CN104880161A - Method for measuring solid material surface roughness by using elliptical polarization parameter - Google Patents

Abstract

The invention provides a method for measuring solid material surface roughness by using elliptical polarization parameters, and relates to a method for measuring solid material surface roughness. Objectives are to solve problems in the prior art that an atomic force microscope in an existing measuring method is slow in speed, a scanning electron microscope requires a measured sample to be conductive, and precision of a light-section microscope is not high. The method is realized through the following technical scheme: step 1, performing analog computation on rough surface characteristic parameters of different solid materials, that is, through a three-dimensional finite-difference time-domain method to obtain space electromagnetic field distribution of the near-field of a solid material rough surface; step 2, through near-to-far-field transformation to obtain a complex electric field E of a far field, calculating radiation polarization characteristic on a mirror reflection direction, and establishing a database; step 3, after a solid material is produced, measuring the optical elliptical polarization parameters on the surface of the solid material, and comparing with the database, to obtain root-mean-square roughness and correlation length. The method is applied in the field of measuring surface roughness.

Description

A kind of method utilizing ellipsometric parameter to measure solid material surface roughness

Technical field

The present invention relates to the method measuring solid material surface roughness.

Background technology

Surfaceness refer to that finished surface has compared with Small Distance and small peak valley unevenness.Real surface is all coarse, and the tool such as wearing quality, sealing, anti-fatigue ability of material surface roughness to this sample has a direct impact, and also affects the assembly quality of part, vibration & noise and power consumption and serviceable life etc.Moreover, surfaceness also has critical role in fields such as optical properties of material, infrared target imagings.The measurement of surfaceness becomes an important process of part quality detection.R.m.s. roughness (root-mean-square, σ) and auto-correlation length (correlation length, τ) can be used to characterize.The definition of r.m.s. roughness is:

$\mathrm{\σ}=\sqrt{\⟨\mathrm{\ζ}{\left(r\right)}^2\⟩}$

Wherein, ζ (r) is the surface elevation at r place, meets following condition:

<ζ(r)>＝0

In reality, the r.m.s. roughness of a lot of material surface all meets Gaussian distribution:

$\&lang;\mathrm{\&zeta;}\left(r\right)\mathrm{\&zeta;}\left(r^{\&prime;}\right)\&rang;={\mathrm{\&sigma;}}^2\exp \&lsqb;-\left(\frac{{\left|x_1-x_2\right|}^2}{{\mathrm{\&tau;}}^2}\right)+\left(\frac{{\left|y_1-y_2\right|}^2}{{\mathrm{\&tau;}}^2}\right)\&rsqb;$

τ is auto-correlation length.

Optics ellipsometry method is that Rothen proposed first in 1945, and he has designed and produced First ellipsometer, and the thickness of 0.3A that used this ellipsometer measurement to arrive, than interference light mensuration at least more than accurate ten times.The measurement parameter used is optics ellipsometric parameter, and existing measuring method is as slow in contact measurement method speed such as atomic force microscope, probe-type contourgraphs; Scanning electron microscope needs to measure sample the restrictive condition such as can to conduct electricity; Optical means is as light-section microscope, and existing instrument generally can only measure mean accuracy 0.5 micron and above roughness, and precision is not high.

Summary of the invention

The object of the invention is in order to solve prior art measuring method speed slow, need to measure sample and can conduct electricity and mean accuracy 0.5 micron and above roughness can only be measured, the problem that precision is not high, and propose a kind of method utilizing ellipsometric parameter measure surface roughness.

Above-mentioned goal of the invention is achieved through the following technical solutions:

A kind of method utilizing ellipsometric parameter to measure solid material surface roughness is specifically carried out according to following steps:

Step one, analog computation is carried out to different solid material rough surface features parameter, namely tried to achieve the spatial electromagnetic field distribution in this solid material rough surface near field by Three-dimensional Time Domain method of finite difference;

Wherein, described near field is be less than the electromagnetic field in 10 wavelength coverages;

External electromagnetic field refers to telegram in reply field and magnetic field

Rough surface features parameter refers to r.m.s. roughness and auto-correlation length;

Step 2, tried to achieve the telegram in reply field in far field by Near-far fields transfer extract the radiation polarisation characteristic of the telegram in reply field component calculating specular reflection direction of specular reflection direction from far field space elect magnetic field, radiation polarisation characteristic uses optics ellipsometric parameter to represent, and building database;

Wherein, described far field is often referred to distance sample is 10 ⁵electromagnetic field outside individual wavelength;

Step 3, after solid material has been produced, the optics ellipsometric parameter of the instrument of measured surface radiation polarisation characteristic to this solid material surface is utilized to measure, and compare with the optics ellipsometric parameter in database, obtain r.m.s. roughness and the auto-correlation length of this solid material surface.

A kind of method utilizing ellipsometric parameter to measure solid material surface roughness is specifically carried out according to following steps:

Step one, analog computation is carried out to different solid material rough surface features parameter, namely tried to achieve the spatial electromagnetic field distribution in this solid material rough surface near field by Three-dimensional Time Domain method of finite difference (FDTD);

Wherein, described near field is be less than the electromagnetic field in 10 wavelength coverages;

External electromagnetic field refers to telegram in reply field and magnetic field

Rough surface features parameter refers to r.m.s. roughness and auto-correlation length;

Step 2, tried to achieve the telegram in reply field in far field by Near-far fields transfer extract the radiation polarisation characteristic of the telegram in reply field component calculating specular reflection direction of specular reflection direction from far field space elect magnetic field, radiation polarisation characteristic uses optics ellipsometric parameter to represent, and building database;

Wherein, described far field is often referred to distance sample is 10 ⁵electromagnetic field outside individual wavelength;

Step 3, after solid material has been produced, optics ellipsometric parameter is recorded successively by the scanning area of measured surface radiation polarisation characteristic instrument, and compare with the optics ellipsometric parameter in database, obtain r.m.s. roughness and the auto-correlation length of this solid material surface, in computer, need according to the precision of solid material the error range setting corresponding optics ellipsometric parameter;

Error range is: | the optics ellipsometric parameter of the ellipsometric parameter calculated in database-record |≤accuracy value that arranges is needed according to solid material precision;

If when the optics ellipsometric parameter recorded is in error allowed band, then this solid material surface roughness meets the requirements;

If when the optics ellipsometric parameter recorded is not in error allowed band, then this solid material surface roughness is undesirable;

Computer record is used to occur the solid material numbering of error or directly use mechanical arm to be taken out by this solid material, Real-Time Monitoring solid material surface roughness.

Invention effect

Adopt a kind of method utilizing ellipsometric parameter to measure solid material surface roughness of the present invention,

The present invention uses FDTD method for numerical simulation to try to achieve the spatial electromagnetic field distribution in rough surface near field; Obtain far field electromagnetic field by Near-far fields transfer, then extract the telegram in reply field of specular reflection direction from far field space elect magnetic field component calculates the radiation polarisation characteristic of the telegram in reply field component of specular reflection direction, and radiation polarisation characteristic uses optics ellipsometric parameter to represent, building database; Then utilize the ellipsometric parameter of the apparatus measures part sample measuring ellipsometric parameter, and measurement result and database are contrasted, obtain roughness, described roughness uses r.m.s. roughness and auto-correlation length to represent.Synthesizing map 3, Fig. 4 are known, and ellipsometric parameter all can produce regular change with r.m.s. roughness σ and auto-correlation length τ, and ellipsometric parameter all can produce regular change with the change of root-mean-square height and auto-correlation length.This regularity ensure that the feasibility obtaining solid parameter roughness by measuring ellipsometric parameter.

Optics ellipsometry is indirect measurement method, has the advantages such as speed is fast, harmless, and faster than atomic force microscope, probe-type contourgraph speed, ellipsometric parameter has high sensitivity; Compared with scanning electron microscope, the present invention does not need to measure sample and can conduct electricity; Through calculating herein, use wavelength is the incident wave of 4 μm, and precision of its detection silicon rough surface can reach 10nm, and the precision of most of light-section microscope is about 0.5 μm, and the precision of ellipsometry improves an order of magnitude.If detection optical constant and the larger material of air difference, as metal etc., the detection accuracy of ellipsometry can further improve.When other conditions are identical, if the incident wave using wavelength shorter, ellipsometry detection accuracy also can further improve.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is r.m.s. roughness is σ=0.05 μm, the rough surface schematic diagram of auto-correlation length τ=0.5 μm;

Fig. 3 is incident wave wavelength is 4 microns, and when τ=0.05 μm and τ=1 μm, ellipsometric parameter is with the changing trend diagram of σ;

Fig. 4 is incident wave wavelength is 4 microns, and when σ=0.1 μm and σ=0.2 μm, ellipsometric parameter is with the variation tendency of τ.

Embodiment

Embodiment one: composition graphs 1 illustrates present embodiment, a kind of method utilizing ellipsometric parameter to measure solid material surface roughness is specifically carried out according to following steps:

Step one, analog computation is carried out to different solid material rough surface features parameter, namely tried to achieve the spatial electromagnetic field distribution in this solid material rough surface near field by Three-dimensional Time Domain method of finite difference (FDTD);

Wherein, described near field is be less than the electromagnetic field in 10 wavelength coverages;

External electromagnetic field refers to telegram in reply field and magnetic field

Rough surface features parameter refers to r.m.s. roughness and auto-correlation length;

Step 2, tried to achieve the telegram in reply field in far field by Near-far fields transfer extract the radiation polarisation characteristic of the telegram in reply field component calculating specular reflection direction of specular reflection direction from far field space elect magnetic field, radiation polarisation characteristic uses optics ellipsometric parameter to represent, and building database;

Wherein, described far field is often referred to distance sample is 10 ⁵electromagnetic field outside individual wavelength;

Step 3, after solid material has been produced, the optics ellipsometric parameter of the instrument of measured surface radiation polarisation characteristic to this solid material surface is utilized to measure, and compare with the optics ellipsometric parameter in database, obtain r.m.s. roughness and the auto-correlation length of this solid material surface.

Embodiment two: present embodiment and embodiment one are unlike the telegram in reply field of being tried to achieve far field in described step 2 by Near-far fields transfer extract the radiation polarisation characteristic of the telegram in reply field component calculating specular reflection direction of specular reflection direction from far field space elect magnetic field, radiation polarisation characteristic uses optics ellipsometric parameter to represent, and building database;

Detailed process is:

The radiation polarisation characteristic calculating specular reflection direction adopts following formula to calculate:

Radiation polarisation characteristic uses optics ellipsometric parameter to represent; Optics ellipsometric parameter is divided into: optics ellipsometric parameter reflectance ratio real part Ψ and optics ellipsometric parameter reflectance ratio imaginary part △; Telegram in reply field be divided into with with set when calculating;

$\mathrm{\&rho;}=tan\mathrm{\&Psi;}\exp \left(i\mathrm{\&Delta;}\right)=\frac{{\stackrel{\&RightArrow;}{r}}_p}{{\stackrel{\&RightArrow;}{r}}_s}=\frac{{\stackrel{\&RightArrow;}{E}}_{rp}}{{\stackrel{\&RightArrow;}{E}}_{ip}}/\frac{{\stackrel{\&RightArrow;}{E}}_{rs}}{{\stackrel{\&RightArrow;}{E}}_{is}}$

In formula: for p direction complex reflection coefficient, for s direction complex reflection coefficient, for p direction reflected field vector, for p direction incident electric field vector, for s direction reflected field vector, for s direction incident electric field vector, r digital reflex, i refers to incidence.

Embodiment three: a kind of method utilizing ellipsometric parameter to measure solid material surface roughness is specifically carried out according to following steps:

Step one, analog computation is carried out to different solid material rough surface features parameter, namely tried to achieve the spatial electromagnetic field distribution in this solid material rough surface near field by Three-dimensional Time Domain method of finite difference (FDTD);

Wherein, described near field is be less than the electromagnetic field in 10 wavelength coverages;

External electromagnetic field refers to telegram in reply field and magnetic field

Rough surface features parameter refers to r.m.s. roughness and auto-correlation length;

Step 2, tried to achieve the telegram in reply field in far field by Near-far fields transfer extract the radiation polarisation characteristic of the telegram in reply field component calculating specular reflection direction of specular reflection direction from far field space elect magnetic field, radiation polarisation characteristic uses optics ellipsometric parameter to represent, and building database;

Wherein, described far field is often referred to distance sample is 10 ⁵electromagnetic field outside individual wavelength;

Step 3, after solid material has been produced, optics ellipsometric parameter is recorded successively by the scanning area of measured surface radiation polarisation characteristic instrument, and compare with the optics ellipsometric parameter in database, obtain r.m.s. roughness and the auto-correlation length of this solid material surface, in computer, need according to the precision of solid material the error range setting corresponding optics ellipsometric parameter;

Error range is: | the optics ellipsometric parameter of the optics ellipsometric parameter calculated in database-record |≤accuracy value that arranges is needed according to solid material precision

If when the optics ellipsometric parameter recorded is in error allowed band, then this solid material surface roughness meets the requirements;

If when the optics ellipsometric parameter recorded is not in error allowed band, then this solid material surface roughness is undesirable;

Computer record is used to occur the solid material numbering of error or directly use mechanical arm to be taken out by this solid material, Real-Time Monitoring solid material surface roughness.

Embodiment four: present embodiment and embodiment three are unlike the telegram in reply field of being tried to achieve far field in described step 2 by Near-far fields transfer extract the radiation polarisation characteristic of the telegram in reply field component calculating specular reflection direction of specular reflection direction from far field space elect magnetic field, radiation polarisation characteristic uses optics ellipsometric parameter to represent, and building database; Detailed process is:

The radiation polarisation characteristic calculating specular reflection direction adopts following formula to calculate:

Radiation polarisation characteristic uses optics ellipsometric parameter to represent; Optics ellipsometric parameter is divided into: optics ellipsometric parameter reflectance ratio real part Ψ and optics ellipsometric parameter reflectance ratio imaginary part △; Telegram in reply field be divided into with with set when calculating;

$\mathrm{\&rho;}=tan\mathrm{\&Psi;}\exp \left(i\mathrm{\&Delta;}\right)=\frac{{\stackrel{\&RightArrow;}{r}}_p}{{\stackrel{\&RightArrow;}{r}}_s}=\frac{{\stackrel{\&RightArrow;}{E}}_{rp}}{{\stackrel{\&RightArrow;}{E}}_{ip}}/\frac{{\stackrel{\&RightArrow;}{E}}_{rs}}{{\stackrel{\&RightArrow;}{E}}_{is}}$

In formula: for p direction complex reflection coefficient, for s direction complex reflection coefficient, for p direction reflected field vector, for p direction incident electric field vector, for s direction reflected field vector, for s direction incident electric field vector, r digital reflex, i refers to incidence.

Embodiment 1: the first situation, when τ is constant, calculates the situation of change of ellipsometric parameter with σ.Fig. 3 be τ=0.05 μm and τ=1 μm time, ellipsometric parameter is with the situation of change of σ.Horizontal ordinate is σ, and ordinate is ellipsometric parameter numerical value.In Fig. 3, the ellipsometer that the data of σ=0.05 μm, τ=0.05 μm are Fig. 2 institute presentation surface calculates result.In Fig. 2, r.m.s. roughness is the height that σ affects roughness fluctuating, and auto-correlation length τ affects the density degree risen and fallen.

As can be seen from Figure 3, in ellipsometric parameter, when τ=0.05 μm, reflectance ratio real part Ψ increases with the increase of σ, and reflectance ratio imaginary part △ reduces with the increase of σ.When τ=1 μm, reflectance ratio real part Ψ reduces with the increase of σ, and reflectance ratio imaginary part △ reduces with the increase of σ.

The second situation, when σ is constant, calculates the situation of change of ellipsometric parameter with τ.Fig. 4 be σ=0.1 μm and σ=0.2 μm time, ellipsometric parameter is with the situation of change of τ.As can be seen from the figure, in ellipsometric parameter, when σ=0.1 μm, reflectance ratio real part Ψ increases rear reduction with the increase line of τ, and reflectance ratio imaginary part △ increases with the increase of τ.When σ=0.2 μm, reflectance ratio real part Ψ reduces with the increase of τ, and reflectance ratio imaginary part △ increases with the increase of τ.

Synthesizing map 3, Fig. 4 are known, and ellipsometric parameter all can produce regular change with r.m.s. roughness σ and auto-correlation length τ.This change makes to become possibility by measuring ellipsometric parameter inverting roughness.When sample is through measuring the instrument of ellipsometric parameter, measures the ellipse inclined numerical value obtaining sample, and contrasting with above-mentioned result of calculation.Roughness value corresponding to ellipsometric parameter is the roughness of this sample.

Claims (4)

1. utilize ellipsometric parameter to measure a method for solid material surface roughness, it is characterized in that: a kind of method utilizing ellipsometric parameter to measure solid material surface roughness is specifically carried out according to following steps:

Step one, analog computation is carried out to different solid material rough surface features parameter, namely tried to achieve the spatial electromagnetic field distribution in this solid material rough surface near field by Three-dimensional Time Domain method of finite difference;

Wherein, described near field is be less than the electromagnetic field in 10 wavelength coverages;

External electromagnetic field refers to telegram in reply field and magnetic field

Rough surface features parameter refers to r.m.s. roughness and auto-correlation length;

Step 2, tried to achieve the telegram in reply field in far field by Near-far fields transfer extract the radiation polarisation characteristic of the telegram in reply field component calculating specular reflection direction of specular reflection direction from far field space elect magnetic field, radiation polarisation characteristic uses optics ellipsometric parameter to represent, and building database;

Wherein, described far field is often referred to distance sample is 10 ⁵electromagnetic field outside individual wavelength;

Step 3, after solid material has been produced, the optics ellipsometric parameter of the instrument of measured surface radiation polarisation characteristic to this solid material surface is utilized to measure, and compare with the optics ellipsometric parameter in database, obtain r.m.s. roughness and the auto-correlation length of this solid material surface.

2. a kind of method utilizing ellipsometric parameter to measure solid material surface roughness according to claim 1, be is characterized in that: the telegram in reply field of being tried to achieve far field in described step 2 by Near-far fields transfer extract the radiation polarisation characteristic of the telegram in reply field component calculating specular reflection direction of specular reflection direction from far field space elect magnetic field, radiation polarisation characteristic uses optics ellipsometric parameter to represent, and building database; Detailed process is:

The radiation polarisation characteristic calculating specular reflection direction adopts following formula to calculate:

Radiation polarisation characteristic uses optics ellipsometric parameter to represent; Optics ellipsometric parameter is divided into: optics ellipsometric parameter reflectance ratio real part Ψ and optics ellipsometric parameter reflectance ratio imaginary part △; Telegram in reply field be divided into with with set when calculating;

$\mathrm{\&rho;}=tan\mathrm{\&Psi;}\exp \left(i\mathrm{\&Delta;}\right)=\frac{{\stackrel{\&RightArrow;}{r}}_p}{{\stackrel{\&RightArrow;}{r}}_s}=\frac{{\stackrel{\&RightArrow;}{E}}_{rp}}{{\stackrel{\&RightArrow;}{E}}_{ip}}/\frac{{\stackrel{\&RightArrow;}{E}}_{rs}}{{\stackrel{\&RightArrow;}{E}}_{is}}$

In formula: for p direction complex reflection coefficient, for s direction complex reflection coefficient, for p direction reflected field vector, for p direction incident electric field vector, for s direction reflected field vector, for s direction incident electric field vector, r digital reflex, i refers to incidence.

3. utilize ellipsometric parameter to measure a method for solid material surface roughness, it is characterized in that: a kind of method utilizing ellipsometric parameter to measure solid material surface roughness is specifically carried out according to following steps:

Step one, analog computation is carried out to different solid material rough surface features parameter, namely tried to achieve the spatial electromagnetic field distribution in this solid material rough surface near field by Three-dimensional Time Domain method of finite difference;

Wherein, described near field is be less than the electromagnetic field in 10 wavelength coverages;

External electromagnetic field refers to telegram in reply field and magnetic field

Rough surface features parameter refers to r.m.s. roughness and auto-correlation length;

Step 2, tried to achieve the telegram in reply field in far field by Near-far fields transfer extract the radiation polarisation characteristic of the telegram in reply field component calculating specular reflection direction of specular reflection direction from far field space elect magnetic field, radiation polarisation characteristic uses optics ellipsometric parameter to represent, and building database;

Wherein, described far field is often referred to distance sample is 10 ⁵electromagnetic field outside individual wavelength;

Step 3, after solid material has been produced, optics ellipsometric parameter is recorded successively by the scanning area of measured surface radiation polarisation characteristic instrument, and compare with the optics ellipsometric parameter in database, obtain r.m.s. roughness and the auto-correlation length of this solid material surface, in computer, need according to the precision of solid material the error range setting corresponding optics ellipsometric parameter;

Error range is: | the optics ellipsometric parameter of the optics ellipsometric parameter calculated in database-record |≤accuracy value that arranges is needed according to solid material precision;

If when the optics ellipsometric parameter recorded is in error allowed band, then this solid material surface roughness meets the requirements;

If when the optics ellipsometric parameter recorded is not in error allowed band, then this solid material surface roughness is undesirable;

Computer record is used to occur the solid material numbering of error or directly use mechanical arm to be taken out by this solid material, Real-Time Monitoring solid material surface roughness.

4. a kind of method utilizing ellipsometric parameter to measure solid material surface roughness according to claim 3, be is characterized in that: the telegram in reply field of being tried to achieve far field in described step 2 by Near-far fields transfer extract the radiation polarisation characteristic of the telegram in reply field component calculating specular reflection direction of specular reflection direction from far field space elect magnetic field, radiation polarisation characteristic uses optics ellipsometric parameter to represent, and building database; Detailed process is:

The radiation polarisation characteristic calculating specular reflection direction adopts following formula to calculate:

Radiation polarisation characteristic uses optics ellipsometric parameter to represent; Optics ellipsometric parameter is divided into: optics ellipsometric parameter reflectance ratio real part Ψ and optics ellipsometric parameter reflectance ratio imaginary part △; Telegram in reply field be divided into with with set when calculating;

$\mathrm{\&rho;}=tan\mathrm{\&Psi;}\exp \left(i\mathrm{\&Delta;}\right)=\frac{{\stackrel{\&RightArrow;}{r}}_p}{{\stackrel{\&RightArrow;}{r}}_s}=\frac{{\stackrel{\&RightArrow;}{E}}_{rp}}{{\stackrel{\&RightArrow;}{E}}_{ip}}/\frac{{\stackrel{\&RightArrow;}{E}}_{rs}}{{\stackrel{\&RightArrow;}{E}}_{is}}$

In formula: for p direction complex reflection coefficient, for s direction complex reflection coefficient, for p direction reflected field vector, for p direction incident electric field vector, for s direction reflected field vector, for s direction incident electric field vector, r digital reflex, i refers to incidence.