Abstract

The proximity effect in successively developed direct-write electron-beam lithography gratings is measured. The grating relief shapes are obtained from the measured power in several of the gratings' diffraction orders. Describing the proximity effect by a convolution with a double Gaussian point-spread function, we determine the parameters of the point-spread function. The writing part of the point-spread function is found to increase significantly with increasing development time, the background part much less.

© 1995 Optical Society of America

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References

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  1. P. D. Maker, R. E. Muller, “Phase holograms in polymethyl methacrylate,” J. Vac. Sci. Technol. B 10, 2516–2519 (1992).
    [CrossRef]
  2. M. Larsson, M. Ekberg, F. Nikolajeff, S. Hård, “Successive development optimization of resist kinoforms manufactured with direct-writing electron-beam lithography,” Appl. Opt. 33, 1176–1179 (1994).
    [CrossRef] [PubMed]
  3. M. Ekberg, F. Nikolajeff, M. Larsson, S. Hård, “Proximity-compensated transmission grating manufactured with direct-writing electron-beam lithography,” Appl. Opt. 33, 103–107 (1994).
    [CrossRef] [PubMed]
  4. G. Owen, “Methods for proximity effect correction in electron lithography,” J. Vac. Sci. Technol. B 8, 1889–1892 (1990).
    [CrossRef]

1994 (2)

1992 (1)

P. D. Maker, R. E. Muller, “Phase holograms in polymethyl methacrylate,” J. Vac. Sci. Technol. B 10, 2516–2519 (1992).
[CrossRef]

1990 (1)

G. Owen, “Methods for proximity effect correction in electron lithography,” J. Vac. Sci. Technol. B 8, 1889–1892 (1990).
[CrossRef]

Ekberg, M.

Hård, S.

Larsson, M.

Maker, P. D.

P. D. Maker, R. E. Muller, “Phase holograms in polymethyl methacrylate,” J. Vac. Sci. Technol. B 10, 2516–2519 (1992).
[CrossRef]

Muller, R. E.

P. D. Maker, R. E. Muller, “Phase holograms in polymethyl methacrylate,” J. Vac. Sci. Technol. B 10, 2516–2519 (1992).
[CrossRef]

Nikolajeff, F.

Owen, G.

G. Owen, “Methods for proximity effect correction in electron lithography,” J. Vac. Sci. Technol. B 8, 1889–1892 (1990).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Reliefs of a 50%-duty-cycle 8.0-μm-period binary exposed grating at three different development times T, obtained from measured diffraction power data and precalculated phases. The electron energy is 25 kV.

Fig. 2
Fig. 2

Etch depth versus development time for large areas, evenly exposed by D = 80 μC/cm2. The data point at T = 1383 s was extrapolated from depths reached at several lower doses. The electron energy is 25 kV.

Fig. 3
Fig. 3

α versus development time T. The electron energy is 25 kV.

Fig. 4
Fig. 4

β versus development time T. The electron energy is 25 kV.

Fig. 5
Fig. 5

Stylus measurement of a blazed-grating exposed structure. The grating period is 16 μm and the electron energy is 50 kV.

Fig. 6
Fig. 6

Stylus measurement of a blazed-grating exposed structure. The grating period is 32 μm, the development time is 240 s, and the electron energy is 50 kV.

Fig. 7
Fig. 7

Computer simulation of the convolution of a 32-μm-period grating with PSF's with different β. The period is much larger than α, and η = 1.0: (a) β = 8 μm, (b) β = 12 μm, (c) β = 16 μm.

Fig. 8
Fig. 8

(a) Measured and calculated diffraction power and (b) reliefs for a 4-μm-period blazed grating (G2). In (b) the upper relief is the convolved grating profile that gives rise to the calculated diffracted powers, the lower is calculated from measured powers and precalculated phases. Dmin = 203 μC/cm2, Dmax = 456 μC/cm2, T = 240 s, and the electron energy is 50 kV.

Fig. 9
Fig. 9

α versus the product of average exposure dose and development time. Dots denote data for the grating G1, and crosses data for the grating G2. The electron energy is 50 kV.

Fig. 10
Fig. 10

Resist depth versus dose characteristic for evenly exposed, wide areas. The electron energy is 50 kV, and the development time is 240 s.

Fig. 11
Fig. 11

Binary grating relief before, h0(x), and after, h(x), convolution with the PSF.

Equations (18)

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PSF ( r ) = 1 π ( 1 + η ) [ 1 α 2 exp ( r 2 α 2 ) + η β 2 exp ( r 2 β 2 ) ] .
β = Λ π [ ln ( 4 η / π ( 1 + η ) ( h / h 0 ) 1 ) ] 1 / 2 .
α = h 0 ( 1 + η ) π 1 { [ d h ( x ) d x ] max π Λ h 0 ( h h 0 1 1 + η ) } .
η = 2 h b / h t 1 ,
h ( x , y ) = h 0 ( x x , y y ) PSF ( x , y ) d x d y = 1 1 + η [ 1 α π h 0 ( x x ) exp ( x 2 α 2 ) d x + η 1 β π h 0 ( x x ) exp ( x 2 β 2 ) d x ] = h ( x ) ,
I 1 h 0 exp ( x 2 α 2 ) d x = h 0 α π .
h 0 ( x ) = h 0 2 + n = 1 , 3 , 2 h 0 ( 1 ) ( n 1 ) / 2 n π cos ( n 2 π x Λ ) .
I 2 = h 0 β π { 1 2 + n = 1 , 3 , 2 ( 1 ) ( n 1 ) / 2 n π exp [ ( n β π Λ ) 2 ] } .
h = h ( 0 ) h ( Λ / 2 ) = h 0 1 + η { 1 + η 4 π exp [ ( β π Λ ) 2 ] } ,
β = Λ π { ln [ 4 η / π ( 1 + η ) ( h / h 0 ) 1 ] } 1 / 2 ,
I 1 0 h 0 exp [ ( x x ) 2 α 2 ] d x = x h 0 exp [ t 2 α 2 ] d t .
dI 1 d x | x = 0 = h 0 exp ( x 2 α 2 ) | x = 0 = h 0 .
h 0 ( x ) = h 0 2 ( 1 + n = 1 , 3 , 4 n π sin n π x Λ / 2 ) .
dI 2 d x | x = 0 = 4 h 0 Λ n = 1 , 3 β π exp [ ( n π β Λ ) 2 ] .
[ d h ( x ) d x ] max = d h ( x ) d x | x = 0 = h 0 1 + η { 1 α π + η 4 Λ n = 1 , 3 exp [ ( n π β Λ ) 2 ] } .
α = h 0 ( 1 + η ) π 1 [ [ d h ( x ) d x ] max π Λ h 0 ( h h 0 1 1 + η ) ] ,
h t = C η , h b = C ( η + 2 × 1 ) ,
η = 2 h b / h t 1 ,

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