CN102662303B - Calculating method of two-dimensional photomask near-field distribution of multi-absorbed layer - Google Patents

Abstract

The invention relates to a calculating method of two-dimensional photomask near-field distribution of a multi-absorbed layer, which is capable of quickly calculating the near-field distribution when any planar wave incomes. The calculating method comprises the following steps: 1. partitioning a mask, constructing a corresponding two-dimensional planes and discretizing the two-dimensional planes; 2. solving the Toeplitz matrixes of four grating regions; 3. calculating the diagonal matrixes Kx and Ky and incidence area matrixes YI and ZI of the matrixes; 4. calculating the characteristic matrix of each layer of grating; 5. calculating the constant matrix in the fourth layer of grating through an enhanced transmittance matrix approach; 6. calculating the amplitudes of the electromagnetic fields of diffraction levels in the fourth layer of grating; and 7. calculating the complex amplitude distribution and light intensity distribution of the near filed of the mask.

Description

The computing method of many absorption layer two dimension photomask near field distribution

Technical field

The present invention relates to a kind of computing method of many absorption layer two dimension photomask near field distribution, belong to photoetching resolution and strengthen technical field.

Background technology

The develop rapidly of semiconductor industry, mainly has benefited from the progress of the Micrometer-Nanometer Processing Technology of microelectric technique, and photoetching technique is one of manufacturing technology of most critical in chip preparation.Due to constantly bringing forth new ideas of optical lithography techniques, it breaks through the optical exposure limit of people's expection again and again, makes it the mainstream technology becoming current exposure.

Etching system is mainly divided into: illuminator (light source), mask, optical projection system and wafer four part.Light incides on mask and diffraction occurs, and diffraction light to enter after optical projection system interference imaging on wafer, then after development and etch processes, just by Graphic transitions on wafer.

Complicated structure on mask, according to the periodicity in all directions, mask can be divided into one dimension, X-Y scheme.One-dimensional pattern only has periodically in one direction, and fairly simple, common lines/space (Line/Space) structure is exactly one-dimensional pattern.X-Y scheme all has periodically in the two directions, is some more complicated geometric figures, more close with practical devices structure.Contact hole (Contact Hole), L figure, splicing figure and H figure are all two-dimensional structures.In addition, intensive figure, half intensive figure and isolation pattern three class can be divided into again according to pattern density.

In order to understand the Physical Mechanism that said process occurs better, need Modling model, and the propagation wherein of analog simulation light.And lithography simulation has become development, has optimized the important tool of photoetching process.Here our propagation of primary study light in contact hole structure mask.

Analog simulation mask diffraction mainly contains two kinds of methods: kirchhoff method (Kirchhoff approach) and strict electromagnetic method (Rigorous electromagnetic field).Mask as infinitely thin, is directly determined by mask layout (mask layout) through the amplitude of electric field, phase place by Kirchhoff method.In binary mask (binary masks, BIM), the light intensity of transmission region is 1, and phase place is 0, and light tight region light intensity is 0.In alternating phase-shift mask (alternating phase shift masks, Alt.PSM), the etched area of transmission region is 1 through intensity, phase place is π, the non-etched area of transmission region is 1 through intensity, and phase place is 0, light tight region be all 0 through intensity.The principal feature of Kirchhoff method is that the intensity of mask zones of different, phase place change are very steep.

When mask feature size is much larger than wavelength, and thickness much smaller than wavelength time, polarisation of light characteristic is not obvious, and now Kirchhoff is approximate is very accurate.Along with photoetching technique develop into 45nm time, the characteristic dimension of mask is close to optical source wavelength (ArF), and mask thickness also reaches wavelength magnitude, add and adopt large-numerical aperture (Numerical Aperture, NA) liquid immersion lithography, polarisation of light effect is fairly obvious, and strict electromagnetic field model must be adopted to simulate the diffraction of mask.

Strict electromagnetic field model considers 3D (Three Dimensional) effect of mask and the impact of material completely.The numerical method adopted mainly comprises: Finite-Difference Time-Domain Method (finite-difference time domain method, FDTD), rigorous coupled wave method (rigorous coupled wave analysis, RCWA), waveguide method (the waveguide method, and finite element method (finite element methods, FEM) WG).In FDTD, Maxwell (Maxwell) equation is carried out discretize in space, on the time, the equation of these discretizes carries out integration to the time and just obtains mask diffractional field, the size of step-length when the precision of solution depends on discretize.Mask electrical magnetic field, specific inductive capacity are carried out Fourier series expansion and obtain eigenvalue equation, then obtain the solution of problem by solving eigenvalue equation by RCWA and WG, the exponent number when precision of solution depends on that Fourier launches.FEM more complicated, understanding is got up also very difficult, not all the fashion.By the electromagnetic field model that these are strict, or obtain amplitude, the phase place in mask near field, or directly obtain amplitude, the phase place of far field construction light.

Prior art (J.Opt.Soc.Am.A, 1994,11,9:2494-2502; JOURNAL OF MUDANJIANG COLLEGE OF EDUCATION, 2009,6:57-59) disclose one and utilize RCWA analysis of two-dimensional grating diffration characteristic.Wherein only give and how to solve grating diffration efficiency, describe the far-field characteristic of grating, and the near field distribution characteristic of sometimes our more concerned mask.Here we provide a kind of computing method of many absorption layer two dimension photomask near field distribution.

Summary of the invention

The present invention relates to a kind of computing method of many absorption layer two dimension photomask near field distribution, the method can calculate near field distribution during arbitrary plane ripple (any incident angle, arbitrary orientation angle and random polarization angle) incidence fast.

Realize technical scheme of the present invention as follows:

The computing method of many absorption layer two dimension photomask near field distribution, concrete steps are:

Step 1, by two dimensional surface corresponding for mask subregion structure, and discretize: first mask is decomposed into six regions, wherein comprises four two-dimensional grating layers, then construct corresponding two dimensional surface, finally these four two dimensional surfaces are carried out discretize; 4th layer is dielectric, and its cycle on x, y direction is all two times of three first layers two-dimensional grating corresponding cycle, and the 4th floor grating presents 0 °, non-phase shift district and 180 °, phase shift the district characteristic be alternately arranged, i.e. crossed grating in x, y-axis;

Step 2, solve the Toeplitz Toeplitz matrix of four grating regions: first Fourier series expansion is carried out to the specific inductive capacity of four grating regions, elastivity, then solve the Toeplitz matrix of four grating regions;

Step 3, solve respectively by each order of diffraction time wave vector along x-axis component, the diagonal matrix K that forms along y-axis component _x, K _y, and the diagonal matrix Y that each order of diffraction time wave vector forms along z-axis component _i, Z _i: first according to Bu Luokai (Floquet) condition, solve the wave vector of (m, n) individual order of diffraction time tangentially, the component of normal direction, wherein m, n are the integer between (-∞ ,+∞); And then solution matrix K _x, K _y, last solution matrix Y _i, Z _i;

Step 4, solve the eigenmatrix of every layer of grating;

Step 5, utilize enhanced transmittance matrix method, solve the constant matrices in the 4th layer of grating;

Step 6, solve the electromagnetic field amplitude of each order of diffraction in the 4th layer of grating time;

Step 7. solves COMPLEX AMPLITUDE and the light distribution in mask near field.

Adopt Cr/MoSi Alt.PSM when analyzing in step 1, the material of three first layers is Cr or MoSi, belongs to and damages material.

In step 7, method for solving comprises the following steps:

Step 701: solve the component S of mask near field electric field along normal direction _{4, z};

Step 702: solve mask near field electric field component E _xcOMPLEX AMPLITUDE;

Step 703: solve mask near field electric field component E _ycOMPLEX AMPLITUDE;

Step 704: solve mask near field electric field component E _zcOMPLEX AMPLITUDE;

Step 705: utilize mask near field electric field component E _x, E _y, E _zcOMPLEX AMPLITUDE, obtain mask near field intensity distribution, namely $I=E_x{E}_x^{*}+E_y{E}_y^{*}+E_z{E}_z^{*}.$

Beneficial effect of the present invention:

The invention provides a kind of computing method of many absorption layer two dimension photomask near field distribution, the method can calculate near field distribution during arbitrary plane ripple (any incident angle, arbitrary orientation angle and random polarization angle) incidence fast.Only need obtain the constant matrices of last one deck crossed grating, just can solve the near field distribution obtaining mask, and not need first to solve the two-dimentional diffractional field obtaining mask outgoing district.For the mask containing L layer grating, the diffractional field solving mask outgoing district needs L to connect multiply matrix, and the present invention only needs (L-1) individual multiply matrix that connects, and reduces calculated amount and accelerates computing velocity.In addition, utilize enhanced transmittance matrix method to solve constant matrices in L layer grating, it also avoid the problems such as numerical value is unstable.

Accompanying drawing explanation

Fig. 1 is many absorption layers two dimension photomask (alternating phase-shift contact hole mask) schematic diagram, and (a) is contact hole mask vertical view, and (b) is contact hole mask side view;

Fig. 2 solves the process flow diagram of many absorption layers two dimension photomask (alternating phase-shift contact hole mask) near field distribution;

The two dimensional surface of Fig. 3 each two-dimensional grating layer correspondence, the two dimensional surface that (a) three first layers two-dimensional grating is corresponding, (b) the 4th layer of two dimensional surface that crossed grating is corresponding;

Near field distribution when Fig. 4 is TE polarized light normal incidence many absorption layers alternating phase-shift contact hole mask, the three-dimensional distribution map of (a) mask near field light intensity, the light distribution on (b) mask exit facet (x-y);

Near field distribution when Fig. 5 is TM polarized light normal incidence many absorption layers alternating phase-shift contact hole mask, the three-dimensional distribution map of (a) mask near field light intensity, the light distribution on (b) mask exit facet (x-y);

Near field distribution when Fig. 6 is nonpolarized light normal incidence many absorption layers alternating phase-shift contact hole mask, the three-dimensional distribution map of (a) mask near field light intensity, the light distribution on (b) mask exit facet (x-y).

Embodiment

Below in conjunction with accompanying drawing, the present invention is further elaborated.

Schematic diagram as shown in Figure 1 for many absorption layers two dimension photomask (alternating phase-shift contact hole mask).The upper and lower surface of grating is two kinds of different materials respectively, and refractive index is respectively n ₁, n ₁₁.The normal direction of grating planar is along z-axis, and along xy plane, x, y, z meets right-hand rule to grating vector (the grating vector).Alternating phase-shift mask is mainly divided into absorption layer, phase shift layer.Front materials at two layers generally is Cr, and thickness is respectively d ₁(d ₁=z ₁-z ₀), d ₂(d ₂=z ₂-z ₁), but the difference such as refractive index, extinction coefficient.Third layer (z ₂< z < z ₃) being generally MoSi, thickness is d ₃=z ₃-z ₂.4th layer is phase-shifted region, and its etching depth is d ₄, to realize the phase shift of 180 °.First, second and third layer is lossy media, and ground floor cycle, dutycycle in x-axis are respectively Λ _1x, f _1x, in y-axis, cycle, dutycycle are respectively Λ _1y, f _1y.The second layer cycle, dutycycle in x-axis are respectively Λ _2x, f _2x, in y-axis, cycle, dutycycle are respectively Λ _2y, f _2y.Third layer cycle, dutycycle in x-axis are respectively Λ _3x, f _3x, in y-axis, cycle, dutycycle are respectively Λ _3y, f _3y.The cycle of three first layers respectively in x, y-axis, dutycycle are all identical, i.e. Λ _1x=Λ _2x=Λ _3x, f _1x=f _2x=f _3x, Λ _1y=Λ _2y=Λ _3y, f _1y=f _2y=f _3y.4th layer is dielectric, and its cycle, dutycycle in x-axis are respectively Λ _4x, f _4x, in y-axis, cycle, dutycycle are respectively Λ _4y, f _4y, and Λ _4y=2 Λ _1y, Λ _4x=2 Λ _1x.Top layer (L '=0), bottom (L '=5) are incidence zone, outgoing district respectively, and be infinite expanding along the negative sense of z-axis, forward.

A branch of linearly polarized light incides in two-dimensional mask and diffraction occurs, incident angle is θ, position angle (plane of incidence and x-axis angle) is δ, polarization angle (angle of incident electric field vector and plane of incidence) is ψ, ψ=90 ° are worked as corresponding to TE polarized light, and ψ=0 ° corresponds to TM polarized light.

Solve the flow process of many absorption layers two dimension photomask (alternating phase-shift contact hole mask) near field distribution as shown in Figure 2.

Step 1. is by two dimensional surface corresponding for mask subregion structure, and discretize.

Step 101: mask is decomposed into six regions, wherein comprises four two-dimensional grating layers, as shown in Figure 1.Adopt Cr/MoSi Alt.PSM during analysis, the material of three first layers is Cr or MoSi, belongs to and damages material.4th layer is dielectric, and its cycle on x, y direction is all two times of three first layers two-dimensional grating corresponding cycle.Because the 4th floor grating presents 0 °, non-phase shift district and 180 °, the phase shift district characteristic be alternately arranged, so we are referred to as crossed grating in x, y-axis.

Step 102: the two dimensional surface that structure is corresponding, wherein the Two dimensional Distribution of three first layers grating is as shown in Fig. 3 (a), and the Two dimensional Distribution of the 4th layer of grating is as shown in Fig. 3 (b).In Fig. 3 (a), (b), the size of institute zoning is identical, and concrete coordinate is: x ∈ [-x ₃, x ₃], y ∈ [-y ₃, y ₃].On x, y-axis direction, the cycle of the etched area of substrate shown in Fig. 3 (b) is two times of the cycle of absorption layer shown in Fig. 3 (a) respectively.We suppose x herein ₃=Λ _1x, y ₃=Λ _1y.

Step 103: these four two dimensional surfaces are carried out discretize.-x in x-axis ₃to x ₃between, with 1 for interval samples, and give the concrete coordinate figure of each imparting.-y in y-axis ₃to y ₃between, with 1 for interval samples, and give the concrete coordinate figure of each imparting.So just four two dimensional surfaces are carried out discretize, and all corresponding concrete coordinate.

Step 2. solves the Toeplitz matrix of four grating regions.

Step 201: Fourier series expansion is carried out to the specific inductive capacity of four grating regions, elastivity.Because the cycle of four layers of two-dimensional grating on x, y direction is different, the lowest common multiple in four layers of grating cycle on correspondence direction during series expansion, should be chosen.When doing Fourier series expansion, selected unit area is as shown in dotted line in Fig. 1 (a).

The Fourierism series of specific inductive capacity is:

${\mathrm{\&epsiv;}}_l(x,y)=\underset{p,q}{\mathrm{\&Sigma;}}{\mathrm{\&epsiv;}}_{l,p,q}\exp \left[j2\mathrm{\&pi;}(\mathrm{px}/{\mathrm{\&Lambda;}}_x+\mathrm{qy}/{\mathrm{\&Lambda;}}_y)\right](l=\mathrm{1,2,3})---\left(1\right)$

${\mathrm{\&epsiv;}}_{l^{\&prime;}}(x,y)=\underset{p,q}{\mathrm{\&Sigma;}}{\mathrm{\&epsiv;}}_{l^{\&prime;}p,q}\exp \left[j2\mathrm{\&pi;}(\mathrm{px}/{\mathrm{\&Lambda;}}_x+\mathrm{qy}/{\mathrm{\&Lambda;}}_y)\right](l^{\&prime;}=4)---\left(2\right)$

Wherein ε _{l, pq}the individual Fourier component of l layer grating relative dielectric constant (p, q), ε _{l ', pq}it is the individual Fourier component of the l ' layer grating relative dielectric constant (p, q).

The Fourierism series of elastivity is:

$1/{\mathrm{\&epsiv;}}_l(x,y)=\underset{p,q}{\mathrm{\&Sigma;}}{\mathrm{\&xi;}}_{l,p,q}\exp \left[j2\mathrm{\&pi;}(\mathrm{px}/{\mathrm{\&Lambda;}}_x+\mathrm{qy}/{\mathrm{\&Lambda;}}_y)\right](l=\mathrm{1,2,3})---\left(3\right)$

$1/{\mathrm{\&epsiv;}}_{l^{\&prime;}}(x,y)=\underset{p,q}{\mathrm{\&Sigma;}}{\mathrm{\&xi;}}_{l^{\&prime;}p,q}\exp \left[j2\mathrm{\&pi;}(\mathrm{px}/{\mathrm{\&Lambda;}}_x+\mathrm{qy}/{\mathrm{\&Lambda;}}_y)\right](l^{\&prime;}=4)---\left(4\right)$

Wherein ξ _{l, pq}it is (p, q) individual Fourier component of l layer grating relative dielectric constant inverse.Wherein ξ _{l ', pq}it is (p, q) individual Fourier component of the l ' layer grating relative dielectric constant inverse.Here the cycle on x, y direction this be the lowest common multiple in four layers of grating cycle on correspondence direction, i.e. Λ _y=Λ _4y, Λ _x=Λ _4x.

Step 202: the Toeplitz matrix solving four grating regions.The Toeplitz matrix that the specific inductive capacity of every layer of grating, the harmonic component (harmonic components) of elastivity form is respectively E _l, E _{l '}, A _l, A _{l '}(l=1,2,3, l '=4) are all (L _l× L _l) rank matrix, l (l ') represents l (l ') layer two-dimensional grating, L _l=L _xl _y, L _x, L _ythe harmonic number retained on x, y direction respectively.E _l, E _{l '}, A _l, A _{l '}its element is respectively ε _{l, m-p, n-q}, ε _{l ', m-p, n-q}, ξ _{l, m-p, n-q}, ξ _{l ', m-p, n-q}.

Step 3. solution matrix K _x, K _yand Y _i, Z _i

Step 301: according to Bu Luokai (Floquet) condition, solve the wave vector of the individual order of diffraction of (m, n) (m, n are the integer between (-∞ ,+∞)) time tangentially, the component of normal direction;

Wave vector tangentially, i.e. the component α of x, y-axis _m, β _nfor $\left\{\begin{array}{c}{\mathrm{\&alpha;}}_m={\mathrm{\&alpha;}}_0-2\mathrm{\&pi;m}/{\mathrm{\&Lambda;}}_x\\ {\mathrm{\&beta;}}_n={\mathrm{\&beta;}}_0-2\mathrm{\&pi;n}/{\mathrm{\&Lambda;}}_y\end{array}\right.---\left(5\right)$

Wherein α ₀=n ₁ksin θ cos δ, β ₀=n ₁ksin θ sin δ (6)

Wherein k is incident light wave wave vector in a vacuum, n ₁be the refractive index of incidence zone, θ is incident angle, and δ is position angle.

Wave vector along normal direction, i.e. the component r of z-axis _mn, t _mnfor:

$r_{\mathrm{mn}}=\left\{\begin{array}{cc}{[{\left(n_{I}k\right)}^2-{\mathrm{\&alpha;}}_m^2-{\mathrm{\&beta;}}_n^2]}^{1/2}& {\mathrm{\&alpha;}}_m^2+{\mathrm{\&beta;}}_n^2\&le;{\left(n_{I}k\right)}^2\\ -j{[{\mathrm{\&alpha;}}_m^2+{\mathrm{\&beta;}}_n^2-{\left(n_{I}k\right)}^2]}^{1/2}& {\mathrm{\&alpha;}}_m^2+{\mathrm{\&beta;}}_n^2>{\left(n_{I}k\right)}^2\end{array}\right.---\left(7\right)$

$t_{\mathrm{mn}}=\left\{\begin{array}{cc}{[{\left(n_{\mathrm{II}}k\right)}^2-{\mathrm{\&alpha;}}_m^2-{\mathrm{\&beta;}}_n^2]}^{1/2}& {\mathrm{\&alpha;}}_m^2+{\mathrm{\&beta;}}_n^2\&le;{\left(n_{\mathrm{II}}k\right)}^2\\ -j{[{\mathrm{\&alpha;}}_m^2+{\mathrm{\&beta;}}_n^2-{\left(n_{\mathrm{II}}k\right)}^2]}^{1/2}& {\mathrm{\&alpha;}}_m^2+{\mathrm{\&beta;}}_n^2>{\left(n_{\mathrm{II}}k\right)}^2\end{array}\right.---\left(8\right)$

Wherein I, II represent incidence zone, transmission area (mask substrate district) respectively.

Step 302: solution matrix K _x, K _y.K _x, K _y(L _l× L _l) rank diagonal matrix, its diagonal element is α _m, β _n.

Step 303: solution matrix Y _i, Z _i.Y _i, Z _ifor diagonal matrix, diagonal element is respectively

Step 4. solves the eigenmatrix of every layer of grating

The eigenmatrix of every layer of two-dimensional grating is: N _l=F _lg _l(l=1,2,3) (9) N _{l '}=F _{l '}g _{l '}(l '=4) (10)

Wherein $F_l=\left[\begin{array}{cc}{K}_y{A}_l{K}_x& I-K_y{A}_l{K}_y\\ K_x{A}_l{K}_x-I& -K_x{A}_l{K}_y\end{array}\right](l=\mathrm{1,2,3})---\left(11\right)$

$G_l=\left[\begin{array}{cc}{K}_x{K}_y& \mathrm{\&alpha;}{A}_l^{-1}+(1-\mathrm{\&alpha;})E_l-K_y^2\\ K_x^2-\mathrm{\&alpha;}{E}_l-(1-\mathrm{\&alpha;})A_l^{-1}& -K_x{K}_y\end{array}\right](l=\mathrm{1,2,3})---\left(12\right)$

$F_{l^{\&prime;}}=\left[\begin{array}{cc}{K}_y{E}_{l^{\&prime;}}^{-1}{K}_x& I-K_y{E}_{l^{\&prime;}}^{-1}{K}_y\\ K_x{E}_{l^{\&prime;}}^{-1}{K}_x-I& -K_x{E}_{l^{\&prime;}}^{-1}{K}_y\end{array}\right](l^{\&prime;}=4)---\left(14\right)$

$G_{l^{\&prime;}}=\left[\begin{array}{cc}{K}_x{K}_y& A_{l^{\&prime;}}^{-1}-K_y^2\\ K_x^2-A_{l^{\&prime;}}^{-1}& -K_x{K}_y\end{array}\right](l^{\&prime;}=4)---\left(15\right)$

Step 5. utilizes enhanced transmittance matrix method, solves the constant matrices M=[A in the 4th layer of grating ₄; B ₄].Utilize enhanced transmittance matrix method, the expression formula between incidence zone and the 4th layer of grating electromagnetic field is:

$\left[\begin{array}{c}\sin \mathrm{\&psi;}{\mathrm{\&delta;}}_{m0}{\mathrm{\&delta;}}_{n0}\\ j\sin \mathrm{\&psi;}{n}_I\cos \mathrm{\&theta;}{\mathrm{\&delta;}}_{m0}{\mathrm{\&delta;}}_{n0}\\ -j{n}_I\cos \mathrm{\&psi;}{\mathrm{\&delta;}}_{m0}{\mathrm{\&delta;}}_{n0}\\ \cos \mathrm{\&psi;}\cos \mathrm{\&theta;}{\mathrm{\&delta;}}_{m0}{\mathrm{\&delta;}}_{n0}\end{array}\right]+\left[\begin{array}{cc}I& 0\\ -j{Y}_I& 0\\ 0& I\\ 0& -j{Z}_I\end{array}\right]R=\left[\begin{array}{c}{f}_I\\ g_I\end{array}\right]M_I---\left(16\right)$

Wherein

$\left[\begin{array}{c}{f}_L\\ g_L\end{array}\right]M_L=\left[\begin{array}{cc}{V}_{L,1}& V_{L,1}{X}_L\\ W_{L,1}& -W_{L,1}{X}_L\\ W_{L,2}& -W_{L,2}{X}_L\\ V_{L,2}& V_{L,2}{x}_L\end{array}\right]\left[\begin{array}{c}I\\ b_L{a}_L^{-1}{X}_L\end{array}\right]M_L(L=\mathrm{1,2,3})---\left(17\right)$

$\left[\begin{array}{c}{a}_L\\ b_L\end{array}\right]={\left[\begin{array}{cc}{V}_{L,1}& V_{L,1}\\ W_{L,1}& -W_{L,1}\\ W_{L,2}& -W_{L,2}\\ V_{L,2}& V_{L,2}\end{array}\right]}^{-1}\left[\begin{array}{c}{f}_{L+1}\\ g_{L+1}\end{array}\right]---\left(18\right)$

$\left[\begin{array}{c}{f}_4\\ g_4\end{array}\right]=\left[\begin{array}{cc}{V}_{\mathrm{4,1}}& V_{\mathrm{4,1}}{X}_4\\ W_{\mathrm{4,1}}& {-W}_{\mathrm{4,1}}{X}_4\\ W_{\mathrm{4,2}}& -W_{4.2}{X}_4\\ V_{\mathrm{4,2}}& V_{\mathrm{4,2}}{X}_4\end{array}\right]---\left(19\right)$

$M=a_3^{-1}{X}_3{a}_2^{-1}{X}_2{a}_1^{-1}{X}_1{M}_1---\left(20\right)$

Wherein $\begin{array}{cc}{V}_{L,1}=F_c{W}_{L,y}-F_s{W}_{L,x}& V_{L,2}=F_c{W}_{L,x}+F_s{W}_{L,y}\\ W_{L,1}=F_c{V}_{L,x}+F_s{V}_{L,y}& W_{L,2}=F_c{V}_{L,y}-F_s{V}_{L,x}\\ W_{L,x}=\left[w_{L,x}\right]& W_{L,y}=\left[w_{L,y}\right]\\ V_{L,x}=\left[v_{L,x}\right]& V_{L,y}=\left[v_{L,y}\right]\end{array}---\left(21\right)$

L represents L layer two-dimensional grating, X _lrepresent the diagonal matrix in L layer two-dimensional grating, diagonal element is exp (-kq _{l, l}d _l). $W_L=\left[\begin{array}{c}{w}_{L,y}\\ w_{L,x}\end{array}\right]$ And q _{l, l}be respectively L layer two-dimensional grating eigenmatrix N _leigenvector and eigenvalue, $V_L=\left[\begin{array}{c}{v}_{L,y}\\ v_{L,x}\end{array}\right]=F_L^{-1}{Q}_L{W}_L,$ Q _lbe diagonal element be q _{l, l}diagonal matrix.F _c, F _sthat diagonal element is respectively diagonal matrix.Work as m=0, δ _m0=1, m ≠ 0, δ _m0=0; Work as n=0, δ _n0=1, n ≠ 0, δ _n0=0.R is intermediate variable, M=[A ₄; B ₄] be the unknown constant in the to be solved the 4th layer of grating.

Step 6. solves the electromagnetic field amplitude that in the 4th layer of grating, each order of diffraction is secondary.In 4th layer of grating, electric field is S along the component of x, y-axis _{4, x}, S _{4, y}, magnetic field is U along the component of x, y-axis _{4, x}, U _{4, y}, be respectively:

$\left[\begin{array}{c}{S}_{4,x}\\ S_{4,y}\\ U_{4,x}\\ U_{4,y}\end{array}\right]=\left[\begin{array}{cc}{W}_{4,x}{X}_4& W_{4,x}\\ W_{4,y}{X}_4& W_{4,y}\\ -V_{4,x}{X}_4& V_{4,x}\\ -V_{4,y}{X}_4& V_{4,Y}\end{array}\right]\&CenterDot;M---\left(22\right)$

Step 7. solves COMPLEX AMPLITUDE and the light distribution in mask near field

Step 701: solve the component of mask near field electric field along normal direction

Step 702: solve mask near field electric field component E _xcOMPLEX AMPLITUDE.Any point (x, y) electric field component E in Fig. 3 (b) _xcOMPLEX AMPLITUDE be: E _x=S _{4, x}exp [-jk (K _xx+K _yy)].And then solve the COMPLEX AMPLITUDE of other coordinate points in Fig. 3 (b) thus, namely obtain mask near field E _xcOMPLEX AMPLITUDE.

Step 703: solve mask near field electric field component E _ycOMPLEX AMPLITUDE.Any point (x, y) electric field component E in Fig. 3 (b) _ycOMPLEX AMPLITUDE be: E _y=S _{4, y}exp [-jk (K _xx+K _yy)].And then solve the COMPLEX AMPLITUDE of other coordinate points in Fig. 3 (b) thus, namely obtain mask near field E _ycOMPLEX AMPLITUDE.

Step 704: solve mask near field electric field component E _zcOMPLEX AMPLITUDE.Any point (x, y) electric field component E in Fig. 3 (b) _zcOMPLEX AMPLITUDE be: E _z=S _{4, z}exp [-jk (K _xx+K _yy)].And then solve the COMPLEX AMPLITUDE of other coordinate points in Fig. 3 (b) thus, namely obtain mask near field E _zcOMPLEX AMPLITUDE.

Step 705: utilize mask near field electric field component E _x, E _y, E _zcOMPLEX AMPLITUDE, obtain mask near field intensity distribution, namely $I=E_x{E}_x^{*}+E_y{E}_y^{*}+E_z{E}_z^{*}.$

The present invention calculates in many absorption layers Cr/MoSi alternating phase-shift contact hole mask, near field distribution when TE, TM polarization and nonpolarized light normal incidence many absorption layers alternating phase-shift contact hole mask.Wherein top layer Cr refractive index, extinction coefficient and thickness are respectively 1.871,1.13 and 20nm.Bottom Cr refractive index, extinction coefficient and thickness are respectively 1.477,1.762 and 40nm.MoSi refractive index, extinction coefficient and thickness are respectively 2.343,0.586 and 68nm.Mask linewidths CD _x=416nm, CD _y=876nm, Λ _1x=576nm, Λ _1y=1120nm, etched area groove depth d ₄=156nm, the dutycycle of mask three first layers grating in x, y-axis is all 0.5, and the size in three first layers grating hole and the ratio in space are 1: 1.Near field distribution when Fig. 4 is TE polarized light normal incidence many absorption layers alternating phase-shift contact hole mask, (a) is the three-dimensional distribution map of mask near field light intensity, and (b) is the light distribution on mask exit facet (x-y).Near field distribution when Fig. 5 is TM polarized light normal incidence many absorption layers alternating phase-shift contact hole mask, (a) is the three-dimensional distribution map of mask near field light intensity, and (b) is the light distribution on mask exit facet (x-y).Near field distribution when Fig. 6 is nonpolarized light normal incidence many absorption layers alternating phase-shift contact hole mask, (a) is the three-dimensional distribution map of mask near field light intensity, and (b) is the light distribution on mask exit facet (x-y).

Although describe the specific embodiment of the present invention by reference to the accompanying drawings, for those skilled in the art, under the premise of not departing from the present invention, can also do some distortion, replacement and improvement, these are also considered as belonging to protection scope of the present invention.

Claims (1)

1. the computing method of the two dimension of absorption layer more than photomask near field distribution, it is characterized in that, concrete steps are:

Step 1, by two dimensional surface corresponding for mask subregion structure, and discretize: first mask is decomposed into six regions, wherein comprises four two-dimensional grating layers, then construct corresponding two dimensional surface, finally these four two dimensional surfaces are carried out discretize; 4th layer is dielectric, and its cycle on x, y direction is all two times of three first layers two-dimensional grating corresponding cycle, and the 4th floor grating presents 0 °, non-phase shift district and 180 °, phase shift the district characteristic be alternately arranged, i.e. crossed grating in x, y-axis; Wherein said mask is Cr/MoSi alternating phase-shift mask, and the material of three first layers is Cr or MoSi, belongs to and damages material;

Step 2, solve the Toeplitz Toeplitz matrix of four grating regions: first Fourier series expansion is carried out to the specific inductive capacity of four grating regions, elastivity, then solve the Toeplitz matrix of four grating regions;

Step 3, solve respectively by each order of diffraction time wave vector along x-axis component, the diagonal matrix K that forms along y-axis component _x, K _y, and the diagonal matrix Y that each order of diffraction time wave vector forms along z-axis component _i, Z _i: first according to Bu Luokai (Floquet) condition, solve the wave vector of (m, n) individual order of diffraction time tangentially, the component of normal direction, wherein m, n are the integer between (-∞ ,+∞); And then solution matrix K _x, K _y, last solution matrix Y _i, Z _i;

Step 4, solve the eigenmatrix of every layer of grating;

The eigenmatrix of every layer of two-dimensional grating is: N _l=F _lg _l(l=1,2,3) (9) N _l'=F _l'g _l'(l'=4) (10)

Wherein $F_l=\left[\begin{array}{cc}{K}_y{A}_l{K}_x& I-K_y{A}_l{K}_y\\ K_x{A}_l{K}_x-I& -K_x{A}_l{K}_y\end{array}\right](l=\mathrm{1,2,3})---\left(11\right)$

$G_l=\left[\begin{array}{cc}{K}_x{K}_y& {\mathrm{\&alpha;A}}_l^{-1}+(1-\mathrm{\&alpha;})E_l-K_y^2\\ K_x^2-{\mathrm{\&alpha;E}}_l-(1-\mathrm{\&alpha;})A_l^{-1}& -K_x{K}_y\end{array}\right](l=\mathrm{1,2,3})---\left(12\right)$

$\mathrm{\&alpha;}=\frac{f_{1y}{\mathrm{\&Lambda;}}_{1y}}{f_{1x}{\mathrm{\&Lambda;}}_{1x}+f_{1y}{\mathrm{\&Lambda;}}_{1y}}---\left(13\right)$

$F_{l^{\&prime;}}=\left[\begin{array}{cc}{K}_y{E}_{l^{\&prime;}}^{-1}{K}_x& I-K_y{E}_{l^{\&prime;}}^{-1}{K}_y\\ K_x{E}_{l^{\&prime;}}^{-1}{K}_x-I& -K_x{E}_{l^{\&prime;}}^{-1}{K}_y\end{array}\right](l^{\&prime;}=4)---\left(14\right)$

$G_{l^{\&prime;}}=\left[\begin{array}{cc}{K}_x{K}_y& A_{l^{\&prime;}}^{-1}-K_y^2\\ K_x^2-A_{l^{\&prime;}}^{-1}& -K_x{K}_y\end{array}\right](l^{\&prime;}=4)---\left(15\right)$

Wherein E _l, E _l', A _l, A _l'be respectively the specific inductive capacity of every layer of grating, elastivity harmonic component composition Toeplitz matrix, Λ _1x, f _1xground floor grating is cycle and dutycycle in x-axis, Λ _1y, f _1yground floor grating is cycle and dutycycle in y-axis;

Step 5, utilize enhanced transmittance matrix method, solve the constant matrices M=[A in the 4th layer of grating ₄; B ₄];

Utilize enhanced transmittance matrix method, the expression formula between incidence zone and the 4th layer of grating electromagnetic field is:

$\left[\begin{array}{c}\sin \mathrm{\&psi;}{\mathrm{\&delta;}}_{m0}{\mathrm{\&delta;}}_{n0}\\ j\sin \mathrm{\&psi;}{n}_I\cos \mathrm{\&theta;}{\mathrm{\&delta;}}_{m0}{\mathrm{\&delta;}}_{n0}\\ -{\mathrm{jn}}_I\cos \mathrm{\&psi;}{\mathrm{\&delta;}}_{m0}{\mathrm{\&delta;}}_{n0}\\ \cos \mathrm{\&psi;}\cos {\mathrm{\&theta;\&delta;}}_{m0}{\mathrm{\&delta;}}_{n0}\end{array}\right]+\left[\begin{array}{cc}I& 0\\ -{\mathrm{jY}}_1& 0\\ 0& I\\ 0& -{\mathrm{jZ}}_1\end{array}\right]R=\left[\begin{array}{c}{f}_1\\ g_1\end{array}\right]M_1---\left(16\right)$

Wherein

$\left[\begin{array}{c}{f}_L\\ g_L\end{array}\right]M_L=\left[\begin{array}{cc}{V}_{L,1}& V_{L,1}{X}_L\\ W_{L,1}& -W_{L,1}{X}_L\\ W_{L,2}& -W_{L,2}{X}_L\\ V_{L,2}& V_{L,2}{X}_L\end{array}\right]\left[\begin{array}{c}I\\ b_L{a}_L^{-1}{X}_L\end{array}\right]M_L,(L=\mathrm{1,2,3})---\left(17\right)$

$\left[\begin{array}{c}{a}_L\\ b_L\end{array}\right]={\left[\begin{array}{cc}{V}_{L,1}& V_{L,1}\\ W_{L,1}& -W_{L,1}\\ W_{L,2}& -W_{L,2}\\ V_{L,2}& V_{L,2}\end{array}\right]}^{-1}\left[\begin{array}{c}{f}_{L+1}\\ g_{L+1}\end{array}\right]---\left(18\right)$

$\left[\begin{array}{c}{f}_4\\ g_4\end{array}\right]=\left[\begin{array}{cc}{V}_{\mathrm{4,1}}& V_{\mathrm{4,1}}{X}_4\\ W_{\mathrm{4,1}}& -W_{\mathrm{4,1}}{X}_4\\ W_{\mathrm{4,2}}& -W_{\mathrm{4,2}}{X}_4\\ V_{\mathrm{4,2}}& V_{\mathrm{4,2}}{X}_4\end{array}\right]---\left(19\right)$

$M=a_3^{-1}{X}_3{a}_2^{-1}{X}_2{a}_1^{-1}{X}_1{M}_1---\left(20\right)$

Wherein $\begin{array}{cc}{V}_{L,1}=F_c{W}_{L,y}-F_s{W}_{L,x}& V_{L,2}=F_c{W}_{L,x}+F_s{W}_{L,y}\\ W_{L,1}=F_c{V}_{L,x}+F_s{V}_{L,y}& W_{L,2}=F_c{V}_{L,y}-F_s{V}_{L,x}\\ W_{L,x}=\left[w_{L,x}\right]& W_{L,y}=\left[w_{L,y}\right]\\ V_{L,x}=\left[v_{L,x}\right]& V_{L,y}=\left[v_{L,y}\right]\end{array}---\left(21\right)$

L represents L layer two-dimensional grating, X _lrepresent the diagonal matrix in L layer two-dimensional grating, diagonal element is exp (-kq _l,ld _l);

$W_L=\left[\begin{array}{c}{w}_{L,y}\\ w_{L,x}\end{array}\right]$ And q _l,lbe respectively L layer two-dimensional grating eigenmatrix N _leigenvector and eigenvalue,

$V_L=\left[\begin{array}{c}{v}_{L,y}\\ v_{L,x}\end{array}\right]=F_L^{-1}{Q}_L{W}_L,$ Q _lbe diagonal element be q _l,ldiagonal matrix; F _c, F _sthat diagonal element is respectively diagonal matrix; Work as m=0, δ _m0=1, when m ≠ 0, δ _m0=0; Work as n=0, δ _n0=1, when n ≠ 0, δ _n0=0; R is intermediate variable, M=[A ₄; B ₄] be the unknown constant in the to be solved the 4th layer of grating; ψ is the incident angle of the polarization angle of incident light, θ incident light, n _iit is the refractive index of incidence zone;

Step 6, solve the electromagnetic field amplitude of each order of diffraction in the 4th layer of grating time; In 4th layer of grating, electric field is S along the component of x, y-axis _{4, x}, S _{4, y}, magnetic field is U along the component of x, y-axis _{4, x}, U _{4, y}, be respectively:

$\left[\begin{array}{c}{S}_{4,x}\\ S_{4,y}\\ U_{4,x}\\ U_{4,y}\end{array}\right]=\left[\begin{array}{cc}{W}_{4,x}{X}_4& W_{4,x}\\ W_{4,y}{X}_4& W_{4,y}\\ -V_{4,x}{X}_4& V_{4,x}\\ -V_{4,y}{X}_4& V_{4,y}\end{array}\right]\&CenterDot;M---\left(22\right)$

Step 7. solves COMPLEX AMPLITUDE and the light distribution in mask near field;

In described step 7, method for solving comprises the following steps:

Step 701: solve the component S of mask near field electric field along normal direction _{4, z};

Step 702: solve mask near field electric field component E _xcOMPLEX AMPLITUDE;

Step 703: solve mask near field electric field component E _ycOMPLEX AMPLITUDE;

Step 704: solve mask near field electric field component E _zcOMPLEX AMPLITUDE;

Step 705: utilize mask near field electric field component E _x, E _y, E _zcOMPLEX AMPLITUDE, obtain mask near field intensity distribution, namely $I=E_x{E}_x^{*}+E_y{E}_y^{*}+E_z{E}_z^{*}.$