CN115406366A - ISOA method for measuring parameters of single-layer film based on in-situ common-angle SPR - Google Patents
ISOA method for measuring parameters of single-layer film based on in-situ common-angle SPR Download PDFInfo
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- G01N21/41—Refractivity; Phase-affecting properties, e.g. optical path length
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Abstract
The invention discloses an ISOA method for measuring parameters of a single-layer film based on in-situ common-angle SPR, which comprises the following steps: firstly, measuring the reflection spectrum and interference fringe information of a single-layer film by utilizing an SPR measuring device in an in-situ co-angle manner, obtaining an incident wavelength-reflectivity and incident wavelength-phase difference relation curve through data processing, initializing data of an improved population search algorithm, selecting reflection spectrum and phase difference data from the relation curve, carrying out normalization processing to obtain a reflectivity value and a phase difference value data set which are in the same order of magnitude, using the reflectivity value and the phase difference value data set as input values of the improved population search algorithm, and setting a resolving termination condition; and finally, operating an improved crowd search algorithm to perform inversion calculation based on the target function, and solving the parameter vector a by searching the minimum value of the target function, namely obtaining that n is the refractive index, k is the extinction coefficient and d is the thickness. The method is convenient to operate, can obtain the film parameters under continuous multiple wavelengths through one-time operation, and has the advantages of high accuracy and high efficiency.
Description
Technical Field
The invention belongs to the technical field of material analysis and measurement, relates to measurement of optical constants and thickness parameters of a metal film material, and particularly relates to an ISOA (inverse sequence analysis and optimization) method for jointly measuring parameters of a single-layer film based on an in-situ common-angle SPR (surface plasmon resonance) phase and a reflection spectrum.
Background
With the wide application of nanoscale thin films in the fields of microelectronics, optoelectronics, aerospace, medical instruments and high polymer materials, thin film technology has become a research hotspot in the fields of current scientific and technological research and industrial production. The continuous improvement and rapid development of thin film technology also put more demands on various parameters of the thin film, for example, the optical constant of the thin film changes with the change of wavelength, and the optical constant of the thin film is influenced by the difference of thickness, thereby playing a decisive role in the optical, mechanical and electromagnetic properties of the thin film. Therefore, the simultaneous and accurate detection of the thickness and optical constants of the multi-wavelength nanoscale thin film has become a crucial technology.
At present, the prior art generally adopts a fixed incident wavelength to change an incident angle to collect reflectivity or phase variation to realize the detection of the optical constant and thickness of the metal film under the excitation SPR effect. For example, patent document CN108827166A discloses a SPR phase measurement method for measuring the thickness and optical constant of a metal thin film SAPSO, that is, a similar method is used for measurement. On one hand, the method needs to change the incident angle continuously, so that the incident point of the incident light on the film surface changes, but is limited by the preparation process, the thickness and the optical property of each part of the film surface cannot be guaranteed to be absolutely uniform, and further the in-situ measurement cannot be realized, and meanwhile, the change of the incident angle can cause the continuous change of the position of the reflectivity or the phase acquisition device, so that the measurement error is easily introduced into the experimental process, and the accuracy of the measurement result is further influenced. On the other hand, the method can solve the optical constants and thickness at one wavelength at a time. For solving the optical parameters of the metal film under multiple wavelengths, a common SPR spectroscopy introduces a large imaginary part error of an optical constant when analyzing or fitting the optical constant of the film, so that the problem of low solving precision is caused.
Rapid and accurate measurement of single layer film parameters at multiple wavelengths remains a challenge. Therefore, the method simultaneously acquires the phase difference and the reflection spectrum information of the single-layer metal film under the multi-wavelength under the condition of in-situ angle sharing, and can calculate and obtain the optical constant and the thickness of the single-layer film of the fixed film sample measuring point under the continuous spectrum by simultaneously inputting the incident wavelength-phase difference and the incident wavelength-reflection light intensity curve of the single-layer metal film on the basis of an improved crowd search algorithm, thereby effectively solving the problem of one-time quick solution of the single-layer film parameters corresponding to each wavelength under the continuous multi-wavelength.
Disclosure of Invention
In view of the above, the present invention aims to provide an ISOA method for measuring parameters of a single-layer thin film based on in-situ co-angular SPR.
The technical scheme is as follows:
an ISOA method for measuring parameters of a single-layer film based on in-situ common-angle SPR is characterized by comprising the following steps:
s1, in-situ co-angle measurement of reflection spectrum and interference fringe information: measuring interference fringe information and a reflection spectrum of TM polarized wave of a single-layer film sample in a continuous wavelength lambda range by using an SPR measuring device, and keeping an incident angle and an incident point of incident light unchanged in the measuring process, wherein the incident angle is an angle capable of exciting an SPR effect;
s2, processing data to obtain an incident wavelength-reflectivity and incident wavelength-phase difference relation curve: processing the reflection spectrum and the interference fringe information obtained in the step S1 to obtain the relation curve;
s3, initializing data of the improved crowd search algorithm: selecting reflection spectrum and phase difference data from the relation curve, carrying out normalization processing to obtain a data set of a reflectivity value and a phase difference value which are in the same magnitude, using the data set as an input value of an improved crowd search algorithm, and setting a resolving termination condition;
and S4, performing inversion calculation based on an objective function by adopting an improved population search algorithm, wherein the size of the objective function reflects the similarity between the inversion calculation and the reflectivity value and between the phase difference values measured by experiments, the objective function takes the parameter vector a to be measured of the single-layer film sample as a function parameter, and the parameter vector a, a = (n, k, d) is solved by searching the minimum value of the objective function, wherein n is the refractive index, k is the extinction coefficient, and d is the thickness.
Preferably, in step S4, the reflectivity value and the phase difference value data set obtained in step S3 are substituted into the objective function, a search range of a solution space { n, k, d } is initialized, an improved population search algorithm is adopted to perform inversion calculation based on the objective function, and the accuracy of solution is determined according to the size of the objective function, so as to obtain the refractive index n, the extinction coefficient k and the thickness d of the single-layer film sample when the objective function is minimum;
the objective function formula is as follows (1):
Δφ cal (i, a) represents the phase difference value of the TE polarized wave and the TM polarized wave under the SPR effect calculated by the algorithm inversion,
Δφ exp (i) Showing the phase difference value of the TE polarized wave and the TM polarized wave under the SPR effect of the ith reference point extracted from the incident wavelength-phase difference curve measured by experiments,
a represents the vector containing the parameters to be determined, a = (n, k, d).
In the formula (1), data R exp (i, a) and Δ φ exp (i) Can be obtained from incident wavelength-reflectivity and incident wavelength-phase difference relation curvesIs directly obtained.
Preferably, the step S4 specifically comprises the steps of,
s41, initializing each parameter: setting the maximum iteration times and the minimum approximation error, initializing the population number of the population search algorithm, and initializing a solution space { n, k, d };
s42, randomly placing M (M)>0 and natural number) searcher in the solution space, calculating and evaluating the objective function value of M searcher positions, and placing the ith searcher position at the individual optimum position g besti Put the best among all searchers at the global best position z best And recording the minimum objective function value min (F) corresponding to the global optimum position at the moment fitness ) And the corresponding solution vector a;
s43, calculating the searching direction d of each searcher i in the j-dimensional space ij Adaptive search step size alpha ij Further updating the position of the individual searcher and updating the solution vector a;
s44, aiming at each searcher, the objective function value and the optimal position g which has been experienced previously besti Is the objective function value F fitness (g besti ) Comparing, and if the position is better, taking the position as the current optimal position; (ii) a
S45, aiming at each searcher, the objective function value and the globally experienced optimal position z best Is the objective function value F fitness (z best ) Comparing, and if the position is better, taking the position as the current global optimal position; (ii) a
S46, judging whether a termination condition is met, if so, stopping searching and outputting an optimal solution vector; otherwise, repeating the steps S43-S45 to continue the iterative computation until the end.
Preferably, in step S43, the calculation formula of the adaptive search step in the improved population search algorithm is as follows:
where ω is the inertial weight, x min 、x max The positions u corresponding to the minimum and maximum objective function values respectively ij Searching the membership degree of the ith objective function value of the space in the j dimension;
wherein uij Calculated according to the equations (3) and (4),
u ij ＝rand(u i ,1),j＝1,....D (3)，
in formulae (3) and (4), u i Is the membership value, u, of the ith objective function min 、u max Respectively, minimum and maximum membership values, rand (u) i 1) is [ u i ,1]And (4) the random number, T is the current evolution algebra, and T is the total evolution algebra.
Preferably, in step S43, the direction d is searched for ij Determined according to the formula (5),
wherein ,
is [0,1 ]]Random real numbers over intervals;
d i,ego 、d i,alt and di,pro The direction of interest, and the direction of pre-movement for each searcher i are respectively expressed as formulas (6) to (8):
d i,ego (t)＝g i,best -x i (t) (6)，
d i,alt (t)＝z i,best -x i (t) (7)，
d i,pro ＝x i (t 1 )-x i (t 2 ) (8)，
wherein ,gi,best Is the current best position; z is a radical of i,best For historical optimum position, t 1 and t2 Are respectively [ t, t-1 ]]And [ t-1, t-2 ]]Value within the range, x i (t 1) and xi (t 2 ) Are respectively [ x ] i (t-2),x i (t-1)]And [ x ] i (t-1),x i (t)]The best search position within the interval.
Preferably, the above-mentioned solution termination condition is an iteration number and a minimum approximation error value, and the iteration calculation is terminated when either one of the iteration number and the minimum approximation error value is satisfied.
Preferably, in step S1, the wavelength λ of the incident light is a continuous wavelength band,
the unit is nm.
Preferably, the single-layer thin film sample is a metal film layer plated on a substrate, and in the step S1, when the SPR measuring apparatus is used for measurement, the substrate-metal film layer-dielectric layer is used as a three-phase thin film structure for detection.
Preferably, in step S4, SPR reflectivity values under TM polarized waves are calculated by algorithmic inversion
Phase difference value delta phi of TE and TM polarized waves under SPR effect cal Calculated according to the equations (9) to (14),
wherein h and g respectively represent p and m or a combination of m and s, p, m and s respectively represent a substrate, a metal film layer and a dielectric layer, r represents a reflection coefficient, epsilon represents a dielectric constant, and k represents h(g)z Wave vector, k, representing the z direction x Representing the wave vector of the incident light;
real part of dielectric constant ∈ real ＝n 2 -k 2 Dielectric constant imaginary part ε imag =2nk, n, k denote refractive index and extinction coefficient, respectively.
Compared with the prior art, the invention has the beneficial effects that:
(1) The in-situ common-angle SPR measurement mode with a fixed incident angle and an incident point is adopted, so that the measurement is convenient and quick, the measurement error caused by the fact that the incident angle and the incident point are continuously changed in the single-wavelength measurement mode in the prior art is avoided, and the influence of the measurement method on the accuracy of the measurement result is reduced;
(2) The method adopts incident light of continuous wave bands for measurement, selects an SPR phase and reflection spectrum combined representation mode, synchronously realizes the solution of the optical constant and the thickness of the metal film under multiple wavelengths, avoids the defect that in the SPR spectrum method in the prior art, larger optical constant imaginary part errors are introduced when the optical constant of the film is analyzed and fitted through reflectivity calculation under multiple wavelengths, and improves the solution precision;
(3) The improved crowd search algorithm is adopted, the problem that the improved crowd search algorithm is easy to fall into local optimum through the gradual self-adaptive search step length is solved, the valley region is prevented from being skipped, the optimum solution can be accurately found, the convergence speed in the iterative calculation process is high, and the optimization precision is high;
(4) The measurement method is improved from two aspects of SPR measurement operation and algorithm calculation, and meanwhile, the measurement efficiency and accuracy are improved;
(5) The method can provide effective theoretical guidance and reference for solving the optical constants and the thicknesses of the multilayer films in the future, and has the characteristics of good optimization effect, strong applicability and the like.
Drawings
FIG. 1 is a flow chart of an ISOA method for measuring parameters of a single-layer thin film based on in-situ co-angular SPR phase and reflectance spectroscopy in accordance with the present invention;
FIG. 2 is a schematic diagram of a three-layer structure of prismatic metal film for use in the present invention;
FIG. 3 is a graph of an iterative comparison of objective functions of an improved population search algorithm obtained at multiple wavelengths according to the present invention and a conventional population search algorithm;
FIG. 4 is a graph of multi-wavelength optical constants obtained by the present invention;
FIG. 5 is a graph of thickness at multiple wavelengths obtained by the present invention;
fig. 6 is a graph comparing the wavelength-reflectance curve and the wavelength-phase difference curve obtained in the experiment with the calculated curve.
Detailed Description
The present invention will be further described with reference to the following examples and the accompanying drawings.
An ISOA method for measuring parameters of a single-layer film based on in-situ common-angle SPR is carried out according to the following steps:
s1, in-situ co-angular measurement of reflection spectrum and interference fringe information: and measuring interference fringe information of the single-layer thin film sample on incident light in a wavelength lambda range and a reflection spectrum of the TM polarized wave by using an SPR measuring device, and keeping an incident angle and an incident point of the incident light unchanged in the measuring process, wherein the incident angle is an angle capable of exciting an SPR effect. The single-layer film sample can be a metal film layer plated on a substrate, and a structure model is detected by adopting a most basic substrate-metal film-dielectric layer three-phase film structure during measurement.
S2, processing data to obtain an incident wavelength-reflectivity and incident wavelength-phase difference relation curve: and processing the reflection spectrum and the interference fringe information obtained in the step S1 to obtain the relation curve.
S3, initializing data of the improved crowd search algorithm: selecting reflection spectrum and phase difference data from the relation curve, carrying out normalization processing to obtain a data set of a reflectivity value and a phase difference value which are in the same order of magnitude, using the data set as an input value of an improved crowd search algorithm, and setting a resolving termination condition. And solving the termination condition into iteration times and a minimum approximation error value, wherein the iteration times and the minimum approximation error value meet one of the conditions, namely, the iterative computation is terminated.
And S4, performing inversion calculation based on an objective function by adopting an improved population search algorithm, wherein the size of the objective function reflects the similarity between the inversion calculation and the reflectivity value and between the phase difference values measured by experiments, the objective function takes the parameter vector a to be measured of the single-layer film sample as a function parameter, and the parameter vector a, a = (n, k, d) is solved by searching the minimum value of the objective function, wherein n is the refractive index, k is the extinction coefficient, and d is the thickness.
In step S4 of this embodiment, the reflectance value and the phase difference value data set obtained in step S3 are substituted into the objective function, and the search range of the solution space { n, k, d } is initialized. Performing inversion calculation based on the target function by adopting an improved population search algorithm, and judging the accuracy of a solution according to the size of the target function to obtain the refractive index n, the extinction coefficient k and the thickness d of the single-layer film sample when the target function is minimum;
the objective function formula is as follows (1):
where Q is the total number of wavelengths involved,
Δφ cal (i, a) represents the phase difference value of the TE polarized wave and the TM polarized wave under the SPR effect calculated by algorithm inversion,
Δφ exp (i) Showing the phase difference value of the TE polarized wave and the TM polarized wave under the SPR effect of the ith reference point extracted from the incident wavelength-phase difference curve measured by experiments,
a represents the vector containing the parameters to be determined, a = (n, k, d).
Step S4 specifically includes:
s41, initializing each parameter: reading the reflection light rate R of the TM polarized wave and the phase difference delta phi between the TE polarized wave and the TM polarized wave under the single-layer metal film excited SPR effect under the multi-wavelength, setting the maximum iteration times and the minimum approximation error, initializing the population number of the population search algorithm, and initializing a solution space { n, k, d }. For example, in this embodiment, the maximum number of iterations =200, the minimum approximation error <0.01, and the population number =100 of the initialized population search algorithm, the initialized solution space { n, k, d }, the solution domain of n [0,0.5], the solution domain of k [1,6], and the solution domain of d [0,50].
S42, randomly placing M searchers in a solution space, calculating and evaluating objective function values of the positions of the M searchers, and placing the position of the ith searcher at the optimal position g of an individual besti Put the best location among all searchers at the global best location z best And recording the minimum objective function value min (F) corresponding to the global optimum position at the moment fitness ) And the corresponding solution vector a. M =100 in this embodiment.
S43, calculating the searching direction d of each searcher i in the j-dimensional space ij Adaptive search step size alpha ij Updating the position of the individual searcher, namely updating a solution vector a in a solution space { n, k, d } with a certain search direction and search step length for each searcher; in this embodiment, the solution space { n, k, d } is three-dimensional, so the value range of j is 1 to 3;
s44, aiming at each searcher, the value of the objective function and the optimal position g which has been experienced before besti Is the objective function value F fitness (g besti ) To carry outComparing, if the position is better, taking the position as the current optimal position;
s45, for each searcher, the objective function value and the global experienced optimal position z best Is the objective function value F fitness (z best ) Comparing, and if the position is better, taking the position as the current global optimal position;
s46, judging whether a termination condition is met, if so, stopping searching and outputting an optimal solution vector; otherwise, repeating the steps S43-S45 to continue the iterative computation until the end.
In step S43, the calculation formula of the adaptive search step in the improved population search algorithm is as follows (2):
wherein, omega is inertia weight and is 0.9; x is a radical of a fluorine atom min 、x max The positions u corresponding to the minimum and maximum objective function values respectively ij Searching the membership degree of the ith objective function value of the space in the j dimension;
wherein uij Calculated according to the equations (3) and (4),
u ij ＝rand(u i ,1),j＝1,....D (3)，
in formulae (3) and (4), u i Is the membership value, u, of the ith objective function min 、u max Respectively, minimum and maximum membership values, rand (u) i 1) is [ u i ,1]The random number is the current evolution algebra, and T is the total evolution algebra; d is the dimension of the solution space, D =3 in this embodiment.
In step S43, the direction d is searched ij Can be determined according to equation (5),
wherein ,
the value of the carbon dioxide is 0.5,
the value is 0.5;
d i,ego 、d i,alt and di,pro The directions of interest, and pre-movement for each searcher i are expressed as formulas (6) to (8), respectively:
d i,ego (t)＝g i,best -x i (t) (6)，
d i,alt (t)＝z i,best -x i (t) (7)，
d i,pro ＝x i (t 1 )-x i (t 2 ) (8)，
wherein ,gi,best Is the current best position; z is a radical of i,best For historical best position, t 1 and t2 Are respectively [ t, t-1 ]]And [ t-1, t-2]Value within the range, x i (t) represents the search position of the searcher i in the t-th generation, x i (t 1) and xi (t 2 ) Are respectively [ x ] i (t-2),x i (t-1)]And [ x ] i (t-1),x i (t)]The best search position within the interval.
In the step S4, the SPR reflectivity value under the TM polarized wave is calculated through algorithm inversion
Phase difference delta phi of TE and TM polarized waves under SPR effect cal Can be calculated according to the expressions (9) to (14),
wherein h and g respectively represent p and m or a combination of m and s, the p, m and s respectively represent a substrate, a metal film layer and a dielectric layer, i represents an imaginary number, r represents a reflection coefficient, epsilon represents a dielectric constant, and k represents h(g)z Wave vector, k, representing the z direction x Representing an incident light wave vector;
from the above equation, it can be seen that the reflectivity and phase depend on the thickness d of the metal film, the incident wavelength λ and the dielectric constant of the metal film, and the real part ε of the dielectric constant real ＝n 2 -k 2 Dielectric constant imaginary part ε imag N, k each represents a refractive index and an extinction coefficient.
The measurement process of the method is specifically described by taking the three-phase structure of the single-layer metal film shown in fig. 2 as an example. The three-phase film structure is a structure of a substrate, a metal film layer and a dielectric layer. In this embodiment, the substrate is made of BK7 glass with refractive index n p =1.5151; the medium is selected from air, and its refractive index n a =1. When the medium layer is made of other substances, the corresponding medium refractive index value can be used.
In the step S1, the wavelength λ of the incident light is a continuous band, and the range of the incident light is selected to be 400 to 1000nm in this embodiment.
The optical constants and the thickness of the film under the target multi-wavelength are solved by improving a crowd search algorithm, the program is operated for 50 times, and each iteration is performed for 200 times, so that an iteration curve chart is obtained and is shown in figure 3. Meanwhile, the optical constant and the thickness of the film under the target multi-wavelength are calculated by a traditional crowd search algorithm to be used as comparison.
As can be seen from fig. 3, the method proposed by the present invention can converge to the optimal solution and the objective function value can reach 0.022 in about 40 generations, whereas the traditional crowd search algorithm can converge to the optimal solution and the objective function minimum value skill can reach 0.13 in about 120 generations. The improved crowd search algorithm has the characteristics of high convergence rate, high optimization precision and the like.
Fig. 4 shows the optical constants of the multi-wavelength metal film obtained by the method, and fig. 5 shows the thicknesses of the multi-wavelength metal film obtained by the method at different wavelengths, wherein the average value of the thicknesses is d =40.251 ± 0.416nm.
As can be seen from fig. 6, the phase difference and reflectance curve obtained by the inversion of the improved population search algorithm almost completely coincides with the curve obtained by the experiment, which indicates that the structural parameter precision of the single-layer film obtained by the inversion method of the present invention is high.
In conclusion, the method simultaneously acquires the phase difference and the reflection spectrum information of the single-layer metal film under the multi-wavelength under the condition of in-situ angle sharing, and can calculate and obtain the optical constant and the thickness of the single-layer film of the fixed film sample measuring point under the continuous spectrum by simultaneously inputting the incident wavelength-phase difference and the incident wavelength-reflectivity curve of the single-layer metal film on the basis of the improved crowd search algorithm, thereby effectively solving the problem of one-time quick solution of the single-layer film parameters corresponding to each wavelength under the continuous multi-wavelength, and having the advantages of high efficiency and high accuracy.
Finally, it should be noted that the above-mentioned description is only a preferred embodiment of the present invention, and those skilled in the art can make various similar representations without departing from the spirit and scope of the present invention.
Claims (9)
1. An ISOA method for measuring parameters of a single-layer film based on in-situ common-angle SPR is characterized by comprising the following steps of:
s1, in-situ co-angle measurement of reflection spectrum and interference fringe information: measuring interference fringe information and a reflection spectrum of TM polarized wave of a single-layer film sample in a continuous wavelength lambda range by using an SPR measuring device, and keeping an incident angle and an incident point of incident light unchanged in the measuring process, wherein the incident angle is an angle capable of exciting an SPR effect;
s2, processing data to obtain an incident wavelength-reflectivity and incident wavelength-phase difference relation curve: processing the reflection spectrum and the interference fringe information obtained in the step S1 to obtain the relation curve;
s3, initializing data of the improved crowd search algorithm: selecting reflection spectrum and phase difference data from the relation curve, carrying out normalization processing to obtain a data set of a reflectivity value and a phase difference value which are in the same order of magnitude, using the data set as an input value of an improved crowd search algorithm, and setting a resolving termination condition;
and S4, performing inversion calculation based on an objective function by adopting an improved population search algorithm, wherein the size of the objective function reflects the similarity between the inversion calculation and a reflectivity value and between phase difference values measured in an experiment, the objective function takes a parameter a to be measured of the single-layer film sample as a function parameter, and the parameter vector a, a = (n, k, d) is solved by searching the minimum value of the objective function, wherein n is a refractive index, k is an extinction coefficient, and d is a thickness.
2. The ISOA method for measuring parameters of a single-layer thin film based on in-situ co-angular SPR according to claim 1, wherein: in the step S4, substituting the reflectivity value and the phase difference value data set obtained in the step S3 into the objective function, initializing a search range of a solution space { n, k, d }, performing inversion calculation based on the objective function by adopting an improved population search algorithm, and judging the accuracy of the solution according to the size of the objective function to obtain the refractive index n, the extinction coefficient k and the thickness d of the single-layer film sample when the objective function is minimum;
the objective function formula is as follows (1):
where Q is the total number of wavelengths involved,
Δφ cal (i, a) represents the phase difference value of the TE polarized wave and the TM polarized wave under the SPR effect calculated by the algorithm inversion,
Δφ exp (i) Showing the phase difference value of the TE polarized wave and the TM polarized wave under the SPR effect of the ith reference point extracted from the incident wavelength-phase difference curve measured by experiments,
a represents the vector containing the parameters to be determined, a = (n, k, d).
3. The ISOA method for measuring parameters of single-layer thin films based on in-situ co-angular SPR according to claim 2, wherein: the step S4 specifically includes the steps of,
s41, initializing each parameter: setting the maximum iteration times and the minimum approximation error, initializing the population number of the population search algorithm, and initializing a solution space { n, k, d };
s42, randomly placing M (M)>0 and natural number) searcher in the solution space, calculating and evaluating the objective function value of M searcher positions, and placing the ith searcher position at the individual optimum position g besti Put the best location among all searchers at the global best location z best And recording the minimum corresponding to the global optimum position at the momentValue of objective function min (F) fitness ) And the corresponding solution vector a;
s43, calculating the searching direction d of each searcher i in the j-dimensional space ij Adaptive search step size alpha ij Further updating the position of the individual searcher and updating the solution vector a;
s44, aiming at each searcher, the objective function value and the optimal position g which has been experienced previously besti Is the objective function value F fitness (g besti ) Comparing, and if the position is better, taking the position as the current optimal position; (ii) a
S45, for each searcher, the objective function value and the global experienced optimal position z best Is the objective function value F fitness (z best ) Comparing, and if the position is better, taking the position as the current global optimal position;
s46, judging whether a termination condition is met, if so, stopping searching and outputting an optimal solution vector; otherwise, repeating the steps S43-S45 to continue the iterative computation until the end.
4. The ISOA method for measuring parameters of a single-layer thin film based on in-situ co-angle SPR according to claim 3, wherein: in step S43, the calculation formula of the adaptive search step in the improved population search algorithm is as follows (2):
where ω is the inertial weight, x min 、x max The positions u corresponding to the minimum and maximum objective function values respectively ij The membership degree of the ith objective function value of the j-dimensional search space is obtained;
wherein uij Calculated according to the equations (3) and (4),
u ij ＝rand(u i ,1),j＝1,....D (3)，
in formulae (3) and (4), u i Membership value, u, for the ith objective function value min 、u max Respectively, minimum and maximum membership values, rand (u) i 1) is [ u i ,1]And T is the current evolution algebra and the total evolution algebra.
5. The ISOA method for measuring parameters of a single-layer thin film based on in-situ co-angle SPR according to claim 4, wherein: in said step S43, the direction d is searched ij Determined according to the formula (5),
wherein ,
is [0,1 ]]Random real numbers over intervals;
d i,ego 、d i,alt and di,pro The directions of interest, and pre-movement for each searcher i are expressed as formulas (6) to (8), respectively:
d i,ego (t)＝g i,best -x i (t) (6)，
d i,alt (t)＝z i,best -x i (t) (7)，
d i,pro ＝x i (t 1 )-x i (t 2 ) (8)，
wherein ,gi,best For the current optimum position, z i,best For historical optimum position, t 1 and t2 Are respectively [ t, t-1 ]]And [ t-1, t-2]Value within the range, x i (t 1) and xi (t 2 ) Are each [ x ] i (t-2),x i (t-1)]And [ x ] i (t-1),x i (t)]The best search position within the interval.
6. The ISOA method for measuring parameters of single-layer thin films based on in-situ co-angular SPR according to any one of claims 1-5, wherein: and the resolving termination condition comprises iteration times and a minimum approximation error value, and the iteration times and the minimum approximation error value meet one of the conditions, namely, the iterative computation is terminated.
7. The ISOA method for measuring parameters of single-layer thin films based on in-situ co-angular SPR according to any one of claims 1-5, wherein: in step S1, the wavelength λ of the incident light is a continuous band,
the unit is nm.
8. The ISOA method for measuring parameters of a single-layer thin film based on in-situ co-angle SPR according to claim 2, wherein: the single-layer thin film sample is a metal film layer plated on a substrate, and in the step S1, when the SPR measuring device is used for measurement, a substrate-metal film layer-dielectric layer is used as a three-phase thin film structure for detection.
9. The ISOA method for measuring parameters of single-layer thin films based on in-situ co-angular SPR according to claim 2, wherein: in the step S4, the SPR reflectance value under the TM polarized wave is calculated through algorithm inversion
Phase difference delta phi of TE and TM polarized waves under SPR effect cal According to the following formulae (9) to (14),
wherein h and g respectively represent p and m or a combination of m and s, p, m and s respectively represent a substrate, a metal film layer and a dielectric layer, r represents a reflection coefficient, epsilon represents a dielectric constant, and k represents h(g)z Wave vector, k, representing the z direction x Representing the wave vector of the incident light;
real part of dielectric constant ∈ real ＝n 2 -k 2 Dielectric constant imaginary part ε imag N, k each represents a refractive index and an extinction coefficient.
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| CN103226007A (en) * | 2013-04-19 | 2013-07-31 | 天津大学 | SPR phase measurement method for measuring thickness of nano metal film |
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| US20190049302A1 (en) * | 2016-02-04 | 2019-02-14 | Industrial Cooperation Foundation Chonbuk National University | Integrated one-piece polarizing interferometer and snapshot spectro-polarimeter applying same |
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| CN103226007A (en) * | 2013-04-19 | 2013-07-31 | 天津大学 | SPR phase measurement method for measuring thickness of nano metal film |
| US20190049302A1 (en) * | 2016-02-04 | 2019-02-14 | Industrial Cooperation Foundation Chonbuk National University | Integrated one-piece polarizing interferometer and snapshot spectro-polarimeter applying same |
| CN106091953A (en) * | 2016-07-19 | 2016-11-09 | 天津大学 | A kind of SPR phase measuring method for measuring nanoscale double-layer metal film thickness |
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