Molecular energetics of the growth mechanism of stearic acid thin films prepared by vacuum-deposition

1298

Applied Surface Science 33/34 (1988) 1298 1306 North-Holland, Amsterdam

MOLECULAR ENERGETICS OF THE G R O W T H M E C H A N I S M OF STEARIC ACID THIN FILMS P R E P A R E D BY V A C U U M - D E P O S I T I O N Yoshio SAITO 1 Kimio I N A O K A : Chihiro K A I T O and M a s a k a z u O K A D A ~ I Department of Physi(w, Kvoto lnsntute of Technology, Matsugasakl. Sakyo-ku, k@oto 006, Japan Yuge Mercantile Marine College, Yuge-cho, Ochigun, Ehime 794-25, Japan FaculO' of Applied Biological Science, Iliroshima Universio,, 2-17 Midon-ch¢; Fukuvama 720, Japan Received 23 August 1987: accepted for publication 15 October 1987

Stearic acid crystals grew with different types of orientation on various subslrates. The molecules lie parallel to the substrates (P-orientation) or stand normal to those (N-orientation}. The proportion of P-orientation in the thin fihn decreases with increasing substrate temperature and also with decreasing deposition rates. Energy calculations have been carried out in order to describe the growth mechanism of the stearic acid on a KCI surface. The net charge distribution m the molecule is presented. The total potential energy, as well as the Coulomb and Lennard-Joncs 6-12 potential contributions have been calculated for a single molecule with different orientations. It was clarified that the potential energy became minimal when the molecule was parallel to the substrate. The growth mechanism is discussed on the basis of the calculated potential energy.

1. Introduction M a n y works have been d o n e on the p r e p a r a t i o n of thin m o l e c u l a r films. O n e of the aims is to utilize them as thin insulating films [1]. In d o i n g so, two m e t h o d s have mainly been applied: L a n g m u i r - B l o d g e t t multilayer d e p o s i t i o n [2] and p h y s i c a l - v a p o u r d e p o s i ti o n s [1]. Because of the recent necessity of fabricating the devices in a dry system, the latter m e t h o d has d r a w n special a t t e n t i o n [3]. T o o b t a i n thin m o l e c u l a r films of desired characteristics, c o n t r o l of the m o l ecu l a r o r i e n t a t i o n by an epitaxial growth t e c h n i q u e b e c o m e s very important. In previous papers [4,5], the m e c h a n i s m of epitaxial growth of hexadec a c h l o r o - c o p p e r - p h t h a l o c y a n i n e (C1-CuPc) on (001) KCI surfaces has been elucidated. T h e C1-CuPc crystals grew with different types of o r i e n t a t i o n such as P- and N - o r i e n t a t i o n s . In the P-orientation, the C I - C u P c molecules lie parallel to the substrate while they are n o r m a l to the substrate in the N - o r i e n t a t i o n . T h e P-oriented crystal increase with increasing substrate temperature and with decreasing d e p o s i t i o n rate. T h e i n t e r p r e t a t i o n of these 0 1 6 9 - 4 3 3 2 / 8 8 / $ 0 3 . 5 0 q~ Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)

Y. Saito et al. / Molecular energetics of growth mechanism of stearic acid

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phenomena was made in terms of molecular energy calculation results [4,5]. In vacuum-deposition of long-chain molecules, such as stearic acid [6], nhexatriacontane and polyethylene [7], P- and N-oriented crystals were also observed by transmission electron microscopy. N o convincing interpretation, however, for the mechanisms that lead to the film orientation, has been given. In the present paper the growth mechanism of stearic acid on a KC1 substrate is discussed using the energy calculations of molecular interactions.

2. Characteristics of molecular orientation The stearic acid (SA) was vacuum-deposited to a thickness of 1000 A onto KC1, mica and SA single crystal surfaces. After deposition, the films were decorated with Ge to judge the orientation of the SA crystals [6]. The grown crystals are monoclinic and the unit cell dimensions are a = 9.36 ,~, b = 4.95 A, c = 50.78 A, and fl = 128.25 o [8]. The surface energy of the plane parallel to the SA molecules in the SA crystals is higher than that of the (001) plane normal to the SA crystals [9]. The SA crystal grows preferentially along the [100] and the [010] directions, then grows in a plate shape. The fractional areas of the P-oriented crystals shearing the total area of deposited films were measured at substrate temperatures (T,) ranging from - 1 0 to 45 ° C, at a constant molecular flux rate ( J ) of 3.34 x 1012 molecules cm -2 s -1. Fig. 1 shows the results obtained on the (001) KC1 substrates. The P-oriented crystals are dominant at lower T~, whereas the N-oriented crystals at higher ~. This tendency is almost independent of substrate material. Several fatty acids, such as palmitic CH3(CH2)14COOH, arachic C H 3 ( C H 2 ) l s C O O H and behenic CH3(CH2)2oCOOH acids, were also vacuum-deposited onto the (001) KC1 surfaces at various T~ [8]. The effect of 100

0 .~

.o ~ ~

22 50

0 0 i Un,

0

-10

0

Substrate

10 20

30

Temperature

40

50 (°C)

Fig. 1. Fraction of the surface area occupied by the P-oriented stearic acid crystals as a function of temperature. C16: palmitic acid, C18: stearic acid, C20: arachic acid and Cn: behenic acid.

] 300

Y. Saito et al. / Molecular energetics of growth mechanism ofstearic acid

100

o~) t~

o w ".~,~

10"C :mica

50

0)-,-4

o°~ o",

,I'"

f 0

I

~C:SA(OO~) 10

Molecular

20 Flux

30 Rate

40

50

x l 0 E=

,7 ( r a o l e c u l e s / c m 2 . s )

Fig. 2. Effect of the molecular flux rate on the concentration of P-oriented stearic acid crystals at different t e m p e r a t u r e s .

T~ is the same in all samples. The concentration curves shift to the high temperature side with increasing chain length of the fatty acids, as shown in fig. 1. The influence of J was also examined at various ~ . The rates J were changed from 1.6 × 1012 to 55 × 1012 molecules cm : s 1. The results for the SA (001) and for mica are shown in fig. 2, indicating that the flux rate accelerates the occurrence of the P-oriented crystals. With increasing temperature, this effect became less significant. Higher ~ and lower J favour the growth of N-oriented crystals whereas lower 7"~ and higher J the P-oriented ones. This tendency is opposite to that for CI-CuPc as mentioned above.

3. C a l c u l a t i o n of potential energy

The potential energy associated with a single SA molecule, for various orientations and positions on the (001) KCI surface has been calculated as the sum of Coulomb and Lennard-Jones 6-12 potential energies. The induced dipolar contribution was neglected because of its very small contribution as reported in a previous paper [4]. An SA single molecule is assumed to be a rigid linear zig-zag chain (all-trans). The atomic coordinates of the SA molecule were chosen from the X-ray structure data of the c-form crystal determined by Malta et al. [10], because the vacuum-deposed films are of the c-polymorph. The coQrdinates of the hydrogen atoms were calculated from the molecular bond and angle data. The atomic coordination are shown in table 1.

Y. Saito et al. / Molecular energeties of growth mechanism of stearic acid Table 1 Atomic coordinates and the net charges of a stearic acid molecule Atom

x

y

z

Charge

C(1)

0.731

0.000

1.969

0.856

C(2)

- 0.076

0.154

3.306

- 0.080

C(3)

0.808

0.026

4.566

0.041

C(4)

- 0.042

0.152

5.852

0.024

C(5)

0.083

- 0.029

7.115

0.028

C(6)

- 0.048

0.118

8.377

0.027

C(7)

0.826

- 0.063

9.635

0.026

C(8)

- 0.053

0.085

10.897

0.026

C(9)

0.821

- 0.097

12.154

0.026

C(10)

- 0.059

0.051

13.417

0.026

C(11)

0.815

14.674

0.025

C(12)

- 0.064

0.017

15.937

0.028

C(13)

0.810

- 0.164

17.194

0.007

C(14)

- 0.069

- 0.017

18.457

0.030

C(15)

0.804

- 0.198

19.714

0.022

C(16)

- 0.075

- 0.051

20.977

- 0.013

0.799

C(17)

-0.130

- 0.232

22.234

0.175

C(18)

- 0.80

- 0.085

23.497

- 0.337

C(19)

- 0.199

- 0.031

0.939

- 0.593

O(H)(1)

- 0.199

- 0.031

0.939

- 0.593

0(2)

1.946

0.000

1.733

- 0.636

H(0)(1)

0.000

0.000

0.000

0.325

H(2)

- 0.842

- 0.621

3.337

0.031

H(3)

- 0.551

1.135

3.310

0.032

H(4)

1.559

0.816

4.557

0.003

H(5)

1.302

- 0.946

4.559

- 0.002

H(6)

- 0.505

1.138

5.878

- 0.011

H(7)

1.613

0.730

7.126

- 0.009

H(8)

1.286

- 1.019

7.102

- 0.009

H(9)

- 0.830

- 0.641

8.365

- 0.012

H(10)

- 0.502

1.109

8.390

- 0.012

H(11)

1.608

0.696

9.646

- 0.011

H(12)

1.280

- 1.053

9.622

- 0.011

H(13)

- 0.835

- 0.675

10.885

- 0.012

H(14)

- 0.508

1.075

10.910

- 0.012

H(15)

1.602

0.066

12.166

- 0.012

H(16)

1.275

- 1.087

12.142

- 0.012

H(17)

- 0.841

- 0.709

13.405

- 0.013

H(18)

- 0.513

1.041

13.430

- 0.012

H(19)

1.597

0.629

14.686

- 0.012

H(20)

1.270

- 1.121

14.662

- 0.014

H(21)

- 0.846

- 0.742

15.925

- 0.014

H(22)

- 0.519

1.007

15.950

- 0.013

H(23)

1.592

0.595

17.206

- 0.014

H(24)

1.276

- 1.060

17.183

0.009

H(25)

- 0.851

- 0.776

18.445

- 0.013

H(26)

- 0.524

0.973

18.469

- 0.012

H(27)

1.586

0.561

19.726

- 0.017

1301

1302

Y. Saito et al. / Molecular energetics of growth mechanism of stearic acid

Table 1 (continued) Atom

x

v

:

Charge

H(28) H(29) H(30) H(31 ) H(32) H(33) H(34) H(35)

1.259 - 0.857 - 0.529 1.581 1.254 0.702 0.375 0.700

1.188 - 0.8 l0 0.940 0.527 1.222 0.674 - 1.075 0.019

19.702 20.965 20.989 22.246 22.222 23.509 23.485 24.387

- 0.017 0.004 (l.004 0.0t2 - 0.012 0.057 (l.057 0.097

Th e g e o m e t r y of the SA substrate system requires six i n d e p e n d e n t spatial variables ( x , y, z~ 0, +, ~ ) to define the position and o r i e n t a t i o n of the SA chain with respect to the substrate surface. T h e g e o m e t r y is shown in fig. 3. T h e electrostatic p o t e n ti a l at some external position ( x , v , z ) d u e to the entire (001) KCI is given by [11] d~(x, y, z) = 2 5 . 6 6 e x p ( - ~ - z )

cos x cos y,

(~)

where the x and y axes are parallel to the a- and b-axes of KC1. Thus, the total C o u l o m b energy is o b t a i n e d by m u l t i p l y i n g the p o t e n t i a l at a given a t o m by the net charge on the atom, and s u m m i n g over all a t o m s in the molecule. D e t e r m i n a t i o n of the C o u l o m b i c c o n t r i b u t i o n requires k n o w l e d g e of the net charge on all the a to m s of the molecule. N o m o l e c u l a r orbital cal cu l at i o n of SA, however, has been reported. We calculated the d i s t r i b u t i o n of the net charges on the a t o m s in the g r o u n d state by using the M I N D O / 2 m e t h o d [12], a n d the results are shown in table 1.

f Fig. 3. Spatial parameters (x, y, z, O, ~, w), used to describe the position of a molecular chain relative to the substrate surface.

Y. Saito et al. / Molecular energetics of growth mechanism of stearic acid

1303

Table 2 Attractive energy constants and contact radii for like species Atom or ion

A,i (.~ eV)

H C O(H) O(C) K+ CI

1.961 16.073 9.413 16.050

A~j (~lz eV)

Contact radius (~,) 1.2 1.7 1.5 1.5

15.168 77.71

1.33 1.81

The energy c o n t r i b u t i o n due to the L e n n a r d - J o n e s 6-12 potential can be obtained by =

-

(2)

(A,,/4).

Hence, rij is the distance between atom i in the SA molecule a n d ion j in the KC1 substrate. The attractive energy c o n s t a n t A,j is d e d u c e d from the c o m b i n a t i o n rule [13]:

A i / = ( A n A j j ) 1/2,

(3)

where A~, can be c o m p u t e d by m e a n s of the modified Slater K i r k w o o d e q u a t i o n [14] and Ajj has been d e t e r m i n e d by M a y e r [15]. The repulsive energy c o n s t a n t B G is calculated from the c o n d i t i o n that U,i is a m i n i m u m at the e q u i l i b r i u m distance, which is the sum of the ionic radii for ions in KC1 a n d the v a n der Waals radii for C, O a n d H [16] in the SA molecule. Ai~ a n d A# are listed in table 2. The total L e n n a r d - J o n e s potential energy can be calculated b y using the hemispherical cap a p p r o x i m a t i o n [17].

I

(a)

--

% i i

[

0

CL

[

I

30

I

I

GO

I

l

90 0

1

60

1

[

I

30

Fig. 4. Total potential energy for a single stearic acid molecule on the (001) KC1 surface. The parameter is the angle between the molecular chain and the (001) KCI surface. (a) The H(35) atom of the methyl group and (b) the H(1) atom of the carboxyl group of the SA molecule are above the C1- ion.

1304

Y. Saito et al. / Molecular energetics of growth mechanism of stearic acid

For given (x, y), 0 and +, the total potential energy was calculated for the molecule at different z and ~0, and the minimal energy value is plotted. In fig. 4, the total potential energies are plotted as a function of 0. In the curves (+ = 45 °) the H(35) atom of the methyl group (a) and the H(1) atom of the carboxyl group (b) of the SA molecule are above the C1 ion. When the molecule is normal to the substrates or in N-orientation, the total potential energy is 0.2 eV. When the molecule is parallel to the substrate, the potential energy has the minimum value. The minimum energy values are about 1 eV, which is a reasonable value compared with the values of polyethylene [17], polyxymethylene and polythiomethylene [18]. Although the Coulomb potential above the surface of the ionic crystal is generally higher than for other substances, there is little contribution of the Coulomb energy to the total energy. This tendency is almost independent of the molecular position (x, y ) and azimuthal angle +.

4. Discussion The molecules must be adsorbed on the substrate at the initial growth stage of the vacuum-deposited films. If the adsorption energies are small, the adsorbed molecules re-evaporate from the substrate. The mean desorption time is given by [19]: r = Vo 1 e x p ( U / k T ) ,

(4)

where v0 is the vibration coefficient, U the adsorption energy, k the Boltzmann constant, and T the absolute temperature. The vibration coefficient is estimated from the experimental data from the deposition conditions as shown in figs. 1 and 2. The mean desorption times are shown in table 3. There are few differences in the mean desorption times among the substrate materials, as the experimental results are very similar to each other. It is noted that the desorption times increase with increasing energy of adsorption and with decreasing 77,. The mean arrival time, for a single evaporated molecule to arrive at the site of adsorbed molecules depends on the molecular flux rate and the molecular orientation. The mean arrival time decreases with increasing J. When the mean arrival time is longer than the mean desorption time, the adsorbed molecules re-evaporate from the substrate. Before desorption, when an adsorbed molecule meets successively with other molecules and is joined to them, the coagulated molecules become a stable crystal nucleus. In the present experiments, the arrival time is estimated to be in the range from 0.4 to 34 s, corresponding to the molecular flux rates and the molecular orientations. Under these conditions SA molecules are never adsorbed in N-orientation on the substrates. The N-oriented molecules are immediately re-evaporated from

]L Saito et al. / Molecular energetics of growth mechanism of stearic acid

1305

Table 3 M e a n d e s o r p t i o n times

U (eV)

• (s) 270 K

290 K

310K

0.1 0.2

5 . 0 x l O 15 3.7 X 10 -13

3.7X10-15 2.0X 10 13

2 . 8 X 1 0 is 1.2X 10-13

0.3 0.4

2.7X10 2.0x10

1.1XIO-H 6 . 0 X 1 0 lo

5.1xlO 2.1x10

0.5 0.6 0.7 0.8

1.5xlO -7 1.1xlO s 7.9X10 -4 5.9 X lO 2

3 . 3 x 1 0 -8 1.8X10-6 9.8 X 10 5 5.3 X 1 0 - 3

9.0XlO -9 3.8x10 7 1.6xlO-S 6.8 X lO - 4

0.9 1.0

4.3 3.2X 10 +2

2.9X 10 -1 1 . 6 x l O ÷1

2.9X 10 2 1.2

11 9

-

12 lo

the substrate or drop back on it. On the other hand, P-oriented molecules can be adsorbed on the substrates at T~ below 35 o C, when J is less than 22 x 1012 molecules cm -2 s -1. The number of the P-oriented crystals decreases with increasing ~ at a constant J, since the desorption time decreases with increasing ~ , and thus nucleation in the P-orientation becomes difficult. At a constant ~ , the nucleation becomes easier at higher J, since the mean arrival time becomes longer as discussed above. As T~ rises, P-oriented molecules become unstable, because the mean desorption time becomes shorter. Therefore, the molecules easily move, rising up and lying down on the substrate. During the surface migration, the molecules meet with other adsorbed molecules more frequently and join together so as to form a crystal nucleus in Pa n d / o r N-orientation. The growth rate of the N-oriented crystals is faster than that of the P-oriented crystals as described before. Once an N-oriented crystal is nucleated, it occupies a larger portion of the substrate. The adsorption energy increases with increasing chain length of the fatty acids, because almost all of the total energy originates from the Lennard-Jones contribution as discussed above. At higher adsorption energy, the desorption t i m e becomes longer, and hence, the desorption temperature becomes higher. The shift of the concentration curves to the high temperature side with increasing chain length (fig. 1) is attributed to the increase of the total energy. The adsorption energies of N- and P-oriented SA molecules are about 0.1 eV and about 1 eV, respectively, while those of the CI-CuPc molecule are about 1 and 4 eV for N- and P-orientation, respectively. The large difference in the adsorption energies between the two substances justifies the difference in the growth mechanisms with respect to the molecular orientation, as mentioned in section 2. In the present interpretation, entropy terms have been disregarded. Although the value of % is generally 1013-1014 s 1 the present value was

1306

IL Saito et al. / Molecular energetics of growth mechanism of stearic acid

1.5 × 1016 s 1. T h e f a c t s h o w s t h a t a n S A m o l e c u l e m a y n o t b e t r e a t e d as a rigid molecule. Flexibility must be taken into account, leading to a contribut i o n f r o m t h e e n t r o p y t e r m for t h e s t a b i l i t y o f t h e m o l e c u l a r o r i e n t a t i o n . A m o r e d e t a i l e d i n v e s t i g a t i o n will b e n e e d e d f o r a c o m p l e t e e x p l a n a t i o n o f t h e growth mechanism.

Acknowledgement T h e a u t h o r s w o u l d s i n c e r e l y like to t h a n k University for valuable discussions.

Dr.

K.

Sato

of

Hiroshima

References [1] P.S. Vincett and G.G. Roberts, Thin Solid Films 68 (1980) 135. [2] A. Barrand, C. Rosilio and A. Ruaudel-Teixier, Solid State Technol. 22 (1979) 12/). [3] S.L. Buchner, V.K. Agarwal and C.H. Huang, in: Abstracts Annual Rept. Conf. on Electrical Insulation and Dielectric Phenomena, Buck Hill Falls, PA, 1983. [4] Y. Saito and M. Shiojiri, J. Crystal Growth 67 (1984) 91. [5] Y. Saito, Appl. Surface Sci. 22/23 (1985) 574. [6] F. Matsuzaki, K. Inaoka, M. Okada and K. Sato, J. Crystal Growth 69 (1984) 231. [7] Y. Uyeda and M. Ashida, J. Electron Microsc. 29 (1980) 38. [8] T. lnoue, K. Yase, K. Inaoka and M. Okada, J. Crystal Growth 83 (1987) 306. [9] W. Beckmann and R. Boistelle, J. Crystal Growth 67 (1984) 271. [10] V. Malta, G. Celoni, R. Zannetti and A.F. Martelli, J. Chem. Soc. (B) (1971) 548. [11] J.E. Lennard-Jones and B.M. Dent, Trans. Faraday Soc. 24 (1928) 92. [12] N. Bodor, M.J.S. Dewar, A. Harget and E. Haselbach, J. Am. Chem. Soc. 92 (1970) 3854. [13] H.L. Kramer and D.R. Herschbach, J. Chem. Phys. 55 (1970) 2792. [14] R.A. Scott and H.A. Scheraga, J. Chem. Phys. 42 (1965) 2209. [15] J.E. Mayer, J. Chem. Phys. 1 (1933) 270. [16] A. Bondi, J. Phys. Chem. 68 (1964) 441. [17] K.A. Mauritz, E. Baer and A.J. Hopfinger, J. Polymer Sci. 11 (1973) 2185. [18] K.A. Mauritz and A.J. Hopfinger, J. Polymer Sci. 13 (1975) 787. [19] A.A. Chernov, Modern Crystallograph III (Crystal Growth), Vol. 36 of Solid-State Sciences (Springer, Berlin, 1984).