M. Radmilović-Radjenović

Theoretical study of the electron field emission phenomena in the generation of a micrometer scale discharge

The phenomenon of field emission plays a significant role in the deviation of the breakdown voltage from that predicted by Paschens law within the range of high electric fields. High fields obtained in small gaps may enhance the secondary electron emission and such enhancement could lead to a lowering of the breakdown voltage and a departure from the Paschen curve. In this paper, the dc breakdown characteristics of the discharge in the micrometric regime were extensively studied by the theoretical approach including ion-enhanced field emission. In addition, semi-empirical expressions for the dependence of the breakdown voltage on the gap spacing and on the pressure based on the numerical solutions of the equation that describes the dc breakdown criteria have been proposed.

The influence of ion-enhanced field emission on the high-frequency breakdown in microgaps

This paper contains the results of the detailed simulation study of the role of ion-enhanced field emission on the breakdown voltage in argon, xenon and krypton at high frequencies. Calculations were performed by using a one-dimensional particle-in-cell/Monte Carlo collisions (PIC/MCC) code with the secondary emission model adjusted to include field emission effects in microgaps. The obtained simulation results clearly show that electrical breakdown across micron-size gaps may occur at voltages far below the minimum predicted by the conventional Paschen curve. The observed breakdown voltage reduction may be attributed to the onset of ion-enhanced field emission.

Level Set Approach to Anisotropic Wet Etching of Silicon

In this paper a methodology for the three dimensional (3D) modeling and simulation of the profile evolution during anisotropic wet etching of silicon based on the level set method is presented. Etching rate anisotropy in silicon is modeled taking into account full silicon symmetry properties, by means of the interpolation technique using experimentally obtained values for the etching rates along thirteen principal and high index directions in KOH solutions. The resulting level set equations are solved using an open source implementation of the sparse field method (ITK library, developed in medical image processing community), extended for the case of non-convex Hamiltonians. Simulation results for some interesting initial 3D shapes, as well as some more practical examples illustrating anisotropic etching simulation in the presence of masks (simple square aperture mask, convex corner undercutting and convex corner compensation, formation of suspended structures) are shown also. The obtained results show that level set method can be used as an effective tool for wet etching process modeling, and that is a viable alternative to the Cellular Automata method which now prevails in the simulations of the wet etching process.

Experimental and theoretical studies of the direct-current breakdown voltage in argon at micrometer separations

In this paper, the dc breakdown in argon has been measured in the discharge system consisting of two parallel planar Cu electrodes at separations from 20 to 500 μm varying the pressure from 4.5 to 690 torr. The measured breakdown voltage curves were systematically analyzed and a corresponding scaling law was suggested. The estimation of the secondary emission coefficient γ as a function of the reduced electric field was based on experimental data and simple theoretical studies. Additionally, particle-in-cell/Monte Carlo collision simulations were performed to understand in more detail the processes involved in the dc discharge breakdown. Good agreement was found between experimental and simulation results.

Experimental and theoretical studies of the breakdown voltage characteristics at micrometre separations in air

This paper presents experimental results and computer simulation for the direct current (DC) breakdown voltages in dry, synthetic and ambient air and discharge gaps ranging from 1 to 100 μm. The measured breakdown voltage curves were systematically analyzed and the effective electron yields from cathode for dry and synthetic air as a function of the reduced electric field have been estimated. As complement to the experimental results, simulations have been performed using a kinetic particle-in-cell (PIC) code. For the electrode gaps less than 20 μm, both experimental and simulation results revealed an interesting departures from the Paschen law on the left-hand side of the Paschen curve. The present results should be useful for the determination of minimum ignition voltages in microplasma sources as well as the maximum safe operating voltages and critical dimensions in other microdevices, high-power switches and circuit breakers.

Nonconvex Hamiltonians in three dimensional level set simulations of the wet etching of silicon

It is shown that profile evolution during anisotropic wet etching of silicon can be described by the nonconvex Hamiltonian arising in the Hamilton-Jacobi equation for the level set function. Etching rate function is determined on the basis of the silicon symmetry properties. An extension of the sparse field method for solving three dimensional level set equations in the case of nonconvex Hamiltonians is presented.

Top down nano technologies in surface modification of materials

This article contains a broad overview of etch process as one of the most important top-down technologies widely used in semiconductor manufacturing and surface modification of nanostructures. In plasma etching process, the complexity comes from the introduction of new materials and from the constant reduction in dimensions of the structures in microelectronics. The emphasis was made on two types of etching processes: dry etching and wet etching illustrated by three dimensional (3D) simulation results for the etching profile evolution based on the level set method. The etching of low-k dielectrics has been demonstrated via modelling the porous materials. Finally, simulation results for the roughness formation during isotropic etching of nanocomposite materials as well as smoothing of the homogeneous materials have also been shown and analyzed. Simulation results, presented here, indicate that with shrinking microelectronic devices, plasma and wet etching interpretative and predictive modeling and simulation have become increasingly more attractive as a tool for design, control and optimization of plasma reactors.

A Particle-in-Cell Simulation of the High-Field Effect in Devices With Micrometer Gaps

Devices with micrometer and submicrometer gaps can face a serious challenge due to electrical breakdown during manufacturing, handling, and operation. Therefore, it is necessary to be aware of the breakdown voltage at different gaps. Since the Paschens law is not valid for gaps smaller than several micrometers, modified Paschen curve should be used to predict breakdown voltage for microdevices. One of the possible mechanisms responsible for the reduction of the maximum operation voltage at small gaps is the field emission (FE). In this paper, particle-in-cell/Monte Carlo collision simulations, including the ejection of electrons from the cathode due to a high electric field, have been carried out to estimate the significance of the FE effect on the breakdown voltage in microgaps.

The effect of magnetic field on the electrical breakdown characteristics

This paper presents a simple phenomenological model and detailed simulation studies of the breakdown of a gas under the simultaneous action of electric and magnetic fields. In deriving expressions for the breakdown voltage variations of both the ionization coefficient and the secondary electron yield in a magnetic field are taken into account. Calculations were carried out by using the XOOPIC code with the old and the improved secondary emission models adjusted to involve the influence of the magnetic field on the secondary electron production. It was shown that the incorporation of the variation of the secondary electron yield with magnetic field leads to the better agreement with existing experimental results.

Modelling of a low-pressure argon breakdown in combined fields

This paper reports the results of the detailed theoretical and simulation study of the dependence of the breakdown voltage on the product of the gas pressure and the electrode separation (pd) under the simultaneous application of radio-frequency (rf) and dc fields. Calculations were performed by using a one-dimensional particle-in-cell/Monte Carlo collision code with three velocity components with a new secondary emission model. Our simulation results show that in combined discharges during breakdown an ambiguity region of the left-hand branch of the breakdown curve appears not only by increasing the rf voltage but also by decreasing it. In other words, with lowering of the pressure, the rf voltage first decreases and passes through an inflection point and a minimum on the breakdown curve and then it grows and approaches the turning point on the breakdown curve. In addition, simulation results are also compared with the theoretical predictions based on the phenomenological method. Analytical expressions for the rf breakdown voltage with a superimposed weak dc electric field corresponding to the minimum, to the inflection point and to the turning point on the breakdown curve have been derived.