阅读说明：本技术 椭偏仪中延迟器偏差角度及延迟相位量的定标方法 (Calibration method for deviation angle and delay phase quantity of delayer in ellipsometer ) 是由 李晶 凌航 张书博 宋晓晓 张欣彤 刘春敏 于 2021-01-21 设计创作，主要内容包括：本发明属于仪器定标技术领域,具体为一种椭偏仪中延迟器偏差角度及延迟相位量的定标方法。本发明先将入射到样品的探测光束的s偏振方向与p偏振方向作为系统的X/Y坐标轴,取下延迟器,利用布儒斯特角法将检偏器调整到坐标系的0°方向,再利用马吕斯定律定标起偏器定标、并调整到系统坐标系的45°方向；加入延迟器,取下样品,调节起偏器方位角,使用该系统进行测量。使用RCE型椭偏系统测量这组等效样品时,坐标偏差角出现在光强分量的比值关系中,可以求出坐标偏差角；最后将修正好延迟器坐标偏差的系统,从计算等效椭偏参数的结果中得到相位延迟器的实际延迟量β。本发明操作简单且精度高,能很好地改善椭偏仪的误差修正。(The invention belongs to the technical field of instrument calibration, and particularly relates to a calibration method for a delay device deviation angle and a delay phase quantity in an ellipsometer. Firstly, the s-polarization direction and the p-polarization direction of a detection beam incident to a sample are taken as the X/Y coordinate axis of a system, a retarder is taken down, an analyzer is adjusted to the 0-degree direction of a coordinate system by utilizing a Brewster's angle method, and then a polarizer is calibrated by utilizing Malus law and adjusted to the 45-degree direction of the coordinate system of the system; and adding a retarder, taking down the sample, adjusting the azimuth angle of the polarizer, and measuring by using the system. Coordinate deviation angle when measuring the set of equivalent samples using RCE-type ellipsometry system When the ratio relation of the light intensity components occurs, the coordinate deviation angle can be calculated (ii) a Finally correcting the coordinate deviation of the retarderThe system obtains the actual delay amount of the phase retarder from the result of calculating the equivalent ellipsometric parameter β . The method is simple to operate and high in precision, and error correction of the ellipsometer can be well improved.)

1. A calibration method for the deviation angle and the delay phase amount of a retarder in an ellipsometer is disclosed, wherein the ellipsometer is a PSCA ellipsometer which is constructed by a polarizer P, a sample S, a phase retarder C and an analyzer A; the system coordinate system defines the direction of light propagation as the positive z-axis direction of the system; parallel to the sample surface and vertical to the incident plane, i.e. the s-light polarization direction of the incident light is the X axis, and the positive direction is vertical to the optical platform; the polarization direction of p light of incident light is taken as an axis Y, and the positive direction is Z multiplied by X; for the whole system, the phase retarder C is taken down, and the PSCA ellipsometry system is degenerated into a PSA ellipsometry system at the moment; in a PSA (pressure swing adsorption) ellipsometry measurement system, a polarizer P and an analyzer A are respectively adjusted to 45-degree and 0-degree directions in a system coordinate system by utilizing a Brewster angle method and a Malus law; for the rotating device retarder C, a coordinate system x is set individually thereto_c×y_c＝z_c(ii) a Adjusting the reflected light through the surface of the retarder C in the light path to be parallel to the incident light, z of the retarder coordinate system_cThe axis coincides with the Z axis of the system coordinate system; x is the number of_cThe deviation angle between the coordinate axis and the X axis is represented by the symbol θ_mcDenotes the azimuth angle theta of the retarder C_cDefined as retarder fast axis and x_cThe included angle of the axes; the method is characterized in that the specific steps of calibration are as follows:

in the elliptic polarization system of the PSCA layout, the azimuth angle adjustment of the phase retarder C specifically comprises the following steps: removing a sample, enabling incident light to pass through a polarizer P, a delayer C and an analyzer A, enabling emergent light to enter a silicon photoelectric detector, rotating the delayer C for a circle, and sampling at equal intervals; determining the frequency component of the intensity signal using a discrete Fourier transform, wherein I'₂sin4θ_C、I′₃cos4θ_CL 'in the frequency component'₂、I′₃The components are calculated to obtain a ratio relation, and the obtained result satisfiesThe functional relationship of (a); adjusting polarizer P coordinate azimuth angle theta_PDrawing outFunction image of, function initial phase quantityDeviation angle theta between the coordinate axis including the retarder C and the coordinate axis of the entire system_mc(ii) a By fitting the mathematical form of the function, the phase quantity is obtainedFinally, the phase quantity contained in the phase is obtainedDeviation angle theta in_mcA specific value of (a);

(II) solving the actual phase quantity of the phase delayer C in the elliptic polarization system of the PSCA layout; the method specifically comprises the following steps: theta obtained in (a)_mcCarrying in a system correction calculation result, and finishing the coordinate deviation correction in the system at the moment; in the system of (one), the rotation theta_PAt different theta_PMeasured under the value, the system is equivalent to measuring a set of samples whose ellipsometric parameters Ψ_i＝θ_PΔ ═ 0 °; correcting coordinate deviation theta_mcThen, the system measurement result Ψ_oTrue Ψ from equivalent samples_iThe deviation of the value, only affected by the specific phase value β of the retarder C; fine tuning the phase value β such that Ψ_o＝Ψ_iAs a result, the value of β at this time is the actual amount of phase delay.

Technical Field

The invention belongs to the technical field of instrument calibration, and particularly relates to a calibration method for a delay device deviation angle and a delay phase quantity in an ellipsometer.

Background

Since the first ellipsometry proposed by Drude professor in 1901, the development and application of ellipsometers have been greatly developed in various fields, and the ellipsometry has been greatly improved in speed and precision from the early measurement of extinction method to the measurement of ellipsometric parameters by photometry with the advance of computer and electronic technology. In an ellipsometry system, optical devices such as a polarizing prism and a retarder are used. The coordinate axes of the devices are adjusted to be consistent with the coordinate axes of the system, or the deviation between the devices and the coordinate system of the system is obtained through calibration, the result is corrected, and the method plays a very important role in improving the measurement accuracy.

Disclosure of Invention

The invention aims to provide a calibration method for the deviation angle between the coordinate system and the system coordinate of a retarder in an ellipsometer under PSCA layout and the delay phase amount, which is simple to operate and high in precision, and the error correction of the ellipsometer is well improved.

The calibration method for the deviation angle and the delay phase quantity of the coordinate system and the system coordinate of the delayer in the PSCA under the PSCA layout is called as the calibration method for the deviation angle and the delay phase quantity of the delayer in the PSCA ellipsometer for short; the PSCA Ellipsometer here refers to an Ellipsometer (RCE) constructed by a polarizer P, a sample S, a phase retarder C, and an analyzer a; the system coordinate system defines the direction of light propagation as the positive z-axis direction of the system; parallel to the sample surface and perpendicular to the incident plane, i.e. the s-light polarization direction of the incident light is the X-axis and the positive direction is perpendicular to the optical platform upwards. The p-polarization direction of the incident light is the Y-axis, and the positive direction is Z X, as shown in FIG. 1.

For the entire system, the retarder C is removed, at which point the PSCA ellipsometry system degenerates to a PSA ellipsometry system. In a PSA ellipsometry system, the polarizer P and the analyzer A are respectively adjusted to 45-degree and 0-degree directions in a system coordinate system by utilizing a Brewster angle method and a Malus law. For the rotating device retarder C, a coordinate system x is set individually thereto_c×y_c＝z_cAs shown in fig. 1. Adjusting the reflected light through the surface of the retarder C in the light path to be parallel to the incident light, z of the retarder coordinate system_cThe axis coincides with the Z-axis of the system coordinate system. x is the number of_cThe deviation angle between the coordinate axis and the X axis is represented by the symbol θ_mcAnd (4) showing. Azimuth angle theta of retarder C_cDefined as retarder fast axis and x_cThe angle of the axes.

When theta is_mcWhen the angle is 0 deg., the output light intensity of the rotary delayer is dependent on theta_cThe theoretical derivation of the change is:

I(θ_C)＝I₀+I₁sin 2θ_C+I₂sin 4θ_C+I₃cos 4θ_c+I₄cos 2θ_c, (1)

wherein the content of the first and second substances,

wherein eta and sigma are intermediate quantities, and are respectively as follows:

beta is the actual delay phase amount of the retarder.

During the actual assembly process, θ_mcNot strictly 0 °, the relationship between the output light intensity signal and the theoretical signal is:

I′(θ_c)＝I(θ_c+θ_mc)＝I₀′+I₁′sin 2θ_C+I₂′sin 4θ_C+I₃′cos 4θ_C+I₄′cos 2θ_C, (9)

wherein the content of the first and second substances,

I′₁＝I₁cos 2θ_mc-I4 sin 2θ_mc, (10)

I′₂＝I₂ cos 4θ_mc-I₃ sin 4θ_mc, (11)

I′₃＝I₂ sin 4θ_mc+I₃cos 4θ_mc, (12)

I′₄＝I₁ sin 2θ_mc+I₄cos 2θ_mc, (13)

the system was then emptied of sample S. Laser emitted by the light source directly enters the retarder C and the subsequent measurement system through the polarizer P, as shown in FIG. 2. Adjusting azimuth angle theta of polarizer_p. At the moment, the rotating delayer is sampled at equal intervals (for example, 1600 points are collected), and the relation I' (theta) between the light intensity value and the azimuth angle of the delayer is recorded_c) The product isThe process is equivalent to an ellipsometry system measuring a set of samples with ellipsometry parameter value Δ being 0 ° (Δ is the phase difference between the s-polarization direction and the p-polarization direction reflection coefficient of the probe beam), and Ψ being θ_P(Ψ is the ratio of the polarization direction of the s-light component of the probe beam to the reflectance mode of the sample for the polarization direction of the p-light component, θ_PAzimuth of the polarizer in the system coordinate system). Reflection coefficient of s polarization direction of equivalent sample(Is the reflection coefficient of the polarization component of s light, and gamma is the reflection coefficient of the light source at theta_PThe magnitude of the polarization component in the direction) as shown in fig. 3.

For light intensity component expression I₂′、I₃' term, substitution of equivalent parameters is made according to parameters of equivalent samples, Ψ ═ θ_P，Obtaining:

introducing the relation:

by angle θ of the rotating polarizer_pGenerating a set of equivalent samples of different psi values, and making a functionAnd (4) an image. As seen from the specific expression, the function is a tangent functionThe phase starting item contains the quantity theta to be calibrated_mcUsing a mathematical fit of the tangent function to determine the initial phaseWhereinComplete theta_mcAnd (4) solving. Determining theta_mcThereafter, the retarder is rotated by-theta_mcThe retarder coordinate system now coincides with the system coordinate system.

After the coordinate of the retarder is corrected, only the retardation phase beta of the retarder is left in the whole system to influence the final ellipsometry parameters. The form of the ellipsometric parameter Ψ calculated from the light intensity components is:

knowing the values of Ψ for the equivalent ellipsometric parameters for the actual equivalent process_i＝θ_P(Ψ_iTo change different azimuth angles theta_PEllipsometric parameter values for a set of equivalent samples). The delayer is trimmed to change the value of beta until the system measurement result coincides with the known equivalent result, i.e., Ψ_o＝Ψ_i(Ψ_oFor placement of RCE ellipsometer pairs using PSCA_iMeasured value of (b), the value of β at that time is the actual retarder delay phase.

Based on the analysis, the calibration method of the deviation angle between the coordinate system of the retarder in the ellipsometer under the PSCA layout and the system coordinate and the delay phase amount comprises the steps of firstly taking the s-polarization direction and the P-polarization direction of a detection beam incident to a sample as the X/Y coordinate axes of the system respectively, taking down the retarder C, degenerating the system into a PSA-type ellipsometry system, adjusting the analyzer A to the 0-degree direction of the system coordinate system by using a Brewster angle method, then calibrating the polarizer P by using the Malus law, and adjusting to the 45-degree direction of the system coordinate system; and adding a retarder C, taking down the sample S, adjusting the azimuth angle of the polarizer, and measuring by using the system. The above process is equivalent to an ellipsometry system in measurementA set of equivalent samples having an ellipsometric parameter of Δ 0 ° and Ψ θ_pChanging theta_pGenerating an equivalent set of samples for different Ψ values; coordinate deviation angle theta when measuring the set of equivalent samples using an RCE-type ellipsometry system_mcAppearing in the ratio relation of the light intensity components, the coordinate deviation angle theta can be calculated_mc(ii) a And finally, obtaining the actual delay beta of the phase retarder from the result of calculating the equivalent ellipsometry parameters by the system for correcting the coordinate deviation of the retarder C.

The method comprises the following specific steps:

in the elliptic polarization system of the PSCA layout, the azimuth angle adjustment of the phase retarder C specifically comprises the following steps: removing a sample, enabling incident light to pass through a polarizer P, a delayer C and an analyzer A, enabling emergent light to enter a silicon photoelectric detector, rotating the delayer C for a circle, and sampling at equal intervals (for example, collecting 1600 light intensity values); determining the frequency component of the intensity signal using a discrete Fourier transform, wherein I'₂sin 4θ_C、I′₃cos 4θ_CL 'in the frequency component'₂、I′₃The components are calculated to obtain a ratio relation, and the obtained result satisfiesThe functional relationship of (a); adjusting polarizer P coordinate azimuth angle theta_PDrawing outFunction image of, function initial phase quantityDeviation angle theta between the coordinate axis including the retarder C and the coordinate axis of the entire system_mc(ii) a By fitting the mathematical form of the function, the phase quantity is obtainedFinally, the phase quantity contained in the phase is obtainedDeviation angle theta in_mcA specific value of (a);

(II) solving the actual phase quantity of the phase delayer C in the elliptic polarization system of the PSCA layout; the method specifically comprises the following steps: theta obtained in (a)_mcCarrying in a system correction calculation result, and finishing the coordinate deviation correction in the system at the moment; in the system of (one), the rotation theta_PAt different theta_PMeasured under the value, the system is equivalent to measuring a set of samples whose ellipsometric parameters Ψ_i＝θ_PΔ ═ 0 °; correcting coordinate deviation theta_mcThen, the system measurement result Ψ_oTrue Ψ from equivalent samples_iThe deviation of the value, only affected by the specific phase value β of the retarder C; fine tuning the phase value β such that Ψ_o＝Ψ_iAs a result, the value of β at this time is the actual amount of phase delay.

The method is simple to operate and high in precision, and can well improve the error correction of the ellipsometer.

Drawings

Fig. 1 is a schematic diagram of a PSCA layout ellipsometer optical path system.

Fig. 2 is a schematic diagram of the system in which the laser emitted from the light source directly enters the retarder C through the polarizer P after the system removes the sample S and the subsequent measurement system.

FIG. 3 is a graph showing equivalent reflection coefficientsAnd the azimuth angle theta of the rotating polarizer_PAnd (5) a relational graph.

FIG. 4 shows the relationship between light intensity componentsMeasured data and fitted curves.

FIG. 5 shows the equivalent ellipsometry parameters Ψ of the system after the angle error correction and only the phase delay error β exists_i＝θ_PTo the fitted curve.

Figure 6 is a graph of the corrected delay phase,equivalent ellipsometric parameter Ψ for the time system_i＝θ_PTo the fitted curve.

Reference numbers in the figures: the device comprises a semiconductor laser 1, a polarizer P (Glan Taylor prism), a sample S to be detected 3, a retarder C (633nm quarter wave plate) 4, an analyzer A (Glan Taylor prism) 5, a photoelectric detector 6, a system coordinate system X axis 7, a retarder coordinate system X axis 8, a retarder fast axis direction 9, a stepping motor 10 and a polarizer light-transmitting polarization direction 11.

Detailed Description

The invention is further described below with reference to the figures and examples.

Firstly, the polarization light transmission axis of the analyzer is calibrated and adjusted to the direction parallel to the s polarization direction of the incident light of the sample through a classical Brewster angle method and a Malus law, then the sample is moved out, and the polarization light transmission direction of the analyzer at the moment is taken as the X axis of the system, namely the direction of 0 degree. The polarizer is adjusted to be approximately parallel to the X-axis of the system as 0 °. Under the coordinate system of the polarizer, the light source, the analyzer, the polarizer and the silicon photodetector are sequentially arranged, as shown in fig. 3. Rotating the polarizer, recording the light intensity value. According to the Malus law formula, the expression of the output light intensity is obtained as follows: for the measured data, the theoretical formula is used for fitting to obtainIs theta_mpAs shown in FIG. 4, obtain θ_mp-1.9688 °. According to the result, the polarizer is adjusted to a position with an included angle of 45 degrees with the X axis of the system coordinate system.

The light path is adjusted in turn for a circle by the light source, the polarizer, the retarder, the analyzer and the silicon photoelectric detector, and the light intensity value is recorded. The light intensity component is determined by means of a discrete Fourier transform, wherein the function is derived by means of theoretical derivationRelationships betweenFor the measured data; fitting by the theoretical formula to obtainI.e., -2 theta_mc to obtain-2 theta_mc2.2336 deg., as shown in fig. 4. Through simple calculation, theta is obtained_mc＝-1.1168°。

To this end we have derived the angle of deviation of the coordinates of the polarizer and retarder in the system from the coordinate system determined by the orientation of the analyzer. Using theta_mcAfter correcting the system at-1.1168 °, the ellipsometric system error source obtained still has η determined by the phase delay β of the retarder.

After the coordinates are corrected, the calculation formula for solving psi through the light intensity component is as follows:

it can be seen that the calculated psi is related to η determined by the phase delay of the retarder, and the ellipsometry parameter psi of the equivalent sample can be known_i＝θ_P. Adjusting the delayer to change beta to make the data calculation result of the system measurement obtain psi_i＝Ψ_oThe value of β at this time is the actual phase delay amount of the retarder. FIG. 5 shows the initial useIt can be seen that the data Ψ for the measurement calculation_oOffset Ψ_i＝θ_PThe functional relationship is large. When the phase delay is fine-tuned toIn time, the data deviation Ψ calculated by the measurement can be seen_i＝θ_PThe functional relationship is small as shown in fig. 6. Considering the influence of noise, it is reasonable to have an error around 0 °; experiment ofThe results show that the actual phase delay of the retarder is

So far, the method completes the deviation angle theta between the coordinate system of the rotating retarder C of the PSCA layout ellipsometer and the system coordinate system_mcAnd scaling of the actual value of the delay phase quantity beta.