Abstract

An analytical approach to the impact of polarization aberration on lithographic imaging is proposed. The linear relationship between image placement error (IPE) of alternating phase-shifting mask (Alt-PSM) and odd aberration items of polarization aberrations, as well as that between best focus shift (BFS) of Alt-PSM and even aberration items of polarization aberrations are established by analytical equations, respectively. The validity of the linear relationships is demonstrated by numerical results. The differences and connections between scalar aberration and polarization aberration are briefly discussed based on these linear relationships.

© 2012 Optical Society of America

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  1. D. O. S. Melville, A. E. Rosenbluth, A. Waechter, M. Millstone, J. Tirapu-Azpiroz, K. Tian, K. Lai, T. Inoue, M. Sakamoto, K. Adam, and A. Tritchkov, J. Vac. Sci. Technol. B 29, 6 (2011).
    [CrossRef]
  2. J. Kye, G. McIntyre, Y. Norihiro, and H. J. Levinson, Proc. SPIE 6154, 61540E (2006).
    [CrossRef]
  3. G. R. McIntyre, J. Kye, H. Levinson, and A. R. Neureuther, J. Microlithogr. Microfabr. Microsyst. 5, 3 (2006).
    [CrossRef]
  4. T. M. Tawfik and E. Tejnil, Proc. SPIE 7122, 712245 (2008).
    [CrossRef]
  5. M. Totzeck, P. Gräupner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, J. Microlithogr. Microfabr. Microsyst. 4, 3 (2005).
    [CrossRef]
  6. A. K. Wong, Optical Imaging in Projection Micro-lithography (SPIE, 2005).
  7. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic, 2000).
  8. J. Ruoff and M. Totzeck, J. Micro/Nanolithogr., MEMS MOEMS 8, 3 (2009).
    [CrossRef]

2011 (1)

D. O. S. Melville, A. E. Rosenbluth, A. Waechter, M. Millstone, J. Tirapu-Azpiroz, K. Tian, K. Lai, T. Inoue, M. Sakamoto, K. Adam, and A. Tritchkov, J. Vac. Sci. Technol. B 29, 6 (2011).
[CrossRef]

2009 (1)

J. Ruoff and M. Totzeck, J. Micro/Nanolithogr., MEMS MOEMS 8, 3 (2009).
[CrossRef]

2008 (1)

T. M. Tawfik and E. Tejnil, Proc. SPIE 7122, 712245 (2008).
[CrossRef]

2006 (2)

J. Kye, G. McIntyre, Y. Norihiro, and H. J. Levinson, Proc. SPIE 6154, 61540E (2006).
[CrossRef]

G. R. McIntyre, J. Kye, H. Levinson, and A. R. Neureuther, J. Microlithogr. Microfabr. Microsyst. 5, 3 (2006).
[CrossRef]

2005 (1)

M. Totzeck, P. Gräupner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, J. Microlithogr. Microfabr. Microsyst. 4, 3 (2005).
[CrossRef]

Adam, K.

D. O. S. Melville, A. E. Rosenbluth, A. Waechter, M. Millstone, J. Tirapu-Azpiroz, K. Tian, K. Lai, T. Inoue, M. Sakamoto, K. Adam, and A. Tritchkov, J. Vac. Sci. Technol. B 29, 6 (2011).
[CrossRef]

Arfken, G. B.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic, 2000).

Dittmann, O.

M. Totzeck, P. Gräupner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, J. Microlithogr. Microfabr. Microsyst. 4, 3 (2005).
[CrossRef]

Flagello, D.

M. Totzeck, P. Gräupner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, J. Microlithogr. Microfabr. Microsyst. 4, 3 (2005).
[CrossRef]

Göhnermeier, A.

M. Totzeck, P. Gräupner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, J. Microlithogr. Microfabr. Microsyst. 4, 3 (2005).
[CrossRef]

Gräupner, P.

M. Totzeck, P. Gräupner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, J. Microlithogr. Microfabr. Microsyst. 4, 3 (2005).
[CrossRef]

Heil, T.

M. Totzeck, P. Gräupner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, J. Microlithogr. Microfabr. Microsyst. 4, 3 (2005).
[CrossRef]

Inoue, T.

D. O. S. Melville, A. E. Rosenbluth, A. Waechter, M. Millstone, J. Tirapu-Azpiroz, K. Tian, K. Lai, T. Inoue, M. Sakamoto, K. Adam, and A. Tritchkov, J. Vac. Sci. Technol. B 29, 6 (2011).
[CrossRef]

Kamenov, V.

M. Totzeck, P. Gräupner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, J. Microlithogr. Microfabr. Microsyst. 4, 3 (2005).
[CrossRef]

Krähmer, D.

M. Totzeck, P. Gräupner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, J. Microlithogr. Microfabr. Microsyst. 4, 3 (2005).
[CrossRef]

Kye, J.

J. Kye, G. McIntyre, Y. Norihiro, and H. J. Levinson, Proc. SPIE 6154, 61540E (2006).
[CrossRef]

G. R. McIntyre, J. Kye, H. Levinson, and A. R. Neureuther, J. Microlithogr. Microfabr. Microsyst. 5, 3 (2006).
[CrossRef]

Lai, K.

D. O. S. Melville, A. E. Rosenbluth, A. Waechter, M. Millstone, J. Tirapu-Azpiroz, K. Tian, K. Lai, T. Inoue, M. Sakamoto, K. Adam, and A. Tritchkov, J. Vac. Sci. Technol. B 29, 6 (2011).
[CrossRef]

Levinson, H.

G. R. McIntyre, J. Kye, H. Levinson, and A. R. Neureuther, J. Microlithogr. Microfabr. Microsyst. 5, 3 (2006).
[CrossRef]

Levinson, H. J.

J. Kye, G. McIntyre, Y. Norihiro, and H. J. Levinson, Proc. SPIE 6154, 61540E (2006).
[CrossRef]

McIntyre, G.

J. Kye, G. McIntyre, Y. Norihiro, and H. J. Levinson, Proc. SPIE 6154, 61540E (2006).
[CrossRef]

McIntyre, G. R.

G. R. McIntyre, J. Kye, H. Levinson, and A. R. Neureuther, J. Microlithogr. Microfabr. Microsyst. 5, 3 (2006).
[CrossRef]

Melville, D. O. S.

D. O. S. Melville, A. E. Rosenbluth, A. Waechter, M. Millstone, J. Tirapu-Azpiroz, K. Tian, K. Lai, T. Inoue, M. Sakamoto, K. Adam, and A. Tritchkov, J. Vac. Sci. Technol. B 29, 6 (2011).
[CrossRef]

Millstone, M.

D. O. S. Melville, A. E. Rosenbluth, A. Waechter, M. Millstone, J. Tirapu-Azpiroz, K. Tian, K. Lai, T. Inoue, M. Sakamoto, K. Adam, and A. Tritchkov, J. Vac. Sci. Technol. B 29, 6 (2011).
[CrossRef]

Neureuther, A. R.

G. R. McIntyre, J. Kye, H. Levinson, and A. R. Neureuther, J. Microlithogr. Microfabr. Microsyst. 5, 3 (2006).
[CrossRef]

Norihiro, Y.

J. Kye, G. McIntyre, Y. Norihiro, and H. J. Levinson, Proc. SPIE 6154, 61540E (2006).
[CrossRef]

Rosenbluth, A. E.

D. O. S. Melville, A. E. Rosenbluth, A. Waechter, M. Millstone, J. Tirapu-Azpiroz, K. Tian, K. Lai, T. Inoue, M. Sakamoto, K. Adam, and A. Tritchkov, J. Vac. Sci. Technol. B 29, 6 (2011).
[CrossRef]

Ruoff, J.

J. Ruoff and M. Totzeck, J. Micro/Nanolithogr., MEMS MOEMS 8, 3 (2009).
[CrossRef]

M. Totzeck, P. Gräupner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, J. Microlithogr. Microfabr. Microsyst. 4, 3 (2005).
[CrossRef]

Sakamoto, M.

D. O. S. Melville, A. E. Rosenbluth, A. Waechter, M. Millstone, J. Tirapu-Azpiroz, K. Tian, K. Lai, T. Inoue, M. Sakamoto, K. Adam, and A. Tritchkov, J. Vac. Sci. Technol. B 29, 6 (2011).
[CrossRef]

Tawfik, T. M.

T. M. Tawfik and E. Tejnil, Proc. SPIE 7122, 712245 (2008).
[CrossRef]

Tejnil, E.

T. M. Tawfik and E. Tejnil, Proc. SPIE 7122, 712245 (2008).
[CrossRef]

Tian, K.

D. O. S. Melville, A. E. Rosenbluth, A. Waechter, M. Millstone, J. Tirapu-Azpiroz, K. Tian, K. Lai, T. Inoue, M. Sakamoto, K. Adam, and A. Tritchkov, J. Vac. Sci. Technol. B 29, 6 (2011).
[CrossRef]

Tirapu-Azpiroz, J.

D. O. S. Melville, A. E. Rosenbluth, A. Waechter, M. Millstone, J. Tirapu-Azpiroz, K. Tian, K. Lai, T. Inoue, M. Sakamoto, K. Adam, and A. Tritchkov, J. Vac. Sci. Technol. B 29, 6 (2011).
[CrossRef]

Totzeck, M.

J. Ruoff and M. Totzeck, J. Micro/Nanolithogr., MEMS MOEMS 8, 3 (2009).
[CrossRef]

M. Totzeck, P. Gräupner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, J. Microlithogr. Microfabr. Microsyst. 4, 3 (2005).
[CrossRef]

Tritchkov, A.

D. O. S. Melville, A. E. Rosenbluth, A. Waechter, M. Millstone, J. Tirapu-Azpiroz, K. Tian, K. Lai, T. Inoue, M. Sakamoto, K. Adam, and A. Tritchkov, J. Vac. Sci. Technol. B 29, 6 (2011).
[CrossRef]

Waechter, A.

D. O. S. Melville, A. E. Rosenbluth, A. Waechter, M. Millstone, J. Tirapu-Azpiroz, K. Tian, K. Lai, T. Inoue, M. Sakamoto, K. Adam, and A. Tritchkov, J. Vac. Sci. Technol. B 29, 6 (2011).
[CrossRef]

Weber, H. J.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic, 2000).

Wong, A. K.

A. K. Wong, Optical Imaging in Projection Micro-lithography (SPIE, 2005).

J. Micro/Nanolithogr., MEMS MOEMS (1)

J. Ruoff and M. Totzeck, J. Micro/Nanolithogr., MEMS MOEMS 8, 3 (2009).
[CrossRef]

J. Microlithogr. Microfabr. Microsyst. (2)

M. Totzeck, P. Gräupner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, J. Microlithogr. Microfabr. Microsyst. 4, 3 (2005).
[CrossRef]

G. R. McIntyre, J. Kye, H. Levinson, and A. R. Neureuther, J. Microlithogr. Microfabr. Microsyst. 5, 3 (2006).
[CrossRef]

J. Vac. Sci. Technol. B (1)

D. O. S. Melville, A. E. Rosenbluth, A. Waechter, M. Millstone, J. Tirapu-Azpiroz, K. Tian, K. Lai, T. Inoue, M. Sakamoto, K. Adam, and A. Tritchkov, J. Vac. Sci. Technol. B 29, 6 (2011).
[CrossRef]

Proc. SPIE (2)

J. Kye, G. McIntyre, Y. Norihiro, and H. J. Levinson, Proc. SPIE 6154, 61540E (2006).
[CrossRef]

T. M. Tawfik and E. Tejnil, Proc. SPIE 7122, 712245 (2008).
[CrossRef]

Other (2)

A. K. Wong, Optical Imaging in Projection Micro-lithography (SPIE, 2005).

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic, 2000).

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Figures (2)

Fig. 1.
Fig. 1.

(a) Illustration of a typical optical lithography imaging system. Two Alt-PSM masks oriented in (b) x and (c) y directions.

Fig. 2.
Fig. 2.

(a) IPE and (b) BFS in the Alt-PSM image as functions of aberrations Pha(a0) and Im(a1). The dots and solid lines represent the IPE and BFS calculated by image intensity in Eq. (6) and linear relationships in Eq. (9), respectively. (λ=193nm, w=45nm, p=90nm, NA=1.35, σ=0.3).

Equations (11)

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I(x^i,y^i,Δz)=+TCC(f^,g^;f^,g^,Δz)O(f^,g^)×M(f^+f^,g^+g^)JJones(f^+f^,g^+g^)×EO*(f^,g^)M*(f^+f^,g^+g^)×JJones*(f^+f^,g^+g^)E*×ei2π[(f^f^)x^i+(g^g^)y^i]df^dg^df^dg^df^dg^,
TCC(f^,g^;f^,g^,Δz)=+J(f^,g^)H(f^+f^,g^+g^,Δz)×H*(f^+f^,g^+g^,Δz)df^dg^.
H(f^,g^,Δz)=exp(i2πΔz1NA2(f^2+g^2)/NA2),
O(f^)=iw^p^n=+δ(f^n2p^)sinc(w^f^)sin(πp^f^)nZ,
M(f^,g^)=1f^2+g^2[g^2f^g^f^g^f^200].
I(x^i,Δz)=A0[A1+A2++J(f^,g^)ei4πf0(f^Δz+x^i)×M0(f^,g^,f^0,f^0)PA(f^,g^,f^0,f^0)df^dg^++J(f^,g^)ei4πf0(f^Δz+x^i)M0(f^,g^,f^0,f^0)×PA(f^,g^,f^0,f^0)df^dg^],
f^0=1/(2p^)A0=(w^·sinc(w^f^0)/p^)2,M0(f^,g^,f^,f^)=(f^+f^)2(f^+f^)2[(f^+f^)2+g^2][(f^+f^)2+g^2],PA(f^,g^,f^,f^)=[a0(f^+f^,g^)a1(f^+f^,g^)]×[a0(f^+f^,g^)a1(f^+f^,g^)]*,A1=+J(f^,g^)M0(f^,g^,f^0,f^0)PA(f^,g^,f^0,f^0)df^dg^,A2=+J(f^,g^)M0(f^,g^,f^0,f^0)PA(f^,g^,f^0,f^0)df^dg^.
A:Amp(a0)=1m=137zmRm(f^,g^),B:Re(a1)=m=137zmRm(f^,g^),C:Pha(a0)=exp(i(2π/λ)m=137zmRm(f^,g^)),D:Im(a1)=i(π/λ)m=137zmRm(f^,g^).
IPE=m=137SIPEm·zmBFS=m=137SBFSm·zm,
SIPEmA=SIPEmB=SBFSmA=SBFSmB0,SIPEmC=12λf^0·+J(f^,g^)M0(f^,g^,f^0,f^0)×[Rm(f^+f^0,g^)Rm(f^f^0,g^)]df^dg^/(+J(f^,g^)M0(f^,g^,f^0,f^0)df^dg^),SIPEmD=SIPEmC/2,SBFSmC=12λf^0·+J(f^,g^)·M0(f^,g^,f^0,f^0)·f^×[Rm(f^+f^0,g^)Rm(f^f^0,g^)]df^dg^/(+J(f^,g^)·M0(f^,g^,f^0,f^0)·f^2·df^dg^),SBFSmD=SBFSmC/2.
{mandm+1are the odd aberrations inxandydirection.SIPEm+1Cy=SIPEmCxSIPEm+1Dy=SIPEmDx,{spherical aberration items :SBFSmCy=SBFSmCxSBFSmDy=SBFSmDx,astigmatism aberration items:SBFSmCy=SBFSmCxSBFSmDy=SBFSmDx,

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