CN103245310A - Method of measuring surface characteristics of sample by adopting X-ray reflectometer - Google Patents

Abstract

The invention relates to a measurement method adopting an X-ray reflectometer, and aims to solve the problems that the existing reflectometer can only carry on research on a plane sample, and the time for measuring the sample is overlong. The method of measuring surface characteristics of a sample by adopting the X-ray reflectometer comprises the steps as follows: I, adopting the X-ray reflectometer to irradiate surface of the sample; II, detecting intensity of the reflected light through a detecting device; III, calculating and measuring the detected intensity of the reflected light; and IV, correcting the measured deviation. The method of measuring surface characteristics of the sample by adopting the X-ray reflectometer is applied to the field of optical measurement.

Description

A kind of method that use X ray reflection instrument measures sample surfaces characteristic

Technical field

The present invention relates to the measuring method using X ray reflection instrument.

Background technology

X ray reflection instrument is used for determination sample thickness degree and its internal structure about electron density.The principle of X ray reflection instrument was most described earlier than 1954 by Parratt, up to the present, and a prerequisite of the technology is that bottom surface used in the range of dispersion wavelength is sufficiently flat.Recently, widely using due to the planar bottom surface on molecular scale, such as widely using for silicon chip so that the technology is popularized.

At present, the measurement of surface roughness, film thickness and curved surface density mainly uses AFM, and the shortcoming of AFM measurement is that equipment is expensive, and test speed is slow, and it is a great defect that can only carry out research to plane.In addition, systematically scanning sample surfaces meaned determination sample thickness it is generally necessary to 30 to 60 minutes, therefore it is not suitable for the measurement table surface thickness of the pipeline system in practice production, and it is as a rule very difficult with θ -2 θ solids (geometry of plane of reflection substrate), calculate also more difficult, cumbersome time-consuming, therefore the time of measurement sample is longer.These instruments must be adjusted to multiple positions, it is therefore desirable to consume substantial amounts of energy, so as to cause cost to increase.

The content of the invention

Plane can only be studied the present invention is to solve existing reflectometer and measure the problem of sample time is long, and there is provided a kind of measuring method of use X ray reflection instrument.

The method for measuring sample surfaces characteristic using X ray reflection instrument comprises the following steps：

First, sample surfaces are irradiated using X ray reflection instrument；

2nd, intensity of reflected light is detected by detection means；

3rd, the intensity of reflected light detected is calculated and measured：

When more than critical reflection angle, X ray reflection instrument is measured using the effect of intensity of reflected light exponential damping, is obtained measurement data, is simulated with mathematical modeling, and is calculated by Parratt formula, obtains mathematical modeling data；Wherein, the Parratt formula are as follows：

$R_{n-1,n}={a_{n-1}}^4\left[\frac{R_{n,n+1}+F_{n-1,n}}{R_{n,n+1}{F}_{n-1,n}+1}\right]$

$R_{\mathrm{flat}}\left(q_z\right)={|q_z-\sqrt{\frac{{q^2}_z-{q^2}_c-\frac{32i{\mathrm{\π}}^2\mathrm{\β}}{{\mathrm{\λ}}^2}}{{q^2}_z+{q^2}_c-\frac{32i{\mathrm{\π}}^2\mathrm{\β}}{{\mathrm{\λ}}^2}}}|}^{\text{2}}---\left(1\right)$

Wherein, R is reflectivity, and n is natural number, and F is Fresnel attenuation coefficients, and a is half vertical depth, and q is the angle correction of test light, and z is critical angle, and i is imaginary number, for minus 1 square root；

Measured by the convergence to mathematics model data and measurement data, obtain sample surfaces characteristic, that is, complete the measurement using X ray reflection instrument；

4th, measured deviation is corrected：

The correction that the measured deviation correction includes surface curvature and influenceed on reflected signal strength is corrected with footprint；

The correction that the surface curvature influences on reflected signal strength：It is corrected by formula (2)：

Wherein, a can be defined as in formula (2)：

$a=|-\frac{\sqrt{k}\&times;\sqrt{{\mathrm{<figure-callout\; id="3"\; label="kl"\; filenames="HDA00003119496500023.png,HDA00003119496500031.png"\; state="\{\{state\}\}">kl</figure-callout>}}^3\&times;(2\sqrt{k}\&times;\sin \left(\mathrm{\&gamma;}\right)+l+3\&times;l\&times;\cos {\left(\mathrm{\&gamma;}\right)}^2)}-2\cos \left(\mathrm{\&gamma;}\right)\&times;{\mathrm{kl}}^2+l\sin \left(\mathrm{\&gamma;}\right)\&times;\sqrt{{\mathrm{<figure-callout\; id="3"\; label="kl"\; filenames="HDA00003119496500023.png,HDA00003119496500031.png"\; state="\{\{state\}\}">kl</figure-callout>}}^3\&times;(2\&times;\sqrt{k}\&times;\sin \left(\mathrm{\&gamma;}\right)+l+31\cos {\left(\mathrm{\&gamma;}\right)}^2)}}{l\&times;(2\&times;\sqrt{k}\&times;l\sin \left(\mathrm{\&gamma;}\right)+k+l^2+{31}^2\cos {\left(\mathrm{\&gamma;}\right)}^2)}|$

K represents to bend the curvature degree of sample in formula (2)

D is the arc length of bending sample, and b is the length of bending sample arc length, and l is the distance between detector and sample, and γ is the angle measured in units of radian；

The footprint correction：The angular range of the detector detection intensity of reflected light of X ray reflection instrument is integrated the reflected radiation of each detection unit of X ray reflection instrument irradiation zone by following equation (3~5), is corrected：

Wherein, " U " and " O " is each detection unit low angle position and high angle position.

Invention effect：

It is fast using the surface roughness of the measuring method measurement sample of the X ray reflection instrument of the present invention, film thickness and curved surface density-velocity, and it is measured by reflectometer, the limitation of geometry need not be met, many structures and object may be by reflectometer and analyzed, and X ray reflection instrument (XR) is that a kind of accuracy is nanoscale, nondestructive surface texture measuring instrument device.The instrument can provide the information such as film thickness, electron density difference, roughness, and the information on sample interior regular texture can be obtained by the measurement of bragg peak position.2~3s is only needed using present invention measurement sample correlation properties, the characteristics of just because of X ray reflection instrument pinpoint accuracy, non-destructive, thus it has greatly advantage in film and study of surfaces field.

Inventive principle：

One contact surface or at least additional layer film are needed using X ray reflection instrument measurement sample, and at least there is one-dimensional curved surface region or deflected and form one-dimensional curved surface in sample.The film added in surface region has outer surface and inner surface, with electromagnetic radiation irradiation curved surface region, electromagnetic radiation is reflected in inner surface and outer surface, and is detected by detection means, and the radiation detected is carried out offset correction to offset the curvature of surface region.By the characteristic for the radiation detected being corrected and being calculated surveyed sample layer.The curvature of curved surface is probably intrinsic curvature or is forced curvature.The reflection for being mainly characterized by all research angles of curvature is all to carry out simultaneously, therefore can observe the angled reflection of institute simultaneously.The reflection of all research angles can be observed simultaneously using the detector of area sensitive.

Brief description of the drawings

Fig. 1 is the Traditional x-ray reflection θ -2 θ schematic diagrames in embodiment one；Wherein, A is X-ray tube, and B is detection means, and C is sample；

Fig. 2 is the X ray reflection instrument schematic diagram for being used to measure bending sample at a high speed in embodiment one；Wherein, A is X-ray tube, and B is detection means, and C is sample, and D is incident X-ray beam, and E is X-ray beam pointing instrumentation, and F is because the X-ray beam that sample curvature is caused disperses；

Fig. 3 is that the high speed in embodiment one measures the schematic diagram for bending sample X ray reflection instrument；Wherein, A is X-ray tube, and B is detection means, and C is sample, D is X-ray beam pointing instrumentation, E is that, because the X-ray beam that sample curvature is caused disperses, F is the mathematical center point of sample curvature, and G is the sample surfaces for the greater curvature amplified, H is the sample surfaces for the smaller curvature amplified, I is vertical irradiation sample surfaces, and J is incident X-ray beam, and K is the X-ray beam of reflection；

Fig. 4 is the Data correction schematic diagram in embodiment one；Wherein, u represents high angle angle, o represents low angle angle, γ is by the scope of o and the u each detection unit detection limited, region is irradiated by light above a expression certain resolutions detector detection sample, b is expressed as being irradiated by light region with certain resolution detector detection sample intermediate region, and c is expressed as being irradiated by light region with certain resolution detector detection sample lower zone；

Fig. 5 is the reflectivity curve of curved surface cover glass of the surface with a thin layer polymer film in embodiment one；

Fig. 6 is the practical measurement surface smooth flat sample data figure in embodiment one；Wherein, black color dots are measured value in figure, and Grey Point is the analogue value；

Fig. 7 is the sample data figure that practical measurement in embodiment one has layer polymerization thing film；Wherein, black color dots are measured value in figure, and Grey Point is the analogue value；

Fig. 8 is the visualization figure for the sample correlation values that practical measurement in embodiment one has layer polymerization thing film；

Fig. 9 is the practical measurement bending samples datagram in embodiment one；Wherein, black color dots are measured value in figure, and Grey Point is the analogue value；

Figure 10 is that the practical measurement radius of curvature in embodiment one is 19cm sample data figures；Wherein, black color dots are measured value in figure, and Grey Point is the analogue value；

Figure 11 is the visualization figure that practical measurement radius of curvature in embodiment one is 19cm sample correlation values.

Embodiment

Embodiment one：The method of the use X ray reflection instrument measurement sample surfaces characteristic of present embodiment comprises the following steps：

First, sample surfaces are irradiated using X ray reflection instrument；

2nd, intensity of reflected light is detected by detection means；

3rd, the intensity of reflected light detected is calculated and measured：

When more than critical reflection angle, X ray reflection instrument is measured using the effect of intensity of reflected light exponential damping, is obtained measurement data, is simulated with mathematical modeling, and is calculated by Parratt formula, obtains mathematical modeling data；Wherein, the Parratt formula are as follows：

$R_{n-1,n}={a_{n-1}}^4\left[\frac{R_{n,n+1}+F_{n-1,n}}{R_{n,n+1}{F}_{n-1,n}+1}\right]$

$R_{\mathrm{flat}}\left(q_z\right)={|q_z-\sqrt{\frac{{q^2}_z-{q^2}_c-\frac{32i{\mathrm{\&pi;}}^2\mathrm{\&beta;}}{{\mathrm{\&lambda;}}^2}}{{q^2}_z+{q^2}_c-\frac{32i{\mathrm{\&pi;}}^2\mathrm{\&beta;}}{{\mathrm{\&lambda;}}^2}}}|}^{\text{2}}---\left(1\right)$

Wherein, R is reflectivity, and n is natural number, and F is Fresnel attenuation coefficients, and a is half vertical depth, and q is the angle correction of test light, and z is critical angle, and i is imaginary number, for minus 1 square root；

Measured by the convergence to mathematics model data and measurement data, obtain sample surfaces characteristic, that is, complete the measurement using X ray reflection instrument；

4th, measured deviation is corrected：

The correction that the measured deviation correction includes surface curvature and influenceed on reflected signal strength is corrected with footprint；

The correction that the surface curvature influences on reflected signal strength：It is corrected by formula (2)：

Wherein, a can be defined as in formula (2)：

$a=|-\frac{\sqrt{k}\&times;\sqrt{{\mathrm{<figure-callout\; id="3"\; label="kl"\; filenames="HDA00003119496500023.png,HDA00003119496500031.png"\; state="\{\{state\}\}">kl</figure-callout>}}^3\&times;(2\sqrt{k}\&times;\sin \left(\mathrm{\&gamma;}\right)+l+3\&times;l\&times;\cos {\left(\mathrm{\&gamma;}\right)}^2)}-2\cos \left(\mathrm{\&gamma;}\right)\&times;{\mathrm{kl}}^2+l\sin \left(\mathrm{\&gamma;}\right)\&times;\sqrt{{\mathrm{<figure-callout\; id="3"\; label="kl"\; filenames="HDA00003119496500023.png,HDA00003119496500031.png"\; state="\{\{state\}\}">kl</figure-callout>}}^3\&times;(2\&times;\sqrt{k}\&times;\sin \left(\mathrm{\&gamma;}\right)+l+31\cos {\left(\mathrm{\&gamma;}\right)}^2)}}{l\&times;(2\&times;\sqrt{k}\&times;l\sin \left(\mathrm{\&gamma;}\right)+k+l^2+{31}^2\cos {\left(\mathrm{\&gamma;}\right)}^2)}|$

K represents to bend the curvature degree of sample in formula (2)

D is the arc length of bending sample, and b is the length of bending sample arc length, and l is the distance between detector and sample, and γ is the angle measured in units of radian；

The footprint correction：The angular range of the detector detection intensity of reflected light of X ray reflection instrument is integrated the reflected radiation of each detection unit of X ray reflection instrument irradiation zone by following equation (3~5), is corrected：

Wherein, " U " and " O " is each detection unit low angle position and high angle position.

In present embodiment, the standardization is related to light path (q) index irrelevant with wavelength, and q's is calculated as follows：

$q=\frac{4\mathrm{\&pi;}\&times;\sin \mathrm{\&Theta;}}{\mathrm{\&lambda;}}$

Need to use the incidence angle θ and wavelength X of X-ray in the measurements, because the wavelength of measurement and the change of refractive index are smaller, compared with visible ray, the angular domain that can be observed is relatively much smaller.The refractive index (except neutron hydrogen) of X-ray is less than 1.Therefore the interface includes one and total reflection θ_cThe related material of critical angle.If incidence angle θ is less than θ_c, then ray will not penetrate sample, but all reflect (see Fig. 1).If incidence angle θ is more than θ_c, ray can then penetrate sample surfaces.In the case of vacuum measurement, no refractive index when can calculate the critical reflection angle (n=1) for obtaining material.

Being calculated as follows for the critical edges of X-ray is shown：

cosΘ_c=n=1- δ

In formula, δ represents the electron density of measurement sample surfaces.The decay is described by Fresnel attenuation functions, (the q ＞ 3q when q values are higher than critical value_c) when, the reflection loss of ideal plane can be calculated by following formula：

$R_{\mathrm{flat}}\left(q_z\right)={|q_z-\sqrt{\frac{{q^2}_z-{q^2}_c-\frac{32i{\mathrm{\&pi;}}^2\mathrm{\&beta;}}{{\mathrm{\&lambda;}}^2}}{{q^2}_z+{q^2}_c-\frac{32i{\mathrm{\&pi;}}^2\mathrm{\&beta;}}{{\mathrm{\&lambda;}}^2}}}|}^{\text{2}}$

Wherein q's is calculated as：

q_cIt is the Scattering of Vector of critical angle.β is the absorption coefficient of sample, and i represents imaginary number.The formula is in q ＞ 3q_cShi Chengli.When q values are relatively low, deviation is produced due to absorption, the formula is used to measure fully-flattened；

(1) influence of roughness：

Due to deviateing the scattering of minute surface, Rough Horizontal Plane reflected light compared with plane is reduced.Accordingly, it would be desirable to set a parameter to roughness.One of definition to roughness is to carry out Gaussian Profile statistics to surface different height (z-axis) in the 2 dimensional region limited by x and y-axis.Roughness parameter ∑²By height z P distributions, average height

Determined jointly with the deviation dz of height：

Surface roughness is (q ＜ 3q for the influence that sample surfaces reflect_c)：

$R_{\mathrm{rough}}{q}_z=R^{\mathrm{flat}}{q}_z{e}^{-q_z{,}_o{q}_{z,1}{\mathrm{\&Sigma;}}^2}$

Q in formula_zAnd q_{Z, 1,0}It is the vector mutually changed by sample material and air.

When q values are larger, formula can be reduced to：

$R_{\mathrm{rough}}{q}_z=R^{\mathrm{flat}}{q}_z{e}^{-q_z{,}_o{\mathrm{\&Sigma;}}^2}$

(2) influence of the sample surfaces film to reflection：

If the reflectivity of film is different from the reflectivity of bottom surface, the reflection characteristic that top layer is covered with film sample will change a lot, and the interference of film top layer and bottom reflection to ripple can cause the reduction or rise of reflected intensity.

Due to ripple, transmission range is different from the distance reflected on surface between film layer, so as to generate interference.Different path distances generates a phase shift, so as to generate destructive interference and constructive interference between two ripples.Interference figure depends on absorption when incidence angle, layer thickness d, different refractive index 6 and low q values.Specifically influence during high q values is as follows：

$R_{\mathrm{flat}}=\frac{{r^2}_{\mathrm{0,1}}+{r^2}_{\mathrm{1,2}}+2{\mathrm{xr}}_{\mathrm{0,1}}{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00003119496500022.png,HDA00003119496500023.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{1,2}}\cos 2k_{z,1}\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00003119496500022.png,HDA00003119496500023.png"\; state="\{\{state\}\}">h</figure-callout>}}{1+{r^2}_{\mathrm{0,1}}{r^2}_{\mathrm{1,2}}+2{\mathrm{xr}}_{\mathrm{0,1}}{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00003119496500022.png,HDA00003119496500023.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{1,2}}\cos 2k_{z,1}h}$

Being expressed as follows for floor height is shown：

2k_{Z, 1}H=q_{Z, 1}h

Wherein r_0,1And r_0,2The reflectance factor at=interface, k_zIt is the wave vector in z-axis (height) direction, h is the thickness of film.Due to the relation between the interference mode and thickness degree (Kiessig edges) of reflectivity curve, angular difference (sin θ between Kiessig edges maximum or minimum value can be calculated_i+1-sinθ_i) thickness degree：

$d=\frac{\mathrm{\&lambda;}}{2({\sin \mathrm{\&Theta;}}_{i+1}-{\sin \mathrm{\&Theta;}}_i)}$ (wherein i=1,2,3 ...)

If not applying to angular difference using wave vector q, formula can be reduced to

(3) influence of the roughness for film layer：

The definition of interference figure depends on the roughness of air-film interface.The roughness at interface is lower, and the definition of interference figure is higher.Therefore, it is necessary to determine the definition of interference and the roughness at interface.In mathematical method, the Gaussian Profile of height is used to describe the roughness between 2 interfaces around average height.This mainly by by wireless thin layer (dz) and the electron density (dP) with Gaussian Profile as model handle.

Therefore, the electron density at interface meets Gaussian Profile, and an interface is reflected on another interface without obvious.This effect is as follows：

$R\left(q_z\right)=R_F\left(q_z\right){\left|\frac{1}{{\mathrm{\&rho;}}_s}\&Integral;_{-\&infin;}^{\&infin;}\frac{\mathrm{d\&rho;}\left(z\right)}{\mathrm{dz}}{e}^{{\mathrm{iq}}_{z}z}\mathrm{dz}\right|}^2$

$R\left(\mathrm{qz}\right)=\frac{\left(4\mathrm{\&pi;}{r}_e\right)}{{q_z}^2}\&Integral;\&Integral;\mathrm{\&rho;}\left(z\right)\mathrm{\&rho;}\left(z^{\&prime;}\right)e^{\mathrm{iqz}(z-z^{\&prime;})}\mathrm{dzd}{z}^{\&prime;}$

Dz ' is dz first deviation

In present embodiment, the electromagnetic radiation in a kind of measuring method of use X ray reflection instrument is at least reflected from two different angles by inner surface and outer surface, and is detected by least one moveable detector, or is measured by a position sensitive detectors；

Survey device in present embodiment, is at least installed at the position relative to two different angles of curved surface；

In present embodiment, the interference spectrum for the electromagnetic radiation reflected from surface region is beyond predetermined angular range；

In present embodiment, the interference spectrum for the two different angles mentioned can calculate acquisition thickness of sample；

In present embodiment, at least the electron density of the sample layer different from electric surface density is detected with a detector；

In present embodiment, the fluctuation for the sheet electron density mentioned can be measured by a variety of methods；

In present embodiment, top layer roughness can be measured by the fluctuation of sheet electron density.

Four groups of different samples are determined using present embodiment, measurement result is as shown in table 1：

Table 1

Present embodiment effect：

It is fast using the surface roughness of the measuring method measurement sample of the X ray reflection instrument of present embodiment, film thickness and curved surface density-velocity, and it is measured by reflectometer, the limitation of geometry need not be met, many structures and object may be by reflectometer and analyzed, and X ray reflection instrument (XR) is that a kind of accuracy is nanoscale, nondestructive surface texture measuring instrument device.The instrument can provide the information such as film thickness, electron density difference, roughness, and the information on sample interior regular texture can be obtained by the measurement of bragg peak position.2~3s is only needed using present embodiment measurement sample correlation properties, the characteristics of just because of X ray reflection instrument pinpoint accuracy, non-destructive, thus it has greatly advantage in film and study of surfaces field.

Present embodiment principle：

One contact surface or at least additional layer film are needed using X ray reflection instrument measurement sample, and at least there is one-dimensional curved surface region or deflected and form one-dimensional curved surface in sample.The film added in surface region has outer surface and inner surface, with electromagnetic radiation irradiation curved surface region, electromagnetic radiation is reflected in inner surface and outer surface, and is detected by detection means, and the radiation detected is carried out offset correction to offset the curvature of surface region.By the characteristic for the radiation detected being corrected and being calculated surveyed sample layer.The curvature of curved surface is probably intrinsic curvature or is forced curvature.The reflection for being mainly characterized by all research angles of curvature is all to carry out simultaneously, therefore can observe the angled reflection of institute simultaneously.The reflection of all research angles can be observed simultaneously using the detector of area sensitive.

Embodiment two：Present embodiment from unlike embodiment one：It is 0~30nm that sample, which includes bending sample or substrate, surface curvature or the film of bending, the roughness of carrying bending sample,²Substrate.Other steps and parameter are identical with embodiment one.

Embodiment three：Present embodiment from unlike embodiment two：At least there is one-dimensional curved surface or one-dimensional curved surface formed by deflection in sample described in step one.Other steps and parameter are identical with embodiment two.

Embodiment four：Present embodiment from unlike embodiment three：The electromagnetic radiation of X ray reflection instrument described in step one is monochromatic electromagnetic radiation.Other steps and parameter are identical with embodiment three.

Embodiment five：Present embodiment from unlike embodiment four：The electromagnetic radiation of X ray reflection instrument described in step one is produced by Cu target K system's radiographic sources or Mo target K systems radiographic source.Other steps and parameter are identical with embodiment four.

Embodiment six：Present embodiment from unlike embodiment five：Detection means described in step 2 is at least installed at the position relative to two different angles of sample curved surface.Other steps and parameter are identical with embodiment five.

Embodiment seven：Present embodiment from unlike embodiment six：Surface characteristic described in step 3 includes thickness of sample, surface roughness, sample characteristics of for example and electric surface density.Other steps and parameter are identical with embodiment six.

Embodiment eight：Present embodiment from unlike embodiment seven：The detector of X ray reflection instrument described in step one is to include one kind in luminous point diode, scintillation detector and semiconductor detector or wherein several combinations.Other steps and parameter are identical with embodiment seven.

Embodiment nine：Present embodiment from unlike embodiment eight：X ray reflection instrument in step one includes an electromagnetic radiation source, at least one lens or mirror-image system and detection means.Other steps and parameter are identical with embodiment eight.

Claims (9)

1. a kind of method that use X ray reflection instrument measures sample surfaces characteristic, it is characterised in that the method using X ray reflection instrument measurement sample surfaces characteristic comprises the following steps：

First, sample surfaces are irradiated using X ray reflection instrument；

2nd, intensity of reflected light is detected by detection means；

3rd, the intensity of reflected light detected is calculated and measured：

When more than critical reflection angle, X ray reflection instrument is measured using the effect of intensity of reflected light exponential damping, is obtained measurement data, is simulated with mathematical modeling, and is calculated by Parratt formula, obtains mathematical modeling data；Wherein, the Parratt formula are as follows：

$R_{n-1,n}={a_{n-1}}^4\left[\frac{R_{n,n+1}+F_{n-1,n}}{R_{n,n+1}{F}_{n-1,n}+1}\right]$

$R_{\mathrm{flat}}\left(q_z\right)={|q_z-\sqrt{\frac{{q^2}_z-{q^2}_c-\frac{32i{\mathrm{\&pi;}}^2\mathrm{\&beta;}}{{\mathrm{\&lambda;}}^2}}{{q^2}_z+{q^2}_c-\frac{32i{\mathrm{\&pi;}}^2\mathrm{\&beta;}}{{\mathrm{\&lambda;}}^2}}}|}^{\text{2}}---\left(1\right)$

Wherein, R is reflectivity, and n is natural number, and F is Fresnel attenuation coefficients, and a is half vertical depth, and q is the angle correction of test light, and z is critical angle, and i is imaginary number, for minus 1 square root；

Measured by the convergence to mathematics model data and measurement data, obtain sample surfaces characteristic, that is, complete the measurement using X ray reflection instrument；

4th, measured deviation is corrected：

The correction that the measured deviation correction includes surface curvature and influenceed on reflected signal strength is corrected with footprint；

The correction that the surface curvature influences on reflected signal strength：It is corrected by formula (2)：

Wherein, a can be defined as in formula (2)：

$a=|-\frac{\sqrt{k}\&times;\sqrt{{\mathrm{kl}}^3\&times;(2\sqrt{k}\&times;\sin \left(\mathrm{\&gamma;}\right)+l+3\&times;l\&times;\cos {\left(\mathrm{\&gamma;}\right)}^2)}-2\cos \left(\mathrm{\&gamma;}\right)\&times;{\mathrm{kl}}^2+l\sin \left(\mathrm{\&gamma;}\right)\&times;\sqrt{{\mathrm{kl}}^3\&times;(2\&times;\sqrt{k}\&times;\sin \left(\mathrm{\&gamma;}\right)+l+31\cos {\left(\mathrm{\&gamma;}\right)}^2)}}{l\&times;(2\&times;\sqrt{k}\&times;l\sin \left(\mathrm{\&gamma;}\right)+k+l^2+{31}^2\cos {\left(\mathrm{\&gamma;}\right)}^2)}|$

K represents to bend the curvature degree of sample in formula (2)

D is the arc length of bending sample, and b is the length of bending sample arc length, and l is the distance between detector and sample, and γ is the angle measured in units of radian；

The footprint correction：The angular range of the detector detection intensity of reflected light of X ray reflection instrument is integrated the reflected radiation of each detection unit of X ray reflection instrument irradiation zone by following equation (3~5), is corrected：

Wherein, " U " and " O " is each detection unit low angle position and high angle position.

2. the method that a kind of use X ray reflection instrument according to claim 1 measures sample surfaces characteristic, it is characterised in that it is 0~30nm that sample described in step one, which includes bending sample or substrate, surface curvature or the film of bending, the roughness of carrying bending sample,²Substrate.

3. the method that a kind of use X ray reflection instrument according to claim 2 measures sample surfaces characteristic, it is characterised in that sample described in step one at least has one-dimensional curved surface or one-dimensional curved surface is formed by deflection.

4. the method that a kind of use X ray reflection instrument according to claim 3 measures sample surfaces characteristic, it is characterised in that the electromagnetic radiation of X ray reflection instrument described in step one is monochromatic electromagnetic radiation.

5. the method that a kind of use X ray reflection instrument according to claim 4 measures sample surfaces characteristic, it is characterised in that the electromagnetic radiation of X ray reflection instrument described in step one is produced by Cu target K system's radiographic sources or Mo target K systems radiographic source.

6. the method that a kind of use X ray reflection instrument according to claim 5 measures sample surfaces characteristic, it is characterised in that detection means described in step 2 is at least installed at the position relative to two different angles of sample curved surface.

7. the method that a kind of use X ray reflection instrument according to claim 6 measures sample surfaces characteristic, it is characterised in that surface characteristic described in step 3 includes thickness of sample, surface roughness, sample characteristics of for example and electric surface density.

8. the method that a kind of use X ray reflection instrument according to claim 7 measures sample surfaces characteristic, it is characterised in that the detector of X ray reflection instrument described in step one is to include one kind in luminous point diode, scintillation detector and semiconductor detector or wherein several combinations.

9. the method that a kind of use X ray reflection instrument according to claim 8 measures sample surfaces characteristic, it is characterised in that the X ray reflection instrument in step one includes an electromagnetic radiation source, at least one lens or mirror-image system and detection means.

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