This paper presents guidelines for the deep reactive ion etching (DRIE) of silicon MEMS structures, employing SF 6 O 2 -based high-density plasmas at cryogenic temperatures. Procedures of how to tune the equipment for optimal results with respect to etch rate and profile control are described. Profile control is a delicate balance between the respective etching and deposition rates of a SiO F passivation layer on the sidewalls and bottom of an etched structure in relation to the silicon removal rate from unpassivated areas. Any parameter that affects the relative rates of these processes has an effect on profile control. The deposition of the SiO F layer is mainly determined by the oxygen content in the SF 6 gas flow and the electrode temperature. Removal of the SiO F layer is mainly determined by the kinetic energy (self-bias) of ions in the SF 6 O 2 plasma. Diagrams for profile control are given as a function of parameter settings, employing the previously published "black silicon method". Parameter settings for high rate silicon bulk etching, and the etching of micro needles and micro moulds are discussed, which demonstrate the usefulness of the diagrams for optimal design of etched features. Furthermore it is demonstrated that in order to use the oxygen flow as a control parameter for cryogenic DRIE, it is necessary to avoid or at least restrict the presence of fused silica as a dome material, because this material may release oxygen due to corrosion during operation of the plasma source. When inert dome materials like alumina are used, etching recipes can be defined for a broad variety of microstructures in the cryogenic temperature regime. Recipes with relatively low oxygen content (1-10% of the total gas volume) and ions with low kinetic energy can now be applied to observe a low lateral etch rate beneath the mask, and a high selectivity (more than 500) of silicon etching with respect to polymers and oxide mask materials is obtained. Crystallographic preference etching of silicon is observed at low wafer temperature ( 120 C). This effect is enhanced by increasing the process pressure above 10 mtorr or for low ion energies (below 20 eV).[720]Index Terms-Cryogenic etching, profile control, reactive ion etching (RIE).

A construction is proposed for a supersymmetric generalization of the cubic Schrödinger equation, resulting in two supersymmetric systems, one of which contains a free parameter. Both systems are proven to admit an infinite set of (higher-order) local and nonlocal symmetries and a seemingly infinite set of conservation laws, the lowest-order terms of which are given explicitly. Moreover, the theory of coverings (equivalent to the prolongation method of Wahlquist and Estabrook) is applied to both systems. Both are seen to admit an infinite-dimensional covering algebra, the structure of which is determined explicitly, resulting in a related supersymmetric system of differential equations, as well as an auto-Bäcklund transformation for each equation. This indicates the complete integrability of both systems.

The prolongation method of Wahlquist and Estabrook is applied to the Landau–Lifshitz equation. The resulting prolongation algebra is shown to be isomorphic to a subalgebra of the tensor product of the Lie algebra so(3) with the elliptic curve vα2−vβ2=jβ−jα (α,β=1,2,3), which is essentially a subalgebra of the Lie algebra applied by Date et al. in a different context. Taking a matrix representation of so(3) gives rise to a Lax pair of the Landau–Lifshitz equation in agreement with the results found by Sklyanin. A system of related equations is deduced which can be used for the computation of auto-Bäcklund transformations of the Landau–Lifshitz equation.

The well known prolongation technique of Wahlquist and Estabrook for nonlinear evolution equations is generalized for supersymmetric equations and applied to the supersymmetric extension of the K d V equation of Manin-Hadul. Using the theory of Kac-Moody Lie superalgebra, the explicit form of the resulting Lie superalgebra is determined. It is shown to be isomorphic to R M R x Covs(C(2),u), where R M R is an eight dimensional radical. An auto-Backlund transformation is derived from the prolongation structure and the relationship with known solution methods of the S K d V equation is analysed. In addition it is indicated how a superposition principle for the S K d V equation can be obtained.

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