M. L. Brake

The Gaseous Electronics Conference radio‐frequency reference cell: A defined parallel‐plate radio‐frequency system for experimental and theoretical studies of plasma‐processing discharges

A “reference cell” for generating radio-frequency (rf) glow discharges in gases at a frequency of 13.56 MHz is described. The reference cell provides an experimental platform for comparing plasma measurements carried out in a common reactor geometry by different experimental groups, thereby enhancing the transfer of knowledge and insight gained in rf discharge studies. The results of performing ostensibly identical measurements on six of these cells in five different laboratories are analyzed and discussed. Measurements were made of plasma voltage and current characteristics for discharges in pure argon at specified values of applied voltages, gas pressures, and gas flow rates. Data are presented on relevant electrical quantities derived from Fourier analysis of the voltage and current wave forms. Amplitudes, phase shifts, self-bias voltages, and power dissipation were measured. Each of the cells was characterized in terms of its measured internal reactive components. Comparing results from different cells provides an indication of the degree of precision needed to define the electrical configuration and operating parameters in order to achieve identical performance at various laboratories. The results show, for example, that the external circuit, including the reactive components of the rf power source, can significantly influence the discharge. Results obtained in reference cells with identical rf power sources demonstrate that considerable progress has been made in developing a phenomenological understanding of the conditions needed to obtain reproducible discharge conditions in independent reference cells.

Abel's inversion applied to experimental spectroscopic data with off axis peaks

Abstract Many mathematical techniques for solving Abels integral equation have been proposed over the years in the literature. Often these methods handle test functions with known solutions and Gaussian type profiles quite accurately. For experimental data and non-Gaussian shapes, however, these methods are inadequate. An experimental study of the uniformity of the plasma emission on the Gaseous Electronics Conference Reference Cell has as its goal to provide immediate feedback regarding the plasma uniformity. Therefore a rapid, accurate, and sturdy computational method of data analysis is required. The first round of experiments indicate off axis or donut shaped plasmas within the reference cell. The analysis and conclusions are presented herein.

A reconstruction algorithm for a spatially resolved plasma optical emission spectroscopy sensor

Abstract The reconstruction algorithm used for a new spatially resolved plasma optical emission spectroscopy sensor is described. The sensor has a wedge shaped field of view which is rotated horizontally across the plasma. The resulting signal as a function of angle defines an ill-posed linear problem that must be solved to determine the emissivity as a function of radius in the plasma. This problem is solved by modified Tikhonov regularization using a finite difference regularizer which discourages rapid variation in the reconstructed emission. The optimal regularization parameter is determined by minimizing the product of the norm of the residual and the norm of this regularizer. The robustness of the algorithm against noise introduced into idealized data is demonstrated, both for a standard Abel inversion problem and for test data based on the sensor model. The algorithm is used to reconstruct emitted power density profiles and to perform actinometry in a Lam TCP 9400 plasma processing tool; these reconstructions show qualitatively correct behaviors.

Multipactor experiment on a dielectric surface

A novel experiment to investigate single-surface multipactor on a dielectric surface was developed and tested. The compact apparatus consists of a small brass microwave cavity in a high vacuum system. The cavity is ∼15 cm in length with an outer diameter of ∼10 cm. A pulsed variable frequency microwave source at ∼2.4 GHz, 2 kW peak excites the TE111 mode with a strong electric field parallel to a dielectric plate (∼0.2 cm thickness) that is inserted at midlength of the cavity. The microwave pulses are monitored by calibrated microwave diodes. An electron probe measures electron current and provides temporal measurements of the multipactor electron current with respect to the microwave pulses. Phosphor on the dielectric surface is used to detect multipactor electrons by photoemission. The motivation of this experiment is to test recent theoretical calculations of single-surface multipactor on a dielectric.

Microwave resonant-cavity-produced air discharges

Air discharges produced in an Asmussen microwave cavity (0-300 W, 2.45 GHz, CW) between 0.5 and 100 torr were investigated. Gas temperatures (1000-2500 K) were estimated from rotational temperatures obtained from optical emission spectroscopy (OES). These agreed with a simple model of the heat transfer of the gas where joule heating was included as the source term. Vibrational temperatures (3700-7300 K) were also determined from OES and followed the electron energy trends. Electron density (10/sup 11/-10/sup 13/ cm/sup -3/), collisional frequency (10/sup 11/-10/sup 12/ s/sup -1/), and plasma conductivity (0.09-0.3 ( Omega -m)/sup -1/) were calculated from a self-consistent electromagnetic model of the cavity where the plasma was assumed to be a lossy dielectric. Absorbed power, electric, and optical probe measurements were used as the input parameters to the model. >

Radial optical emission profiles of radio frequency glow discharges

Radial optical emission profiles are determined from Abel inverted emission spectroscopy of a parallel plate radio frequency system known as a GEC Reference Cell. These profiles in general show a nonuniform plasma, annular in shape. Etching results of silicon wafers also follow this annular pattern. This effect is explained by numerically computed large radial and axial electric fields near the edge of the electrodes, produced by the presence of the grounded dark shields.

Electron density and collision frequency of microwave‐resonant‐cavity‐produced discharges

A review of perturbation diagnostics applied to microwave resonant cavity discharges is presented. The classical microwave perturbation technique examines the shift in the resonant frequency and cavity quality factor of the resonant cavity caused by low‐electron density discharges. However, the modifications presented allow the analysis to be applied to discharges with electron densities beyond the limit predicted by perturbation theory. An ‘‘exact’’ perturbation analysis is presented which models the discharge as a separate dielectric, thereby removing the restrictions on electron density imposed by the classical technique. The ‘‘exact’’ method also uses measurements of the shifts in the resonant conditions of the cavity. Third, an electromagnetic analysis is presented which uses a characteristic equation, based upon Maxwell’s laws, and predicts the discharge conductivity based upon measurements of a complex axial wave number. By allowing the axial wave number of the electromagnetic fields to be complex,...

Spatially resolved fluorine actinometry

A method has been developed to obtain spatially resolved optical emission spectra. This method is used in a diagnostic known as actinometry, where the relative concentration of fluorine can be obtained by examining the ratio of two spectral lines having similar excitation thresholds and excitation cross sections. Generally, the etch rate of silicon is correlated to the concentration of fluorine. In this modified actinometry method, radial emissivity profiles of the discharge are obtained 1 cm above the wafer surface by using a rotating stage to capture small wedges of light from the etching discharge, and analyzing these wedges using a regularized reconstruction algorithm. The relative fluorine concentration is obtained by comparing the ratio of a fluorine (703.75 nm) to argon (750.39 nm) emission line. The atomic fluorine radial profiles correlate to hard masked silicon etch radial profiles processed in a Lam TCP 9400 SE inductively coupled plasma processing tool using an SF6/Ar chemistry. Fluorine loadi...

A spatially resolved optical emission sensor for plasma etch monitoring

A spatially resolved optical emission spectroscopy sensor has been developed, and the resulting reconstructed radial emission profiles from an ArI and ArII line compare well with Ar sputter etch uniformity profiles. The new sensor collects light from a wedge shaped field of view, and is rotated around a single collection point in order to observe the entire plasma through a relatively small viewpoint.

Emission spectroscopy of long pulse relativistic electron‐beam‐produced argon plasmas

Visible emission spectroscopy of long pulse, relativistic, electron‐beam (300 ns, 1 kA, 300 keV) ‐produced argon plasmas has been performed over a wide pressure range (1–750 Torr). The emission spectra were observed between 350 and 600 nm with a spectrograph coupled to an optical multichannel analyzer, which was gated with pulses of 50 and 500 ns. Singly ionized argon lines were observed at all pressures and all times during the beam current. The relative line intensities for the (4s–4p) transitions fit those described by an equilibrium distribution at approximately 2 eV. The emission lines originating from the higher excited states of (4s’–4p’) and (4s‘–4p‘) were much larger than expected in a 2‐eV plasma, and this enhancement can be attributed to the presence of the beam electrons.