refractive index With coefficient correlation γ of stress_X,Y<0th, and | γ_n,S| there is negatively correlated linear relationship with stress in → 1, i.e. film refractive index, with The increase of film layer compression, the refractive index of film layer is also presented the trend of increase.

(8) fiducial probability is set as 95% (significance 5%), the Ta for obtaining₂O₅Film fiducial confidence ellipse is shown in Fig. 3.

(9) Ta is analysis shows from above-mentioned correlation statistics₂O₅There is strong linear correlation with stress in film refractive index, under Linear regression is carried out in the face of relation of the refractive index with stress, regression equation is：

Y=a+b × X (6)

Wherein X is refractive index, and Y is stress, and a is intercept, and b is slope, a=4.012, b=-6.269.HfO₂Film is reflected The linear regression result of rate and stress relation is shown in Fig. 4 respectively.

To sum up, the correlation between optical thin film different qualities can be obtained by this method, is not the characteristics of the invention It is limited to specific thin-film technique experimental design, by using the Correlation Analysis Technology of statistical mathematics, is prepared by same process Film characteristics test result is analyzed, and the correlation between two kinds of characteristics of film is obtained.This method is special for optical thin film The analysis of correlation between property has universality.

The above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For member, on the premise of without departing from the technology of the present invention principle, some improvement and deformation can also be made, these improve and deform Also should be regarded as protection scope of the present invention.

Claims (6)

1. between a kind of optical thin film characteristic correlation determination method, it is characterised in that comprise the following steps：

S1：The Sample Storehouse of optical thin film characteristic under same preparation technology is set up, optical thin film characteristic is according to different characteristics Numerical matrix；

S2：Two property samples matrixes are chosen, sample number is identical in feature matrix, and the sample spy of same position in a matrix Property is the characteristic under preparation technology parameter of the same race, calculates the Pearson came product moment sample correlation coefficient of two matrixes；

S3：Significance test is carried out to sample correlation coefficient, the t distribution inspections proposed using Fischer, according to t testing model meters Calculate sample statistic；

S4：In assumed statistical inspection, P is defined as in null hypothesis H₀Make random sampling in the totality of defined, be more than or equal to The minimum level of signifiance of available sample statistic；In any given level of signifiance α, if p<α, then refuse null hypothesis H₀, say Correlation between two characteristics of bright film is notable；If p >=α, null hypothesis H can not be refused₀, illustrate to roll over two characteristics of film Between no significant correlation；

S5：Under level of significance α, the fiducial confidence ellipse of correlation between two characteristics of film is analyzed, with correlation Increase, the ratio of semi-minor axis length of fiducial confidence ellipse gradually increases, and the correlation between the bigger explanation film characteristics of ratio of semi-minor axis length is just It is bigger；

S6：Have a case that correlation carries out linear regression analysis to film characteristics, obtain the correlation number between film characteristics Value function.

2. between optical thin film characteristic as claimed in claim 1 correlation determination method, it is characterised in that step S1 In, two property samples storehouses of optical thin film under same preparation technology to be set up, X and Y matrixes are designated as, the size of matrix is sample Number N, x_jAnd y_jFor the film characteristics under same preparation parameter, the sample matrix such as following formula of characteristic：

$X=\left[\begin{array}{c}{x}_1\\ x_2\\ ...\\ x_j\\ ...\\ x_N\end{array}\right],Y=\left[\begin{array}{c}{y}_1\\ y_2\\ ...\\ y_j\\ ...\\ y_N\end{array}\right]---\left(1\right)$

3. between optical thin film characteristic as claimed in claim 2 correlation determination method, it is characterised in that step S2 In, covariance and standard deviation are estimated based on sample, be calculated the sample matrix correlation coefficient r of two characteristics_X,Y, table It is as follows up to formula：

$r_{X,Y}=\frac{\underset{j=1}{\overset{N}{\&Sigma;}}\&lsqb;(x_j-\underset{j=1}{\overset{N}{\&Sigma;}}{x}_j/N)(y_j-\underset{j=1}{\overset{N}{\&Sigma;}}{y}_j/N)\&rsqb;}{\sqrt{\underset{i=1}{\overset{N}{\&Sigma;}}{(x_j-\underset{j=1}{\overset{N}{\&Sigma;}}{x}_j/N)}^2}\sqrt{\underset{i=1}{\overset{N}{\&Sigma;}}{(y_j-\underset{j=1}{\overset{N}{\&Sigma;}}{y}_j/N)}^2}}---\left(2\right)$

4. between optical thin film characteristic as claimed in claim 3 correlation determination method, it is characterised in that step S3 In, set up hypothesis testing model：

H₀:ρ=0；H₁:ρ≠0 (3)

5. between optical thin film characteristic as claimed in claim 4 correlation determination method, it is characterised in that step S3 In, build t test statistics as follows：

$t=\frac{\sqrt{N-2}}{\sqrt{1-r_{X,Y}^2}}|r_{X,Y}-0|---\left(4\right)$

6. between optical thin film characteristic as claimed in claim 5 correlation determination method, it is characterised in that step S4 In, in assumed statistical inspection, P is defined as in null hypothesis H₀Make random sampling in the totality of defined, obtain more than or equal to existing The minimum level of signifiance of sample statistic, as formula (3) is two-sided test of hypothesis, can obtain：

P=P { | t | >=α }=2P { | t | >=α } (5).