Nano-Scale Machining Via Electron Beam and Laser Processing

[+] Author and Article Information
Basil T. Wong, M. Pinar Mengüç

Department of Mechanical Engineering, University of Kentucky, 151RGAN Building, Lexington, KY 40506

R. Ryan Vallance

Mechanical and Aerospace Engineering, The George Washington University, 738 Academic Center, 801 22nd St., N.W., Washington, DC 20052

J. Heat Transfer 126(4), 566-576 (May 12, 2004) (11 pages) doi:10.1115/1.1777581 History: Received January 21, 2003; Revised May 12, 2004
Copyright © 2004 by ASME
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Schematic for the nano-scale machining process considered. A workpiece is positioned on top of a substrate. The substrate is assumed transparent to the incident laser. Two different evaporation methods are considered: (a) electron-beam impinges perpendicularly on the top of the workpiece, and (b) electron-beam and laser impinge normally on the workpiece at opposite directions.
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The grid setup used in modeling the electron-beam transport, the laser propagation, and the heat conduction inside the workpiece. The grid is sub-divided into two zones: (1) A and B with uniform spacings in both r and z-directions, and (2) C and D with non-uniform spacings where the grid is stretched along r and z-directions with independent factors. A is where the MC simulation in the electron-beam transport is performed while B extends A uniformly in both r and z-directions in order to account for the laser heating. The boundary conditions are (a) adiabatic at r=0 due to symmetry and (b) adiabatic at r=R1+R2+R3,z=0 and z=L1+L2+L3 since it is assumed that there are no convection and radiation losses.
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Schematic for the radiative transfer inside the workpiece. The impinging laser has a radial dimension of Rlaser and a wavelength of 355 nm. Since the absorption of radiant energy in a metal is strong, a one-dimensional radiation model with exponential decaying of radiant energy in the direction of propagation is employed; scattering of photons is neglected. The complex index of refraction of gold is at the wavelength of the laser. Rs→w is the reflectivity at the interface between gold and quartz when the incident direction is from quartz to gold.
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Normalized electron energy Ψ×109 (nm−3) (see Eq. (11)) deposited inside gold film Results are obtained from the Monte Carlo simulation in the electron-beam transport. The incident beam has a Gaussian profile in the r-direction with (a) a 1/e2 radius of Relectron=100 nm and the initial kinetic energy of E0=4 keV, (b) Relectron=50 nm and E0=4 keV, and (c) Relectron=100 nm and E0=6 keV.
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(a) Temperature distribution (K) within gold film at t=0.9 ns. The electron-beam impinges on the top of workpiece (i.e., z=0). A Gaussian beam profile is considered with a 1/e2 radius of Relectron=100 nm and an initial kinetic energy of E0=4 keV. The power of the beam is set to Ė=0.5 W. The Δt used in the simulation is 0.005 ps. The thicknesses of the workpiece and the substrate, which are gold and quartz, are assumed to be 500 nm and 10 μm, respectively. In the figure there is a sharp bending for the isothermal lines at z=500 nm, which is where the interface of the two different materials. Note that this is the snapshot of the temperature field right at the moment when the first computational element nearest the origin overcomes the latent heat of evaporation and starts to evaporate. The small inset in top right-hand corner portrays an up-close temperature field for an area of (r×z)=(120 nm×120 nm) near the origin. (b) Temperature distribution (K) within gold at t=0.7 ns using the same conditions in (a) except that Relectron=50 nm,E0=4 keV, and Ė=0.305 W. (c) Temperature distribution (K) within gold at t=1.0 ns using the same conditions in (a) but with Relectron=100 nm,E0=6 keV, and Ė=0.615 W.
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Temperature distribution (K) within gold film at t=0.5 ns. Both the electron-beam and the laser are considered. The input parameters are the same as those in Fig. 5(a). The power of the laser is 1.5 W and it covers a radius of Rlaser=300 nm from the z-axis. With the assistance from the laser, the time required for the first element at the origin to evaporate is improved from t=0.9 ns (as in Fig. 5(a)) to 0.5 ns.
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(a) Temperature distribution (K) within gold at t=1 ns. Both the electron-beam and the laser heating are considered. The thickness of gold film is reduced to 200 nm and the power of the electron-beam is set to 0.25 W. The rest of the input parameters follow those given in Fig. 6(b). The time required for evaporation as a function of the input power from the electron-beam for the 200-nm gold film.
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Transient temperatures at the origin around an infinitesimal area with radius of Δr=1.25 nm and depth of Δz=1.25 nm. The first case is set as the reference at which the inputs for the electron-beam are Relectron=100 nm,E0=4 keV and Ė=0.5 W. The gold film thickness is assumed to be 500 nm. The second has the same inputs as the reference except that the beam is focused narrower with Relectron=50 nm. The third is the same as the first case but with laser heating. The power of the laser used is 1.5 W. The fourth has a gold film thickness of 200 nm while the rest of the inputs are the same as the third case. The electron-beam of the final case has Relectron=100 nm,E0=6 keV and Ė=0.615 W with the laser turned off.




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