CN104238282A - Quick strict simulation method for extremely ultraviolet photoetching mask diffraction spectrum containing defect - Google Patents

Abstract

The invention relates to a quick strict simulation method for a extremely ultraviolet photoetching mask diffraction spectrum containing a defect . The method comprises the following steps: dividing a multilayer film containing defects into a no-defect part and a defect part, and modeling by a partition method and an equivalent film layer method; during modeling, firstly, obtaining a mask absorption layer diffraction spectrum through thin mask proximity and phase compensation, and then, through the diffraction of the multilayer film containing the defects, finally obtaining the extremely ultraviolet photoetching mask diffraction spectrum containing the defect through the thin mask proximity and the phase compensation. The invention provides the quick strict simulation method which can quickly and effectively simulate the extremely ultraviolet photoetching diffraction spectrum containing the defect mask.

Description

Extreme ultraviolet photolithographic is containing the quick strict emulation mode of defect mask diffraction spectra

Technical field

The present invention relates to extreme ultraviolet photolithographic mask, particularly a kind of extreme ultraviolet photolithographic is containing the quick strict emulation mode of defect mask diffraction spectra.

Background technology

It is the most promising Next Generation Lithography that extreme ultraviolet (EUV) photoetching is described as, and defects on mask is one of main bugbear hindering extreme ultraviolet photolithographic technical development.Extreme ultraviolet photolithographic mask defect is mainly divided into two kinds: amplitude type defect and phase type defect, amplitude type defect distribution in absorption layer and multi-layer film surface, the amplitude of major effect mask diffraction spectra; Phase type defect distribution is inner in multilayer film, causes the distortion of multilayer film, the phase place of major effect multilayer film diffraction spectra.Compared to amplitude type defect, phase type defect on the impact of mask diffraction spectra more complicated and be difficult to repair, therefore need certain method to compensate, and simulation bit-type defect is the Main Basis of compensation and the demand of large area mask emulation for the impact of mask diffraction spectra quickly and accurately.

At present, strict emulation mode that what extreme ultraviolet photolithographic mask emulation usually adopted is solves the distribution of mask diffractional field if FDTD method is (see in first technology 1, T.Pistor, Y.Deng, and A.Neureuther, " Extreme ultraviolet mask defect simulation:low-profile defects ", J.Vac.Sci.Technol.B18, 2926-2929 (2000)), waveguide method is (see in first technology 2, Peter Evanschitzky and Andreas Erdmann, " Fast near field simulation of optical and EUV masks using the waveguide method ", Proc.of SPIE Vol.6533, 65330Y (2007)).Obtain mask diffractional field distribution accurately in first technology mainly through calculating maxwell equation group, calculated amount is large, and computing velocity is slow, is unfavorable for large-area mask simulation calculation and data statistic analysis.

Summary of the invention

The object of the present invention is to provide a kind of extreme ultraviolet photolithographic containing the quick strict emulation mode of defect mask diffraction spectra.The present invention can emulate the impact of defects on mask on mask imaging effectively, and improves the simulation velocity containing defect mask diffraction spectra.

Technical solution of the present invention is as follows:

Extreme ultraviolet photolithographic is containing a quick strict emulation mode for defect mask diffraction spectra, and the method comprises following steps:

1) mask absorption layer diffraction spectra is emulated:

The affixture machine of the thin mask model of equivalence of mask absorption layer is:

(see in first technology 3, Yuting Cao, Xiangzhao Wang, Andreas Erdmann, Peng Bu, and Yang Bu, " Analytical model for EUV mask diffraction field calculation ", the formula (3) in Proc.of SPIE Vol.8171,81710N (2011), should be merged in by reference herein at the full content of first technology 3)

Wherein, $t\left(x\right)=\left\{\begin{array}{cc}{t}_a& \frac{-p}{2w}<x<\frac{p}{2w}\\ t_b& \frac{-1}{2w}<x<\frac{-p}{2w}\mathrm{and}\frac{p}{2w}<x<\frac{1}{2w}\end{array}\right.,$ X-axis is the coordinate axis of horizontal direction, true origin is positioned at isolated empty centre position, t'(x) be the approximate affixture machine of the thin mask model of equivalence of mask absorption layer, t (x) is the transmission coefficient of unlimited thin mask, p is the size of the isolated sky on mask, w is the figure periodic dimensions on mask, t _afor the equivalent transmission coefficient within the scope of p, t _bfor p _absequivalent transmission coefficient in scope, p _absfor the width of absorption layer in the figure cycle, i.e. p _abs=w-p, Ae ^{j φ}for the border corrected impulse of the thin mask model of equivalence, A is the amplitude of corrected impulse, and φ is the phase place of corrected impulse.

Wherein, δ (x)=0 when δ (x) is defined as x ≠ 0, and

To affixture machine t'(x) carry out the diffraction spectra that Fourier transform obtains equivalent thin mask model and be:

$F_{\mathrm{thin}}\left(m\right)=(t_a-t_b)\frac{p}{x}\sin c\left(m\frac{p}{w}\right)+t_b\sin c\left(m\right)+2\mathrm{A\; exp}\left(\mathrm{j\&phi;}\right)\cos \left(\mathrm{\&pi;m}\frac{p}{w}\right),$

Wherein, m is the order of diffraction time of the diffraction spectra of equivalent thin mask model, and the span of m is determined by the required order of diffraction time, and usual span is integer range required arbitrarily between-w/ λ and w/ λ, and λ is the operation wavelength of extreme ultra violet lithography.

Incident light is inclination unit plane ripple, and inclination angle is expressed as the angle of incident light direction and z-axis with the angle theta of incident light direction projection in x-o-y plane and x-axis, the diffraction spectra of mask absorption layer is:

$F_{\mathrm{thick}}({\mathrm{\&alpha;}}_m,{\mathrm{\&beta;}}_m;{\mathrm{\&alpha;}}_{\mathrm{in}},{\mathrm{\&beta;}}_{\mathrm{in}})=e^{-j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\frac{d_{\mathrm{abs}}}{2}\sqrt{1-{\mathrm{\&alpha;}}_{\mathrm{in}}^2-{\mathrm{\&beta;}}_{\mathrm{in}}^2}}{F}_{\mathrm{thin}}({\mathrm{\&alpha;}}_m-{\mathrm{\&alpha;}}_{\mathrm{in}},{\mathrm{\&beta;}}_m-{\mathrm{\&beta;}}_{\mathrm{in}})e^{-j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\frac{d_{\mathrm{abs}}}{2}\sqrt{1-{\mathrm{\&alpha;}}_m^2-{\mathrm{\&beta;}}_m^2}},$

Wherein, F _thin(α _m-α _in, β _m-β _in)=F _thin(α _m-α _in) δ (β _m-β _in), for light is from the additive phase of the equivalent face position of the equivalent thin mask model of mask absorption layer 1 surface arrival, for light is from the additive phase of the equivalent face position arrival mask absorption layer lower surface of the thin mask model of equivalence, α _inand β _inbe respectively the x-axis of incident light and the direction cosine in y-axis direction, and α _mfor the direction cosine of x-axis direction m level time diffraction light, and α _m=m λ, β _mfor the direction cosine of y-axis direction m level time diffraction light, β during X-Y scheme _m=β _in, d _absfor the thickness of mask absorption layer.

Wherein,

$F_{\mathrm{thin}}({\mathrm{\&alpha;}}_m-{\mathrm{\&alpha;}}_{\mathrm{in}})=(t_a-t_b)\frac{p}{w}\sin c\left(\frac{{\mathrm{\&alpha;}}_m-{\mathrm{\&alpha;}}_{\mathrm{in}}}{\mathrm{\&lambda;}}\frac{p}{w}\right)+t_b\sin c\left(\frac{{\mathrm{\&alpha;}}_m-{\mathrm{\&alpha;}}_{\mathrm{in}}}{\mathrm{\&lambda;}}\right)+2\mathrm{A\; exp}\left(\mathrm{j\&phi;}\right)\cos \left(\mathrm{\&pi;}\frac{{\mathrm{\&alpha;}}_m-{\mathrm{\&alpha;}}_{\mathrm{in}}}{\mathrm{\&lambda;}}\frac{p}{w}\right)$

For the Fourier transform of affixture machine, i.e. the diffraction spectra of equivalent thin mask model.

The numeric distribution that strict emulation obtains mask absorption layer diffraction spectra is carried out, by F by Commercial photolithography simulation software Dr.LiTHO _thick(α _m, β _m; α _in, β _in) to mate to the diffraction spectra of three the corresponding arbitrarily orders of diffraction in the diffraction spectra numeric distribution obtained time and obtain ternary linear function group, solving equations can obtain the parametric t in affixture machine expression formula _a, t _band Ae ^{j φ}value, and this parameter value only needs again to solve when changing material and the thickness of mask absorption layer, namely for same material and thickness, a demand solution primary parameter.

2) emulation is containing the diffraction spectra after the reflection of defect multilayer film:

To zero defect part be divided into containing defect multilayer film and contain defect part, be wherein the horizontal extent of the complex reflection coefficient of defective effect multilayer film containing the scope of defect part, the scope containing defect part as Gaussian defect be defect center towards periphery extended range be the scope obtained containing the full width at half maximum of defect multi-layer film surface defect.The complex reflection coefficient of zero defect part is tried to achieve by equivalent rete method, and for same incident angle, the complex reflection coefficient of whole zero defect part is identical.

To be divided into N aliquot along the x-axis direction containing defect part, N is odd number, is parallel between each rete in the multilayer film of each aliquot, and the thickness of each layer is determined by each thicknesses of layers of the center of this aliquot multilayer film.The complex reflection coefficient of each aliquot multilayer film can be tried to achieve by equivalent rete method.Wherein in one-period, the width of zero defect part is w ₁, the width containing defect part is w ₂, then the every part of width contained after defect part decile is w ₂/ N.

Can try to achieve the complex reflection coefficient of zero defect part 21 by equivalent rete method and contain a series of aliquot multilayer film 2201,2202 in defect part 22, the complex reflection coefficient of 2203, obtaining the diffraction spectra after containing defect multilayer film 22 reflection is thus:

Wherein, a=2w ₂/ w, t are the coordinate in x-axis direction, and value is α _qand β _qbe respectively the q order diffraction light after reflecting containing defect multilayer film 2 along the x-axis direction with the direction cosine in y-axis direction, q is the order of diffraction time containing defect multilayer film 2 diffraction spectra, and span is identical with m, for the angle of diffraction of m order diffraction light, and for the incident angle adopting equivalent rete method to try to achieve is time the complex reflection coefficient of zero defect part 21, for the incident angle adopting equivalent rete method to try to achieve is time t coordinate place containing the complex reflection coefficient of defect part 22, h ₀t () is the flaw height at the upper surface t coordinate place containing defect part 22 containing defect multilayer film 1.

3) emulation is containing defect mask diffraction spectra:

The diffraction light reflected containing defect multilayer film 2, again through the diffraction of mask absorption layer 1, obtains containing defect mask diffraction spectra at the upper surface of mask absorption layer 1:

$G({\mathrm{\&alpha;}}_n,{\mathrm{\&beta;}}_n)={\&Integral;F}_{\mathrm{thick}}({\mathrm{\&alpha;}}_n,{\mathrm{\&beta;}}_n;{\mathrm{\&alpha;}}_q,{\mathrm{\&beta;}}_q)F_{\mathrm{ML}}({\mathrm{\&alpha;}}_q,{\mathrm{\&beta;}}_q;{\mathrm{\&alpha;}}_m,{\mathrm{\&beta;}}_m)d{\mathrm{\&alpha;}}_{m}d{\mathrm{\&beta;}}_m,$

Wherein, n is the order of diffraction time containing defect mask diffraction spectra, and span is identical with m, α _n, β _nbe respectively n order diffraction light along the x-axis direction with the direction cosine in y-axis direction.

G (α _n, β _n) namely to emulate containing defect mask diffraction spectra.

The step that described equivalent rete method solves the complex reflection coefficient of multilayer film is as follows:

1. establish multilayer film to have M layer, M layer is adjacent with substrate, and the 1st layer adjacent with vacuum, if vacuum is the 0th layer, substrate is M+1 layer.

2. M-1 layer is looked as a whole F to the 0th layer ₁, then substrate, M layer and F ₁constitute a monofilm, the complex reflection coefficient of this monofilm is

${\tilde{r}}_M\left({\mathrm{\&theta;}}_{M-1}\right)=\frac{r_{(M-1)M}\left({\mathrm{\&theta;}}_{M-1}\right)+r_{M(M+1)}\left({\mathrm{\&theta;}}_M\right)\&CenterDot;s_M\left({\mathrm{\&theta;}}_M\right)}{1+r_{(M-1)M}\left({\mathrm{\&theta;}}_{M-1}\right)\&CenterDot;r_{M(M+1)}\left({\mathrm{\&theta;}}_M\right)\&CenterDot;s_M\left({\mathrm{\&theta;}}_M\right)},$

Wherein, r _{(M-1) M}(θ _m-1) for light is with θ _m-1the complex reflection coefficient of M layer is incided by M-1 layer in angle, r _{m (M+1)}(θ _m) for light is with θ _mthe complex reflection coefficient of substrate is incided by M layer in angle, θ _mcan by inciding the incident angle of multilayer film according to n _m-1sin (θ _m-1)=n _msin (θ _m) try to achieve, n _m-1, n _mbe respectively M-1 layer medium complex index of refraction m layer medium complex index of refraction real part, s _m(θ _m) change for the phase place of light round trip in M tunic, and d _mbe the thickness of M tunic.

3. M-2 layer is looked as a whole F to the 0th layer ₂, substrate and M layer look as a whole P ₂, then M-1 layer, F ₂and P ₂form a monofilm, its complex reflection coefficient is

${\tilde{r}}_{M-1}\left({\mathrm{\&theta;}}_{M-2}\right)=\frac{r_{(M-2)(M-1)}\left({\mathrm{\&theta;}}_{M-2}\right)+{\tilde{r}}_M\left({\mathrm{\&theta;}}_{M-1}\right)\&CenterDot;s_{M-1}\left({\mathrm{\&theta;}}_{M-1}\right)}{1+r_{(M-2)(M-1)}\left({\mathrm{\&theta;}}_{M-2}\right)\&CenterDot;{\tilde{r}}_M\left({\mathrm{\&theta;}}_{M-1}\right)\&CenterDot;s_{M-1}\left({\mathrm{\&theta;}}_{M-1}\right)},$

Wherein, r _{(M-2) (M-1)}(θ _m-2) for light is with θ _m-2the complex reflection coefficient of M-1 layer is incided by M-2 layer in angle, θ _m-1can by inciding the incident angle of multilayer film according to n _m-2sin (θ _m-2)=n _m-1sin (θ _m-1) try to achieve, n _m-2, n _m-1be respectively M-2 layer medium complex index of refraction m-1 layer medium complex index of refraction real part, s _m-1(θ _m-1) change for the phase place of light round trip in M-1 tunic, and $s_{M-1}\left({\mathrm{\&theta;}}_{M-1}\right)=\exp (-j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\&CenterDot;2{\tilde{n}}_{M-1}{d}_{M-1}\cos {\mathrm{\&theta;}}_{M-1}),$ D _m-1be the thickness of M-1 tunic.

4. an overall F is regarded the i-th-1 layer as to the 0th layer _m-i+1, substrate looks as a whole P to the i-th+1 layer _m-i+1, then i-th layer, F _m-i+1and P _m-i+1form a monofilm, its complex reflection coefficient is

${\tilde{r}}_i\left({\mathrm{\&theta;}}_{i-1}\right)=\frac{r_{(i-1)i}\left({\mathrm{\&theta;}}_{i-1}\right)+{\tilde{r}}_{i+1}\left({\mathrm{\&theta;}}_i\right)\&CenterDot;s_i\left({\mathrm{\&theta;}}_i\right)}{1+r_{(i-1)i}\left({\mathrm{\&theta;}}_{i-1}\right)\&CenterDot;{\tilde{r}}_{i+1}\left({\mathrm{\&theta;}}_i\right)\&CenterDot;s_i\left({\mathrm{\&theta;}}_i\right)},$

Wherein, r _{(i-1) i}(θ _i-1) for light is with θ _i-1angle by complex index of refraction is the i-th-1 tunic medium incident to complex index of refraction be the complex reflection coefficient of the i-th tunic medium, for light is with θ _iangle by the i-th tunic medium incident to P _m-i+1complex reflection coefficient, θ _i-1for angle of light, θ _ifor with θ _i-1angle is by the i-th-1 tunic medium incident to the refraction angle in the i-th tunic medium, and it meets n _i-1sin (θ _i-1)=n _isin (θ _i), n _i-1, n _ibe respectively real part, s _i(θ _i) change for the phase place of light round trip in the i-th tunic, and d _ibe the thickness of the i-th tunic, i be M-2 to 1 integer.

5. value by i=M-2, repeats 4. process, until i=2, as i=1, substrate is looked as a whole P to the 2nd layer _m, then the 1st layer, vacuum layer (the 0th layer) and P _mform a monofilm, its complex reflection coefficient:

${\tilde{r}}_1\left({\mathrm{\&theta;}}_0\right)=\frac{r_{01}\left({\mathrm{\&theta;}}_0\right)+{\tilde{r}}_2\left({\mathrm{\&theta;}}_1\right)\&CenterDot;s_1\left({\mathrm{\&theta;}}_1\right)}{1+r_{01}\left({\mathrm{\&theta;}}_0\right)\&CenterDot;{\tilde{r}}_2\left({\mathrm{\&theta;}}_1\right)\&CenterDot;s_1\left({\mathrm{\&theta;}}_1\right)},$

Wherein, r ₀₁(θ ₀) for light is with θ ₀angle by complex index of refraction is vacuum layer incide complex index of refraction and be the complex reflection coefficient of the 1st layer of medium, for light is with θ ₁angle by the 1st tunic medium incident to P _m-2complex reflection coefficient, P _m-2for the entirety that substrate forms to the 3rd tunic, θ ₀for angle of light, θ ₁for with θ ₀the refraction angle in the 1st tunic medium is incided by vacuum in angle, and it meets n ₀sin (θ ₀)=n ₁sin (θ ₁), n ₀, n ₁be respectively real part, s ₁(θ ₁) change for the phase place of light round trip in the 1st tunic, and d ₁be the thickness of the 1st tunic.

Thus, the complex reflection coefficient adopting equivalent rete method to calculate multilayer film is:

Wherein for inciding the incident angle on multilayer film.

With compared with first technology, the present invention has the following advantages:

The present invention, containing the quick strict emulation mode of defect mask diffraction spectra, improves the simulation velocity containing defect mask diffraction spectra, thus can realize the emulation of large scale containing defect mask fast.

Accompanying drawing explanation

Fig. 1 is that extreme ultraviolet photolithographic of the present invention is containing defect mask basic structure schematic diagram

Fig. 2 is the quick strict realistic model ultimate principle of the present invention and structural representation

Fig. 3 is of the present invention containing defect part equal portions segmentation schematic diagram

Embodiment

Below in conjunction with embodiment and accompanying drawing, the invention will be further described, but should not limit the scope of the invention with this embodiment.

First refer to Fig. 1 and Fig. 2, Fig. 1 is that extreme ultraviolet photolithographic of the present invention is containing defect mask basic structure schematic diagram, mainly comprise mask absorption layer 1, containing defect multilayer film 2 and substrate 3, Fig. 2 is the quick strict realistic model ultimate principle of the present invention and structural representation, wherein the defect contained in defect multilayer film 2 is Gaussian defect, and substrate defects height is 40nm, full width at half maximum is 40nm, surface imperfection height is 5nm, full width at half maximum is 90nm, mask absorption layer 1 adopts the modeling of equivalent thin mask model 4, split plot design and the modeling of equivalent rete method is adopted containing defect multilayer film 2.

The present invention is containing the quick strict emulation mode of defect mask diffraction spectra, and concrete steps comprise:

1) mask absorption layer diffraction spectra is emulated:

The affixture machine of the thin mask model 4 of equivalence of mask absorption layer 1 is:

$t^{\&prime;}\left(x\right)=t\left(x\right)+{\mathrm{Ae}}^{\mathrm{j\&phi;}}\mathrm{\&delta;}(x-\frac{w}{2})+{\mathrm{Ae}}^{\mathrm{j\&phi;}}\mathrm{\&delta;}(x+\frac{w}{2}),$

Wherein, $t\left(x\right)=\left\{\begin{array}{cc}{t}_a& \frac{-p}{2w}<x<\frac{p}{2w}\\ t_b& \frac{-1}{2w}<x<\frac{-p}{2w}\mathrm{and}\frac{p}{2w}<x<\frac{1}{2w}\end{array}\right.,$ X-axis is the coordinate axis of horizontal direction, true origin is positioned at isolated empty centre position, t'(x) be the approximate affixture machine of the thin mask model of equivalence 4 of mask absorption layer 1, t (x) is the transmission coefficient of unlimited thin mask, p is the size of the isolated sky on mask, for 88nm, w are the figure periodic dimensions on mask, for 400nm, t _afor the equivalent transmission coefficient within the scope of p, t _bfor p _absequivalent transmission coefficient in scope, p _absfor the width of absorption layer in the figure cycle, i.e. p _abs=w-p is 312nm, Ae ^{j φ}for the border corrected impulse of the thin mask model 4 of equivalence, A is the amplitude of corrected impulse, and φ is the phase place of corrected impulse.

Wherein, δ (x)=0 when δ (x) is defined as x ≠ 0, and

To affixture machine t'(x) carry out the diffraction spectra that Fourier transform obtains equivalent thin mask model 4 and be:

$F_{\mathrm{thin}}\left(m\right)=(t_a-t_b)\frac{p}{x}\sin c\left(m\frac{p}{w}\right)+t_b\sin c\left(m\right)+2\mathrm{A\; exp}\left(\mathrm{j\&phi;}\right)\cos \left(\mathrm{\&pi;m}\frac{p}{w}\right),$

Wherein, m is the order of diffraction time of the diffraction spectra of equivalent thin mask model 4, and the span of m is (-15,15), and λ is the operation wavelength of extreme ultra violet lithography, is 13.5nm.

Incident light 6 is inclination unit plane ripple, and inclination angle is expressed as the angle of incident light direction and z-axis be 6 degree and incident light direction projection be 0 degree in the angle theta of x-o-y plane and x-axis, the diffraction spectra of mask absorption layer 1 is:

$F_{\mathrm{thick}}({\mathrm{\&alpha;}}_m,{\mathrm{\&beta;}}_m;{\mathrm{\&alpha;}}_{\mathrm{in}},{\mathrm{\&beta;}}_{\mathrm{in}})=e^{-j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\frac{d_{\mathrm{abs}}}{2}\sqrt{1-{\mathrm{\&alpha;}}_{\mathrm{in}}^2-{\mathrm{\&beta;}}_{\mathrm{in}}^2}}{F}_{\mathrm{thin}}({\mathrm{\&alpha;}}_m-{\mathrm{\&alpha;}}_{\mathrm{in}},{\mathrm{\&beta;}}_m-{\mathrm{\&beta;}}_{\mathrm{in}})e^{-j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\frac{d_{\mathrm{abs}}}{2}\sqrt{1-{\mathrm{\&alpha;}}_m^2-{\mathrm{\&beta;}}_m^2}},$

Wherein, F _thin(α _m-α _in, β _m-β _in)=F _thin(α _m-α _in) δ (β _m-β _in), for light is from the additive phase of the equivalent face position of the equivalent thin mask model 4 of mask absorption layer 1 upper surface arrival, for light is from the additive phase of equivalent face position arrival mask absorption layer 1 lower surface of the thin mask model 4 of equivalence, α _inand β _inbe respectively the x-axis of incident light 6 and the direction cosine in y-axis direction, and α _mfor the direction cosine of x-axis direction m level time diffraction light, and α _m=m λ, β _mfor the direction cosine of y-axis direction m level time diffraction light, β during X-Y scheme _m=β _in, d _absfor the thickness of mask absorption layer 1, be 70nm.

Wherein,

$F_{\mathrm{thin}}({\mathrm{\&alpha;}}_m-{\mathrm{\&alpha;}}_{\mathrm{in}})=(t_a-t_b)\frac{p}{w}\sin c\left(\frac{{\mathrm{\&alpha;}}_m-{\mathrm{\&alpha;}}_{\mathrm{in}}}{\mathrm{\&lambda;}}\frac{p}{w}\right)+t_b\sin c\left(\frac{{\mathrm{\&alpha;}}_m-{\mathrm{\&alpha;}}_{\mathrm{in}}}{\mathrm{\&lambda;}}\right)+2\mathrm{A\; exp}\left(\mathrm{j\&phi;}\right)\cos \left(\mathrm{\&pi;}\frac{{\mathrm{\&alpha;}}_m-{\mathrm{\&alpha;}}_{\mathrm{in}}}{\mathrm{\&lambda;}}\frac{p}{w}\right)$

For the Fourier transform of affixture machine, i.e. the diffraction spectra of equivalent thin mask model 4.

The numeric distribution that strict emulation obtains mask absorption layer 1 diffraction spectra is carried out, by F by Commercial photolithography simulation software Dr.LiTHO _thick(α _m, β _m; α _in, β _in) to mate to the diffraction spectra of three the corresponding arbitrarily orders of diffraction in the diffraction spectra numeric distribution obtained time and obtain ternary linear function group, solving equations can obtain the parametric t in affixture machine expression formula _a, t _band Ae ^{j φ}value, for

$t_a=b_0-b_2+i\frac{\mathrm{\&pi;}}{2}{b}_1,$

$t_b=b_0-b_2-i\frac{\mathrm{\&pi;}}{2}{b}_1,$

${\mathrm{Ae}}^{\mathrm{j\&phi;}}=\frac{1}{2}{b}_2,$

And this parameter value only needs again to solve when changing material and the thickness of mask absorption layer 1, namely for same material and thickness, a demand solution primary parameter.

2) emulation is containing the diffraction spectra after the reflection of defect multilayer film:

To be divided into zero defect part 21 containing defect multilayer film 2 and contain defect part 22, the scope wherein containing defect part 22 be the scope that defect center expands 90nm distance towards periphery.The complex reflection coefficient of zero defect part 21 is tried to achieve by equivalent rete method, and for same incident angle, the complex reflection coefficient of whole zero defect part is identical.

To be divided into 45 aliquots along the x-axis direction containing defect part 22, be parallel between each rete in the multilayer film of each aliquot, and the thickness of each layer is determined by each thicknesses of layers of the center of this aliquot multilayer film.The complex reflection coefficient of each aliquot multilayer film can be tried to achieve by equivalent rete method.Wherein in one-period, the width of zero defect part 21 is w ₁, be 220nm, the width containing defect part 22 is w ₂, be 180nm, then the every part of width contained after defect part 22 decile is 4nm.

Wherein, the equivalent rete method step that solves the complex reflection coefficient of multilayer film is as follows:

1. establish multilayer film to have M layer, M be the 80,80th layer adjacent with substrate, the 1st layer is adjacent with vacuum, if vacuum is the 0th layer, substrate is the 81st layer, and multilayer film is made up of Mo/Si duplicature, and odd number layer is Mo layer, and even numbers layer is Si layer.

2. M-1 layer is looked as a whole F to the 0th layer ₁, then substrate, M layer and F ₁constitute a monofilm, the complex reflection coefficient of this monofilm is

${\tilde{r}}_M\left({\mathrm{\&theta;}}_{M-1}\right)=\frac{r_{(M-1)M}\left({\mathrm{\&theta;}}_{M-1}\right)+r_{M(M+1)}\left({\mathrm{\&theta;}}_M\right)\&CenterDot;s_M\left({\mathrm{\&theta;}}_M\right)}{1+r_{(M-1)M}\left({\mathrm{\&theta;}}_{M-1}\right)\&CenterDot;r_{M(M+1)}\left({\mathrm{\&theta;}}_M\right)\&CenterDot;s_M\left({\mathrm{\&theta;}}_M\right)},$

Wherein, r _{(M-1) M}(θ _m-1) for light is with θ _m-1the complex reflection coefficient of M layer is incided by M-1 layer in angle, r _{m (M+1)}(θ _m) for light is with θ _mthe complex reflection coefficient of substrate is incided by M layer in angle, θ _mcan by inciding the incident angle of multilayer film according to n _m-1sin (θ _m-1)=n _msin (θ _m) try to achieve, n _m-1, n _mbe respectively M-1 layer medium complex index of refraction m layer medium complex index of refraction real part, s _m(θ _m) change for the phase place of light round trip in M tunic, and d _mbe the thickness of M tunic.

3. M-2 layer is looked as a whole F to the 0th layer ₂, substrate and M layer look as a whole P ₂, then M-1 layer, F ₂and P ₂form a monofilm, its complex reflection coefficient is

${\tilde{r}}_{M-1}\left({\mathrm{\&theta;}}_{M-2}\right)=\frac{r_{(M-2)(M-1)}\left({\mathrm{\&theta;}}_{M-2}\right)+{\tilde{r}}_M\left({\mathrm{\&theta;}}_{M-1}\right)\&CenterDot;s_{M-1}\left({\mathrm{\&theta;}}_{M-1}\right)}{1+r_{(M-2)(M-1)}\left({\mathrm{\&theta;}}_{M-2}\right)\&CenterDot;{\tilde{r}}_M\left({\mathrm{\&theta;}}_{M-1}\right)\&CenterDot;s_{M-1}\left({\mathrm{\&theta;}}_{M-1}\right)},$

Wherein, r _{(M-2) (M-1)}(θ _m-2) for light is with θ _m-2the complex reflection coefficient of M-1 layer is incided by M-2 layer in angle, θ _m-1can by inciding the incident angle of multilayer film according to n _m-2sin (θ _m-2)=n _m-1sin (θ _m-1) try to achieve, n _m-2, n _m-1be respectively M-2 layer medium complex index of refraction m-1 layer medium complex index of refraction real part, s _m-1(θ _m-1) change for the phase place of light round trip in M-1 tunic, and $s_{M-1}\left({\mathrm{\&theta;}}_{M-1}\right)=\exp (-j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\&CenterDot;2{\tilde{n}}_{M-1}{d}_{M-1}\cos {\mathrm{\&theta;}}_{M-1}),$ D _m-1be the thickness of M-1 tunic.

4. an overall F is regarded the i-th-1 layer as to the 0th layer _m-i+1, substrate looks as a whole P to the i-th+1 layer _m-i+1, then i-th layer, F _m-i+1and P _m-i+1form a monofilm, its complex reflection coefficient is

${\tilde{r}}_i\left({\mathrm{\&theta;}}_{i-1}\right)=\frac{r_{(i-1)i}\left({\mathrm{\&theta;}}_{i-1}\right)+{\tilde{r}}_{i+1}\left({\mathrm{\&theta;}}_i\right)\&CenterDot;s_i\left({\mathrm{\&theta;}}_i\right)}{1+r_{(i-1)i}\left({\mathrm{\&theta;}}_{i-1}\right)\&CenterDot;{\tilde{r}}_{i+1}\left({\mathrm{\&theta;}}_i\right)\&CenterDot;s_i\left({\mathrm{\&theta;}}_i\right)},$

Wherein, r _{(i-1) i}(θ _i-1) for light is with θ _i-1angle by complex index of refraction is the i-th-1 tunic medium incident to complex index of refraction be the complex reflection coefficient of the i-th tunic medium, for light is with θ _iangle by the i-th tunic medium incident to P _m-i+1complex reflection coefficient, θ _i-1for angle of light, θ _ifor with θ _i-1angle is by the i-th-1 tunic medium incident to the refraction angle in the i-th tunic medium, and it meets n _i-1sin (θ _i-1)=n _isin (θ _i), n _i-1, n _ibe respectively real part, s _i(θ _i) change for the phase place of light round trip in the i-th tunic, and d _ibe the thickness of the i-th tunic, i be M-2 to 1 integer.

5. value by i=M-2, repeats 4. process, until i=2, as i=1, substrate (M+1 layer) is looked as a whole P to the 2nd layer _m, then the 1st layer, vacuum layer (the 0th layer) and P _mform a monofilm, its complex reflection coefficient:

${\tilde{r}}_1\left({\mathrm{\&theta;}}_0\right)=\frac{r_{01}\left({\mathrm{\&theta;}}_0\right)+{\tilde{r}}_2\left({\mathrm{\&theta;}}_1\right)\&CenterDot;s_1\left({\mathrm{\&theta;}}_1\right)}{1+r_{01}\left({\mathrm{\&theta;}}_0\right)\&CenterDot;{\tilde{r}}_2\left({\mathrm{\&theta;}}_1\right)\&CenterDot;s_1\left({\mathrm{\&theta;}}_1\right)},$

Wherein, r ₀₁(θ ₀) for light is with θ ₀angle by complex index of refraction is vacuum layer incide complex index of refraction and be the complex reflection coefficient of the 1st layer of medium, for light is with θ ₁angle by the 1st tunic medium incident to P _m-2complex reflection coefficient, P _m-2for the entirety that substrate forms to the 3rd tunic, θ ₀for angle of light, θ ₁for with θ ₀the refraction angle in the 1st tunic medium is incided by vacuum in angle, and it meets n ₀sin (θ ₀)=n ₁sin (θ ₁), n ₀, n ₁be respectively real part, s ₁(θ ₁) change for the phase place of light round trip in the 1st tunic, and d ₁be the thickness of the 1st tunic.Thus, the complex reflection coefficient adopting equivalent rete method to calculate multilayer film is:

Wherein for inciding the incident angle on multilayer film.

6. can try to achieve the complex reflection coefficient of zero defect part 21 by equivalent rete method and contain a series of aliquot multilayer film 2201,2202 in defect part 22, the complex reflection coefficient of 2203.Can obtain the diffraction spectra after containing defect multilayer film 22 reflection is thus:

Wherein, a=2w ₂/ w, t are the coordinate in x-axis direction, and value is α _qand β _qbe respectively the q order diffraction light after reflecting containing defect multilayer film 2 along the x-axis direction with the direction cosine in y-axis direction, q is the order of diffraction time containing defect multilayer film 2 diffraction spectra, and span is identical with m, for the angle of diffraction of m order diffraction light, and for the incident angle adopting equivalent rete method to try to achieve is time the complex reflection coefficient of zero defect part 21, for the incident angle adopting equivalent rete method to try to achieve is time t coordinate place containing the complex reflection coefficient of defect part 22, h ₀t () is the flaw height at the upper surface t coordinate place containing defect part 22 containing defect multilayer film 1.

3) emulation is containing defect mask diffraction spectra:

The diffraction light reflected containing defect multilayer film 2, again through the diffraction of mask absorption layer 1, obtains containing defect mask diffraction spectra at the upper surface of mask absorption layer 1:

$G({\mathrm{\&alpha;}}_n,{\mathrm{\&beta;}}_n)={\&Integral;F}_{\mathrm{thick}}({\mathrm{\&alpha;}}_n,{\mathrm{\&beta;}}_n;{\mathrm{\&alpha;}}_q,{\mathrm{\&beta;}}_q)F_{\mathrm{ML}}({\mathrm{\&alpha;}}_q,{\mathrm{\&beta;}}_q;{\mathrm{\&alpha;}}_m,{\mathrm{\&beta;}}_m)d{\mathrm{\&alpha;}}_{m}d{\mathrm{\&beta;}}_m,$

Wherein, n is the order of diffraction time containing defect mask diffraction spectra, and span is identical with m, α _n, β _nbe respectively n order diffraction light along the x-axis direction with the direction cosine in y-axis direction.

G (α _n, β _n) namely to emulate containing defect mask diffraction spectra.

In this embodiment, adopt described method to emulate diffraction spectra with the Dr.LiTHO strict simulation ratio of extreme ultraviolet photolithographic containing defect mask, simulation velocity improves 20 times, and error is less than 4%.

The illustrative embodiments that above embodiment is only used to principle of the present invention is described and adopts, but the present invention is not limited thereto.For those skilled in the art; without departing from the spirit and substance in the present invention; can make various modification and improvement, therefore all equivalent technical schemes also belong to category of the present invention, and scope of patent protection of the present invention should be defined by the claims.

Claims (2)

1. an extreme ultraviolet photolithographic is containing the quick strict emulation mode of defect mask diffraction spectra, this extreme ultraviolet photolithographic comprises mask absorption layer (1), containing defect multilayer film (2) and substrate (3) successively containing the formation of defect mask along incident light direction, described mask absorption layer (1) is periodicity list structure, it is characterized in that: the method adopts the modeling of equivalent thin mask model (4) to described mask absorption layer (1), adopt split plot design in conjunction with the modeling of equivalent rete method to described containing defect multilayer film (2), the method comprises the steps:

1) mask absorption layer diffraction spectra is emulated:

The approximate affixture machine of the thin mask model of equivalence (4) of described mask absorption layer (1) is t'(x):

Wherein, x-axis is the coordinate axis of horizontal direction, and true origin is positioned at isolated empty centre position, and t (x) is the transmission coefficient of unlimited thin mask, and p is the size of the isolated sky on mask, and w is the size in the figure cycle on mask, t _afor the equivalent transmission coefficient within the scope of isolated empty size p, t _bfor p _absequivalent transmission coefficient in scope, p _absfor the width of absorption layer in the figure cycle, i.e. p _abs=w-p, Ae ^{j φ}for the border corrected impulse of the thin mask model of equivalence (4), A is the amplitude of described corrected impulse, and φ is the phase place of described corrected impulse;

δ (x)=0 when δ (x) is defined as x ≠ 0, and

To affixture machine t'(x) carry out the diffraction spectra that Fourier transform obtains the thin mask model of described equivalence (4) and be:

Wherein, m is the order of diffraction time of the diffraction spectra of the thin mask model of described equivalence (4), the span of m is determined by the required order of diffraction time, and usual span is integer range required arbitrarily between-w/ λ and w/ λ, and λ is the operation wavelength of extreme ultra violet lithography;

Incident light (6) is inclination unit plane ripple, and inclination angle is expressed as the angle of incident light direction and z-axis with the angle theta of incident light direction projection in x-o-y plane and x-axis, the diffraction spectra of described mask absorption layer (1) is:

Wherein, F _thin(α _m-α _in, β _m-β _in)=F _thin(α _m-α _in) δ (β _m-β _in), for light to arrive the additive phase of the equivalent face position of the thin mask model of described equivalence (4) from described mask absorption layer (1) upper surface, for light to arrive the additive phase of described mask absorption layer (1) lower surface from the equivalent face position of the thin mask model of described equivalence (4), α _inand β _inbe respectively the x-axis of described incident light (6) and the direction cosine in y-axis direction, and α _mfor the direction cosine of x-axis direction m level time diffraction light, and α _m=m λ, β _mfor the direction cosine of y-axis direction m level time diffraction light, β during X-Y scheme _m=β _in, d _absfor the thickness of described mask absorption layer (1);

Wherein,

For the Fourier transform of affixture machine, i.e. the diffraction spectra of the thin mask model of described equivalence (4);

The numeric distribution that strict emulation obtains described mask absorption layer (1) diffraction spectra is carried out, by F by Commercial photolithography simulation software Dr.LiTHO _thick(α _m, β _m; α _in, β _in) to mate to the diffraction spectra of three the corresponding arbitrarily orders of diffraction in the diffraction spectra numeric distribution obtained time and obtain ternary linear function group, solving equations obtains the parametric t in affixture machine expression formula _a, t _band Ae ^{j φ}value, and this parameter value only change described mask absorption layer (1) material and thickness time need again to solve, namely for same material and thickness, a demand solution primary parameter;

2) emulation is containing the diffraction spectra after the reflection of defect multilayer film:

The described defect multilayer film (2) that contains is divided into zero defect part (21) and contains defect part (22), the wherein said scope containing defect part (22) is the horizontal extent of the complex reflection coefficient of defective effect multilayer film, as Gaussian defect containing the scope of defect part be defect center towards periphery extended range be the scope obtained containing the full width at half maximum of defect multi-layer film surface defect, the complex reflection coefficient of described zero defect part (21) is tried to achieve by equivalent rete method, and for same incident angle, the complex reflection coefficient of whole zero defect part is identical;

N aliquot is divided into along the x-axis direction containing defect part (22) by described, N is odd number, parallel between each rete in the multilayer film of each aliquot, and the thickness of each layer is determined by each thicknesses of layers of the center of this aliquot multilayer film, the complex reflection coefficient of each aliquot multilayer film is tried to achieve by equivalent rete method, and wherein in one-period, the width of described zero defect part (21) is w ₁, the described width containing defect part (22) is w ₂, then described is w containing every part of width after defect part (22) decile ₂/ N;

The complex reflection coefficient of described zero defect part (21) and the described complex reflection coefficient containing a series of aliquot multilayer film (2201,2202,2203) in defect part (22) is tried to achieve by equivalent rete method; Described in obtaining thus containing the diffraction spectra after defect multilayer film (22) reflection be:

Wherein, a=2w ₂/ w, t are the coordinate in x-axis direction, and value is α _qand β _qbe respectively described containing the q order diffraction light after defect multilayer film (2) reflection along the x-axis direction with the direction cosine in y-axis direction, q is the described order of diffraction containing defect multilayer film (2) diffraction spectra time, and span is identical with m, for the angle of diffraction of m order diffraction light, and for the incident angle adopting equivalent rete method to try to achieve is the complex reflection coefficient of Shi Suoshu zero defect part (21), for the incident angle adopting equivalent rete method to try to achieve is time t coordinate place described in containing the complex reflection coefficient of defect part (22), h ₀t () is the flaw height at the described described upper surface t coordinate place containing defect part (22) containing defect multilayer film (1);

3) emulation is containing defect mask diffraction spectra:

The described diffraction light reflected containing defect multilayer film (2), again through the diffraction of described mask absorption layer (1), obtains containing defect mask diffraction spectra at the upper surface of described mask absorption layer (1):

Wherein, n is the order of diffraction time containing defect mask diffraction spectra, and span is identical with m, α _n, β _nbe respectively n order diffraction light along the x-axis direction with the direction cosine in y-axis direction;

G (α _n, β _n) namely to emulate containing defect mask diffraction spectra.

2. extreme ultraviolet photolithographic according to claim 1 is containing the quick strict emulation mode of defect mask diffraction spectra, and it is characterized in that, the step that described equivalent rete method solves the complex reflection coefficient of multilayer film is as follows:

1. establish multilayer film to have M layer, M layer is adjacent with substrate, and the 1st layer adjacent with vacuum, if vacuum is the 0th layer, substrate is M+1 layer;

2. M-1 layer is looked as a whole F to the 0th layer ₁, then substrate, M layer and F ₁constitute a monofilm, the complex reflection coefficient of this monofilm is:

Wherein, r _{(M-1) M}(θ _m-1) for light is with θ _m-1the complex reflection coefficient of M layer is incided by M-1 layer in angle, r _{m (M+1)}(θ _m) for light is with θ _mthe complex reflection coefficient of substrate is incided by M layer in angle, θ _mcan by inciding the incident angle of multilayer film according to n _m-1sin (θ _m-1)=n _msin (θ _m) try to achieve, n _m-1, n _mbe respectively M-1 layer medium complex index of refraction m layer medium complex index of refraction real part, s _m(θ _m) change for the phase place of light round trip in M tunic, and d _mbe the thickness of M tunic;

3. M-2 layer is looked as a whole F to the 0th layer ₂, substrate and M layer look as a whole P ₂, then M-1 layer, F ₂and P ₂form a monofilm, its complex reflection coefficient is

Wherein, r _{(M-2) (M-1)}(θ _m-2) for light is with θ _m-2the complex reflection coefficient of M-1 layer is incided by M-2 layer in angle, θ _m-1can by inciding the incident angle of multilayer film according to n _m-2sin (θ _m-2)=n _m-1sin (θ _m-1) try to achieve, n _m-2, n _m-1be respectively M-2 layer medium complex index of refraction m-1 layer medium complex index of refraction real part, s _m-1(θ _m-1) change for the phase place of light round trip in M-1 tunic, and d _m-1be the thickness of M-1 tunic;

4. an overall F is regarded the i-th-1 layer as to the 0th layer _m-i+1, substrate looks as a whole P to the i-th+1 layer _m-i+1, then i-th layer, F _m-i+1and P _m-i+1form a monofilm, its complex reflection coefficient is

Wherein, r _{(i-1) i}(θ _i-1) for light is with θ _i-1angle by complex index of refraction is the i-th-1 tunic medium incident to complex index of refraction be the complex reflection coefficient of the i-th tunic medium, for light is with θ _iangle by the i-th tunic medium incident to P _m-i+1complex reflection coefficient, θ _i-1for angle of light, θ _ifor with θ _i-1angle is by the i-th-1 tunic medium incident to the refraction angle in the i-th tunic medium, and it meets n _i-1sin (θ _i-1)=n _isin (θ _i), n _i-1, n _ibe respectively real part, s _i(θ _i) change for the phase place of light round trip in the i-th tunic, and d _ibe the thickness of the i-th tunic, i be M-2 to 1 integer;

5. value by i=M-2, repeats 4. process, until i=2, as i=1, substrate (M+1 layer) is looked as a whole P to the 2nd layer _m, then the 1st layer, vacuum layer (the 0th layer) and P _mform a monofilm, its complex reflection coefficient:

Wherein, r ₀₁(θ ₀) for light is with θ ₀angle by complex index of refraction is vacuum layer incide complex index of refraction and be the complex reflection coefficient of the 1st layer of medium, for light is with θ ₁angle by the 1st tunic medium incident to P _m-2complex reflection coefficient, P _m-2for the entirety that substrate forms to the 3rd tunic, θ ₀for angle of light, θ ₁for with θ ₀the refraction angle in the 1st tunic medium is incided by vacuum in angle, and it meets n ₀sin (θ ₀)=n ₁sin (θ ₁), n ₀, n ₁be respectively real part, s ₁(θ ₁) change for the phase place of light round trip in the 1st tunic, and d ₁be the thickness of the 1st tunic; Thus, the complex reflection coefficient adopting equivalent rete method to calculate multilayer film is:

Wherein, for inciding the incident angle on multilayer film.