CN104880915A - Method for quickly simulating diffraction spectrum of contact mask containing phase type defects through extreme ultra-violet lithography - Google Patents

Abstract

The invention discloses a method for quickly simulating a diffraction spectrum of a contact mask containing phase type defects through extreme ultra-violet lithography. The method is characterized in that an absorbing layer is modeled through a thin mask approximation method, a multilayer film containing phase type defects is equivalent to a structure formed by combination of a double-layer ellipsoid of revolution and a defect-free multilayer film, and the double-layer ellipsoid of revolution and the defect-free multilayer film are modeled through a mie scattering theory and an equivalent layer method respectively. The invention provides the method capable of effectively simulating the diffraction spectrum of the contact mask containing phase type defects by extreme ultra-violet lithograph, and the simulation speed is increased.

Description

Extreme ultraviolet photolithographic is containing the rapid simulation method of phase type defect contact hole mask diffraction spectra

Technical field

The present invention relates to extreme ultraviolet photolithographic mask, particularly a kind of extreme ultraviolet photolithographic is containing the rapid simulation method of phase type defect contact hole mask diffraction spectra

Background technology

Extreme ultraviolet (EUV) photoetching adopts the exposure light source of 13.5nm wavelength to improve resolution, is deep-UV lithography to the reasonable extension of more short-wave band, is considered to the Next Generation Lithography that most is promising.Defects on mask hinders one of extreme ultraviolet photolithographic main bugbear realizing volume production, and the method compensating defective that main employing is certain is at present on the impact of optical patterning.Emulating the impact of defect on optical patterning is quickly and accurately the condition precedent realizing defect compensating.On the other hand, due to the high cost of extreme ultraviolet photolithographic experiment, in extreme ultraviolet photolithographic R&D process, need to reduce R&D costs by lithography simulation means, shorten the R&D cycle.The simulation calculation of mask diffractional field is the important step of extreme ultraviolet photolithographic emulation.Containing the strict emulation mode of defect mask diffractional field if FDTD method is (see in first technology 1, Yen-Min Lee, Jia-Han Li, Philip C.W.Ng, Ting-Han Pei, Fu-MinWang, Kuen-Yu Tsai and Alek C.Chen, " Using Transmission Line Theory toCalculate Equivalent Refractive Index of EUV Mask Multilayer Structures forEfficient Scattering Simulation by Finite-Difference Time-Domain Method ", Proc.ofSPIE Vol.7520, 75200W (2009)) and WG method (see in first technology 2, Peter Evanschitzkyand Andreas Erdmann, " Fast near field simulation of optical and EUV masks usingthe waveguide method ", Proc.of SPIE Vol.6533, 65330Y (2007)), simulation accuracy is high, but calculated amount is large, computing velocity is slow, and diffraction spectra analytical expression cannot be drawn.Existing rapid simulation method, if monoplane method of approximation is (see in first technology 3, E.M.Gullikson, C.Cerjan, D.G.Stearns, and P.B.Mirkarimi, " Practical approach for modeling extreme ultraviolet lithography maskdefects, " J.Vac.Sci.Technol.B20, 81 (2002)) and Ray-tracing Method (see in first technology 4, M.C.Lam, A.R.Neureuther, Modeling Methodologies and Defect Printability Maps forBuried Defects in EUV Mask Blanks, Proc.SPIE 6151, 61510D (2006)), usual employing numerical computation method, limit the further raising of its speed, also diffraction spectra analytical expression cannot be provided.

Summary of the invention

The object of the present invention is to provide a kind of extreme ultraviolet photolithographic containing the rapid simulation method of phase type defect contact hole mask diffraction spectra.

Technical solution of the present invention is as follows:

1. the thin mask approximate model of mask absorption layer is set up

In extreme ultraviolet photolithographic, absorber thickness is greater than incident wavelength, and traditional Kirchhoff approximation model is no longer accurate, frontier point pulse can be adopted to represent the geometry ripple Transmission field of border diffraction effect to mask and revise.Contact hole has two orthogonal inside surfaces, and the electromagnetic wave boundary condition under same polarized illumination condition in two vertical inside surface is different.Under y-polarisation optical illumination condition, for inside surface in the x-direction, this polarized light is TM polarization, and this polarized light is TE polarization for inside surface in the y-direction.Boundary condition is different, and in contact hole simplified model, the frontier point pulse amplitude of two vertical inside surface is also by difference.Be labeled as Δ respectively _tMand Δ _tE.Under y-polarisation light optical illumination condition, absorption layer transmission coefficient being distributed as on xy coordinate plane

t _ya(x,y)＝t _a+(1-t _a)rect(x/ω _x,y/ω _y)+Δ _TE[δ(x-ω _x/2)+δ(x+ω _x/2)]rect(y/ω _y)+

Δ _TM[δ(y-ω _y/2)+δ(y+ω _y/2)]rect(x/ω _x)

Wherein t _ageometry ripple transmission coefficient, rect (x) is rectangular function, ω _xand ω _ybe respectively contact hole in the x-direction with the pattern character size in y direction, δ (x) is a some impulse function, Δ _tMand Δ _tEthe respectively frontier point pulse amplitude of contact hole inside surface and inside surface in the y-direction in the x-direction.If under x-polarisation optical illumination condition, only need by Δ _tEand Δ _tMtransposition.Carry out Fourier transform to above formula can be absorbed the diffraction spectra F of layer _thin(α _m, β _m), wherein α _mand β _mbe respectively the cosine value of diffraction light and x-axis and y-axis angle.

In addition, the equivalent face position of absorption layer will cause phase delay, and the diffraction spectra function of absorption layer is finally described as

$F_{\mathrm{thick}}({\mathrm{\α}}_m,{\mathrm{\β}}_m;{\mathrm{\α}}_{\mathrm{in}},{\mathrm{\β}}_{\mathrm{in}})=\exp (-i\frac{2\mathrm{\π}}{\mathrm{\λ}}\frac{d_{\mathrm{abs}}}{2}\sqrt{1-{\mathrm{\α}}_{\mathrm{in}}^2-{\mathrm{\β}}_{\mathrm{in}}^2})\·F_{\mathrm{thin}}({\mathrm{\α}}_m,{\mathrm{\β}}_m)\·\exp (-i\frac{2\mathrm{\π}}{\mathrm{\λ}}\frac{d_{\mathrm{abs}}}{2}\sqrt{1-{\mathrm{\α}}_{\mathrm{in}}^2-{\mathrm{\β}}_{\mathrm{in}}^2})$

Wherein m is diffraction spectrum level time, α _mand β _mbe respectively the cosine value of first time diffraction light and x-axis and y-axis angle after absorption layer diffraction, α _inand β _inbe respectively incident light and the cosine value with x-axis and y-axis angle, λ is lambda1-wavelength, d _absfor absorber thickness, i is imaginary unit.

2. the equivalent model containing phase type defect multilayer film is set up

For being 2w containing phase type defect full width at half maximum, containing phase type defect multilayer film highly for h, can be similar to that to think that zero defect multilayer film covers a major axis be 2w, minor axis 2h _dthe double-deck ellipsoid of gyration, Si layer is identical with in zero defect multilayer film with the thickness proportion of Mo layer.Double-deck ellipsoid of gyration refractive index real part

$m_r=\left\{\begin{array}{c}{m}_{\mathrm{Mo}},0\≤v\≤v_{\mathrm{Mo}}\\ m_{\mathrm{Si}},0\≤v\≤v_{\mathrm{Si}}\end{array}\right.$

Wherein m _morepresent the refractive index real part of Mo, m _sirepresent the refractive index real part of Si, v represents the ellipsoid volume surrounded centered by double-deck ellipsoid of gyration center, v _moand v _sirepresent the volume of Mo layer and Si layer respectively.Double-deck ellipsoid of gyration imaginary index represents absorption, and because zero defect multilayer film has 80 layers, the imaginary index of desirable Si and Mo is multiplied by 80 by after height weighting.2h _dmake to mate containing the mode that phase type defect multilayer film is equal with set up equivalent model aerial image dip value to obtain by strictly emulating with the relation between h, dip value is defined as wherein I _backgroundfor aerial image bias light light intensity, I _centerfor aerial image center light intensity.

The polar coordinate system that plane above zero defect multilayer film to be set up with double-deck ellipsoid of gyration center be initial point, under normal incidence condition, the scattered light of the double-deck ellipsoid of gyration has circular symmetry.When y-polarisation incident light normal incidence, part light can incide on the double-deck ellipsoid of gyration, and part light can be directly incident on zero defect multilayer film, and its transmission coefficient is

$t_d\left(R\right)=\left\{\begin{array}{c}1,R>w\\ S_1\left(\arctan \frac{R}{h_d}\right)\·\exp (-\mathrm{ik}\sqrt{R^2+{h_d}^2}+{\mathrm{ikh}}_d)/\left(\mathrm{ik}\sqrt{R^2+{h_d}^2}\right),R\≤w\end{array}\right.$

Wherein R is polar radius vector, and w is the semi-major axis of the double-deck ellipsoid of gyration, h _dfor the semi-minor axis of the double-deck ellipsoid of gyration, S ₁for the amplitude function of the ellipsoid of gyration double-deck under y-polarisation state, i is imaginary unit, and k is wave number, h _dfor double-deck ellipsoid of gyration semi-minor axis.When x-polarisation light is incident, by S ₁be changed to S ₂, S ₂for the amplitude function of the ellipsoid of gyration (4) double-deck under x-polarisation state.After for the first time after the double-deck ellipsoid of gyration, scattered light is designated as θ, S with first time angle of diffraction light after absorption layer ₁(θ), S ₂(θ) infinite series be made up of Bezier (Bessel) function and Legendre (Legendre) function, expression formula is

$\left\{\begin{array}{c}{S}_1\left(\mathrm{\θ}\right)=\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}\frac{2n+1}{n(n+1)}(a_n{\mathrm{\π}}_n+b_n{\mathrm{\τ}}_n)\\ S_2\left(\mathrm{\θ}\right)=\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}\frac{2n+1}{n(n+1)}(a_n{\mathrm{\τ}}_n+b_n{\mathrm{\π}}_n)\end{array}\right.$

Wherein, a _n, b _nbeing called Mie coefficient, is double-deck ellipsoid of gyration refractive index m _rwith the function of semi-major axis w, and π _n, τ _nrelevant with θ, be expressed as

$\left\{\begin{array}{c}{a}_n=\frac{{\mathrm{\ψ}}_n\left(\mathrm{\α}\right){\mathrm{\ψ}}_n^{\′}\left(m_r\mathrm{\α}\right)-m_r{\mathrm{\ψ}}_n^{\′}\left(\mathrm{\α}\right){\mathrm{\ψ}}_n^{\′}\left(m_r\mathrm{\α}\right)}{{\mathrm{\ζ}}_n\left(\mathrm{\α}\right){\mathrm{\ψ}}_n^{\′}\left(m_r\mathrm{\α}\right)-m_r{\mathrm{\ζ}}_n^{\′}\left(\mathrm{\α}\right){\mathrm{\ψ}}_n\left(m_r\mathrm{\α}\right)}\\ b_n=\frac{m_r{\mathrm{\ψ}}_n\left(\mathrm{\α}\right){\mathrm{\ψ}}_n^{\′}\left(m_r\mathrm{\α}\right)-{\mathrm{\ψ}}_n^{\′}\left(\mathrm{\α}\right)\mathrm{\ψ}\left(m_r\mathrm{\α}\right)}{m_r{\mathrm{\ζ}}_n\left(\mathrm{\α}\right){\mathrm{\ψ}}_n^{\′}\left(m_r\mathrm{\α}\right)-{\mathrm{\ζ}}_n^{\′}\left(\mathrm{\α}\right){\mathrm{\ψ}}_n\left(m_r\mathrm{\α}\right)}\\ {\mathrm{\π}}_n=\frac{{P_n}^{\left(1\right)}\left(\cos \mathrm{\θ}\right)}{\sin \mathrm{\θ}}=\frac{d{P}_n\left(\cos \mathrm{\θ}\right)}{d\cos \mathrm{\θ}}\\ {\mathrm{\τ}}_n=\frac{d{P_n}^{\left(1\right)}\left(\cos \mathrm{\θ}\right)}{\mathrm{d\θ}}\end{array}\right.$

Wherein α=2 π w/ λ, ψ _n(x) and ζ _nx () is semi-integer order Bessel's function and Hankel function of the second kind, have

$\left\{\begin{array}{c}{\mathrm{\ψ}}_n\left(x\right)={\left(\frac{\mathrm{\πx}}{2}\right)}^{1/2}{J}_{n+1/2}\left(x\right)\\ {\mathrm{\ζ}}_n\left(x\right)={\left(\frac{\mathrm{\πx}}{2}\right)}^{1/2}{H}_{n+1/2}\left(x\right)\end{array}\right.$

And P _n(cos θ) and the Legendre function about cos θ and single order association Legendre function.

To t _d(R) expression formula is the diffraction spectra F that Fourier transform can obtain the double-deck ellipsoid of gyration _d(α _p, β _p; α _m, β _m), α _pand β _pbe respectively first time through the scattered light of the double-deck ellipsoid of gyration (4) and the cosine value of x-axis and y-axis angle, α _mand β _mbe respectively first time diffraction light after absorption layer and the cosine value of x-axis and y-axis angle.

Equivalent rete method can be adopted to calculate its reflection coefficient for zero defect multilayer film, zero defect multilayer film is θ to angle ₀the reflection coefficient of incident light is

$\tilde{r}\left({\mathrm{\θ}}_0\right)=\frac{r_{\mathrm{airMo}}+{\tilde{r}}_2{s}_{\mathrm{Mo}}^2}{1+r_{\mathrm{airMo}}{\tilde{r}}_2{s}_{\mathrm{Mo}}^2}$

Wherein r _airMofor light to be incided the reflection coefficient of Mo layer by air layer, s _mofor light propagates phase place change once in Si layer, for the reflection coefficient of substrate, zero defect multilayer film ground floor, zero defect multilayer film second layer entirety.

3. extreme ultraviolet photolithographic is tried to achieve containing phase type defect contact hole mask diffraction spectra

Extreme ultraviolet photolithographic containing phase type defect contact hole mask diffraction spectra is

Wherein n is diffraction spectrum level time, α _in, β _infor the cosine value of incident light and x-axis, y-axis angle, α _m, β _mfor first time diffraction light after absorption layer diffraction and x-axis, y-axis angle cosine value, α _p, β _pfor first time scattered light after double-deck ellipsoid of gyration scattering and x-axis, y-axis angle cosine value, for first time scattered light after double-deck ellipsoid of gyration scattering and the cosine value of z-axis angle, have α _q, β _qfor the cosine value of the scattered light of second time after double-deck ellipsoid of gyration scattering and x-axis, y-axis angle, α _n, β _nfor the cosine value of the diffraction light of second time after absorption layer diffraction and x-axis, y-axis angle.

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

(1) provide one fast extreme ultraviolet photolithographic containing phase type defect contact hole mask diffraction spectra emulation mode, the diffraction spectra of extreme ultraviolet photolithographic containing phase type defect mask can be emulated rapidly.

(2) obtain containing phase type defect contact hole mask diffraction spectra analytical expression, for the theoretical analysis containing phase type defect contact hole mask diffraction effect is laid a good foundation.

Accompanying drawing explanation

Fig. 1: extreme ultraviolet photolithographic of the present invention is containing phase type defect contact hole mask basic structure schematic diagram

Fig. 2: the equivalent model structural representation containing phase type defect multilayer film that the present invention sets up

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, Fig. 1 is the basic structure schematic diagram of extreme ultraviolet photolithographic of the present invention containing phase type defect contact hole mask, mainly comprise absorption layer 1, containing phase type defect multilayer film 2 and substrate 3, wherein absorption layer 1 is highly 75nm, the full width at half maximum of phase type defect is 30nm, be highly 1.5nm, the equivalent model structural representation containing phase type defect multilayer film 2 that Fig. 2 sets up for the present invention, comprising the double-deck ellipsoid of gyration 4 and zero defect multilayer film 5, incident light is y-polarisation light, wavelength X=13.5nm.

The concrete steps of emulation mode comprise:

1. the thin mask approximate model of mask absorption layer is set up

In extreme ultraviolet photolithographic, absorption layer 1 thickness is greater than incident wavelength, and traditional Kirchhoff approximation model is no longer accurate, frontier point pulse can be adopted to represent the geometry ripple Transmission field of border diffraction effect to mask and revise.Contact hole has two orthogonal inside surfaces, and the electromagnetic wave boundary condition under same polarized illumination condition in two vertical inside surface is different.Under y-polarisation optical illumination condition, for inside surface in the x-direction, this polarized light is TM polarization, and this polarized light is TE polarization for inside surface in the y-direction.Boundary condition is different, and in contact hole simplified model, the frontier point pulse amplitude of two vertical inside surface is also by difference.Be labeled as Δ respectively _tMand Δ _tE.Under y-polarisation light optical illumination condition, absorption layer 1 transmission coefficient being distributed as on xy coordinate plane

t _ya(x,y)＝t _a+(1-t _a)rect(x/ω _x,y/ω _y)+Δ _TE[δ(x-ω _x/2)+δ(x+ω _x/2)]rect(y/ω _y)+

Δ _TM[δ(y-ω _y/2)+δ(y+ω _y/2)]rect(x/ω _x)

Wherein t _afor geometry ripple transmission coefficient, the once strict emulation of two-dimentional lines mask and frequency spectrum coupling can obtain, and rect (x) is rectangular function, ω _xand ω _ybe respectively contact hole in the x-direction with the pattern character size in y direction, ω _x=ω _y=176nm, δ (x) they are a some impulse function, δ (x)=0 when being defined as x ≠ 0, and Δ _tMand Δ _tEthe respectively frontier point pulse amplitude of contact hole inside surface and inside surface in the y-direction in the x-direction, the once strict emulation of the lower two-dimentional lines mask of x-polarisation illumination and frequency spectrum mate and can obtain Δ _tM, once strict emulation and the frequency spectrum coupling of the lower two-dimentional lines mask of x-polarisation illumination can obtain Δ _tE.Carry out Fourier transform to above formula can be absorbed the diffraction spectra F of layer _thin(α _m, β _m), wherein m is diffraction lighting level time, α _mand β _mbe respectively first time diffraction light after the absorption layer 1 and cosine value of x-axis and y-axis angle.

In addition, the equivalent face position of absorption layer 1 will cause phase delay, and the diffraction spectra function of absorption layer 1 is finally described as

$F_{\mathrm{thick}}({\mathrm{\α}}_m,{\mathrm{\β}}_m;{\mathrm{\α}}_{\mathrm{in}},{\mathrm{\β}}_{\mathrm{in}})=\exp (-i\frac{2\mathrm{\π}}{\mathrm{\λ}}\frac{d_{\mathrm{abs}}}{2}\sqrt{1-{\mathrm{\α}}_{\mathrm{in}}^2-{\mathrm{\β}}_{\mathrm{in}}^2})\·F_{\mathrm{thin}}({\mathrm{\α}}_m,{\mathrm{\β}}_m)\·\exp (-i\frac{2\mathrm{\π}}{\mathrm{\λ}}\frac{d_{\mathrm{abs}}}{2}\sqrt{1-{\mathrm{\α}}_{\mathrm{in}}^2-{\mathrm{\β}}_{\mathrm{in}}^2})$

Wherein m is diffraction lighting level time, α _mand β _mbe respectively first time diffraction light after the absorption layer 1 and cosine value of x-axis and y-axis angle, α _inand β _inbe respectively incident light and the cosine value with x-axis and y-axis angle, λ is lambda1-wavelength, is 13.5nm, d _absfor absorption layer 1 thickness, for 75nm, i are imaginary unit.

2. the equivalent model containing phase type defect multilayer film 2 is set up

For being 2w containing phase type defect full width at half maximum, containing phase type defect multilayer film 2 highly for h, can be similar to that to think that zero defect multilayer film 5 covers a major axis be 2w, minor axis 2h _dthe double-deck ellipsoid of gyration 4, w=30nm, Si layer identical with in zero defect multilayer film 5 with the thickness proportion of Mo layer.The double-deck ellipsoid of gyration 4 refractive index real part

$m_r=\left\{\begin{array}{c}{m}_{\mathrm{Mo}},0\≤v\≤v_{\mathrm{Mo}}\\ m_{\mathrm{Si}},0\≤v\≤v_{\mathrm{Si}}\end{array}\right.$

Wherein m _morepresenting the refractive index real part of Mo, is 0.9238, m _sirepresenting the refractive index real part of Si, is that 0.9990, v represents the ellipsoid volume surrounded centered by the double-deck ellipsoid of gyration 4 center, v _moand v _sirepresent the volume of Mo layer and Si layer respectively.The double-deck ellipsoid of gyration 4 imaginary index represents absorption, and owing to having 80 layers containing phase type defect multilayer film 2, the imaginary index of desirable Si and Mo is multiplied by 80 by after height weighted sum, for-0.29573.2h _dstrictly to emulate by waveguide method with the relation between h and make to mate containing phase type defect multilayer film 2 mode equal with set up equivalent model aerial image dip value to obtain, dip value is defined as wherein I _backgroundfor aerial image bias light light intensity, I _centerfor aerial image center light intensity, 2h _d=1.24nm.

The polar coordinate system that plane above zero defect multilayer film 5 to be set up with the double-deck ellipsoid of gyration 4 center be initial point, under normal incidence condition, the scattered light of the double-deck ellipsoid of gyration 4 has circular symmetry.When y-polarisation incident light normal incidence, part light can incide the double-deck ellipsoid of gyration 4, and part light can be directly incident on zero defect multilayer film 5, and its transmission coefficient is

$t_d\left(R\right)=\left\{\begin{array}{c}1,R>w\\ S_1\left(\arctan \frac{R}{h_d}\right)\·\exp (-\mathrm{ik}\sqrt{R^2+{h_d}^2}+{\mathrm{ikh}}_d)/\left(\mathrm{ik}\sqrt{R^2+{h_d}^2}\right),R\≤w\end{array}\right.$

Wherein R is polar radius vector, and w is the semi-major axis of the double-deck ellipsoid of gyration 4, and w=30nm, i are imaginary unit, and k is wave number, h _dfor the double-deck ellipsoid of gyration 4 semi-minor axis, S ₁for the amplitude function of the ellipsoid of gyration 4 double-deck under y-polarisation state, the scattered light for the first time after the double-deck ellipsoid of gyration 4 is designated as θ, S with first time angle of diffraction light after absorption layer 1 ₁(θ) infinite series be made up of Bezier (Bessel) function and Legendre (Legendre) function, expression formula is

$S_1\left(\mathrm{\θ}\right)=\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}\frac{2n+1}{n(n+1)}(a_n{\mathrm{\π}}_n+b_n{\mathrm{\τ}}_n),$

Wherein, a _n, b _nbeing called Mie coefficient, is the double-deck ellipsoid of gyration 4 refractive index m _rwith the function of semi-major axis w, and π _n, τ _nrelevant with θ, be expressed as

$\left\{\begin{array}{c}{a}_n=\frac{{\mathrm{\ψ}}_n\left(\mathrm{\α}\right){\mathrm{\ψ}}_n^{\′}\left(m_r\mathrm{\α}\right)-m_r{\mathrm{\ψ}}_n^{\′}\left(\mathrm{\α}\right){\mathrm{\ψ}}_n^{\′}\left(m_r\mathrm{\α}\right)}{{\mathrm{\ζ}}_n\left(\mathrm{\α}\right){\mathrm{\ψ}}_n^{\′}\left(m_r\mathrm{\α}\right)-m_r{\mathrm{\ζ}}_n^{\′}\left(\mathrm{\α}\right){\mathrm{\ψ}}_n\left(m_r\mathrm{\α}\right)}\\ b_n=\frac{m_r{\mathrm{\ψ}}_n\left(\mathrm{\α}\right){\mathrm{\ψ}}_n^{\′}\left(m_r\mathrm{\α}\right)-{\mathrm{\ψ}}_n^{\′}\left(\mathrm{\α}\right)\mathrm{\ψ}\left(m_r\mathrm{\α}\right)}{m_r{\mathrm{\ζ}}_n\left(\mathrm{\α}\right){\mathrm{\ψ}}_n^{\′}\left(m_r\mathrm{\α}\right)-{\mathrm{\ζ}}_n^{\′}\left(\mathrm{\α}\right){\mathrm{\ψ}}_n\left(m_r\mathrm{\α}\right)}\\ {\mathrm{\π}}_n=\frac{{P_n}^{\left(1\right)}\left(\cos \mathrm{\θ}\right)}{\sin \mathrm{\θ}}=\frac{d{P}_n\left(\cos \mathrm{\θ}\right)}{d\cos \mathrm{\θ}}\\ {\mathrm{\τ}}_n=\frac{d{P_n}^{\left(1\right)}\left(\cos \mathrm{\θ}\right)}{\mathrm{d\θ}}\end{array}\right.$

Wherein α=2 π w/ λ, ψ _n(x) and ζ _nx () is semi-integer order Bessel's function and Hankel function of the second kind, have

$\left\{\begin{array}{c}{\mathrm{\ψ}}_n\left(x\right)={\left(\frac{\mathrm{\πx}}{2}\right)}^{1/2}{J}_{n+1/2}\left(x\right)\\ {\mathrm{\ζ}}_n\left(x\right)={\left(\frac{\mathrm{\πx}}{2}\right)}^{1/2}{H}_{n+1/2}\left(x\right)\end{array}\right.$

And P _n(cos θ) and the Legendre function about cos θ and single order association Legendre function.

To t _d(R) expression formula is the diffraction spectra F that Fourier transform can obtain the double-deck ellipsoid of gyration 4 _d(α _p, β _p; α _m, β _m), α _pand β _pbe respectively first time through the scattered light of the double-deck ellipsoid of gyration 4 and the cosine value of x-axis and y-axis angle, α _mand β _mbe respectively first time diffraction light after the absorption layer 1 and cosine value of x-axis and y-axis angle.

Equivalent rete method can be adopted to calculate its reflection coefficient for zero defect multilayer film 5, zero defect multilayer film 5 pairs of angles are θ ₀the reflection coefficient of incident light is

$\tilde{r}\left({\mathrm{\θ}}_0\right)=\frac{r_{\mathrm{airMo}}+{\tilde{r}}_2{s}_{\mathrm{Mo}}^2}{1+r_{\mathrm{airMo}}{\tilde{r}}_2{s}_{\mathrm{Mo}}^2}$

Wherein r _airMofor light to be incided the reflection coefficient of Mo layer by air layer, s _mofor light propagates phase place change once in Si layer, for the reflection coefficient of substrate 3, zero defect multilayer film 5 ground floor, zero defect multilayer film 5 second layer entirety.

3. extreme ultraviolet photolithographic is tried to achieve containing phase type defect contact hole mask diffraction spectra

Extreme ultraviolet photolithographic containing phase type defect contact hole mask diffraction spectra is

Wherein n is the order of diffraction time containing phase type defect mask contact hole mask diffraction spectra, α _in, β _infor the cosine value of incident light and x-axis, y-axis angle, α _in, β _infor first time diffraction light after absorption layer 1 diffraction and x-axis, y-axis angle cosine value, α _p, β _pfor first time scattered light after the scattering of the double-deck ellipsoid of gyration 4 and x-axis, y-axis angle cosine value, for first time scattered light after the scattering of the double-deck the ellipsoid of gyration 4 and cosine value of z-axis angle, have α _q, β _qfor the cosine value of the scattered light of second time after the scattering of the double-deck ellipsoid of gyration 4 and x-axis, y-axis angle, α _n, β _nfor the cosine value of the diffraction light of second time after absorption layer 1 diffraction and x-axis, y-axis angle.

G (α _n, β _n) be the extreme ultraviolet photolithographic that will emulate containing phase type defect contact hole mask diffraction spectra.

In this embodiment, adopt described method to emulate extreme ultraviolet photolithographic containing phase type defect contact hole mask diffraction spectra compared with the strict emulation mode of Commercial photolithography simulation software Dr.LiTHO waveguide method, simulation velocity improves about 100 times, and CD phantom error is 0.3nm.

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 (1)

1. an extreme ultraviolet photolithographic is containing the rapid simulation method of phase type defect contact hole mask diffraction spectra, described extreme ultraviolet photolithographic is comprise absorption layer (1) successively along incident light direction containing the formation of phase type defect contact hole mask, containing bit-type defect multilayer film (2) and substrate (3), it is characterized in that: described absorption layer (1) utilizes the modeling of thin mask method of approximation, described be equivalent to containing phase type defect multilayer film (2) structure that a double-deck ellipsoid of gyration (4) and zero defect multilayer film (5) form and also utilize Mie-scattering lidar and equivalent rete method to the double-deck ellipsoid of gyration (4) and zero defect multilayer film (5) modeling respectively, the method comprises the steps:

1. the approximate model setting up absorption layer is absorbed the diffraction spectra function of layer (1), and formula is as follows:

$F_{\mathrm{thick}}({\mathrm{\α}}_m,{\mathrm{\β}}_m;{\mathrm{\α}}_{\mathrm{in}},{\mathrm{\β}}_{\mathrm{in}})=\exp (-i\frac{2\mathrm{\π}}{\mathrm{\λ}}\frac{d_{\mathrm{abs}}}{2}\sqrt{1-{\mathrm{\α}}_{\mathrm{in}}^2-{\mathrm{\β}}_{\mathrm{in}}^2})\·F_{\mathrm{thin}}({\mathrm{\α}}_m,{\mathrm{\β}}_m)\·\exp (-i\frac{2\mathrm{\π}}{\mathrm{\λ}}\frac{d_{\mathrm{abs}}}{2}\sqrt{1-{\mathrm{\α}}_{\mathrm{in}}^2-{\mathrm{\β}}_{\mathrm{in}}^2})$

Wherein, α _inand β _inbe respectively the cosine value of incident light and x-axis and y-axis angle, α _m, β _mfor first time diffraction light after absorption layer (1) diffraction and x-axis, y-axis angle cosine value, λ is lambda1-wavelength, d _absfor absorption layer (1) thickness, i is imaginary unit;

2. the equivalent model containing phase type defect multilayer film (2) is set up:

First, by containing phase type defect full width at half maximum be 2w, highly for h containing phase type defect multilayer film (2), be similar to that to think that zero defect multilayer film (5) covers a major axis be 2w, minor axis 2h _dthe double-deck ellipsoid of gyration (4), Si layer is identical with in zero defect multilayer film (5) with the thickness proportion of Mo layer;

Then, the diffraction spectra letter F of the double-deck ellipsoid of gyration (4) is calculated _d(α _p, β _p; α _m, β _m), α _pand β _pbe respectively first time through the scattered light of the double-deck ellipsoid of gyration (4) and the cosine value of x-axis and y-axis angle, α _mand β _mbe respectively first time diffraction light after absorption layer and the cosine value of x-axis and y-axis angle, specific as follows:

The refractive index real part of the double-deck ellipsoid of gyration (4)

$m_r=\left\{\begin{array}{c}{m}_{\mathrm{Mo}},0\≤v\≤v_{\mathrm{Mo}}\\ m_{\mathrm{Si}},0\≤v\≤v_{\mathrm{Si}}\end{array}\right.$

Wherein m _morepresent the refractive index real part of Mo, m _sirepresent the refractive index real part of Si, v represents the ellipsoid volume surrounded centered by the double-deck ellipsoid of gyration (4) center, v _moand v _sirepresent the volume of Mo layer and Si layer respectively; The double-deck ellipsoid of gyration (4) imaginary index represents absorption, and the imaginary index getting Si and Mo is multiplied by 80 by after height weighted sum;

2h _dmake to mate containing the mode that phase type defect multilayer film (2) is equal with set up equivalent model aerial image dip value to obtain by strictly emulating with the relation between h, dip value is defined as wherein I _backgroundfor aerial image bias light light intensity, I _centerfor aerial image center light intensity;

It is the polar coordinate system of initial point that the plane of zero defect multilayer film (5) top is set up with the double-deck ellipsoid of gyration (4) center, under normal incidence condition, the scattered light of the double-deck ellipsoid of gyration (4) has circular symmetry, when y-polarisation incident light normal incidence, part light can incide the double-deck ellipsoid of gyration (4), part light can be directly incident on zero defect multilayer film (5), and its transmission coefficient is

$t_d\left(R\right)=\left\{\begin{array}{c}1,R>w\\ S_1\left(\arctan \frac{R}{h_d}\right)\·\exp (-\mathrm{ik}\sqrt{R^2+{h_d}^2}+{\mathrm{ikh}}_d)/\left(\mathrm{ik}\sqrt{R^2+{h_d}^2}\right),R\≤w\end{array}\right.$

Wherein, R is polar radius vector, and w is the semi-major axis of the double-deck ellipsoid of gyration (4), h _dfor the semi-minor axis of the double-deck ellipsoid of gyration, S ₁for the amplitude function of the ellipsoid of gyration (4) double-deck under y-polarisation state, i is imaginary unit, and k is wave number; When x-polarisation light is incident, by S ₁be changed to S ₂, S ₂for the amplitude function of the ellipsoid of gyration (4) double-deck under x-polarisation state;

Fourier transform is done to above formula transmission coefficient, namely obtains the diffraction spectra F of the double-deck ellipsoid of gyration (4) _d(α _p, β _p; α _m, β _m);

Finally, adopt equivalent rete method to calculate its reflection coefficient to zero defect multilayer film (5), zero defect multilayer film (5) is θ to angle ₀the reflection coefficient of incident light is

$\tilde{r}\left({\mathrm{\θ}}_0\right)=\frac{r_{\mathrm{airMo}}+{\tilde{r}}_2{s}_{\mathrm{Mo}}^2}{1+r_{\mathrm{airMo}}{\tilde{r}}_2{s}_{\mathrm{Mo}}^2}$

Wherein r _airMofor light to be incided the reflection coefficient of Mo layer by air layer, s _mofor light propagates phase place change once in Si layer, for the reflection coefficient of substrate (3), zero defect multilayer film (5) ground floor and zero defect multilayer film (5) second layer;

3. calculate extreme ultraviolet photolithographic containing phase type defect contact hole mask diffraction spectra, formula is as follows:

Wherein α _in, β _infor the cosine value of incident light and x-axis, y-axis angle, α _m, β _mfor first time diffraction light after absorption layer (1) diffraction and x-axis, y-axis angle cosine value, α _p, β _pfor first time scattered light after the double-deck ellipsoid of gyration (4) scattering and x-axis, y-axis angle cosine value, for first time scattered light after the double-deck ellipsoid of gyration (4) scattering and the cosine value of z-axis angle, α _q, β _qfor the cosine value of the scattered light of second time after the double-deck ellipsoid of gyration (4) scattering and x-axis, y-axis angle, α _n, β _nfor the cosine value of the diffraction light of second time after absorption layer (1) diffraction and x-axis, y-axis angle.