CN104880915B - The rapid simulation method of extreme ultraviolet photolithographic defect containing phase type contact hole mask diffraction spectra - Google Patents
The rapid simulation method of extreme ultraviolet photolithographic defect containing phase type contact hole mask diffraction spectra Download PDFInfo
- Publication number
- CN104880915B CN104880915B CN201510273829.3A CN201510273829A CN104880915B CN 104880915 B CN104880915 B CN 104880915B CN 201510273829 A CN201510273829 A CN 201510273829A CN 104880915 B CN104880915 B CN 104880915B
- Authority
- CN
- China
- Prior art keywords
- mrow
- msub
- ellipsoid
- gyration
- double
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Abstract
A kind of rapid simulation method of extreme ultraviolet photolithographic defect containing phase type contact hole mask diffraction spectra, methods described models absorbed layer by thin mask approximation method, the multilayer film of defect containing phase type is equivalent to the structure that a double-deck ellipsoid of gyration combines with zero defect multilayer film two parts, and the double-deck ellipsoid of gyration and zero defect multilayer film modeled by Mie-scattering lidar and equivalent film layer method respectively.The invention provides a kind of method that can effectively emulate extreme ultraviolet photolithographic defect containing phase type contact hole mask diffraction spectra, simulation velocity is improved.
Description
Technical field
The present invention relates to extreme ultraviolet photolithographic mask, particularly a kind of extreme ultraviolet photolithographic defect containing phase type contact hole mask spreads out
Penetrate the rapid simulation method of spectrum
Background technology
Extreme ultraviolet (EUV) photoetching improves resolution ratio using the exposure light source of 13.5nm wavelength, is deep-UV lithography to shorter
The reasonable extension of wave band, it is considered to be most promising Next Generation Lithography.Defects on mask is to hinder extreme ultraviolet
Quarter realizes one of main bugbear of volume production, mainly uses influence of certain method compensating defective to optical patterning at present.Accurately
Quickly influence of the emulation defect to optical patterning is to realize the prerequisite of defect compensating.On the other hand, due to extreme ultraviolet
The high cost of experiment is carved, it is necessary to reduce R&D costs by lithography simulation means, shorten and grind in extreme ultraviolet photolithographic R&D process
Send out the cycle.The simulation calculation of mask diffractional field is the important step of extreme ultraviolet photolithographic emulation.The diffractional field of mask containing defect is strictly imitated
True method such as FDTD methods are (referring to first technology 1, Yen-Min Lee, Jia-Han Li, Philip C.W.Ng, Ting-Han
Pei,Fu-Min Wang,Kuen-Yu Tsai and Alek C.Chen,“Using Transmission Line Theory
to Calculate Equivalent Refractive Index of EUV Mask Multilayer Structures
for Efficient Scattering Simulation by Finite-Difference Time-Domain Method”,
Proc.of SPIE Vol.7520,75200W (2009)) and WG methods (referring to 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)), simulation accuracy is high, but
It is computationally intensive, calculating speed is slow, and diffraction spectra analytical expression can not be drawn.Existing rapid simulation method, as monoplane is near
Like method (referring to first technology 3, E.M.Gullikson, C.Cerjan, D.G.Stearns, and P.B.Mirkarimi,
“Practical approach for modeling extreme ultraviolet lithography mask
Defects, " J.Vac.Sci.Technol.B20,81 (2002)) and Ray-tracing Method (referring to first technology 4, M.C.Lam,
A.R.Neureuther,Modeling Methodologies and Defect Printability Maps for Buried
Defects in EUV Mask Blanks, Proc.SPIE 6151,61510D (2006)), generally use numerical computation method,
The further raising of its speed is limited, can not also provide diffraction spectra analytical expression.
The content of the invention
It is an object of the invention to provide a kind of the quick of extreme ultraviolet photolithographic defect containing phase type contact hole mask diffraction spectra
Emulation mode.
The technical solution of the present invention is as follows:
1. establish the thin mask approximate model of mask absorber
In extreme ultraviolet photolithographic, absorber thickness is more than incident wavelength, and traditional Kirchhoff approximation model is no longer accurate,
Border diffraction effect can be represented using boundary point pulse to be modified the geometry ripple Transmission field of mask.Contact hole has two mutual
Vertical inner surface, it is different in the electromagnetic wave boundary condition under the conditions of same polarized illumination in two vertical inside surfaces.In y-polarisation
Under the conditions of optical illumination, for inner surface in the x-direction the polarised light be TM polarization, and for inner surface in the y-direction and
It is TE polarizations to say the polarised light.Boundary condition is different, the boundary point pulse amplitude of two vertical inside surfaces in contact hole simplified model
Also by difference.It is respectively labeled as ΔTMAnd ΔTE.Under the conditions of y-polarisation light optical illumination, absorbed layer transmission coefficient is in xy coordinate planes
On be distributed as
tya(x, y)=ta+(1-ta)rect(x/ωx,y/ωy)+ΔTE[δ(x-ωx/2)+δ(x+ωx/2)]rect(y/
ωy)+
ΔTM[δ(y-ωy/2)+δ(y+ωy/2)]rect(x/ωx)
Wherein taGeometry ripple transmission coefficient, rect (x) are rectangular function, ωxAnd ωyRespectively contact hole is in the x-direction and y
The pattern character size in direction, δ (x) are to put an impulse function, ΔTMAnd ΔTEContact hole inner surface and in the y-direction in the x-direction respectively
The boundary point pulse amplitude of inner surface.If, only need to be by Δ under x-polarisation light lighting conditionTEAnd ΔTMTransposition.It is right
Above formula, which carries out Fourier transformation, can be absorbed the diffraction spectra F of layerthin(αm,βm), wherein αmAnd βmRespectively diffraction light and x-axis
With the cosine value of y-axis angle.
In addition, the equivalent face position of absorbed layer will cause phase delay, the diffraction spectral function of absorbed layer is finally described as
Wherein m is diffraction spectra level, αmAnd βmRespectively diffraction light presss from both sides with x-axis and y-axis after absorbed layer diffraction for the first time
Cosine of an angle value, αinAnd βinRespectively incident light and cosine value with x-axis and y-axis angle, λ are lambda1-wavelength, dabsTo inhale
Thickness degree is received, i is imaginary unit.
2. establish the equivalent model of the multilayer film of defect containing phase type
It is 2w for the full width at half maximum (FWHM) of defect containing phase type, is highly the h multilayer film of defect containing phase type, can be approximately considered
It is that to cover a major axis be 2w, short axle 2h to zero defect multilayer filmdThe double-deck ellipsoid of gyration, the thickness proportion of Si layers and Mo layers with
It is identical in zero defect multilayer film.Double-deck ellipsoid of gyration refractive index real part
Wherein mMoRepresent Mo refractive index real part, mSiSi refractive index real part is represented, v is represented with the double-deck ellipsoid of gyration
The ellipsoid volume surrounded centered on the heart, vMoAnd vSiThe volume of Mo layers and Si layers is represented respectively.Double-deck ellipsoid of gyration refractive index is empty
Portion represents to absorb, and because zero defect multilayer film shares 80 layers, desirable Si and Mo imaginary index is multiplied by 80 after being weighted by height.
2hdRelation between h can make the multilayer film of defect containing phase type and establish equivalent model aerial image dip values by strictly emulating
Equal mode is matched to obtain, and dip values are defined asWherein IbackgroundFor aerial image bias light light
By force, IcenterFor light intensity at the inconocenter of space.
Establish using double-deck ellipsoid of gyration center as the polar coordinate system of origin in the plane above zero defect multilayer film, just enter
The scattering light of the double-deck ellipsoid of gyration has circular symmetry under the conditions of penetrating.When y-polarisation incident light normal incidence, part light can incide
On the double-deck ellipsoid of gyration, part light can be directly incident on zero defect multilayer film, and its transmission coefficient is
Wherein R is polar radius vector, and w is the semi-major axis of the double-deck ellipsoid of gyration, hdFor the semi-minor axis of the double-deck ellipsoid of gyration,
S1For the amplitude function of the double-deck ellipsoid of gyration under y-polarisation state, i is imaginary unit, and k is wave number, hdIt is short for the double-deck ellipsoid of gyration half
Axle.When x-polarisation light incidence, by S1It is changed to S2, S2For the amplitude function of the double-deck ellipsoid of gyration (4) under x-polarisation state.The
Once after the double-deck ellipsoid of gyration after scatter light with for the first time after absorbed layer the angle of diffraction light be designated as θ, S1(θ)、S2
The infinite series that (θ) is made up of Bezier (Bessel) function and Legendre (Legendre) function, expression formula are
Wherein, an、bnReferred to as Mie coefficients, it is double-deck ellipsoid of gyration refractive index mrWith semi-major axis w function, and πn、τnWith θ
It is relevant, it is expressed as
Wherein α=2 π w/ λ, ψnAnd ζ (x)n(x) it is semi-integer order Bessel function and Hankel function of the second kind, has
And Pn(cos θ) andIt is Legendre function and single order the association Legendre function on cos θ.
To td(R) expression formula, which does Fourier transformation, can obtain the diffraction spectra F of the double-deck ellipsoid of gyrationd(αP,βP;αm,βm), αPWith
βPRespectively for the first time by the scattering light and x-axis and the cosine value of y-axis angle, α of the double-deck ellipsoid of gyration (4)mAnd βmRespectively
The once diffraction light after absorbed layer and x-axis and the cosine value of y-axis angle.
Its reflectance factor can be calculated using equivalent film layer method for zero defect multilayer film, zero defect multilayer film is θ to angle0
The reflectance factor of incident light is
Wherein rairMoThe reflectance factor of Mo layers, s are incided by air layer for lightMoPhase once is propagated in Si layers for light
Position change,For the reflectance factor that substrate, zero defect multilayer film first layer, the zero defect multilayer film second layer are overall.
3. try to achieve extreme ultraviolet photolithographic defect containing phase type contact hole mask diffraction spectra
Extreme ultraviolet photolithographic defect containing phase type contact hole mask diffraction spectra is
Wherein n is diffraction spectra level, αin、βinFor incident light and x-axis, the cosine value of y-axis angle, αm、βmTo pass through for the first time
The diffraction light crossed after absorbed layer diffraction and x-axis, the cosine value of y-axis angle, αp、βpTo be scattered for the first time by the double-deck ellipsoid of gyration
Scattering light and x-axis, the cosine value of y-axis angle afterwards,For scattering light and z of the first time after the scattering of the double-deck ellipsoid of gyration
Axle clamp cosine of an angle value, hasαq、βqFor second of dissipating after the scattering of the double-deck ellipsoid of gyration
Penetrate light and x-axis, the cosine value of y-axis angle, αn、βnFor second diffraction light after absorbed layer diffraction and x-axis, y-axis angle
Cosine value.
Compared with first technology, the present invention has advantages below:
(1) a kind of quickly extreme ultraviolet photolithographic contact hole mask diffraction spectra emulation mode of defect containing phase type is provided, can
Rapidly to emulate the diffraction spectra of extreme ultraviolet photolithographic defect containing phase type mask.
(2) the contact hole mask diffraction spectra analytical expression of defect containing phase type has been obtained, for the contact hole of defect containing phase type
The theory analysis of mask diffraction effect is laid a good foundation.
Brief description of the drawings
Fig. 1:Extreme ultraviolet photolithographic defect containing phase type contact hole mask basic structure schematic diagram of the present invention
Fig. 2:The equivalent model structural representation for the multilayer film of defect containing phase type that the present invention is established
Embodiment
With reference to embodiment and accompanying drawing, the invention will be further described, but should not limit the present invention's with this embodiment
Protection domain.
First referring to Fig. 1, Fig. 1 is the basic of extreme ultraviolet photolithographic defect containing phase type contact hole mask of the present invention
Structural representation, mainly including absorbed layer 1, the multilayer film of defect containing phase type 2 and substrate 3, the wherein height of absorbed layer 1 is 75nm,
The full width at half maximum (FWHM) of phase type defect is 30nm, is highly 1.5nm, the multilayer film of defect containing phase type 2 that Fig. 2 is established for the present invention
Equivalent model structural representation, including the double-deck ellipsoid of gyration 4 and zero defect multilayer film 5, incident light is y-polarisation light, ripple
Long λ=13.5nm.
The specific steps of emulation mode include:
1. establish the thin mask approximate model of mask absorber
In extreme ultraviolet photolithographic, the thickness of absorbed layer 1 is more than incident wavelength, and traditional Kirchhoff approximation model is no longer accurate
Really, border diffraction effect can be represented using boundary point pulse to be modified the geometry ripple Transmission field of mask.Contact hole has two
Orthogonal inner surface, it is different in the electromagnetic wave boundary condition under the conditions of same polarized illumination in two vertical inside surfaces.In y
Under the conditions of polarized illumination, the polarised light is TM polarizations for inner surface in the x-direction, and for interior table in the y-direction
The polarised light is TE polarizations for face.Boundary condition is different, the boundary point pulse of two vertical inside surfaces in contact hole simplified model
Amplitude is also by difference.It is respectively labeled as ΔTMAnd ΔTE.Under the conditions of y-polarisation light optical illumination, the transmission coefficient of absorbed layer 1 is sat in xy
It is distributed as in mark plane
tya(x, y)=ta+(1-ta)rect(x/ωx,y/ωy)+ΔTE[δ(x-ωx/2)+δ(x+ωx/2)]rect(y/
ωy)+
ΔTM[δ(y-ωy/2)+δ(y+ωy/2)]rect(x/ωx)
Wherein taFor geometry ripple transmission coefficient, the once strict emulation and frequency spectrum matching of two-dimentional lines mask are available,
Rect (x) is rectangular function, ωxAnd ωyThe respectively contact hole pattern character size with y directions in the x-direction, ωx=ωy=
176nm, δ (x) they are a point impulse function, are defined as δ (x)=0 during x ≠ 0, andΔTMAnd ΔTEContact respectively
Hole inner surface and the boundary point pulse amplitude of inner surface in the y-direction in the x-direction, two-dimentional lines mask is once under x-polarisation illumination
Strict emulation and frequency spectrum matching can obtain ΔTM, the once strict emulation and frequency spectrum matching of two-dimentional lines mask can under x-polarisation illumination
Obtain ΔTE.Fourier transformation is carried out to above formula can be absorbed the diffraction spectra F of layerthin(αm,βm), wherein m is diffraction lighting level
It is secondary, αmAnd βmRespectively diffraction light of the first time after absorbed layer 1 and x-axis and the cosine value of y-axis angle.
In addition, the equivalent face position of absorbed layer 1 will cause phase delay, the diffraction spectral function of absorbed layer 1 is finally described as
Wherein m is diffraction light level, αmAnd βmRespectively the diffraction light after absorbed layer 1 presss from both sides with x-axis and y-axis for the first time
Cosine of an angle value, αinAnd βinRespectively incident light and the cosine value with x-axis and y-axis angle, λ is lambda1-wavelength, is
13.5nm dabsIt is 75nm for the thickness of absorbed layer 1, i is imaginary unit.
2. establish the equivalent model of the multilayer film of defect containing phase type 2
Be 2w for the full width at half maximum (FWHM) of defect containing phase type, be highly the h multilayer film of defect containing phase type 2, can approximation recognize
For be zero defect multilayer film 5 cover a major axis be 2w, short axle 2hdThe double-deck ellipsoid of gyration 4, w=30nm, Si layers and Mo layers
Thickness proportion it is identical with zero defect multilayer film 5.The double-deck refractive index real part of the ellipsoid of gyration 4
Wherein mMoMo refractive index real part is represented, is 0.9238, mSiSi refractive index real part is represented, is 0.9990, v tables
Show the ellipsoid volume surrounded centered on the double-deck center of the ellipsoid of gyration 4, vMoAnd vSiThe volume of Mo layers and Si layers is represented respectively.
The double-deck imaginary index of the ellipsoid of gyration 4 represents to absorb, and because the multilayer film of defect containing phase type 2 shares 80 layers, can use Si's and Mo
Imaginary index is -0.29573 by being multiplied by 80 after height weighted sum.2hdRelation between h can be strict by waveguide method
The mode that emulating makes the multilayer film of defect containing phase type 2 equal with established equivalent model aerial image dip values matches to obtain, dip values
It is defined asWherein IbackgroundFor aerial image bias light light intensity, IcenterFor light at the inconocenter of space
By force, 2hd=1.24nm.
The polar coordinate system using the double-deck center of the ellipsoid of gyration 4 as origin is established in the plane above zero defect multilayer film 5, just
The scattering light of the double-deck ellipsoid of gyration 4 has circular symmetry under the conditions of incidence.When y-polarisation incident light normal incidence, part light can enter
The double-deck ellipsoid of gyration 4 is mapped to, part light can be directly incident on zero defect multilayer film 5, and its transmission coefficient is
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, hdFor the double-deck semi-minor axis of the ellipsoid of gyration 4, S1For the amplitude function of the double-deck ellipsoid of gyration 4 under y-polarisation state, pass through for the first time
The angle of diffraction light after absorbed layer 1 is designated as θ, S to the scattering light crossed after the double-deck ellipsoid of gyration 4 with first time1(θ) is by shellfish plug
The infinite series that your (Bessel) function and Legendre (Legendre) function form, expression formula are
Wherein, an、bnReferred to as Mie coefficients, it is the double-deck refractive index m of the ellipsoid of gyration 4rWith semi-major axis w function, and πn、τnWith θ
It is relevant, it is expressed as
Wherein α=2 π w/ λ, ψnAnd ζ (x)n(x) it is semi-integer order Bessel function and Hankel function of the second kind, has
And Pn(cos θ) andIt is Legendre function and single order the association Legendre function on cos θ.
To td(R) expression formula, which does Fourier transformation, can obtain the diffraction spectra F of the double-deck ellipsoid of gyration 4d(αP,βP;αm,βm), αP
And βPRespectively for the first time by the scattering light and x-axis and the cosine value of y-axis angle, α of the double-deck ellipsoid of gyration 4mAnd βmRespectively
The once diffraction light after absorbed layer 1 and x-axis and the cosine value of y-axis angle.
Its reflectance factor can be calculated using equivalent film layer method for zero defect multilayer film 5, zero defect multilayer film 5 is to angle
θ0The reflectance factor of incident light is
Wherein rairMoThe reflectance factor of Mo layers, s are incided by air layer for lightMoPhase once is propagated in Si layers for light
Position change,For the reflectance factor that substrate 3, the first layer of zero defect multilayer film 5, the second layer of zero defect multilayer film 5 are overall.
3. try to achieve extreme ultraviolet photolithographic defect containing phase type contact hole mask diffraction spectra
Extreme ultraviolet photolithographic defect containing phase type contact hole mask diffraction spectra is
Wherein n be the mask contact hole mask diffraction spectra of defect containing phase type diffraction time, αin、βinFor incident light and x
The cosine value of axle, y-axis angle, αin、βinCosine of an angle is pressed from both sides for diffraction light of the first time after the diffraction of absorbed layer 1 and x-axis, y-axis
Value, αp、βpIt is first time to scatter light and x-axis, the cosine value of y-axis angle after the scattering of the double-deck ellipsoid of gyration 4,For first
The cosine value of secondary scattering light and z-axis angle after the scattering of the double-deck ellipsoid of gyration 4, hasαq、
βqFor second of the scattering light after the scattering of the double-deck ellipsoid of gyration 4 and x-axis, the cosine value of y-axis angle, αn、βnPassed through for second
The diffraction light crossed after the diffraction of absorbed layer 1 and x-axis, the cosine value of y-axis angle.
G(αn,βn) it is extreme ultraviolet photolithographic defect containing the phase type contact hole mask diffraction spectra to be emulated.
In this embodiment, using methods described emulate extreme ultraviolet photolithographic defect containing phase type contact hole mask diffraction spectra and
The strict emulation mode of Commercial photolithography simulation software Dr.LiTHO waveguide methods is compared, and simulation velocity improves about 100 times, CD phantom errors
For 0.3nm.
Principle that embodiment of above is intended to be merely illustrative of the present and the illustrative embodiments used, but this hair
It is bright to be not limited thereto.For those skilled in the art, the feelings of spirit and substance of the present invention are not being departed from
Under condition, various changes and modifications can be made therein, therefore all equivalent technical schemes fall within scope of the invention, of the invention
Scope of patent protection should be defined by the claims.
Claims (1)
1. a kind of rapid simulation method of extreme ultraviolet photolithographic defect containing phase type contact hole mask diffraction spectra, described extreme ultraviolet
The composition for carving the contact hole mask of defect containing phase type is more including absorbed layer (1), defect containing phase type successively along incident light direction
Tunic (2) and substrate (3), it is characterised in that:Described absorbed layer (1) is modeled using thin mask approximation method, and described contains phase
Type defect multilayer film (2) is equivalent to the structure of a double-deck ellipsoid of gyration (4) and zero defect multilayer film (5) composition and is utilized respectively
Mie-scattering lidar and equivalent film layer method model to the double-deck ellipsoid of gyration (4) and zero defect multilayer film (5), and this method includes following step
Suddenly:
1. the approximate model for establishing absorbed layer is absorbed, the diffraction spectral function of layer (1), formula are as follows:
<mrow>
<msub>
<mi>F</mi>
<mrow>
<mi>t</mi>
<mi>h</mi>
<mi>i</mi>
<mi>c</mi>
<mi>k</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mi>m</mi>
</msub>
<mo>,</mo>
<msub>
<mi>&beta;</mi>
<mi>m</mi>
</msub>
<mo>;</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>i</mi>
<mfrac>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
<mi>&lambda;</mi>
</mfrac>
<mfrac>
<msub>
<mi>d</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
<mi>s</mi>
</mrow>
</msub>
<mn>2</mn>
</mfrac>
<msqrt>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msubsup>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
</msqrt>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<msub>
<mi>F</mi>
<mrow>
<mi>t</mi>
<mi>h</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mi>m</mi>
</msub>
<mo>,</mo>
<msub>
<mi>&beta;</mi>
<mi>m</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>i</mi>
<mfrac>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
<mi>&lambda;</mi>
</mfrac>
<mfrac>
<msub>
<mi>d</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
<mi>s</mi>
</mrow>
</msub>
<mn>2</mn>
</mfrac>
<msqrt>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msubsup>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
Wherein, αinAnd βinRespectively incident light and x-axis and the cosine value of y-axis angle, αm、βmTo pass through absorbed layer (1) for the first time
Diffraction light after diffraction and x-axis, the cosine value of y-axis angle, λ are lambda1-wavelength, dabsFor absorbed layer (1) thickness, i is imaginary number
Unit;
2. establish the equivalent model of the multilayer film of defect containing phase type (2):
First, it is 2w by the full width at half maximum (FWHM) of defect containing phase type, is highly the h multilayer film of defect containing phase type (2), being approximately considered is
It is 2w, short axle 2h that zero defect multilayer film (5), which covers a major axis,dThe double-deck ellipsoid of gyration (4), the thickness ratio of Si layers and Mo layers
Example is identical with zero defect multilayer film (5);
Then, the diffraction spectra letter F of the double-deck ellipsoid of gyration (4) is calculatedd(αP,βP;αm,βm), αPAnd βPRespectively for the first time by double-deck
The scattering light of the ellipsoid of gyration (4) and x-axis and the cosine value of y-axis angle, αmAnd βmRespectively diffraction of the first time after absorbed layer
Light and x-axis and the cosine value of y-axis angle, it is specific as follows:
The refractive index real part of the double-deck ellipsoid of gyration (4)
<mrow>
<msub>
<mi>m</mi>
<mi>r</mi>
</msub>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mi>M</mi>
<mi>o</mi>
</mrow>
</msub>
<mo>,</mo>
<mn>0</mn>
<mo>&le;</mo>
<mi>v</mi>
<mo>&le;</mo>
<msub>
<mi>v</mi>
<mrow>
<mi>M</mi>
<mi>o</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mi>S</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>,</mo>
<mn>0</mn>
<mo>&le;</mo>
<mi>v</mi>
<mo>&le;</mo>
<msub>
<mi>v</mi>
<mrow>
<mi>S</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein mMoRepresent Mo refractive index real part, mSiSi refractive index real part is represented, v is represented with the double-deck ellipsoid of gyration (4) center
Centered on the ellipsoid volume surrounded, vMoAnd vSiThe volume of Mo layers and Si layers is represented respectively;The double-deck ellipsoid of gyration (4) refractive index
Imaginary part represents to absorb, and takes Si and Mo imaginary index by being multiplied by 80 after height weighted sum;
2hdRelation between h makes the multilayer film of defect containing phase type (2) and establishes equivalent model aerial image by strictly emulating
The equal mode of dip values is matched to obtain, and dip values are defined asWherein IbackgroundFor aerial image background
Light light intensity, IcenterFor light intensity at the inconocenter of space;
The polar coordinate system using the double-deck ellipsoid of gyration (4) center as origin is established in the plane above zero defect multilayer film (5), just
The scattering light of the double-deck ellipsoid of gyration (4) has circular symmetry under the conditions of incidence, when y-polarisation incident light normal incidence, part light meeting
The double-deck ellipsoid of gyration (4) is incided, part light can be directly incident on zero defect multilayer film (5), and its transmission coefficient is
<mrow>
<msub>
<mi>t</mi>
<mi>d</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>R</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = '{' close = ''>
<mtable>
<mtr>
<mtd>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mi>R</mi>
<mo>></mo>
<mi>w</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>S</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>a</mi>
<mi>r</mi>
<mi>c</mi>
<mi>t</mi>
<mi>a</mi>
<mi>n</mi>
<mfrac>
<mi>R</mi>
<msub>
<mi>h</mi>
<mi>d</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>i</mi>
<mi>k</mi>
<msqrt>
<mrow>
<msup>
<mi>R</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<msub>
<mi>h</mi>
<mi>d</mi>
</msub>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>+</mo>
<msub>
<mi>ikh</mi>
<mi>d</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>/</mo>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mi>k</mi>
<msqrt>
<mrow>
<msup>
<mi>R</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<msub>
<mi>h</mi>
<mi>d</mi>
</msub>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mi>R</mi>
<mo>&le;</mo>
<mi>w</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein, R is polar radius vector, and w is the semi-major axis of the double-deck ellipsoid of gyration (4), hdFor the semi-minor axis of the double-deck ellipsoid of gyration,
S1For the amplitude function of the double-deck ellipsoid of gyration (4) under y-polarisation state, i is imaginary unit, and k is wave number;When x-polarisation light incidence,
By S1It is changed to S2, S2For the amplitude function of the double-deck ellipsoid of gyration (4) under x-polarisation state;
Fourier transformation is done to above formula transmission coefficient, that is, obtains the diffraction spectra F that double-layer back turns ellipsoid (4)d(αP,βP;αm,βm;
Finally, its reflectance factor is calculated using equivalent film layer method to zero defect multilayer film (5), zero defect multilayer film (5) is to angle
For θ0The reflectance factor of incident light is
<mrow>
<mover>
<mi>r</mi>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>r</mi>
<mrow>
<mi>a</mi>
<mi>i</mi>
<mi>r</mi>
<mi>M</mi>
<mi>o</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mover>
<mi>r</mi>
<mo>~</mo>
</mover>
<mn>2</mn>
</msub>
<msubsup>
<mi>s</mi>
<mrow>
<mi>M</mi>
<mi>o</mi>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>r</mi>
<mrow>
<mi>a</mi>
<mi>i</mi>
<mi>r</mi>
<mi>M</mi>
<mi>o</mi>
</mrow>
</msub>
<msub>
<mover>
<mi>r</mi>
<mo>~</mo>
</mover>
<mn>2</mn>
</msub>
<msubsup>
<mi>s</mi>
<mrow>
<mi>M</mi>
<mi>o</mi>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
</mfrac>
</mrow>
Wherein rairMoThe reflectance factor of Mo layers, s are incided by air layer for lightMoThe phase propagated for light in Si layers once becomes
Change,For the reflectance factor of substrate (3), zero defect multilayer film (5) first layer and zero defect multilayer film (5) second layer;
3. calculating the extreme ultraviolet photolithographic contact hole mask diffraction spectra of defect containing phase type, formula is as follows:
Wherein αin、βinFor incident light and x-axis, the cosine value of y-axis angle, αm、βmFor for the first time after absorbed layer (1) diffraction
Diffraction light and x-axis, the cosine value of y-axis angle, αp、βpFor the scattering light and x after the double-deck ellipsoid of gyration (4) scattering for the first time
The cosine value of axle, y-axis angle,For the scattering light after the double-deck ellipsoid of gyration (4) scattering for the first time cosine of an angle is pressed from both sides with z-axis
Value,αq、βqFor second of the scattering light and x-axis, y-axis after the double-deck ellipsoid of gyration (4) scattering
The cosine value of angle, αn、βnFor second of diffraction light after absorbed layer (1) diffraction and x-axis, the cosine value of y-axis angle.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN201510273829.3A CN104880915B (en) | 2015-05-26 | 2015-05-26 | The rapid simulation method of extreme ultraviolet photolithographic defect containing phase type contact hole mask diffraction spectra |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN201510273829.3A CN104880915B (en) | 2015-05-26 | 2015-05-26 | The rapid simulation method of extreme ultraviolet photolithographic defect containing phase type contact hole mask diffraction spectra |
Publications (2)
Publication Number | Publication Date |
---|---|
CN104880915A CN104880915A (en) | 2015-09-02 |
CN104880915B true CN104880915B (en) | 2018-03-20 |
Family
ID=53948458
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN201510273829.3A Active CN104880915B (en) | 2015-05-26 | 2015-05-26 | The rapid simulation method of extreme ultraviolet photolithographic defect containing phase type contact hole mask diffraction spectra |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN104880915B (en) |
Families Citing this family (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN109031894B (en) * | 2018-08-13 | 2019-12-20 | 中国科学院上海光学精密机械研究所 | Method for detecting bottom morphology of phase type defect of multilayer film of extreme ultraviolet lithography mask |
CN110297401B (en) * | 2019-06-28 | 2020-05-05 | 中国科学院上海光学精密机械研究所 | Phase type defect detection method for multilayer film of extreme ultraviolet lithography mask |
Family Cites Families (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US9547233B2 (en) * | 2013-03-14 | 2017-01-17 | Kla-Tencor Corporation | Film-growth model using level sets |
CN103197503B (en) * | 2013-03-27 | 2015-05-13 | 中国科学院上海光学精密机械研究所 | Fast simulation method for extreme ultraviolet photoetching thick mask defects |
CN103617309B (en) * | 2013-10-31 | 2016-07-06 | 中国科学院上海光学精密机械研究所 | The quick strict emulation mode of extreme ultraviolet photolithographic faultless mask diffraction spectra |
CN104238282B (en) * | 2014-09-23 | 2016-08-24 | 中国科学院上海光学精密机械研究所 | The extreme ultraviolet photolithographic quick strict emulation mode containing defect mask diffraction spectra |
-
2015
- 2015-05-26 CN CN201510273829.3A patent/CN104880915B/en active Active
Also Published As
Publication number | Publication date |
---|---|
CN104880915A (en) | 2015-09-02 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN104880915B (en) | The rapid simulation method of extreme ultraviolet photolithographic defect containing phase type contact hole mask diffraction spectra | |
CN103197503B (en) | Fast simulation method for extreme ultraviolet photoetching thick mask defects | |
KR20210144918A (en) | Optimizing computational efficiency by multiple truncation of spatial harmonics | |
CN104238282B (en) | The extreme ultraviolet photolithographic quick strict emulation mode containing defect mask diffraction spectra | |
Kosolapova et al. | Numerical modeling of micro turbulence wave number spectra reconstruction using radial correlation reflectometry: I. O-mode reflectometry at the linear plasma density profile | |
Lin et al. | Integration of multiple theories for the simulation of laser interference lithography processes | |
CN104730867B (en) | Rapid simulation method for extreme ultraviolet photoetching mask multilayered film amplitude type defect diffraction pattern | |
CN106773546B (en) | Extreme ultraviolet photolithographic Three-Dimensional contact aperture mask diffraction spectra rapid simulation method | |
CN103617309B (en) | The quick strict emulation mode of extreme ultraviolet photolithographic faultless mask diffraction spectra | |
Lam et al. | Simplified model for absorber feature transmissions on EUV masks | |
CN107345788A (en) | A kind of directional light low-light spot optical critical dimension analytical equipment and detection method | |
CN102654729B (en) | Computing method of dual-layer attenuated phase shift contact hole mask diffraction field with assist features | |
CN102621801B (en) | Calculation method of conical diffraction field of double-layer attenuation phase-shift L/S mask with assist lines | |
O'Mullane et al. | Modeling ellipsometric measurement of novel 3D structures with RCWA and FEM simulations | |
CN101776849A (en) | Light intensity distribution analogy method of heavy-rubber ultraviolet light oblique incidence back etching process | |
Pisarenco | Scattering from finite structures: an extended Fourier modal method | |
Kim et al. | Printability Study of Pattern Defects in the EUV Mask as a Function of hp Nodes | |
CN106338493B (en) | A method of measurement molecular layer refractive index | |
Padron-Griffe et al. | A biologically-inspired appearance model for snake skin | |
Imeci | Transmission through an arbitrarily shaped aperture in a conducting plane separating air and a chiral medium | |
Yu et al. | Mask 3D model based on complex-valued convolution neural network for EUV lithography | |
CN102621799B (en) | Calculation method for double absorption layer attenuation phase-shift mask diffractinonal field and degree of polarization | |
Uchida et al. | Angle-resolved photoemission spectroscopy in low-dimensional periodic structures: a real-time first-principles simulation | |
Øyre | Electromagnetic Scattering Calculations for Arbitrarily Shaped Closed Surfaces using the Method of Moments | |
CN102809894B (en) | Method for computing diffraction of masks of contact holes of multiple absorbing layers |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
C06 | Publication | ||
PB01 | Publication | ||
EXSB | Decision made by sipo to initiate substantive examination | ||
SE01 | Entry into force of request for substantive examination | ||
GR01 | Patent grant | ||
GR01 | Patent grant | ||
TR01 | Transfer of patent right |
Effective date of registration: 20180615 Address after: 518045 Shenzhen, Futian District, Guangdong province Fubao street, Hong Kong Road, C digital technology park, 301F Patentee after: Shenzhen Jingyuan Information Technology Co., Ltd. Address before: 201800 mail box 800-211, Shanghai, Jiading District, Shanghai Patentee before: Shanghai Optical Precision Machinery Inst., Chinese Academy of Sciences |
|
TR01 | Transfer of patent right |