- Email: [email protected]
Modification of SiO2 thickness distribution through evaporation
Accepted Manuscript Modification of SiO2 thickness distribution through evaporation
Xiumei Zhang, Xiaofeng Gu, Shaoqing Xiao PII: DOI: Reference:
S0040-6090(17)30685-5 doi: 10.1016/j.tsf.2017.09.018 TSF 36218
To appear in:
Thin Solid Films
Received date: Revised date: Accepted date:
9 December 2016 31 July 2017 9 September 2017
Please cite this article as: Xiumei Zhang, Xiaofeng Gu, Shaoqing Xiao , Modification of SiO2 thickness distribution through evaporation, Thin Solid Films (2017), doi: 10.1016/ j.tsf.2017.09.018
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Modification of SiO2 thickness distribution through evaporation
PT
Xiumei Zhang, Xiaofeng Gu1, Shaoqing Xiao
RI
Engineering Research Center of IoT Technology Applications (Ministry of Education),
AC
CE
PT E
D
MA
NU
SC
Department of Electronic Engineering, Jiangnan University, Wuxi 214122, China
1
Corresponding author. Email address: [email protected] 1
ACCEPTED MANUSCRIPT
Abstract: The electron beam deposition process of SiO2 thin film with large angle and wide aperture is dominated by self-shadowing effect, which deviates from the traditional thickness distribution model. In this paper we develop a modified model based on the traditional one and calculate the SiO2 relative thickness distribution in
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consideration of the self-shadowing effect. The deviations between the modified
RI
theoretical model and experimental data are largely reduced compared to that
SC
between the classical theory and experimental data. In comparison with the
NU
classical model, the mean deviation of the relative film thickness is reduced by 1.91%, the maximum deviation of the relative film thickness is decreased by
MA
2.38%, and the root mean square deviation of the relative film thickness is reduced by 2.05% in comparison with the classical model, suggesting that this modified
PT E
D
model is more accurate in describing the large angle and wide aperture deposition situations than the classical one. This study may provide a new way to modify the
CE
deposition thickness distribution under similar conditions.
AC
Keywords: self-shadowing effect; large aperture; optical thin film; packing density; uniformity
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1. Introduction The next generation space and ground optical telescopes require an optical system with high spatial resolution, which makes the aperture of the optical system get larger and larger.
T
This in turn draws higher demands on the quality of the optical thin film. A most crucial
IP
problem of the optical thin film is how to control the uniformity of the layer-thickness over
CR
a large area on a substrate. Poor uniformity with a typical wavelength shift may directly reduce the performance of the whole optical system [1-3].
US
The uniformity of the optical thin film is sensitive to a series of deposition conditions
AN
[4-6], such as chamber geometry, deposition rate, substrate temperature and so on. Holland and Steckelmacher [7] first conducted systematic studies on how to predict layer thickness
M
and uniformity. They established a theory which has been used in film uniformity
ED
predictions till today. Since then lots of studies on film thickness and uniformity have also been carried out and some other models have also been established [8-17].
PT
Both the deposition distance and the deposition angle between the evaporation source
CE
and the substrate increase gradually with the diameter of the coating instruments, so the vertical deposition is quite different for these two cases with small and large coating
AC
diameters. For the latter, the structure of the thin films can be taken as a few columns of approximate cylinders parallel to the incident growth direction. The approximate cylinders are usually of several tens of nanometers. With the growth of the thin films, the cylinders become higher and higher and the gaps between the cylindrical columns produce a self-shadowing effect which may further make the growth along the cylinders [18].
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The self-shadowing effect is an important factor responsible for the discrepancy between the calculations and experiments, and a lot of effort has been devoted to investigate this effect in various deposition process such as laser-focused atomic deposition [19] and glancing angle deposited thin films [20]. Due to the self-shadowing effect, the
IP
T
columnar microstructure is equivalent to a porous structure, thus making the packing
CR
density of the film less than 1 which prevent the growth from being of a continuous dense film. However, the skew directions of the cylindrical columns may vary in the cases with
US
different deposition flux angles [21]. This means that there may exist different packing densities at different positions of a wide aperture mirror. Therefore, the deposition process
AN
of SiO2 with large angle and wide aperture deviates greatly from the Holland and
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Steckelmacher’s classical model. In this work, the self-shadowing effect is introduced into
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the classical thickness distribution model for the evaporation deposition case with large angle. According to the classical relationship between the packing density, the deposition
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angle and the refractive index of the thin films, the modified model of layer thickness distribution is deduced. This modified model shows more accuracy and higher universality
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in describing the deposition process with large angle and wide aperture.
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2. Experimental details
SiO2 is chosen as the main evaporation source in this work. As one of the popularly used optical coating materials, it is very representative and has many excellent photoelectric properties such as low refractive index, wide transparent bandgap and high thermal and optical stabilities [22-24]. In fact, in this work, the modified model is actually an amendment on the deposition process and has no direct connection with the evaporation
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source. Large diameter deposition usually requires a flat substrate holder as shown in Fig. 1. Here, the horizontal distance from the evaporation source to the flat center point is described as D, and the distance from the deposition point to the flat center point is described as L. H is the vertical distance from the evaporation source to the substrate holder
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T
plane. The substrate holder diameter is described as X. is the angle between the normal
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direction of the deposition point and the connection of the source and the deposition point. φ is the angle between the normal direction of the evaporation source and the connection of
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the source and the deposition point. r is the distance between the source and the deposition
AN
point. Φ is the angle at which the q point has been rotated.
In this work, thin film was deposited in a wide aperture vacuum box coater with two
M
e-guns at room temperature. Here H is 1200 mm, X is 1600 mm and D is 950 mm. The
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deposition was monitored at a rate of about 0.4 nm/s by IC/6 deposition controller. The ion source was in the same horizontal plane with the evaporation source and the horizontal
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distance to the holder center was approximately 1600mm with a dip angle of about 230 as
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shown in Fig. 1 in our system.
The experiment for SiO2 evaporation was mainly contained two parts. For the first one,
AC
the film was deposited using a stationary substrate holder. In order to reduce the self-shadowing effect, the evaporation flux with a small incident angle θ was also adopted. The samples were positioned respectively away from the holder center with a distance of 0, 100, 200, 300, 400, 500, 600, 700 and 800 mm in horizontal direction. In this situation, the evaporation flux has a relatively small incident angle (even the largest incident angle is only 38° when the sample is at the holder center). So the self-shadowing effect has little
5
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influence and the classical model is still practical. The experiment in this part aims to obtain the characteristic parameters of evaporation source by the classical model. For the second part, the holder was set to rotate with different speeds to verify the modified model. In addition, TiO2 was used as another evaporation source to test the universality of the
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modified model. O2 ion beam assisted deposition was adopted because TiO2 was easy to
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lose oxygen during the evaporation process. The scattering ion O2- was single charge ion. The operating voltage of the ion source was set to be 180V. Under the ion assisted
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condition, the background vacuum was 2.0×10-2 Pa. The spatial distribution characteristics of evaporation source of TiO2 electron gun accorded with cos2.1φ and the beam distribution
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characteristic of ion source parameters accords with cos4.2φ.
3. Theory and calculation
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(Lambda 900 by Perkin Elmer).
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The transmittances of all the as-deposited films were measured by spectrophotometer
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The classical model of thickness distribution established by Holland and Steckelmacher
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is based on the assumptions as follows. 1. The molecules in the evaporation stream travel in a straight line until they collide with
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the substrate surface.
2. The evaporation speed of the source does not vary with time. 3. Every evaporation molecule adheres where it lands and the molecular collisions are ignored. As one can see in Fig. 1, the evaporation source can be taken as a point. Then the layer thickness distribution is usually described as follows:
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t C
cosn cos
(1)
r2
Here, φ, and r are all consistent with that described above in Fig. 1. C is a proportionality constant. For a flat substrate holder, the two angles φ and are the same. In addition,
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cosn is a parameter used to characterize the vapor emission characteristics of a vapor
source which is related to the evaporation rate of the evaporation source and the state of the
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material during evaporation.
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As the work piece aperture becomes larger, the deposition angle φ at lots of points may also become larger. In this case, both the inherent low surface diffusion of the material and
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the shadow effect may make the layer-by-layer structure prone to be cylindrical columns
M
[14]. The cylindrical columns and shadows would have a size distribution which may suppress the nucleation and growth within the gaps, as shown in Fig. 2. In this situation, the
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deposition process deviates greatly from the classical model because the third assumption
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mentioned above is no longer valid.
When considering the shadow effect, the relationship between the packing density p of
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the layer and the angle of deposition flux is expressed as follows: tan E 1 tan
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p
(2)
2
(3)
1 cos (1 ) cos
n (1 p )nv pns
(4)
Where β is the inclination angle of growth cylinder and E1 is a constant related to the intrinsic surface diffusion of material. Eq. (2) (tangent rule equation) is one of the earliest
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attempts to describe the relationship between incident angle and inclination angle of cylinder according to experimental data by Nieuwenhuizen (when E1=2) [25]. Eq. (4) is a very useful expression and it is reasonably accurate for layers with low refractive index. The refractive index of the layer n is related to the cylinder part ns and the void part nv.
IP
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Then, Φi is supposed as the amount of material emitted by the source at one moment and
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pi is the corresponding packing density of the layer at the same time. The relationship between the average packing density of the layer and the amount of emission material can
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be expressed as follows:
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i pi
p
i
i
M
2 1 ) cos i
cos i(1
cos i cos i
ri
2
CE
i C
(6)
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n
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pi
(5)
When the substrate holder is stationary, the layer thickness distribution is usually not
AC
uniform. A common method to improve the uniformity is to rotate the holder [26]. As the sample rotated to the position where it was the farthest away from the source, the deposition angle will become the largest one. In this case, the self-shadowing effect may dominate in the deposition process and influence both the thickness distribution and the refractive index of the as-deposited films.
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When the holder rotates at a constant speed, the packing density P of a point on a circumference in the rotating model can be approximated as the integral mean value of the packing density of every point over the entire circumference under the situation when the holder is stationary and it can be calculated as follows:
( ) d p( )
0
cos n cos
t t0
(7)
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T
( )d
0
0
d r 2p cos n 0 cos 0 r02 p 0
(8)
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0
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p
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Here, t/t0 represents the relative film thickness where t is the layer thickness at one point and t0 is the layer thickness at the substrate holder’s center. According to Fig. 1, the
r
H
2
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relationship between these parameters can be described as Eq. (9): L2 D 2 2DL cos
(9)
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cos cos H / r
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This modified model should be applicable to oblique angle deposition case which deviates
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from the classical model.
4. Results and discussion When using SiO2 as the evaporation source material, the values of the emission parameters of SiO2 were determined (C=3.5 and n=2.1) by fitting the thickness distribution based on a deposition process with stationary substrate because these parameters hardly change no matter the substrate is stationary or rotating. The deposition characteristics of the
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evaporation source SiO2 are presented in Fig. 3. As can be seen from Fig. 3(a), the date between theory and experiment can be in good agreement with each other especially when L is large. On the other hand, when L=0, the deposition angle is calculated to be about 380, and the corresponding P can be estimated to be about 95% by Eq. (3). At this situation, the
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film thickness distribution calculated by the classical model starts to be biased with the
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experimental data for the larger deposition incidence angle. In addition, from Fig. 3(a), we can see that the layer thickness distribution has a low uniformity.
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For the case using a rotated substrate holder at a speed of 0.5 r/min, the refractive indexes can be obtained by the transmittance of the samples at a wavelength of 550 nm and
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the results are shown in Fig. 3(b). Then, the actual average packing density and relative
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packing density can be calculated by Eq. 4 and Eq. 7, respectively. Here, the relative
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packing density is the ratio of layer packing density at a point to that at the holder center. Fig. 3(c) shows the relative packing densities obtained by both theory and experiment data.
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As shown in Fig. 3(c), there’s a slight difference between experiment results and simulation results according to our modified model. In particular, we find no difference in
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the variation trend of the refractive index between them. The packing density becomes
AC
much higher for the sample which is farther away from the holder center. Fig. 3(d) compares the relative thickness distribution between the experimental data, the classical model and our modified one. The curve of the modified model fits the experiment data very well, but the curve of the classical model deviates too much from the experimental data, indicating that the self-shadowing effect could not be ignored in such large-angle deposition.
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In order to be more intuitive, the relative thickness deviations including mean deviation, maximum deviation and root mean square deviation between the modified model and the experimental data are presented in table 1. For the modified model, the mean deviation of the relative film thickness is reduced by
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1.91%, the maximum deviation of the relative film thickness is decreased by 2.38%, and
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the root mean square deviation of the relative film thickness is reduced by 2.05% in comparison with the classical model. These results demonstrate that our modified model is
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sufficient to describe the real whole deposition process in large-angle deposition. In order to verify the modified model, the rotation speeds of 0.3, 1, 2, 3r/min were also
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employed for the case using SiO2 as the evaporation source. The results are shown in Fig. 4.
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As can be seen, all the curves of the modified model fit the experiment data very well no
ED
matter how the rotation speed changes. On another hand, for the case of the evaporation source TiO2, the deposition characteristics are presented in Fig. 5. When the current of the
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ion source was set to be 3A and the substrate holder was stationary, the relative thickness distribution according to the sample position was shown in Fig. 5(a). When the holder
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rotated at the speed of 0.5r/min, with the ion source of 1.5, 3, 4.5 and 6A respectively, the
AC
results were shown in Fig. 5(b). As can be seen from Fig. 5(a) and (b), the experimental results are in good agreement with theoretical simulations by our modified model no matter whether the holder rotates or remains stationary. All the above results further prove that the modified model is suitable to describe the thickness distribution in large-angle deposition.
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5. Conclusion A modified model considering the self-shadowing effect was developed for thin film deposition at large angle of incidence. The modified model is more accurate than the
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classical model in describing the SiO2 thickness distribution of large angle deposition
IP
process. The proposed method is a general approach that can be applied to large surface
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planetary rotation deposition systems as well as other shapes such as curved surfaces. This modified model also has the potential to provide an entirely new platform for probing and
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CE
PT
ED
M
AN
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designing uniformity masks in large and even glancing angle deposition coating processes.
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[2] S.R. Kennedy, M.J. Brett, O. Toader, S. John, Fabrication of Tetragonal square spiral
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photonic crystals, Nano Lett. 2 (1) (2002) 59-62.
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[3] J. Aizpurua, P. Hanarp, D.S. Sutherland, M. Kall, G.W. Bryant, G.d. Abajio, Optical properties of gold nanorings, Phys. Rev. Let. 90 (5) (2003) 057401.
US
[4] S.P. Bugaev, N.S. Sochugov, K.V. Oskomov, A.A. Solovjev, A.N. Zakharov,
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Improvement of coating deposition and target erosion uniformity in rotating cylindrical magnetrons, Laser Part. Beams 21 (2) (2003) 279-283.
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[5] K.S. Fancey, P.A. Robinson, A. Leyland, A.S. James, A. Matthews, A coating thickness
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uniformity model for physical vapor deposition systems—further validity tests, Mater Sci Engineering A Mat. Scoi. Eng. A-Struct 140 (91) (1991) 576-582.
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[6] J. Kim, B.J. Novick, J.M. DeSimone, R.G. Carbonell, Ultrathin film deposition by
642-657.
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liquid CO2 free meniscus coating-uniformity and morphology, Langmuir 22 (2) (2006)
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[7] L. Holland, B.S. W. Steckelmacher, The distribution of thin films condensed on surfaces by the vacuum evaporation method, Vacuum 2 (4) (1952) 346-364. [8] R. Dreu, B. Perpar, I. Zun, S. Srcic, Influence of hydrodynamic conditions in Wurster chamber on uniformity of the pellet film coating thickness, Eur. J. Pharm. Sci. 25 (2) (2005) S92-S94.
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[9] L.C. Zhang, X.K. Cai, Uniformity masks design method based on the shadow matrix for coating materials with different condensation characteristics, The Sci. World J. 2013 (10) (2013) 160792-160795. [10] M.M. Hawkeye, M.J. Brett, Glancing angle deposition: Fabrication, properties, and
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applications of micro- and nanostructured thin films, J. Vac. Sci. Technology A 25 (5）
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(2007) 1317-1335.
[11] Y. Kamimura, H. Okada, S. Naka, Evaluation of uniformity for organic film
US
evaporation using two dimensional different apertures, Vacuum 92 (3) (2013) 26-31. [12] M.O. Jensen, M.J. Brett, Square spiral 3D photonic bandgap crystals at
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telecommunications frequencies, Optics Express 13 (9) (2005) 3348-3354.
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[13] R.N. Tait, T. Smy, M.J. Brett, Modelling and characterization of columnar growth in
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evaporated films, Thin Solid Films 226 (226) (1993) 196-201. [14] E. Lee, Simulation of the thin-film thickness distribution for an OLED thermal
PT
evaporation process, Vacuum 83 (5) (2009) 848-852.
CE
[15] S.R. Kennedy, M.J. Brett, Porous broadband antireflection coating by glancing angle deposition, Appl. Optics 42 (22) (2003) 4573-4579.
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[16] M. Pelliccione, T.M. Lu, Evolution of thin film morphology : modeling and simulations, in: R. Hull， R. M. Osgood, Jr. J. Parisi， H. Warlimont (Eds.), Materials science, Springer New York, New York, 2008, pp. 6-8. [17] T.M. Lu, Y.P. Zhao, J.T. Drotar, T. Karabacak, G.C. Wang, Novel mechanisms on the growth morphology of films, Mat. Res. Soc. Symp. Proc. 749 (3) (2003) W1.2.1W1.2.6.
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[18] T. Karabacak, Thin-film growth dynamics with shadowing and re-emission effects, J. Nanophotonics 5 (1) (2011) 2501. [19] X. Deng, Y. Ma, P. Zhang, W. Zhang, S. Chen, S. Xiao, T. Li, Investigation of shadow effect in laser-focused atomic deposition, Appl. Surf. Sci. 261 (1) (2012) 464-469.
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[20] A. Dolatshahi‐Pirouz, Growth characteristics of glancing angle deposited (GLAD)
CR
thin films, Adv. Mat. Lett. 5 (11) (2014) 634-638.
[21] W.H. Lowdermilk, D. Milam, Graded‐index antireflection surfaces for high‐power
US
laser applications, Appl. Phy. Let. 36 (11) (1980) 891-893.
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[22] M. Krumrey, M. Hoffmann, G. Ulm, K. Hasche, P. Thomsen-Schmidt, Thickness determination for SiO2 films on Si by X-ray reflectometry at the Si K edge, Thin Solid
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Films 459 (1) (2004) 241-244.
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[23] Y. Lu, X.L. Li, X. Zhang, J.B. Wu, P.H. Tan, Optical contrast determination of the thickness of SiO 2 film on Si substrate partially covered by two-dimensional crystal
PT
flakes, Sci. Bull. 60 (8) (2015) 806-811.
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[24] K.J. Kim, K.T. Park, J.W. Lee, Thickness measurement of SiO2 films thinner than 1 nm by X-ray photoelectron spectroscopy, Thin Solid Films 500 (1) (2006) 356-359.
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[25] J. M. Nieuwenhuizen, H. B. Haanstra, Microfractography of thin films, Philips Tech. Rev. 27 (3/4) (1966) 87-91. [26] S.H. Chen, J.S. Liang, Y.J. Mo, D.F. Luo, S.J. Jiang, Onset of shadowing-dominated growth of Ag films in glancing angle deposition: Kinetic Monte Carlo simulation, Appl. Sur. Sci. 264 (4) (2013) 552-556.
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Figure caption Fig. 1 The schematic diagram of the evaporation system. Fig. 2 The schematic diagram of the self-shadowing effect in oblique deposition process. Fig. 3 The deposition characteristics of the evaporation source SiO2. (a) Normalized thickness
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distributions of SiO2 thin film. (b) Indexes of SiO2 thin film as a function of the deposition location.
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(c) The relative packing density of SiO2 thin film with the holder-rotation speed of 0.5r/min. (d) The
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relative thickness distribution of SiO2 thin film with the holder-rotation speed of 0.5r/min. Fig. 4 Relative thickness distribution of SiO2 thin film with different holder-rotation speeds.
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Fig. 5 The deposition characteristics of the evaporation source TiO2. (a) The relative thickness
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distribution of TiO2 thin film with stationary holder. (b) The relative thickness distribution of TiO2 thin film with rotating holder.
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Table caption
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CE
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Table 1. Comparison of the two theoretical models with SiO2 thin film evaporation.
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Fig. 1
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Fig. 2
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Fig. 3
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M
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Fig. 4
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Fig. 5
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Table 1
thickness deviation
The maximum
The root mean
deviation
square deviation 2.52%
2.06%
3.86%
Modified model
-0.15%
0.48%
AC
CE
PT
ED
M
AN
US
CR
Classical model
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The mean deviation
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Relative film
22
0.47%
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Highlights:
1. A modified model of thickness distribution was developed for thin film deposition. 2. The self-shadowing effect was taken into account by the modified model.
IP
T
3. Both experiments and theories are combined to derive the modified model.
AC
CE
PT
ED
M
AN
US
CR
4. The modified model is more accurate in describing large-angle deposition process.
23
Xiumei Zhang, Xiaofeng Gu, Shaoqing Xiao PII: DOI: Reference:
S0040-6090(17)30685-5 doi: 10.1016/j.tsf.2017.09.018 TSF 36218
To appear in:
Thin Solid Films
Received date: Revised date: Accepted date:
9 December 2016 31 July 2017 9 September 2017
Please cite this article as: Xiumei Zhang, Xiaofeng Gu, Shaoqing Xiao , Modification of SiO2 thickness distribution through evaporation, Thin Solid Films (2017), doi: 10.1016/ j.tsf.2017.09.018
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Modification of SiO2 thickness distribution through evaporation
PT
Xiumei Zhang, Xiaofeng Gu1, Shaoqing Xiao
RI
Engineering Research Center of IoT Technology Applications (Ministry of Education),
AC
CE
PT E
D
MA
NU
SC
Department of Electronic Engineering, Jiangnan University, Wuxi 214122, China
1
Corresponding author. Email address: [email protected] 1
ACCEPTED MANUSCRIPT
Abstract: The electron beam deposition process of SiO2 thin film with large angle and wide aperture is dominated by self-shadowing effect, which deviates from the traditional thickness distribution model. In this paper we develop a modified model based on the traditional one and calculate the SiO2 relative thickness distribution in
PT
consideration of the self-shadowing effect. The deviations between the modified
RI
theoretical model and experimental data are largely reduced compared to that
SC
between the classical theory and experimental data. In comparison with the
NU
classical model, the mean deviation of the relative film thickness is reduced by 1.91%, the maximum deviation of the relative film thickness is decreased by
MA
2.38%, and the root mean square deviation of the relative film thickness is reduced by 2.05% in comparison with the classical model, suggesting that this modified
PT E
D
model is more accurate in describing the large angle and wide aperture deposition situations than the classical one. This study may provide a new way to modify the
CE
deposition thickness distribution under similar conditions.
AC
Keywords: self-shadowing effect; large aperture; optical thin film; packing density; uniformity
2
ACCEPTED MANUSCRIPT
1. Introduction The next generation space and ground optical telescopes require an optical system with high spatial resolution, which makes the aperture of the optical system get larger and larger.
T
This in turn draws higher demands on the quality of the optical thin film. A most crucial
IP
problem of the optical thin film is how to control the uniformity of the layer-thickness over
CR
a large area on a substrate. Poor uniformity with a typical wavelength shift may directly reduce the performance of the whole optical system [1-3].
US
The uniformity of the optical thin film is sensitive to a series of deposition conditions
AN
[4-6], such as chamber geometry, deposition rate, substrate temperature and so on. Holland and Steckelmacher [7] first conducted systematic studies on how to predict layer thickness
M
and uniformity. They established a theory which has been used in film uniformity
ED
predictions till today. Since then lots of studies on film thickness and uniformity have also been carried out and some other models have also been established [8-17].
PT
Both the deposition distance and the deposition angle between the evaporation source
CE
and the substrate increase gradually with the diameter of the coating instruments, so the vertical deposition is quite different for these two cases with small and large coating
AC
diameters. For the latter, the structure of the thin films can be taken as a few columns of approximate cylinders parallel to the incident growth direction. The approximate cylinders are usually of several tens of nanometers. With the growth of the thin films, the cylinders become higher and higher and the gaps between the cylindrical columns produce a self-shadowing effect which may further make the growth along the cylinders [18].
3
ACCEPTED MANUSCRIPT
The self-shadowing effect is an important factor responsible for the discrepancy between the calculations and experiments, and a lot of effort has been devoted to investigate this effect in various deposition process such as laser-focused atomic deposition [19] and glancing angle deposited thin films [20]. Due to the self-shadowing effect, the
IP
T
columnar microstructure is equivalent to a porous structure, thus making the packing
CR
density of the film less than 1 which prevent the growth from being of a continuous dense film. However, the skew directions of the cylindrical columns may vary in the cases with
US
different deposition flux angles [21]. This means that there may exist different packing densities at different positions of a wide aperture mirror. Therefore, the deposition process
AN
of SiO2 with large angle and wide aperture deviates greatly from the Holland and
M
Steckelmacher’s classical model. In this work, the self-shadowing effect is introduced into
ED
the classical thickness distribution model for the evaporation deposition case with large angle. According to the classical relationship between the packing density, the deposition
PT
angle and the refractive index of the thin films, the modified model of layer thickness distribution is deduced. This modified model shows more accuracy and higher universality
CE
in describing the deposition process with large angle and wide aperture.
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2. Experimental details
SiO2 is chosen as the main evaporation source in this work. As one of the popularly used optical coating materials, it is very representative and has many excellent photoelectric properties such as low refractive index, wide transparent bandgap and high thermal and optical stabilities [22-24]. In fact, in this work, the modified model is actually an amendment on the deposition process and has no direct connection with the evaporation
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source. Large diameter deposition usually requires a flat substrate holder as shown in Fig. 1. Here, the horizontal distance from the evaporation source to the flat center point is described as D, and the distance from the deposition point to the flat center point is described as L. H is the vertical distance from the evaporation source to the substrate holder
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plane. The substrate holder diameter is described as X. is the angle between the normal
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direction of the deposition point and the connection of the source and the deposition point. φ is the angle between the normal direction of the evaporation source and the connection of
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the source and the deposition point. r is the distance between the source and the deposition
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point. Φ is the angle at which the q point has been rotated.
In this work, thin film was deposited in a wide aperture vacuum box coater with two
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e-guns at room temperature. Here H is 1200 mm, X is 1600 mm and D is 950 mm. The
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deposition was monitored at a rate of about 0.4 nm/s by IC/6 deposition controller. The ion source was in the same horizontal plane with the evaporation source and the horizontal
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distance to the holder center was approximately 1600mm with a dip angle of about 230 as
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shown in Fig. 1 in our system.
The experiment for SiO2 evaporation was mainly contained two parts. For the first one,
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the film was deposited using a stationary substrate holder. In order to reduce the self-shadowing effect, the evaporation flux with a small incident angle θ was also adopted. The samples were positioned respectively away from the holder center with a distance of 0, 100, 200, 300, 400, 500, 600, 700 and 800 mm in horizontal direction. In this situation, the evaporation flux has a relatively small incident angle (even the largest incident angle is only 38° when the sample is at the holder center). So the self-shadowing effect has little
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influence and the classical model is still practical. The experiment in this part aims to obtain the characteristic parameters of evaporation source by the classical model. For the second part, the holder was set to rotate with different speeds to verify the modified model. In addition, TiO2 was used as another evaporation source to test the universality of the
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modified model. O2 ion beam assisted deposition was adopted because TiO2 was easy to
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lose oxygen during the evaporation process. The scattering ion O2- was single charge ion. The operating voltage of the ion source was set to be 180V. Under the ion assisted
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condition, the background vacuum was 2.0×10-2 Pa. The spatial distribution characteristics of evaporation source of TiO2 electron gun accorded with cos2.1φ and the beam distribution
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characteristic of ion source parameters accords with cos4.2φ.
3. Theory and calculation
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(Lambda 900 by Perkin Elmer).
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The transmittances of all the as-deposited films were measured by spectrophotometer
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The classical model of thickness distribution established by Holland and Steckelmacher
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is based on the assumptions as follows. 1. The molecules in the evaporation stream travel in a straight line until they collide with
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the substrate surface.
2. The evaporation speed of the source does not vary with time. 3. Every evaporation molecule adheres where it lands and the molecular collisions are ignored. As one can see in Fig. 1, the evaporation source can be taken as a point. Then the layer thickness distribution is usually described as follows:
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t C
cosn cos
(1)
r2
Here, φ, and r are all consistent with that described above in Fig. 1. C is a proportionality constant. For a flat substrate holder, the two angles φ and are the same. In addition,
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cosn is a parameter used to characterize the vapor emission characteristics of a vapor
source which is related to the evaporation rate of the evaporation source and the state of the
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material during evaporation.
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As the work piece aperture becomes larger, the deposition angle φ at lots of points may also become larger. In this case, both the inherent low surface diffusion of the material and
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the shadow effect may make the layer-by-layer structure prone to be cylindrical columns
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[14]. The cylindrical columns and shadows would have a size distribution which may suppress the nucleation and growth within the gaps, as shown in Fig. 2. In this situation, the
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deposition process deviates greatly from the classical model because the third assumption
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mentioned above is no longer valid.
When considering the shadow effect, the relationship between the packing density p of
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the layer and the angle of deposition flux is expressed as follows: tan E 1 tan
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p
(2)
2
(3)
1 cos (1 ) cos
n (1 p )nv pns
(4)
Where β is the inclination angle of growth cylinder and E1 is a constant related to the intrinsic surface diffusion of material. Eq. (2) (tangent rule equation) is one of the earliest
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attempts to describe the relationship between incident angle and inclination angle of cylinder according to experimental data by Nieuwenhuizen (when E1=2) [25]. Eq. (4) is a very useful expression and it is reasonably accurate for layers with low refractive index. The refractive index of the layer n is related to the cylinder part ns and the void part nv.
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Then, Φi is supposed as the amount of material emitted by the source at one moment and
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pi is the corresponding packing density of the layer at the same time. The relationship between the average packing density of the layer and the amount of emission material can
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i pi
p
i
i
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2 1 ) cos i
cos i(1
cos i cos i
ri
2
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i C
(6)
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n
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pi
(5)
When the substrate holder is stationary, the layer thickness distribution is usually not
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uniform. A common method to improve the uniformity is to rotate the holder [26]. As the sample rotated to the position where it was the farthest away from the source, the deposition angle will become the largest one. In this case, the self-shadowing effect may dominate in the deposition process and influence both the thickness distribution and the refractive index of the as-deposited films.
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When the holder rotates at a constant speed, the packing density P of a point on a circumference in the rotating model can be approximated as the integral mean value of the packing density of every point over the entire circumference under the situation when the holder is stationary and it can be calculated as follows:
( ) d p( )
0
cos n cos
t t0
(7)
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( )d
0
0
d r 2p cos n 0 cos 0 r02 p 0
(8)
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p
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Here, t/t0 represents the relative film thickness where t is the layer thickness at one point and t0 is the layer thickness at the substrate holder’s center. According to Fig. 1, the
r
H
2
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relationship between these parameters can be described as Eq. (9): L2 D 2 2DL cos
(9)
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cos cos H / r
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This modified model should be applicable to oblique angle deposition case which deviates
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from the classical model.
4. Results and discussion When using SiO2 as the evaporation source material, the values of the emission parameters of SiO2 were determined (C=3.5 and n=2.1) by fitting the thickness distribution based on a deposition process with stationary substrate because these parameters hardly change no matter the substrate is stationary or rotating. The deposition characteristics of the
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evaporation source SiO2 are presented in Fig. 3. As can be seen from Fig. 3(a), the date between theory and experiment can be in good agreement with each other especially when L is large. On the other hand, when L=0, the deposition angle is calculated to be about 380, and the corresponding P can be estimated to be about 95% by Eq. (3). At this situation, the
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film thickness distribution calculated by the classical model starts to be biased with the
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experimental data for the larger deposition incidence angle. In addition, from Fig. 3(a), we can see that the layer thickness distribution has a low uniformity.
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For the case using a rotated substrate holder at a speed of 0.5 r/min, the refractive indexes can be obtained by the transmittance of the samples at a wavelength of 550 nm and
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the results are shown in Fig. 3(b). Then, the actual average packing density and relative
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packing density can be calculated by Eq. 4 and Eq. 7, respectively. Here, the relative
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packing density is the ratio of layer packing density at a point to that at the holder center. Fig. 3(c) shows the relative packing densities obtained by both theory and experiment data.
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As shown in Fig. 3(c), there’s a slight difference between experiment results and simulation results according to our modified model. In particular, we find no difference in
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the variation trend of the refractive index between them. The packing density becomes
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much higher for the sample which is farther away from the holder center. Fig. 3(d) compares the relative thickness distribution between the experimental data, the classical model and our modified one. The curve of the modified model fits the experiment data very well, but the curve of the classical model deviates too much from the experimental data, indicating that the self-shadowing effect could not be ignored in such large-angle deposition.
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In order to be more intuitive, the relative thickness deviations including mean deviation, maximum deviation and root mean square deviation between the modified model and the experimental data are presented in table 1. For the modified model, the mean deviation of the relative film thickness is reduced by
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1.91%, the maximum deviation of the relative film thickness is decreased by 2.38%, and
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the root mean square deviation of the relative film thickness is reduced by 2.05% in comparison with the classical model. These results demonstrate that our modified model is
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sufficient to describe the real whole deposition process in large-angle deposition. In order to verify the modified model, the rotation speeds of 0.3, 1, 2, 3r/min were also
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employed for the case using SiO2 as the evaporation source. The results are shown in Fig. 4.
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As can be seen, all the curves of the modified model fit the experiment data very well no
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matter how the rotation speed changes. On another hand, for the case of the evaporation source TiO2, the deposition characteristics are presented in Fig. 5. When the current of the
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ion source was set to be 3A and the substrate holder was stationary, the relative thickness distribution according to the sample position was shown in Fig. 5(a). When the holder
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rotated at the speed of 0.5r/min, with the ion source of 1.5, 3, 4.5 and 6A respectively, the
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results were shown in Fig. 5(b). As can be seen from Fig. 5(a) and (b), the experimental results are in good agreement with theoretical simulations by our modified model no matter whether the holder rotates or remains stationary. All the above results further prove that the modified model is suitable to describe the thickness distribution in large-angle deposition.
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5. Conclusion A modified model considering the self-shadowing effect was developed for thin film deposition at large angle of incidence. The modified model is more accurate than the
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classical model in describing the SiO2 thickness distribution of large angle deposition
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process. The proposed method is a general approach that can be applied to large surface
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planetary rotation deposition systems as well as other shapes such as curved surfaces. This modified model also has the potential to provide an entirely new platform for probing and
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designing uniformity masks in large and even glancing angle deposition coating processes.
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References [1] M. Gu, X. Li, Y. Cao, Optical storage arrays: a perspective for future big data storage, Light-Sci. Appl. 3 (5) (2014) e177.
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[2] S.R. Kennedy, M.J. Brett, O. Toader, S. John, Fabrication of Tetragonal square spiral
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photonic crystals, Nano Lett. 2 (1) (2002) 59-62.
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[3] J. Aizpurua, P. Hanarp, D.S. Sutherland, M. Kall, G.W. Bryant, G.d. Abajio, Optical properties of gold nanorings, Phys. Rev. Let. 90 (5) (2003) 057401.
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[4] S.P. Bugaev, N.S. Sochugov, K.V. Oskomov, A.A. Solovjev, A.N. Zakharov,
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Improvement of coating deposition and target erosion uniformity in rotating cylindrical magnetrons, Laser Part. Beams 21 (2) (2003) 279-283.
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[5] K.S. Fancey, P.A. Robinson, A. Leyland, A.S. James, A. Matthews, A coating thickness
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[6] J. Kim, B.J. Novick, J.M. DeSimone, R.G. Carbonell, Ultrathin film deposition by
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liquid CO2 free meniscus coating-uniformity and morphology, Langmuir 22 (2) (2006)
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[7] L. Holland, B.S. W. Steckelmacher, The distribution of thin films condensed on surfaces by the vacuum evaporation method, Vacuum 2 (4) (1952) 346-364. [8] R. Dreu, B. Perpar, I. Zun, S. Srcic, Influence of hydrodynamic conditions in Wurster chamber on uniformity of the pellet film coating thickness, Eur. J. Pharm. Sci. 25 (2) (2005) S92-S94.
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[9] L.C. Zhang, X.K. Cai, Uniformity masks design method based on the shadow matrix for coating materials with different condensation characteristics, The Sci. World J. 2013 (10) (2013) 160792-160795. [10] M.M. Hawkeye, M.J. Brett, Glancing angle deposition: Fabrication, properties, and
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applications of micro- and nanostructured thin films, J. Vac. Sci. Technology A 25 (5）
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[11] Y. Kamimura, H. Okada, S. Naka, Evaluation of uniformity for organic film
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evaporation using two dimensional different apertures, Vacuum 92 (3) (2013) 26-31. [12] M.O. Jensen, M.J. Brett, Square spiral 3D photonic bandgap crystals at
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telecommunications frequencies, Optics Express 13 (9) (2005) 3348-3354.
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[13] R.N. Tait, T. Smy, M.J. Brett, Modelling and characterization of columnar growth in
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evaporated films, Thin Solid Films 226 (226) (1993) 196-201. [14] E. Lee, Simulation of the thin-film thickness distribution for an OLED thermal
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evaporation process, Vacuum 83 (5) (2009) 848-852.
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[15] S.R. Kennedy, M.J. Brett, Porous broadband antireflection coating by glancing angle deposition, Appl. Optics 42 (22) (2003) 4573-4579.
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[16] M. Pelliccione, T.M. Lu, Evolution of thin film morphology : modeling and simulations, in: R. Hull， R. M. Osgood, Jr. J. Parisi， H. Warlimont (Eds.), Materials science, Springer New York, New York, 2008, pp. 6-8. [17] T.M. Lu, Y.P. Zhao, J.T. Drotar, T. Karabacak, G.C. Wang, Novel mechanisms on the growth morphology of films, Mat. Res. Soc. Symp. Proc. 749 (3) (2003) W1.2.1W1.2.6.
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[18] T. Karabacak, Thin-film growth dynamics with shadowing and re-emission effects, J. Nanophotonics 5 (1) (2011) 2501. [19] X. Deng, Y. Ma, P. Zhang, W. Zhang, S. Chen, S. Xiao, T. Li, Investigation of shadow effect in laser-focused atomic deposition, Appl. Surf. Sci. 261 (1) (2012) 464-469.
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[20] A. Dolatshahi‐Pirouz, Growth characteristics of glancing angle deposited (GLAD)
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thin films, Adv. Mat. Lett. 5 (11) (2014) 634-638.
[21] W.H. Lowdermilk, D. Milam, Graded‐index antireflection surfaces for high‐power
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laser applications, Appl. Phy. Let. 36 (11) (1980) 891-893.
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[22] M. Krumrey, M. Hoffmann, G. Ulm, K. Hasche, P. Thomsen-Schmidt, Thickness determination for SiO2 films on Si by X-ray reflectometry at the Si K edge, Thin Solid
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Films 459 (1) (2004) 241-244.
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[23] Y. Lu, X.L. Li, X. Zhang, J.B. Wu, P.H. Tan, Optical contrast determination of the thickness of SiO 2 film on Si substrate partially covered by two-dimensional crystal
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flakes, Sci. Bull. 60 (8) (2015) 806-811.
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[24] K.J. Kim, K.T. Park, J.W. Lee, Thickness measurement of SiO2 films thinner than 1 nm by X-ray photoelectron spectroscopy, Thin Solid Films 500 (1) (2006) 356-359.
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[25] J. M. Nieuwenhuizen, H. B. Haanstra, Microfractography of thin films, Philips Tech. Rev. 27 (3/4) (1966) 87-91. [26] S.H. Chen, J.S. Liang, Y.J. Mo, D.F. Luo, S.J. Jiang, Onset of shadowing-dominated growth of Ag films in glancing angle deposition: Kinetic Monte Carlo simulation, Appl. Sur. Sci. 264 (4) (2013) 552-556.
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Figure caption Fig. 1 The schematic diagram of the evaporation system. Fig. 2 The schematic diagram of the self-shadowing effect in oblique deposition process. Fig. 3 The deposition characteristics of the evaporation source SiO2. (a) Normalized thickness
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distributions of SiO2 thin film. (b) Indexes of SiO2 thin film as a function of the deposition location.
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(c) The relative packing density of SiO2 thin film with the holder-rotation speed of 0.5r/min. (d) The
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relative thickness distribution of SiO2 thin film with the holder-rotation speed of 0.5r/min. Fig. 4 Relative thickness distribution of SiO2 thin film with different holder-rotation speeds.
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Fig. 5 The deposition characteristics of the evaporation source TiO2. (a) The relative thickness
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distribution of TiO2 thin film with stationary holder. (b) The relative thickness distribution of TiO2 thin film with rotating holder.
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Table caption
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Table 1. Comparison of the two theoretical models with SiO2 thin film evaporation.
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Fig. 1
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Fig. 2
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Fig. 3
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Fig. 4
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Fig. 5
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Table 1
thickness deviation
The maximum
The root mean
deviation
square deviation 2.52%
2.06%
3.86%
Modified model
-0.15%
0.48%
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Classical model
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The mean deviation
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Highlights:
1. A modified model of thickness distribution was developed for thin film deposition. 2. The self-shadowing effect was taken into account by the modified model.
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3. Both experiments and theories are combined to derive the modified model.
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4. The modified model is more accurate in describing large-angle deposition process.
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