, vol.43, no.2, pp.71 77, Simultaneous Measurement of Film Thickness and Surface Profile of Film-Covered Objects by Using White-Light Interfer

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1 , vol.43, no.2, pp.71 77, Simultaneous Measurement of Film Thickness and Surface Profile of Film-Covered Objects by Using White-Light Interferometry ( ) ( ) sugi@cs.titech.ac.jp Abstract In semiconductor and LCD manufacturing processes, film thickness and surface profile of filmcovered objects are needed to be measured simultaneously. By using the vertical scanning whitelight interferometry, an algorithm is developed that enables such simultaneous measurement. It works well for objects covered with not only thick film but also thin film. Experimental results are presented for film-covered surfaces consisting of approximately 70nm SiO 2 film on silicon substrate. Keywords white-light interferometry, surface profiler, transparent film, thickness. 1 [1, 2, 3, 4, 5, 6]

2 2 [7, 8, 9, 10, 11] [12, 13, 14, 15, 16] 1µm 2 1 P D 2 O 1 O 2 O 2 L O 2 L E z = 0 E z z = 0 P z p E d d = z z p λ k k = 2π λ a(k) λ c λ c ± λ b a(k) a(k) = 0 (0 < k < k l, k u < k) (1) k l = 2π, k u = 2π λ c + λ b λ c λ b CCD 1 1(a) r N N(N = 0, 1, 2,...) CCD 1(b) η o (k), η r (k), η m (k) η o (k) η r (k), η m (k) 1(c) η t (k), η a (k), η s (k) n η t (k) η a (k), η s (k)

3 3 Light source To CCD camera η r O1 Movable part η o Beam spliter η m Reference mirror Beam spliter O2 L Path: r (b) System parameters L Reference mirror Incident ray P Path: 0,1,2,... d E Air Path:0 Path:1 Path:2 Path:3 ηa nηt nηt nηt Transparent film Opaque layer D zp z z = 0 (a) Basic set up of an optical system Transparent film Opaque layer ηt ηs ηa ηa ηa ηs (c) Sample parameters ηs 1: Notations used in this paper nη t (k), η a (k) 1(c) r, 0, N(N = 1, 2,...) CCD γ r (k), γ N (k) γ r (k) = {η r (k)} 2 η m (k) (2) γ 0 (k) = η a (k){η o (k)} 2 (3) γ N (k) = n{ η a (k)η s (k)} N 1 {η t (k)} 2 η s (k){η o (k)} 2 (4) SiO 2 Si 3 0,1 2 3 g(z; z p, D) 1 ( ) g(z; z p, D) z f(z; D) z C(D) g(z; z p, D) = f(z z p ; D) + C(D) (5)

4 4 f(z; D) = 2 C(D) = ku k l {a(k)} 2 γ r (k) [ γ 0 (k) cos(2kz) +γ 1 (k) cos{2k(z + nd)} +γ 2 (k) cos{2k(z + 2nD)} ] dk (6) ku k l {a(k)} 2[ {γ r (k)} 2 + {γ 0 (k)} 2 +{γ 1 (k)} 2 + {γ 2 (k)} 2 +2γ 1 (k){γ 0 (k) + γ 2 (k)} cos(2knd) +2γ 0 (k)γ 2 (k) cos{4knd} ] dk (7) 3 D z p 3.1 {z m } N m=1 z m = (m 1) ε m {g m } N m=1 g m = g(z m ; z p, D) + ε m (8) 3.2 D {g m } N m=1 C(D) Ĉ Ĉ = 1 N N g m (9) m=1 (7) Ĉ D DC(Direct Current) DC DC

5 : Interferogram g(z; z p, D) 3.3 z p D g(z; z p, D) f(z z p ; D) z p D g(z; z p ), f(z z p ) 2 g(z; z p ) g(z; z p ) g(z; 0) z pg, z pg0 z pg z p [5] z pg z p z pg z pg0 z p = z pg z pg0 (10) z p [5, 6] z pg, z pg0 (10) z p z p DSE(Difference between Squared Envelopes) 4 D (DC ) (9) Ĉ (7) (7) D ˆD D i ϵ C(D)

6 6 C 1 (D) [D i ϵ, D i + ϵ] max C 1(D) C(D) (11) D i ϵ D D i +ϵ C 1 (D) (11) [18] (7) Ĉ1(D) Ĉ 1 (D) = c 0 (D i ) + c 1(D i ) (D D i ) (12) ϵ c 0 (D i ) = 1 2 c 1 (D i ) = 1 2 [ C(Di + [ C(Di + ϵ ) + C(D i ϵ ) ] (13) 2 2 ϵ 2 ) C(D i ϵ 2 ) ] (14) (12) (9) Ĉ D DC D ˆD = Ĉ c 0(D i ) ϵ + D i (15) c 1 (D i ) ˆD D e 0 C(D) n C (n) (D) 4 C ϵ 0 = (1) (D i ) e 0 C (2) ( λ c ) (16) 2n ϵ 0 < ϵ ϵ 0 (17) [D i ϵ, D i + ϵ] e 0 (17) ϵ e 0 [D i ϵ, D i + ϵ] DC ϵ ϵ 0 (16) e 0 D i 3 z C(D) D C(D) C (1) (D) = 0 C(D) D i (16),(17) 0 DC

7 7 3: Graph of C(D) function 1: Measured T j and (λ c /(4n))j (λ c = 605.9nm, n = 1.458) j T j (λ c /(4n))j D ( DC ) C(D) T j (j = 1, 2, 3,...) [T j 1, T j ] C(D) D D C(D) = Ĉ T j SiO 2 λ c = 605.9nm T j 1 SiO 2 n = (λ c /(4n))j 1 (λ c /(4n))j T j T j (λ c /(4n))j [T j 1, T j ] [ λ c 4n (j 1), λ c j] (j = 1, 2,...) (18) 4n D (18) D C(D) = Ĉ D ( DC )

8 8 2: i c 1 (D i0 ) > 0 c 1 (D i0 ) < 0 C(D) C( D i 0 +D i0 +1 ) 2 i = i 0 i = i C(D) > C( D i 0 +D i0 +1 ) 2 i = i i = i 0 1. D j λ c 4n (j 1) D λ c j (j = 1, 2,...) (19) 4n 2. [ λ c 4n (j 1), λ c j] 4n [T j 1, T j ] 3. DC ϵ [0.0050, ] Tj T j 1 4. M = [T j 1, T j ] M c c 2ϵ 5. D 0 = T j 1 + ϵ {D i } M i=1 D i = D 0 + i 1 M (T j T j 1 ) (20) 6. x i = C(D i ) Ĉ {x i} M i=1 x i x i = 0 i i 0 7. C( D i 0 +D i ) 8. i 2 i D [D i ϵ, D i + ϵ] 9. D ˆD = Ĉ c 0(D i ) ϵ + D i (21) c 1 (D i ) D M DC D i DC

9 9 (21) D i C(D) (16) D i D i ϵ 0 1 C(D) λ c 6 z p (DSE ) z p f(z z p ) z p = 0 f(z) [5, 6] (6) f(z) k 0 f(z) = r(z) cos{2k 0 z α(z)} (22) r(z) = {m c1 (z) + m s2 (z)} 2 +{m c2 (z) m s1 (z)} 2 (23) α(z) = tan 1 m c2(z) m s1 (z) m c1 (z) + m s2 (z) (24) m ci (z) = ku k l ψ i (k) cos{2(k k 0 )z}dk (25) ku m si (z) = ψ i (k) sin{2(k k 0 )z}dk k l (26) ψ 1 (k) = 2{a(k)} 2 γ r (k){γ 0 (k) + γ 1 (k) cos (2nkD) +γ 2 (k) cos (4nkD)} (27) ψ 2 (k) = 2{a(k)} 2 γ r (k){γ 1 (k) sin (2nkD) (28) +γ 2 (k) sin (4nkD)} (29) (25),(26) i i=1,2 r(z) f(z) 2 f(z) 2 2 r(z z p ), r(z) z p, z p0 r(z z p ) r(z) z p z p z p0 z p0 = z p z p z p z p = z p z p0 (30)

10 10 z p z p0 z p z p0 r(z) (23) (29) D r(z) z p0 [5] z p r(z z p ) z p (23) {f m } N m=1 2 r(z z p) z p (1) f(z z p ) [5] J λ c + λ b 4 0 J λ c λ b 2λ b (31) J λ c λ b (J + 1) (32) 4 [5] λ c = 605.9nm, λ b = 37.5nm (λ c λ b )/2λ b = 7.58 (31) J (32) 2 r(z z p ) f(z z p ) 2 (2 ) 2 r(z z p ) {f(z m z p )} m=. z z = z 2j r(z 2j z p ) = {f(z 2j z p )} 2 { 2 } 2 f(z 2m 1 z p ) + (33) π 2(j m) + 1 m=. z z = z 2j+1 r(z 2j+1 z p ) = {f(z 2j+1 z p )} 2 { 2 } 2 f(z 2m z p ) + (34) π 2(j m) + 1 m=

11 11. z r(z z p ) = 2 2 π 2 [ (1 cos πz ) { m= f(z 2m 1 z p ) z z 2m 1 } 2 +(1 + cos πz ) { } 2 ] f(z 2m z p ) z z 2m m= (35) f(z m z p ) f m = g m Ĉ 2 r(z z p) r N (z z p ). z z = z 2j r N (z 2j z p ) = (f 2j ) 2. z z = z 2j+1. z r N (z 2j+1 z p ) = (f 2j+1 ) 2 { N 2 2 } 2 f 2m 1 + (36) π 2(j m) + 1 m=1 { N 2 2 } 2 f 2m + (37) π 2(j m) + 1 m=1 r N (z z p ) = [ 2 2 (1 cos πz { N 2 π 2 ) f 2m 1 z z m=1 2m 1 +(1 + cos πz { N 2 ) } 2 ] f 2m z z 2m m=1 } 2 (38) c c r N (z z p ) z p

12 4: Photograph of a surface profiler SP-500[17] Sample # D Mean of 3: Mesurement errors of ˆD and ẑ p ˆD Standard deviation of ˆD Mean standard deviation of ẑ p 1 103nm 96.8nm 0.

12 12 4: Photograph of a surface profiler SP-500[17] Sample # D Mean of 3: Mesurement errors of ˆD and ẑ p ˆD Standard deviation of ˆD Mean standard deviation of ẑ p 1 103nm 96.8nm 0.24nm 163nm 2 304nm 294.8nm 0.25nm 171nm 3 750nm 738.0nm 0.24nm 162nm 7 4 SP-500[17] SP-500 λ c = 605.9nm, 37.5nm (1) SiO 2 Si DC = 1.425µm 103nm,304nm,750nm mm 0.31mm D z p 10 3 D = 10, 000 ˆD 10 z p 1 10,000 ẑ p ẑ p 10 3 Mean of ˆD, Standard deviation of ˆD, Mean standard

13 : Measured film thickness of sloped sample deviation of ẑ p 5 8 z z DC DC DSE SP-500 [1] G. S. Kino and S. S. C. Chim: The Mirau correlation microscope, Appl. Opt., 29, 3775/3783 (1990). [2] P. J. Caber: Interferometric profiler for rough surfaces, Appl. Opt., 32-19, 3438/3441 (1993).

14 14 [3] P. de Groot and L. Deck: Three-dimensional imaging by sub-nyquist sampling of white-light interferograms, Opt. Lett , 1462/1464 (1993). [4] L. Deck and P. de Groot: High-speed noncontact profiler based on scanning whitelight interferometry, Appl. Opt., 33, 7334/7338 (1994). [5] : 36-1, 16/25 (2000). [6] A. Hirabayashi, H. Ogawa, K. Kitagawa: Fast surface profiler by white-light interferometry by use of a new algorithm based on sampling theory, Appl. Opt., 41-23, 4876/4883 (2002). [7] P. A. Flournoy, R. W. McClure, and G. Wyntjes: White-light interferometric thickness gauge, Appl. Opt., 11-9, 1907/1915 (1972). [8] T. Tsuruta and Y. Ichihara: Accurate measurement of lens thickness by using whitelight fringes, Japn. J. Appl. Phys., Suppl., 14-1, 369/372 (1975). [9] T. M. Merklein: High resolution measurement of multilayer structures, Appl. Opt., 29, 505/511 (1990). [10] M. Itoh, R. Yamada, R. Tian, M. Tsai, and T. Yatagai: Broad-band light-wave correlation topography using wavelet transform, Optical Review 2-2, 135/138 (1995). [11] S. Diddams and J. C. Diels: Dispersion measurements with white-light interferometry, J. Opt. Soc. Am. A, 13, 1120/1129 (1996). [12] B. S. Lee and T. C. Strand: Profilometry with a coherence scanning microscope, Appl. Opt., 29-26, 3784/3788 (1990). [13] 21-7, 481/484 (1992). [14] S.-W. Kim and G.-H. Kim: Thickness-profile measurement of transparent thin-film layers by white-light scanning interferometry, Appl. Opt., 38-28, 5968/5973 (1999). [15] ViEW2003, 87/92 (2003). [16] K. Kitagawa 3-D profiling of a transparent film using white-light interferometry TAI-7-2, 585/590 (2004). (CD ROM)

15 15 [17] SP [18] : (1969).

Table 1 Experimental conditions Fig. 1 Belt sanded surface model Table 2 Factor loadings of final varimax criterion 5 6

Table 1 Experimental conditions Fig. 1 Belt sanded surface model Table 2 Factor loadings of final varimax criterion 5 6 JSPE-54-04 Factor Analysis of Relationhsip between One's Visual Estimation and Three Dimensional Surface Roughness Properties on Belt Sanded Surface Motoyoshi HASEGAWA and Masatoshi SHIRAYAMA This paper