CN101738407A - X-ray diffractometer-based ultra-smooth surface measuring method - Google Patents

Abstract

The invention relates to a method for detecting the roughness of an ultra-smooth surface, in particular to an X-ray diffractometer-based ultra-smooth surface measuring method. The method comprises the following steps: making X rays with wavelengths lambda less than 4 angstroms grazing-incident to the surface of a tested sample on a sample stage as probe beams, wherein the grazing-incident angle of the X ray is less than a critical angle of total reflection of the sample in the waveband of the X ray; gradually scanning and receiving scattered beams reflected from the surface of the sample in a rotating way at a set interval and a set speed, and recording gradual scattering intensities Pi(theta) by a photon counting detector on an X-ray diffractometer; and calculating a surface one-dimensional power spectrum function PSD1D (p) and effective surface roughness sigma(eff) according to a first-order vector perturbation theoretical formula. The method can accurately and quantitatively measure the power spectrum function and the effective surface roughness value of the ultra-smooth surface of which the root mean square of the surface roughness is less than 2 nm, and has the advantages of simple measurement equipment and means and convenient operation.

Description

Measure the method for super-smooth surface based on X-ray diffractometer

Technical field

The present invention relates to detect the method for super-smooth surface roughness, particularly a kind of method of measuring the super-smooth surface roughness with X-ray diffractometer.

Background technology

At present, at semiconductor and short-wave band optical field, the method for measuring the general employing of super-smooth surface is optical interference method and contact method.Interferometric method measuring equipment complex structure, cost is higher; And when adopting contact type measurement, probe contacts with the surface, easy scratch surface.

Aspect scattering method measurement optical surface, R.S.Wriston, Buddhist nun open very, Chen Shuyan etc. studied the method for measuring rough surface under vacuum condition with grenz ray or ultraviolet scattering method ^[1-3]This method is used for measuring more coarse surface (σ based on the scalar scattering theory _Rms＞3nm).But the measuring equipment complexity relates to the problem of vacuumizing, time-consuming and inconvenient operation.J.M.Elson, J.C.stover etc. utilize the scatterometry rough surface of visible light ^[4-10]This method also is based on the scalar scattering theory, is mainly used in the bigger coarse surface (σ of measurement _Rms＞100nm).And for super-smooth surface (σ _Rms＜2nm), scattering phenomenon is mainly caused by the medium-high frequency error.Because detectable surperficial smallest lateral dimension and probing wave appearance are worked as, and no matter are visible light scattering method or grenz ray scattering method, can only provide the scattered information that the medium and low frequency error causes, so we can not obtain more accurate surface microscopic information.

Summary of the invention

The objective of the invention is above-mentioned many disadvantages for the method existence that overcomes habitual at present detection super-smooth surface roughness, propose a kind ofly to measure the method for super-smooth surface, to realize and to carry out more accurate quantitative measurment to the root mean square surfaceness less than the power spectral density function (PSD) and the effective surface roughness value thereof of the super-smooth surface of 2nm based on X-ray diffractometer.

The present invention is based on X-ray diffractometer and measure the method for super-smooth surface, with wavelength X less than

X ray as detecting light beam (otherwise ray has strong absorption when propagating in air) glancing incidence to the sample surface that places on the sample stage, its grazing angle is less than the cirtical angle of total reflection of sample at the X ray wave band, detector on the X-ray diffractometer progressively scans the scattered beam that reception reflects from sample surfaces with interval and the speed rotation of setting, record scattered light intensity ∏ (θ) progressively obtains the one dimension power spectral density PSD according to calculating with following formula (1) and formula (2) _1D(p) and effective surface roughness σ _Eff:

$\mathrm{\&Pi;}\left(\mathrm{\&theta;}\right)=\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="W"\; filenames="H2009102180633E00014.png"\; state="\{\{state\}\}">W</figure-callout>}}_0}\frac{{\mathrm{dW}}_{\mathrm{scat}}}{\mathrm{d\&theta;}}=\frac{k^3{|1-\mathrm{\&epsiv;}|}^2{\left|t\left({\mathrm{\&theta;}}_0\right)t\left(\mathrm{\&theta;}\right)\right|}^2}{16\mathrm{\&pi;}\sin {\mathrm{\&theta;}}_0\sqrt{\cos {\mathrm{\&theta;}}_0\cos \mathrm{\&theta;}}}\&CenterDot;{\mathrm{PSD}}_{1D}\left(p\right)---\left(1\right)$

${{\mathrm{\&sigma;}}_{\mathrm{eff}}}^2=2\mathrm{\&pi;}{\&Integral;}_{p_{\min }}^{p_{\max }}{\mathrm{PSD}}_{1D}\left(p\right)\mathrm{dp}---\left(2\right)$

In the formula: W ₀For inciding lip-deep radiation power;

DW _ScatBe the radiation power in scattering angle d θ scope;

PSD _1D(p) be surperficial one dimension power spectral density function;

θ ₀Be the light grazing angle;

θ is a scattering angle;

P be by one-dimensional grating equation decision with θ and θ ₀Relevant spatial frequency range;

T (θ) is the transmission factor of desirable smooth surface;

ε is the complex permittivity of medium;

κ is a wave vector.

Measuring method of the present invention, can realize the root mean square surfaceness is carried out more accurate quantitative measurment less than the power spectral density function (PSD) and the effective surface roughness value thereof of the super-smooth surface of 2nm by means of X-ray diffractometer, the measuring equipment means are simple, easy to operate, utilize this method can measure the medium-high frequency error of super-smooth surface and the inferior surface structure of research solid.

Description of drawings

Fig. 1 is an optical system synoptic diagram of measuring super-smooth surface on X-ray diffractometer;

Fig. 2 is the PSD figure that the silicon chip of σ=0.67nm is obtained with GXRS method and AFM method;

Fig. 3 is the PSD figure that the silicon chip of σ=0.46nm is obtained with GXRS method and AFM method;

Fig. 4 is the PSD figure that the silicon chip of σ=0.29nm is obtained with GXRS method and AFM method.

Embodiment

By following examples the inventive method is described in further detail.

With reference to Fig. 1, press the following practice at K with the copper target _α

Spectral line makes to measure on the commercial X-ray diffractometer of light source the super-smooth surface roughness:

Testing sample is fixed on the sample stage, surface to be measured is positioned on the plane of entrance slit and the formation of reception slit.Make detecting light beam with θ by adjusting sample stage ₀=0.18 ° of glancing incidence to testing sample 1 surface, its grazing angle θ ₀Less than the cirtical angle of total reflection of sample at the X ray wave band.The width of slit is respectively 20 μ m, 50 μ m, 20 μ m from left to right, and light source-sample interval is from being 185mm, and sample-detector pitch is from also being 185mm.Adjusting is arranged on the crack on the fine setting edge of a knife 2 and sample surface on the sample stage, directly injects the photon counting detector 3 of X-ray diffractometer to avoid detecting light beam.Photon counting detector 3 on the X-ray diffractometer with the interval (18 ") set and speed (18 "/S) the rotation scattered beam that reflects from sample surfaces of scanning reception progressively, record scattered light intensity ∏ (θ) progressively calculates acquisition one dimension power spectral density PSD according to one-level vector perturbation theory formula (1) and formula (2) _1D(p) and effective surface roughness σ _Eff:

$\mathrm{\&Pi;}\left(\mathrm{\&theta;}\right)=\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="W"\; filenames="H2009102180633E00014.png"\; state="\{\{state\}\}">W</figure-callout>}}_0}\frac{{\mathrm{dW}}_{\mathrm{scat}}}{\mathrm{d\&theta;}}=\frac{k^3{|1-\mathrm{\&epsiv;}|}^2{\left|t\left({\mathrm{\&theta;}}_0\right)t\left(\mathrm{\&theta;}\right)\right|}^2}{16\mathrm{\&pi;}\sin {\mathrm{\&theta;}}_0\sqrt{\cos {\mathrm{\&theta;}}_0\cos \mathrm{\&theta;}}}\&CenterDot;{\mathrm{PSD}}_{1D}\left(p\right)---\left(1\right)$

${{\mathrm{\&sigma;}}_{\mathrm{eff}}}^2=2\mathrm{\&pi;}{\&Integral;}_{p_{\min }}^{p_{\max }}{\mathrm{PSD}}_{1D}\left(p\right)\mathrm{dp}---\left(2\right)$

In the formula: W ₀For inciding lip-deep radiation power;

DW _ScatBe the radiation power in scattering angle d θ scope;

PSD _1D(p) be surperficial one dimension power spectral density function;

θ ₀Be the light grazing angle;

θ is a scattering angle;

P be by one-dimensional grating equation decision with θ and θ ₀Relevant spatial frequency range;

T (θ) is the transmission factor of desirable smooth surface;

ε is the complex permittivity of medium;

κ is a wave vector.

Measure the silicon chip sample test example of following three different roughness respectively by above-mentioned way:

The surfaceness and other parameters that record these three samples with atomic force microscope (AFM) are as shown in table 1.Selected sample has the surface (σ of smoother _Rms＜2nm), and the surface does not have significant flaw.

The basic parameter of table 1 sample

And the one dimension power spectral density PSD of three different roughness silicon chips that obtain with above-mentioned glancing incidence X ray scattering (GXRS) method _1D(p) respectively as Fig. 2, Fig. 3, shown in Figure 4; The effective surface roughness σ that calculates by formula (2) _EffAs shown in table 2.

The r.m.s. roughness value that table 2GXRS method and AFM method obtain

As can be seen from Table 2: glancing incidence X ray scattering method survey area is much larger than the AFM sweep limit, therefore obtaining PSD in space intermediate frequency zone glancing incidence X ray scattering (GXRS) method should be higher than AFM and obtain PSD, and in the spatial high-frequency district, both are basically identical then, as Fig. 2, Fig. 3, shown in Figure 4, experimental result conforms to theory.

Claims (3)

1. measure the method for super-smooth surface based on X-ray diffractometer for one kind, it is characterized in that: with wavelength X less than

X ray as the detecting light beam glancing incidence to the sample surface that places on the sample stage, its grazing angle is less than the cirtical angle of total reflection of sample at the X ray wave band, photon counting detector on the X-ray diffractometer progressively scans the scattered beam that reception reflects from sample surfaces with interval and the speed rotation of setting, record scattered light intensity ∏ (θ) progressively obtains surperficial one dimension power spectral density function PSD according to calculating with following formula (1) and formula (2) _1D(P) and effective surface roughness σ _Eff:

$\mathrm{\&Pi;}\left(\mathrm{\&theta;}\right)=\frac{1}{W_0}\frac{{\mathrm{dW}}_{\mathrm{scat}}}{\mathrm{d\&theta;}}=\frac{k^3{|1-\mathrm{\&epsiv;}|}^2{\left|t\left({\mathrm{\&theta;}}_0\right)t\left(\mathrm{\&theta;}\right)\right|}^t}{16\mathrm{\&pi;}\sin {\mathrm{\&theta;}}_0\sqrt{\cos {\mathrm{\&theta;}}_0\cos \mathrm{\&theta;}}}\&CenterDot;{\mathrm{PSD}}_{1D}\left(p\right)---\left(1\right)$

${{\mathrm{\&sigma;}}_{\mathrm{eff}}}^2=2\mathrm{\&pi;}{\&Integral;}_{p_{\min }}^{p_{\max }}{\mathrm{PSD}}_{1D}\left(p\right)\mathrm{dp}---\left(2\right)$

In the formula: W ₀For inciding lip-deep radiation power;

DW _ScatBe the radiation power in scattering angle d θ scope;

PSD _1D(p) be surperficial one dimension power spectral density function;

θ ₀Be the light grazing angle;

θ is a scattering angle;

P be by one-dimensional grating equation decision with θ and θ ₀Relevant spatial frequency range;

T (θ) is the transmission factor of desirable smooth surface;

ε is the complex permittivity of medium;

κ is a wave vector.

2. the method based on X-ray diffractometer measurement super-smooth surface according to claim 1 is characterized in that, adopts wavelength The K of copper target _αSpectral line is as the detecting light beam light source.

3. according to claim 1ly measure the method for super-smooth surface, it is characterized in that, be arranged on the edge of a knife on the sample stage and the crack on sample surface, directly inject detector to avoid detecting light beam by adjusting based on X-ray diffractometer.

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