^{a)}

^{a)}This article is based on material presented at the 57th International Symposium of the American Vacuum Society.

^{1}and Alina A. Alexeenko

^{2,b)}

### Abstract

In a typical electron-beam physical vapor deposition system, there is limited control over how the high-power electron beam heats the metal surface. This leads to thermal nonuniformities at the melt. Three-dimensional direct simulation Monte Carlo simulations were performed with the aim of quantifying the effect of such spatial variations of source temperature in thin film depositions using an electron-beam physical vapor deposition system. The source temperature distribution from a typical deposition process was used in the direct simulation Monte Carlo simulations performed for various mass flow rates. The use of an area-averaged temperature is insufficient for all mass flow rates due to the highly nonlinear relationship between temperature and saturation number density, and hence, the mass flux. The mass flow rate equivalent temperature was determined, and the simulations performed with this temperature were compared with those corresponding to the actual nonuniform temperature distribution. For low mass flow rates, the growth rates depend very weakly on the spatial variation of temperature as long as an equivalent temperature corresponding to the same mass flow rate was used. However, as the mass flow rate increases, the error associated with this approximation increases. For deposition processes with source Knudsen numbers less than 0.05, it is not possible to account for the spatial nonuniformities in temperature using the total mass flow rate without significant errors. For a given mass flow rate, the errors associated with using an equivalent temperature decrease with increasing collector plane distance since the flow is allowed to expand further, thereby decreasing the effects of slit temperature nonuniformities.

The authors would like to acknowledge the support from Kirk Endowment Seed Grant program, Birck Nanotechnology Center at Purdue University.

I. INTRODUCTION

II. EBPVD: OVERVIEW OF THE TECHNIQUE AND PROCESS VARIABLES

III. DSMC SIMULATION PARAMETERS AND FLOW CONDITIONS

IV. RESULTS AND DISCUSSION

V. CONCLUSIONS

### Key Topics

- Photon density
- 18.0
- Electron beam deposition
- 14.0
- Thin film deposition
- 12.0
- Physical vapor deposition
- 8.0
- Sputter deposition
- 8.0

## Figures

(Color online) Schematic of experimental set-up and the computational domain used in the DSMC simulations.

(Color online) Schematic of experimental set-up and the computational domain used in the DSMC simulations.

(Color online) Slit temperature contours for case I(a).

(Color online) Slit temperature contours for case I(a).

Slit temperature and saturation number density distribution at *Z* * = * 0 for cases I(a), II(a), and III(a).

Slit temperature and saturation number density distribution at *Z* * = * 0 for cases I(a), II(a), and III(a).

(Color online) Number density and Knudsen number contours for case I(a).

(Color online) Number density and Knudsen number contours for case I(a).

(Color online) Comparison of number density and Knudsen number contours at the *Z* * = * 0 plane for cases I(a) (———-) and I(b) (–––).

(Color online) Comparison of number density and Knudsen number contours at the *Z* * = * 0 plane for cases I(a) (———-) and I(b) (–––).

(Color online) Comparison of number density and Knudsen number contours at the *Y* * = * 0 plane for cases I(a) (———) and I(b) (–––).

(Color online) Comparison of number density and Knudsen number contours at the *Y* * = * 0 plane for cases I(a) (———) and I(b) (–––).

(Color online) Comparison of mass flux at all collector plate locations for cases I(a) and I(b) for a collector plane distance of *X* * = * 0.14 m. (Top-left) *Y* = 0.0; (top-right)*Y* = 0.05; (bottom-left)*Y* = 0.10; (bottom-right)*Y* = 0.15 m.

(Color online) Comparison of mass flux at all collector plate locations for cases I(a) and I(b) for a collector plane distance of *X* * = * 0.14 m. (Top-left) *Y* = 0.0; (top-right)*Y* = 0.05; (bottom-left)*Y* = 0.10; (bottom-right)*Y* = 0.15 m.

(Color online) Comparison of mass flux at all collector plate locations for cases I(a) and I(c) for a collector plane distance of *X* * = *0.14 m. (Top-left) *Y* = 0.0; (top-right)*Y* = 0.05; (bottom-left)*Y* = 0.10; (bottom-right)*Y* = 0.15 m.

(Color online) Comparison of mass flux at all collector plate locations for cases I(a) and I(c) for a collector plane distance of *X* * = *0.14 m. (Top-left) *Y* = 0.0; (top-right)*Y* = 0.05; (bottom-left)*Y* = 0.10; (bottom-right)*Y* = 0.15 m.

(Color online) Comparison of contours of Knudsen number contours for cases II(a) (———-) and II(b) (–––) in the *Z* * = * 0 and *Y* * = * 0 planes.

(Color online) Comparison of contours of Knudsen number contours for cases II(a) (———-) and II(b) (–––) in the *Z* * = * 0 and *Y* * = * 0 planes.

(Color online) Comparison of mass flux at all collector plate locations for cases II(a) and II(b) for a collector plane distance of *X* * = * 0.14 m*.* (Top-left)*Y* = 0.0; (top-right)*Y* = 0.05; (bottom-left)*Y* = 0.10; (bottom-right)*Y* = 0.15 m.

(Color online) Comparison of mass flux at all collector plate locations for cases II(a) and II(b) for a collector plane distance of *X* * = * 0.14 m*.* (Top-left)*Y* = 0.0; (top-right)*Y* = 0.05; (bottom-left)*Y* = 0.10; (bottom-right)*Y* = 0.15 m.

(Color online) Comparison of mass flux at all collector plate locations for cases III(a) and III(b) for a collector plane distance of *X* * = * 0.14 m*.* (Top-left)*Y* = 0.0; (top-right)*Y* = 0.05; (bottom-left)*Y* = 0.10; (bottom-right)*Y* = 0.15 m.

(Color online) Comparison of mass flux at all collector plate locations for cases III(a) and III(b) for a collector plane distance of *X* * = * 0.14 m*.* (Top-left)*Y* = 0.0; (top-right)*Y* = 0.05; (bottom-left)*Y* = 0.10; (bottom-right)*Y* = 0.15 m.

(Color online) Comparison of contours of Knudsen number contours for cases III(a) (———-) and III(b) (–––) in the *Z* * = * 0 and *Y* * = * 0 planes.

(Color online) Comparison of contours of Knudsen number contours for cases III(a) (———-) and III(b) (–––) in the *Z* * = * 0 and *Y* * = * 0 planes.

(Color online) Comparison of mass flux at all collector plate locations for cases I(a) and I(b) for a collector plane distance of *X* * = *0.28 m. (Top-left) *Y* = 0.0; (top-right) *Y* = 0.05; (bottom-left) *Y* = 0.10; (bottom-right) *Y* = 0.15 m.

(Color online) Comparison of mass flux at all collector plate locations for cases I(a) and I(b) for a collector plane distance of *X* * = *0.28 m. (Top-left) *Y* = 0.0; (top-right) *Y* = 0.05; (bottom-left) *Y* = 0.10; (bottom-right) *Y* = 0.15 m.

## Tables

Summary of the DSMC simulations.

Summary of the DSMC simulations.

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