Maskless etching of silicon using patterned microdischarges

Microdischarges in flexible copper-polyimide structures with hole diameters of 200 µm have been used as stencil masks to pattern bare silicon in CF4/Ar chemistry. The discharges were operated at 20 Torr using the substrate as the cathode, achieving etch rates greater than 7 µm/min. Optical emission spectroscopy provides evidence of excited fluorine atoms. The etch profiles show a peculiar shape attributed to plasma expansion into the etched void. Forming discharges in multiple hole and line shapes permits direct pattern transfer in silicon and could be an alternative to ultrasonic milling and laser drilling

Hollow cathode sustained plasma microjets: Characterization and application to diamond deposition

Extending the principle of operation of hollow cathode microdischarges to a tube geometry has allowed the formation of stable, high-pressure plasma microjets in a variety of gases including Ar, He, and H2. Direct current discharges are ignited between stainless steel capillary tubes (d = 178 µm) which are operated as the cathode and a metal grid or plate that serves as the anode. Argon plasma microjets can be sustained in ambient air with plasma voltages as low as 260 V for cathode-anode gaps of 0.5 mm. At larger operating voltage, this gap can be extended up to several millimeters. Using a heated molybdenum substrate as the anode, plasma microjets in CH4/H2 mixtures have been used to deposit diamond crystals and polycrystalline films. Micro-Raman spectroscopy of these films shows mainly sp3 carbon content with slight shifting of the diamond peak due to internal stresses. Optical emission spectroscopy of the discharges used in the diamond growth experiments confirms the presence of atomic hydrogen and CH radicals

Equivariant Giambelli and determinantal restriction formulas for the Grassmannian

The main result of the paper is a determinantal formula for the restriction to a torus fixed point of the equivariant class of a Schubert subvariety in the torus equivariant integral cohomology ring of the Grassmannian. As a corollary, we obtain an equivariant version of the Giambelli formula.Comment: 16 pages, 3 figures, LaTex, uses epsfig and psfrag; for the revised version: title changed; Proof of Theorem 3 changed; 3 references added and 1 deleted; other minor change