4-1 Summary
The current study carries out the simulations of electron beam physical vapor deposition using direct simulation Monte Carlo method. Due to the demand for highly vacuum environment, background pressure is an important factor that it is worthy to study the effects on the deposited reaction. In the chapter three, we show the reactions and results that the background pressure is considered. It seems that the results correspond to our previous expectations that the depositions are steadier when environment is rare in the chamber. We can verify from the uniformity discussions.
Another subject in this study is uniformity of composition and thickness by changing some parameters. These parameters we adjust are the altitude of substrate, background pressure and distance between the sources. As the EBPVD theorem saying that we can obtain uniform composition and thickness by mixing the evaporated atoms well.
The major findings of the current research are summarized as follows:
1. The tendency of simulated flux distribution will be toward the cosθ distribution as d/λ0 decreases approaching zero.
2. Background gas will cause the appearance of shock wave phenomena. It is a significant factor that will influence the properties of flow field in the chamber.
3. If there is background gas in the chamber, the number of deposited particle on the substrate is less.
4. The particles’ energy is larger in the vacuum condition, but incident angle is almost the same compared with the environment of rare flow field.
5. It will obtain better uniformity of composition at appropriate distance between the source and substrate.
6. To compare with each other under the circumstance of high vacuum environment, the uniformity will have minor differences.
7. As increasing the distance between the sources, the composition of Al and V will exceed the upper bound of composition of Ti6Al4V gradually.
4-2 Recommendation
As completing simulation condition described above, we can work further for the following items:
(1) To change different combinations of temperature of three evaporants, comparing the uniformity of composition and thickness.
(2) In order to simulate the reactions between atoms close to the realistic condition, variable soft sphere model is recommended.
(3) To modify uniform temperature on the source with source temperature distribution.
(4) The effect of recondensation on evaporation rate makes influences on uniformity.
(5) Cluster growth process.
(6) Experimental data used for verifying the simulation results.
References
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[2] Bakish, R., editor. Proc. Electron Beam Melting and Refining State of the Art, Reno, Nevada, October 1995. Bakish Materials Corporation.
[3] Bellot, J. P., Hess, E., Hans, S. and Ablitzer, D., “A Comprehensive Simulation of the Electron Beam Cold Hearth Refining of Titanium Alloy”, In Alec Mitchell and Philippe Auburtin, editors, Proc. 1997 Int’l. Symp. on Liquid Metal Processing and Casting, pp. 166-187, Santa Fe, February 1997. American Vacuum Society.
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[5] Bird, G. A., “Molecular Gas Dynamics and the Direct Simulation of Gas Flows”, Oxford University Press, New York, 1994.
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405-420, 1975.
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[8] Boyd, I. D., “Conservative Species Weighting Scheme for the Direct Simulation
Monte Carlo Method”, Journal of Thermophysics and Heat Transfer, 10, pp. 579-585, 1996.
[9] Brandes, E., editor, “Smithells Metals Reference Book”, Butterworth & Co., Boston, sixth edition, 1983.
[10] Cron, M. and Adams, C. M., “Controlled Electron Beam Co-Deposition of Copper Nickel Films”, Journal of Materials Science, 4, pp. 252-258, 1969.
[11] DeMasi-Marcin, J. T. and Gupta, D. K., “Protective Coatings in the Gas Turbine Engine”, Surface and Coatings Technology, 68/69, pp. 1-9, 1994.
[12] Fan, J., Boyd, I. D. and Shelton, C., “Monte Carlo Modeling of Electron Beam Physical Vapor Deposition of Yttrium”, Journal of Vacuum Science and Technology A, 18, pp. 2937-2945, 2000.
[13] Gilbaud, D., “Effect of Melt Surface Depression on the Vaporization Rate of a Metal Heated by an Electron Beam”, In R. Bakish, editor, Proc. Electron Beam Melting and Refining State of the Art, pp. 227-242, Reno, Nevada, November 1995. Bakish Materials Corporation.
[14] Hass, D. D., Marciano, Y. and Wadley, H. N. G., “Physical Vapor Deposition on Cylindrical Substrates”, Surface and Coatings Technology, 185, pp.283-291, 2004.
[15] Hideo NAKAMURA and Alec MITCHELL, “The Effect of Beam Oscillation Rate on Al Evaporation from a Ti-6Al-4V Alloy in the Electron Beam Melting Process”, ISIJ International, 32, pp. 583-592, 1992.
[16] Hiroshi KANAYAMA, Tatsuhiko KUSAMICHI, Tetsuhiro MURAOKA, Toshio ONOUYE and Takashi NISHIMURA, “Electron Beam Melting of Sponge Titanium”, ISIJ International, 31, pp. 906-914, 1991.
[17] Kannenberg, K. and Boyd, I. D., “Strategies for Efficient Particle Resolution in the Direct Simulation Monte Carlo Method”, Journal of Computational Physics, 157, pp.
727-745, 2000.
[18] Lian, Y.-Y., “Parallel Three-Dimensional Direct Simulation Monte Carlo Method and Its Applications”, Mechanical Engineering, National Chiao-Tung University, Taiwan, Master Thesis, 2001.
[19] Powell, A. C., “Transport Phenomena in Electron Beam Melting and Evaporation”, Massachusetts Institute of Technology, Department of Materials Science and Engineering, Ph.D thesis, 1997.
[20] Powell, A., Minson, P., Trapaga, G. and Pal, U., “Mathematical Modeling of Vapor-Plume Focusing in Electron-Beam Evaporation”, Metallurgical and Materials Transactions, 32A, pp. 1959-1966, 2001.
[21] Schiller, S., Heisig, U. and Panzer, S., “Electron Beam Technology”, John Wiley &
Sons, New York, 1982.
[22] Schulz, U., Fritscher, K. and Peters, M., “EB-PVD Y2O3- and CeO2/Y2O3- Stabilized Zirconia Thermal Barrier Coatings — Crystal Habit and Phase Composition”, Surface and Coatings Technology, 82, pp. 259-269, 1995.
[23] Stohr, J. A., “Vacuum Welding by Electron Beam”, Nuclear Power, 3, pp. 272-274, 1958.
[24] Storer, J., “Electron Beam Deposition for the Fabrication of Titanium MMCs”, In R.
Bakish, editor, Proc. Electron Beam Melting and Refining State of the Art, pp.
235-245, Reno, Nevada, November 1993. Bakish Materials Corporation.
[25] Storer, J., “Update on Metal Matrix Composites Produced by Electron Beam
Evaporation”, In R. Bakish, editor, Proc. Electron Beam Melting and Refining State of the Art, pp. 177-181, Reno, Nevada, November 1996. Bakish Materials Corporation.
[26] Tran Kong, T. and Bird, G. A., “One-Dimensional Outgassing Problem”, Physics of Fluids, 21, pp. 327-333, 1978.
[27] Tripp, D., Cockcroft, S. and Mitchell, A., “The Effect of Pressure on Power Transfer in Electron Beam Remelting”, In R. Bakish, editor, Proc. Electron Beam Melting and Refining State of the Art, pp. 127-138, Reno, Nevada, November 1993. Bakish Materials Corporation.
[28] Tomoo ISAWA, Hideo NAKAMURA and Katsuhiko MURAKAMI, “Aluminum Evaporation from Titanium Alloys in EB Heart Melting Process”, ISIJ International, 32, pp. 607-615, 1992.
[29] Tseng, K.-C., “Analysis of Micro-scale Gas Flows with Pressure Boundaries Using the Direct Simulation Monte Carlo Method”, Mechanical Engineering, National Chiao-Tung University, Taiwan, Master Thesis, 2000.
[30] Wadley, H.N.G. and Groves, J. F., “Monte Carlo Modeling of Atom Transport During Directed Vapor Deposition”, Materials Research Society Symposium - Proceedings, Thin Films - Structure and Morphology, 441, pp. 541-548, 1997.
[31] Wolf, S. and Rauber, R. N., “Process Technology”, Volume 1 of Silicon Processing for the VLSI Era, Lattice Press, Sunset Beach, 1986.
[32] Wu, J.-S. and Hsu Y.-L., “Derivation of Variable Soft Sphere Model Parameters in Direct-Simulation Monte Carlo Method Using Quantum Chemistry Computation”, Japanese Journal of Applied Physics, 42, pp. 7574-7575, 2003.
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[35] http://www.azom.com/details.asp?ArticleID=1547
Appendix A
The Peclet number for heat transfer is derived from the ratio of convective to conductive terms in the energy equation, and thus gives a rough measure of which is more important in a heat transfer problem. When it is much less than one, conduction can be said to dominate; when much greater than one, convection is more important. Because the ratio of interest is that of horizontal convection to vertical conduction, the following modified version of the Peclet number is proposed:
α horizontal and vertical length scales of the problem. The horizontal length scale is the spot radius, and the vertical length scale can be approximated by the penetration depth of temperature fluctuations given by
∆z
/ f 2 α .
To approximate transient surface velocity, one must use the expression for Marangoni shear τ due to the temperature rise near the beam given by zx
x
where σ here is the surface tension and the temperature gradient is approximated as the maximum centerline temperature rise ∆Tmax(given by equation A.10, appendix B) divided by spot radius. One may then apply the constant flux diffusion equation solution from appendix B (equation A.8) to fluid flow, where momentum flux is given by shear τ , which gives
⎥⎥
Using the beam dwell time as our reference time, the surface velocity will simply be
Inserting the shear stress given by equation A.2 into this velocity expression, and the resulting velocity into equation A.1, giving the conclusion
Rf
Appendix B
To estimate the temperature rise during the dwell time of the beam, one can solve the one-dimensional heat conduction equation
cp
The beam is treated as a constant heat source with surface flux 0 2 R pattern length and the scan frequency. Therefore, the maximum surface temperature rise along the beam centerline is
f
Because this expression does not consider the gaussian nature of the beam, and does not account for radiative and evaporative heat losses, it is an overestimate of the
Tables
Table I. The properties of Ti, Al, V.
Name, Symbol, Number titanium, Ti, 22 aluminum, Al, 13 vanadium, V, 23 Group, Period, Block 4, 4, d 13, 3, p 5, 4, d
Crystal structure hexagonal cubic face centered cubic body centered
Atomic radius 140 pm 125 pm 135 pm
Atomic mass 47.867 g/mol 26.9815386 g/mol 50.9415 g/mol
Density 4.506 g/cm³ 2.70 g/cm³ 6.0 g/cm³
Electron configuration [Ar] 3d2 4s2 [Ne] 3s2 3p1 [Ar] 3d3 4s2
Melting point 1941 K 933.47 K 2183 K
Phase solid solid solid
Table II. The composition of Ti6Al4V
CONTENT C <0.08%
Fe <0.25%
N2 <0.05%
O2 <0.2%
Al 5.5-6.76%
V 3.5-4.5%
H2(sheet) <0.015%
H2(bar) <0.0125%
H2(billet) <0.01%
Ti Balance
Table III. Typical physical properties for Ti6Al4V.
PROPERTY TYPICAL VALUE
Density g/cm3 (lb/ cu in) 4.42 (0.159)
Melting Range °C±15°C (°F) 1649 (3000)
Specific Heat J/kg.°C (BTU/lb/°F) 560 (0.134) Volume Electrical Resistivity ohm.cm (ohm.in) 170 (67) Thermal Conductivity W/m.K (BTU/ft.h.°F) 7.2 (67) Mean Co-Efficient of Thermal Expansion 0-100°C /°C
(0-212°F /°F)
8.6x10-6 (4.8)
Mean Co-Efficient of Thermal Expansion 0-300°C /°C (0-572°F /°F)
9.2x10-6 (5.1)
Beta Transus °C±15°C (°F) 999 (1830)
Table IV. Typical mechanical properties for Ti6Al4V.
PROPERTY MINIMUM TYPICAL VALUE
Tensile Strength MPa (ksi) 897 (130) 1000 (145) 0.2% Proof Stress MPa (ksi) 828 (120) 910 (132)
Elongation Over 2 Inches % 10 18
Reduction in Area % 20
Elastic Modulus GPa (Msi) 114 (17)
Hardness Rockwell C 36
Specified Bend Radius <0.070 in x Thickness 4.5 Specified Bend Radius >0.070 in x Thickness 5.0 Welded Bend Radius x Thickness 6
Charpy, V-Notch Impact J (ft.lbf) 24 (18)
Table V. The relevant values of Ti6Al4V compared with different altitude of the substrate: (a) 10 cm ; (b) 27.5 cm ; (c) 40 cm.
Maximum Minimum Average Acceptable ratio
Ti 0.8969262 0.8895243 0.8930359 0.5166667
Al 6.7761280E-02 6.3346483E-02 6.5553702E-02 0.4500000
V 4.2944506E-02 3.9722294E-02 4.1410439E-02 0.6333333
Thickness(nm) 30.143852 15.649038 21.236644 0.5500000 (a)
Maximum Minimum Average Acceptable ratio
Ti 0.8999392 0.8952078 0.8975889 0.8833333
Al 6.4780384E-02 6.1212711E-02 6.2680699E-02 0.8166667
V 4.1203082E-02 3.7962511E-02 3.9730396E-02 0.7500000
Thickness(nm) 4.6865596 3.1084202 3.7459880 0.7000000 (b)
Maximum Minimum Average Acceptable ratio
Ti 0.9018313 0.8946580 0.8975435 0.8500000
Al 6.5985218E-02 5.9271228E-02 6.2852316E-02 0.5833333
V 4.1586936E-02 3.7352987E-02 3.9604116E-02 0.6166667
Thickness(nm) 2.2513418 1.5063452 1.8192412 0.7833334 (c)
Table VI. The relevant values of Ti6Al4V compared with different pressure in the chamber: (a) 5×10−5 torr ; (b) 5×10−6 torr ; (c) vacuum.
Maximum Minimum Average Acceptable ratio
Ti 0.8994763 0.8944911 0.8974000 0.8500000
Al 6.5057889E-02 6.0450226E-02 6.2877662E-02 0.6833333 V 4.1000150E-02 3.7529990E-02 3.9722379E-02 0.7666667 Thickness(nm) 4.7098676 3.0981182 3.7469472 0.6833333
(a)
Maximum Minimum Average Acceptable ratio
Ti 0.9016619 0.8949397 0.8976156 0.8833333
Al 6.5159686E-02 6.0712483E-02 6.2711656E-02 0.7666667 V 4.1075449E-02 3.7580859E-02 3.9672747E-02 0.7166666 Thickness(nm) 4.6932973 3.1256890 3.7502526 0.7000000
(b)
Maximum Minimum Average Acceptable ratio
Ti 0.9004977 0.8945116 0.8975023 0.8333333
Al 6.5024279E-02 6.1098572E-02 6.2862754E-02 0.8166667 V 4.1686617E-02 3.7523944E-02 3.9634921E-02 0.5833333 Thickness(nm) 4.6887019 3.1006788 3.7491774 0.7000000
(c)
Table VII. The relevant values of Ti6Al4V compared with different distances between the sources: (a) 1.732 cm ; (b) 4.330 cm ; (c) 6.928 cm.
Maximum Minimum Average Acceptable ratio
Ti 0.8999392 0.8952078 0.8975889 0.8833333
Al 6.4780384E-02 6.1212711E-02 6.2680699E-02 0.8166667 V 4.1203082E-02 3.7962511E-02 3.9730396E-02 0.7500000 Thickness(nm) 4.6865596 3.1084202 3.7459880 0.7000000
(a)
Maximum Minimum Average Acceptable ratio
Ti 0.8952824 0.8906804 0.8932091 0.9166667
Al 6.7737736E-02 6.3664123E-02 6.5459445E-02 0.8166667 V 4.3435723E-02 4.0098816E-02 4.1331455E-02 0.8333333 Thickness(nm) 4.3954760 2.9617002 3.5538856 0.7333333
(b)
Maximum Minimum Average Acceptable ratio
Ti 0.8931664 0.8882905 0.8910138 0.9166667
Al 6.8866223E-02 6.5300256E-02 6.6667311E-02 0.7666667 V 4.3634392E-02 4.0418547E-02 4.2318914E-02 0.7333333 Thickness(nm) 4.2402091 2.8831408 3.4465084 0.7166666
(c)
Figures
Fig. 1.1 Principle of electron beam evaporation. [Schiller, et al.,1982]
READ GRID DATA
SET INITIAL STATE
MOVE PARTICLES
ENTERING NEW PARTICLES
COLLIDE PARTICLES
STEADY FLOW?
SAMPLE FLOW FIELD
SUFFICIENT SAMPLING?
AVERAGE SAMPLES AND PRINT OUT THE DATA
YES
YES NO
NO
INDEX PARTICLES START
STOP
Fig. 2.1 Conventional DSMC flow chart.
INITIALIZE
Fig. 2.2 Simplified flow chart of the parallel DSMC method for np processors.
unstructured
(unordered) (unordered) (unordered)
Fig. 2.3 Schematic diagram of the proposed cell numbering scheme.
Fig. 2.4 The additional schemes in the parallel DSMC code.
L
1L
2Cell 1 Cell 2
N
1W
11
u
1
φ
∆ t
N
2W
22 2
φ
∆ t
2
21 ,
1 mv mv
φ =
Fig. 2.5 Sketch of the concept of variable time step scheme.
INITIALIZE MPI
Fig. 2.6 The flowchart of the parallel DSMC method with dynamic domain decomposition method.
Splitting Step
W2m1
W2m2
W1m1
(W1-W2)m1
non-collision collision
W2m1 W2m2
W2m1 (W1-W2)m1
W1m1
(W1-W2)m1
Merging Step Colliding Step
Fig. 2.7 Schematic diagram of CWS for non-reactive flow.
Fig.2.8 The flow chart of chemical reaction in the PDSC.
Fig. 3.1 Verification of inflow condition: quarter half sphere for simulation region.
Fig. 3.2 Normalized vapor flux distributions from titanium disk sources at 2050 K with five different diameters, and cos )(θ for reference.
Fig. 3.3 Inflow condition simulation: density distribution.
Fig. 3.4 Inflow condition simulation: temperature distribution.
Fig. 3.5 Inflow condition simulation: z-directional velocity distribution.
Fig. 3.6 Inflow condition simulation: velocity vector.
Fig. 3.7 Three view drawing of the chamber.
(a) (b)
(c) (d)
Fig. 3.8 Inflow condition of quart chamber that contains one source on the bottom: (a) density; (b) temperature; (c) z-directional velocity; (d) velocity vector.
(a)
(b)
(c)
Fig. 3.9 Comparisons of inflow condition with vacuum (left) and background pressur torr (right): (a) density; (b) temperature; (c) z-directional velocity.
10 5
5× −
(a)
(b)
(c)
Fig. 3.10 Comparisons of inflow condition with different background pressure torr (left), torr (middle), torr (right): (a) density; (b) temperature; (c) z-directional velocity.
10 5
5 .
2 × − 5×10−5 7.5×10−5
0 10000 20000 30000 40000 50000 60000 70000
0 1 2 3 4 5
Distance from wafer's center (cm)
Deposited particle
(a)
0 10000 20000 30000 40000 50000 60000
0 1 2 3 4 5
Distance from wafer's center (cm)
Deposited particle
(b)
Fig. 3.11 Comparison of the number deposited particle with (a) vacuum (b) background pressure 7.5×10−5torr.
Fig. 3.12 The specific cell labeled to sample the distribution of energy and incident angle.
(a) (b)
(c) (d)
(e) (f)
(g) (h)
Fig. 3.13 Comparison of energy distribution with vacuum (solid line) and background gas torr (dash line): (a) face 1; (b) face 2; (c) face 3; (d) face 4; (e) face 5; (f) face 6; (g) face 7; (h) face 8.
10 5
11 .
3 × −
(a) (b)
(c) (d)
(e) (f)
(g) (h)
Fig. 3.14 Comparison of incident angle distribution with vacuum (solid line) and background gas torr (dash line): (a) face 1; (b) face 2; (c) face 3; (d) face 4;
(e) face 5; (f) face 6; (g) face 7; (h) face 8.
10 5
11 .
3 × −
Fig. 3.15 The relative position of three sources and substrate in the simulation domain.
(a) (b)
(c) (d)
Fig. 3.16 The position of evaporated atoms at a specific steady time step (a) titanium; (b) aluminum; (c) vanadium; (d) together with titanium, aluminum and vanadium.
Fig. 3.17 Vapor pressure and Langmuir evaporation rates for titanium, aluminum and vanadium over the range 1600-2200℃. Small circles lie at melting points, and gray vanadium curves are extrapolations of solid data.[Powell, 1997]
(a) (b)
(c)
Fig. 3.18 The distributions of composition of alloy on the substrate (a) titanium; (b) aluminum; (c) vanadium.
(a) (b)
(c)
Fig. 3.19 The distribution of error percentage of individual evaporated atom on the substrate (a) titanium; (b) aluminum; (c) vanadium.
Fig. 3.20 The distribution of thickness on the substrate.
(a) (b)
(c)
Fig. 3.21 The distribution of the growth rate at (a) time step 5000~15000; (b) time step 15000~25000; (c) time step 25000~35000.
(a)
(b)
(c)
(d)
Fig. 3.22 The comparisons of composition and thickness. The rows of left, middle and right represent three different altitude of the substrate: 10cm, 27.5cm and 40cm. The columns represent (a) titanium; (b) aluminum; (c) vanadium; (d) thickness.
(a)
(b)
(c)
(d)
Fig. 3.23 The comparisons of composition and thickness. The rows of left, middle and right represent three different background pressure: , torr and vacuum.
The columns represent (a) titanium; (b) aluminum; (c) vanadium; (d) thickness.
10 5
5× − 5×10−6
(a)
(b)
(c)
(d)
Fig. 3.24 The comparisons of composition and thickness. The rows of left, middle and right represent three different distances between sources: 1.732, 4.330 and 6.928cm.
The columns represent (a) titanium; (b) aluminum; (c) vanadium; (d) thickness.