Etching of silicon in alkaline solutions: a critical look at the {111} minimum

Anisotropic wet-chemical etching of silicon in alkaline solutions is a key technology in the fabrication of sensors and actuators. In this technology, etching through masks is used for fast and reproducible shaping of micromechanical structures. The etch rates Image depend mainly on composition and temperature of the etchant. In a plot of etch rate versus orientation, there is always a deep, cusped minimum for the {1 1 1} orientations. We have investigated the height of the {1 1 1} etch-rate minimum, as well as the etching mechanisms that determine it. We found that in situations where masks are involved, the height of the {1 1 1} minimum can be influenced by nucleation at a silicon/mask-junction. A junction which influences etch or growth rates in this way can be recognized as a velocity source, a mathematical concept developed by us that is also applicable to dislocations and grain boundaries. The activity of a velocity source depends on the angle between the relevant {1 1 1} plane and the mask, and can thus have different values at opposite {1 1 1} sides of a thin wall etched in a micromechanical structure. This observation explains the little understood spread in published data on etch rate of {1 1 1} and the anisotropy factor (often defined as Imag

Simulation of anisotropic wet-chemical etching using a physical model

We present a method to describe the orientation dependence of the etch rate of silicon, or any other single crystalline material, in anisotropic etching solutions by analytical functions. The parameters in these functions have a simple physical meaning. Crystals have a small number of atomically smooth faces, which etch (and grow) slowly as a consequence of the removal (or addition) of atoms by rows and layers. However, smooth faces have a roughening transition (well known in statistical physics); at increasing temperature they become rougher, and accordingly the etch and growth rates increase. Consequently, the basic physical parameters of our functions are the roughness of the smooth faces and the velocity of steps on these faces. This small set of parameters describes the etch rate in the two-dimensional space of orientations (on the unit sphere). We have applied our method to the practical case of etch rate functions for silicon crystals in KOH solutions. The maximum deviation between experimental data and simulation using only nine physically meaningful parameters is less than 5% of the maximum etch rate. This method, which in this study is used to describe anisotropic etching of silicon, can easily be adjusted to describe the growth or etching process of any crysta

The energy balance of Hg-free HID lamps and the influence of electrode distance

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Etching pits and dislocations in Si{111}

The nature of etch pits that arise during anisotropic etching in KOH on Si{111} surfaces was investigated. It was verified that bulk stacking faults in the crystal lattice give rise to deep etching pits. Other types of dislocations, of which the nature is still unclear, were also found to be present, but these do not give rise to etching pits

Simulation of crystal shape evoluation in two dimensions

We present a simulation tool for the prediction of the evolution of macroscopic crystal growth and etching shapes that can be represented in a two-dimensional setting. It is assumed that the advance rate of the crystal surface depends solely on the surface orientation, which implies that the classical kinematic wave theory applies. We present an algorithm to calculate the crystal shape at any given point in time in a single time step for initial crystal shapes that are either completely convex or completely concave. We show that calculation of the crystal shape for mixed convex/concave crystal shapes may require a series of time steps. Boundary conditions imposed at imperfections in the crystal surface or at boundaries with a container wall or a mask are treated. The possibility of two or more disconnected crystal shapes that meet at some point in their evolution is also taken into account. The simulation tool is used to predict crystal shape evolution for the technologically relevant case of wet chemical etching of masked silicon {1 0 0} wafers with multiple mask openings. It is shown that the experimental evolution of Si{1 1 0} surfaces cannot be reproduced using any simulation tool based on the assumption that the etch rate depends solely on the surface orientation. The differences between experiments and simulations are explained on the basis of the etching mechanism of Si{1 1 0} surfaces

The velocity source concept

Traditional kinematic wave theory neglects considerations involving free energy of a surface and nucleation at the boundary of a surface. As a consequence, strictly speaking this theory is only applicable to freely floating perfect crystals, and when applied to more complex situations the conclusions may be false. In this paper we argue that boundary conditions, to be taken into account at interface junctions, affect the shape of the crystal. The effect is either microscopic or macroscopic. In the first case, we have a “kinetic meniscus”, a curved transition of the size of the critical radius. In the second case, the growth rate is affected macroscopically and we may consider the boundary as a “velocity source” for the affected interface. These concepts are essential elements in a version of kinematic wave theory that is applicable to all physically relevant situations

Broadband integrating sphere setup for energy balance measurements on HID lamps

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