CN103245310B - A kind of method adopting X ray reflection instrument to measure sample surfaces characteristic - Google Patents

Abstract

Adopt X ray reflection instrument to measure a method for sample surfaces characteristic, the present invention relates to the measuring method adopting X ray reflection instrument.The present invention will solve existing reflectometer can only study plane and measure the long problem of sample time, and provides a kind of measuring method adopting X ray reflection instrument.One, X ray reflection instrument is adopted to irradiate sample surfaces; Two, intensity of reflected light is detected by pick-up unit; Three, the intensity of reflected light detected calculated and measure; Four, measured deviation is corrected.The present invention is applied to field of optical measurements.

Description

A kind of method adopting X ray reflection instrument to measure sample surfaces characteristic

Technical field

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

Background technology

X ray reflection instrument is used for the inner structure of working sample layer thickness and related electronic density thereof.The principle of X ray reflection instrument was described by Parratt early than 1954, and up to the present, a condition precedent of this technology is that bottom surface used in the scope of scattering wavelength is enough smooth.Recently, due to widely using of the planar bottom surface on molecular scale, as widely using of silicon chip, this technology is obtained universal.

At present, what the measurement of surfaceness, film thickness and curved surface density mainly adopted is atomic force microscope, and the shortcoming that atomic force microscope is measured is apparatus expensive, and test speed is slow, can only be a great defect to plane research.In addition, systematically scanning samples surface means that working sample thickness needs 30 to 60 minutes usually, therefore the measured surface layer thickness of pipeline system in practice is produced is not suitable for, and it is as a rule very difficult with θ-2 θ solid (geometric configuration of plane of reflection substrate), calculate also more difficult, loaded down with trivial details consuming time, the time of therefore measuring sample is longer.These instruments must adjust to multiple position, therefore need to consume a large amount of energy, thus cause cost to increase.

Summary of the invention

The present invention will solve existing reflectometer can only study plane and measure the long problem of sample time, and provides a kind of measuring method adopting X ray reflection instrument.

The method adopting X ray reflection instrument to measure sample surfaces characteristic comprises the following steps:

One, X ray reflection instrument is adopted to irradiate sample surfaces;

Two, intensity of reflected light is detected by pick-up unit;

Three, the intensity of reflected light detected calculated and measure:

When exceeding reflection at critical angle, X ray reflection instrument utilizes the effect of intensity of reflected light exponential damping to measure, and obtains measurement data, simulates by mathematical model, and calculated by Parratt formula, obtain mathematical model data; Wherein, described Parratt formula is 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 coefficient, 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, is the square root of negative 1;

By measuring the convergence of mathematics model data and measurement data, obtaining sample surfaces characteristic, namely completing the measurement adopting X ray reflection instrument;

Four, measured deviation is corrected:

Described measured deviation corrects and comprises correction that surface curvature affects reflected signal strength and footprint corrects;

The correction that described surface curvature affects reflected signal strength: corrected by formula (2):

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

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

In formula (2), k represents the curvature degree of bending sample d is the arc length of bending sample, and b is the length of bending sample arc length, and l is the distance between detecting device and sample, and γ is the angle recorded in units of radian;

Described footprint corrects: the angular range of the detecting device detection of reflected light intensity of X ray reflection instrument, by the reflected radiation integration of following formula (3 ~ 5) by each detecting unit of X ray reflection instrument irradiation zone, corrects:

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

Invention effect:

Adopt the surfaceness of the measuring method of X ray reflection instrument of the present invention measurement sample, film thickness and curved surface density-velocity fast, and carry out by reflectometer the restriction measuring then not demand fulfillment geometric configuration, many structures and object can utilize reflectometer analysis, and X ray reflection instrument (XR) is a kind of degree of accuracy is nanoscale, nondestructive surface texture measuring instrument device.This instrument can provide the information such as film thickness, electron density difference, roughness, and the information that can obtain about sample interior regular texture by the measurement of bragg peak position.Adopt the present invention to measure sample correlation properties and only need 2 ~ 3s, just because of X ray reflection instrument pinpoint accuracy, nondestructive feature, thus it has greatly advantage at film and study of surfaces field.

Inventive principle:

Adopt X ray reflection instrument to measure sample and need a surface of contact or an at least additional skim, and at least there is the curved surface region or deflected and form the curved surface of one dimension of one dimension in sample.The film additional at surf zone has outside surface and inside surface, with electromagnetic radiation irradiation curved surface region, electromagnetic radiation is reflected at inside surface and outside surface, and is detected by pick-up unit, carries out offset correction to offset the curvature of surf zone to the radiation detected.The characteristic of surveyed sample layer is calculated by correcting the radiation detected.The curvature of curved surface may be intrinsic curvature or be forced to curvature.The principal character of curvature is that the reflection of all research angles is carried out all simultaneously, therefore can observe angled reflection simultaneously.Utilize the detecting device of area sensitive can observe the reflection of all research angles simultaneously.

Accompanying drawing explanation

Fig. 1 is Traditional x-ray reflection θ-2 θ schematic diagram in embodiment one; Wherein, A is X-ray tube, and B is pick-up unit, and C is sample;

Fig. 2 is the X ray reflection instrument schematic diagram for measuring at a high speed bending sample in embodiment one; Wherein, A is X-ray tube, and B is pick-up unit, and C is sample, and D is incident X-rays bundle, and E is X-ray beam point instrumentation, and F is the X-ray beam dispersion because sample curvature causes;

Fig. 3 is the schematic diagram that the high speed in embodiment one measures bending sample X ray reflection instrument; Wherein, A is X-ray tube, and B is pick-up unit, and C is sample, D is X-ray beam point instrumentation, E is the X-ray beam dispersion because sample curvature causes, and F is the mathematical center point of sample curvature, and G is the sample surfaces compared with deep camber amplified, H is the sample surfaces compared with small curve amplified, I is vertical irradiation sample surfaces, and J is incident X ray light beam, and K is the X ray light 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 the scope that each detecting unit limited by o and u detects, a expression certain resolution detecting device detects above sample and is irradiated by light region, b is expressed as and is irradiated by light region with certain resolution detecting device detection sample zone line, and c is expressed as and is irradiated by light region with certain resolution detecting device detection sample lower zone;

Fig. 5 is the reflectivity curve that in embodiment one, surface has the curved surface cover glass of skim polymer film;

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

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

Fig. 9 is that the practical measurement in embodiment one bends samples data plot; Wherein, in figure, black color dots is measured value, and Grey Point is the analogue value;

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

The visual figure of Figure 11 to be practical measurement radius-of-curvature in embodiment one be 19cm sample correlation values.

Embodiment

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

One, X ray reflection instrument is adopted to irradiate sample surfaces;

Two, intensity of reflected light is detected by pick-up unit;

Three, the intensity of reflected light detected calculated and measure:

When exceeding reflection at critical angle, X ray reflection instrument utilizes the effect of intensity of reflected light exponential damping to measure, and obtains measurement data, simulates by mathematical model, and calculated by Parratt formula, obtain mathematical model data; Wherein, described Parratt formula is 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 coefficient, 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, is the square root of negative 1;

By measuring the convergence of mathematics model data and measurement data, obtaining sample surfaces characteristic, namely completing the measurement adopting X ray reflection instrument;

Four, measured deviation is corrected:

Described measured deviation corrects and comprises correction that surface curvature affects reflected signal strength and footprint corrects;

The correction that described surface curvature affects reflected signal strength: corrected by formula (2):

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

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

In formula (2), k represents the curvature degree of bending sample d is the arc length of bending sample, and b is the length of bending sample arc length, and l is the distance between detecting device and sample, and γ is the angle recorded in units of radian;

Described footprint corrects: the angular range of the detecting device detection of reflected light intensity of X ray reflection instrument, by the reflected radiation integration of following formula (3 ~ 5) by each detecting unit of X ray reflection instrument irradiation zone, corrects:

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

In present embodiment, this standardization relates to uncorrelated light path (q) index with wavelength, and q is calculated as follows:

$q=\frac{4\mathrm{\π}\×\sin \mathrm{\Θ}}{\mathrm{\λ}}$

Need incidence angle θ and the wavelength X of using X-ray in the measurements, due to the wavelength measured and the change of refractive index less, compared with visible ray, the angular domain that can observe is relatively much smaller.The refractive index (except neutron hydrogen) of X-ray is less than 1.Therefore this interface comprises one and total reflection θ _cthe material that critical angle is relevant.If incidence angle θ is less than θ _c, then ray can not penetrate sample, but all reflects (see Fig. 1).If incidence angle θ is greater than θ _c, ray then can penetrate sample surfaces.When vacuum measurement, without refractive index time can calculate the reflection at critical angle (n=1) of material.

Shown in being calculated as follows of the critical edges of X-ray:

cosΘ _c＝n＝1-δ

In formula, the electron density of sample surfaces is measured in δ representative.This decay is described by Fresnel attenuation function, when q value is higher than (q > 3q during critical value _c) time, the reflection loss of ideal plane can be calculated by formula below:

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

Wherein being calculated as of q: q _cit is the Scattering of Vector of critical angle.β is the absorption coefficient of sample, and i represents imaginary number.This formula is at q > 3q _cshi Chengli.When q value is lower, produce deviation due to absorption, this formula is used for measuring fully-flattened;

(1) impact of roughness:

Owing to departing from the scattering of minute surface, Rough Horizontal Plane reflected light compared with plane reduces.Therefore, need to set a parameter to roughness.That effects on surface differing heights (z-axis) carries out Gaussian distribution statistics in the 2 dimensional region limited by x and y-axis to one of definition of roughness.Roughness parameter ∑ ²distributed by the P of height z, average height jointly determine with the deviation dz of height:

The impact that surfaceness reflects for sample surfaces is (q < 3q _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 value is larger, formula can be reduced to:

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

(2) sample surfaces film is on the impact of 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 film top layer and bottom reflection can cause reduction or the rising of reflection strength to the interference of ripple.

Because ripple transmission range between thin layer is different from the distance at surface reflection, thus create interference.Different path distances creates a phase shift, thus creates destructive interference and constructive interference between two ripples.Interference figure depend on incident angle, layer thickness d, different refractive indexes 6 and low q value time absorption.Concrete impact during high q value is as follows:

$R_{\mathrm{flat}}=\frac{{r^2}_{\mathrm{0,1}}+{r^2}_{\mathrm{1,2}}+2{\mathrm{xr}}_{\mathrm{0,1}}{r}_{\mathrm{1,2}}\cos 2k_{z,1}h}{1+{r^2}_{\mathrm{0,1}}{r^2}_{\mathrm{1,2}}+2{\mathrm{xr}}_{\mathrm{0,1}}{r}_{\mathrm{1,2}}\cos 2k_{z,1}h}$

Shown in being expressed as follows of floor height:

2k _z，1h＝q _z，1h

Wherein r _0,1and r _0,2the reflection coefficient at=interface, k _zbe the wave vector in z-axis (highly) direction, h is the thickness of film.Due to the relation between the interference mode of reflectivity curve and layer thickness (Kiessig edge), angular difference (sin θ between Kiessig edge maximal value or minimum value can be calculated _i+1-sin θ _i) layer thickness:

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

If adopt wave vector q and inapplicable angular difference, formula can be reduced to

(3) roughness is for the impact of thin layer:

The sharpness of interference figure depends on the roughness of air-film interface.The roughness at interface is lower, and the sharpness of interference figure is higher.Therefore, the roughness determining sharpness and the interface of interfering is necessary.In mathematical method, around average height, the Gaussian distribution of height is for describing the roughness between 2 interfaces.This mainly by by wireless thin layer (dz) and the electron density (dP) with Gaussian distribution as model process.

Therefore, the electron density at interface meets Gaussian distribution, and an interface is reflected without obvious on another interface.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 first deviation of dz

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

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

In present embodiment, from the interference spectrum of electromagnetic radiation of surf zone reflection beyond predetermined angular range;

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

In present embodiment, at least detect the electron density of the sample layer being different from electric surface density with a detecting device;

In present embodiment, the fluctuation of the sheet electron density mentioned can be measured by multiple method;

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

Utilize present embodiment to determine four groups of different samples, measurement result is as shown in table 1:

Table 1

Present embodiment effect:

Adopt the surfaceness of the measuring method of the X ray reflection instrument of present embodiment measurement sample, film thickness and curved surface density-velocity fast, and carry out by reflectometer the restriction measuring then not demand fulfillment geometric configuration, many structures and object can utilize reflectometer analysis, and X ray reflection instrument (XR) is a kind of degree of accuracy is nanoscale, nondestructive surface texture measuring instrument device.This instrument can provide the information such as film thickness, electron density difference, roughness, and the information that can obtain about sample interior regular texture by the measurement of bragg peak position.Adopt present embodiment to measure sample correlation properties and only need 2 ~ 3s, just because of X ray reflection instrument pinpoint accuracy, nondestructive feature, thus it has greatly advantage at film and study of surfaces field.

Present embodiment principle:

Adopt X ray reflection instrument to measure sample and need a surface of contact or an at least additional skim, and at least there is the curved surface region or deflected and form the curved surface of one dimension of one dimension in sample.The film additional at surf zone has outside surface and inside surface, with electromagnetic radiation irradiation curved surface region, electromagnetic radiation is reflected at inside surface and outside surface, and is detected by pick-up unit, carries out offset correction to offset the curvature of surf zone to the radiation detected.The characteristic of surveyed sample layer is calculated by correcting the radiation detected.The curvature of curved surface may be intrinsic curvature or be forced to curvature.The principal character of curvature is that the reflection of all research angles is carried out all simultaneously, therefore can observe angled reflection simultaneously.Utilize the detecting device of area sensitive can observe the reflection of all research angles simultaneously.

Embodiment two: present embodiment and embodiment one comprise bending sample unlike: sample or carry the substrate of bending sample, surface curvature or bending film, roughness be 0 ~ 30nm ²substrate.Other step and parameter identical with embodiment one.

Embodiment three: present embodiment and embodiment two unlike: at least there is one dimension curved surface or form one dimension curved surface by deflecting in sample described in step one.Other step and parameter identical with embodiment two.

Embodiment four: present embodiment and embodiment three unlike: the electromagnetic radiation of the instrument of X ray reflection described in step one is monochromatic electromagnetic radiation.Other step and parameter identical with embodiment three.

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

Embodiment six: present embodiment and embodiment five unlike: pick-up unit described in step 2 is at least installed in the position relative to sample curved surface two different angles.Other step and parameter identical with embodiment five.

Embodiment seven: present embodiment and embodiment six unlike: character of surface described in step 3 comprises thickness of sample, surfaceness, sample characteristics of for example and electric surface density.Other step and parameter identical with embodiment six.

Embodiment eight: present embodiment and embodiment seven unlike: the instrument of X ray reflection described in step one detecting device is a kind of or wherein several combination comprised in luminous point diode, scintillation detector and semiconductor detector.Other step and parameter identical with embodiment seven.

Embodiment nine: present embodiment and embodiment eight unlike: the X ray reflection instrument in step one comprises an electromagnetic radiation source, at least one lens or mirror-image system and pick-up unit.Other step and parameter identical with embodiment eight.

Claims (9)

1. adopt X ray reflection instrument to measure a method for sample surfaces characteristic, it is characterized in that the method adopting X ray reflection instrument to measure sample surfaces characteristic comprises the following steps:

One, X ray reflection instrument is adopted to irradiate sample surfaces;

Two, intensity of reflected light is detected by pick-up unit;

Three, the intensity of reflected light detected calculated and measure:

When exceeding reflection at critical angle, X ray reflection instrument utilizes the effect of intensity of reflected light exponential damping to measure, and obtains measurement data, simulates by mathematical model, and calculated by Parratt formula, obtain mathematical model data; Wherein, described Parratt formula is as follows:

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

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

Wherein, R is reflectivity, and n is natural number, and F is Fresnel attenuation coefficient, 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, is the square root of negative 1;

By measuring the convergence of mathematics model data and measurement data, obtaining sample surfaces characteristic, namely completing the measurement adopting X ray reflection instrument;

Four, measured deviation is corrected:

Described measured deviation corrects and comprises correction that surface curvature affects reflected signal strength and footprint corrects;

The correction that described surface curvature affects reflected signal strength: corrected by formula (2):

${\mathrm{\&Theta;}}_r=\arctan \left(m\right)=\arctan \left(\frac{-a}{\sqrt{k-a^2}}\right)---\left(2\right)$

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

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

In formula (2), k represents the curvature degree of bending sample d is the arc length of bending sample, and b is the length of bending sample arc length, and l is the distance between detecting device and sample, and γ is the angle recorded in units of radian;

Described footprint corrects: the angular range of the detecting device detection of reflected light intensity of X ray reflection instrument, by the reflected radiation integration of following formula (3 ~ 5) by each detecting unit of X ray reflection instrument irradiation zone, corrects:

$f=\left(\underset{U}{\overset{O}{\&Integral;}}\sqrt{1+\frac{x^2}{k-x^2}\mathrm{dx}}\right)---\left(3\right)$

$U=+\frac{\sqrt{k}\&times;\sqrt{k^2{l}^3\&times;(2\sqrt{k}\&times;\sin \left(u\right)+1)}-\cos \left(u\right)\&times;k^{\frac{3}{2}}\&times;l^2+l\sin \left(u\right)\&times;\sqrt{k^2\&times;l^3\&times;(2\&times;\sqrt{k}\&times;\sin \left(u\right)+1)}}{l\&times;(k^{\frac{3}{2}}\&times;\mathrm{lk}\sin \left(u\right)+\sqrt{k}\&times;l^2)}---\left(4\right)$

$O=+\frac{\sqrt{k}\&times;\sqrt{k^2{l}^3\&times;(2\sqrt{k}\&times;\sin \left(o\right)+1)}-\cos \left(o\right)\&times;k^{\frac{3}{2}}\&times;l^2+l\sin \left(o\right)\&times;\sqrt{k^2\&times;l^3\&times;(2\&times;\sqrt{k}\&times;\sin \left(o\right)+1)}}{l\&times;(k^{\frac{3}{2}}\&times;\mathrm{lk}\sin \left(o\right)+\sqrt{k}\&times;l^2)}---\left(5\right)$

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

2. a kind of method adopting X ray reflection instrument to measure sample surfaces characteristic according to claim 1, is characterized in that sample described in step one comprises the substrate of bending sample or the bending sample of carrying, surface curvature or bending film, roughness are 0 ~ 30nm ²substrate.

3. a kind of method adopting X ray reflection instrument to measure sample surfaces characteristic according to claim 2, is characterized in that sample described in step one at least exists one dimension curved surface or forms one dimension curved surface by deflecting.

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

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

6. a kind of method adopting X ray reflection instrument to measure sample surfaces characteristic according to claim 5, is characterized in that pick-up unit described in step 2 is at least installed in the position relative to sample curved surface two different angles.

7. a kind of method adopting X ray reflection instrument to measure sample surfaces characteristic according to claim 6, is characterized in that character of surface described in step 3 comprises thickness of sample, surfaceness, sample characteristics of for example and electric surface density.

8. a kind of method adopting X ray reflection instrument to measure sample surfaces characteristic according to claim 7, is characterized in that the instrument of X ray reflection described in step one detecting device is a kind of or wherein several combination comprised in photodiode, scintillation detector and semiconductor detector.

9. a kind of method adopting X ray reflection instrument to measure sample surfaces characteristic according to claim 8, is characterized in that the X ray reflection instrument in step one comprises an electromagnetic radiation source, at least one lens or mirror-image system and pick-up unit.