J. van Suchtelen

Micro-morphology of single crystalline silicon surfaces during anisotropic wet chemical etching in KOH: velocity source forests

For silicon etched in KOH the micro-morphology of any surface, no matter the crystallographic orientation, is defined by some sort of persistent corrugations. As a matter of principle, the occurrence of these corrugations is incompatible with the classical kinematic wave theory for the evolution of crystal shapes. Either the re-entrant or the protruding edges or vertices are stabilized by some mechanism that is not accounted for in the microscopic etch rate function, i.e. are velocity sources. Exact Si{1 1 1} surfaces are dominated by etch pits caused by edge dislocations corresponding to oxygen-induced stacking faults. Exact Si{1 0 0} surfaces are dominated by circular indentations, probably owing to fast etching of accumulations of point defects. On exact and vicinal Si{1 0 0}, also pyramidal protrusions are found, which, we hypothesize, are formed and stabilized by silicate particles adhering to the surface. Exact and vicinal Si{1 1 0} surfaces are dominated by a zigzag pattern at low KOH concentration and a hillock pattern at high KOH concentration, which, we hypothesize, are also the result of the presence of silicate particles, created during etching, on the surface. Vicinal Si{1 0 0} and Si{1 1 1} surfaces, finally, are dominated by step bunching patterns, probably owing to time-dependent impurity adsorption.

Micromorphology of single crystalline silicon surfaces during anisotropic wet chemical etching in KOH and TMAH

An optical microscopy study is presented of the micromorphology of silicon surfaces etched in KOH and TMAH, using large hemispherical specimen on which all possible surface orientations are present. Many of the features found on the silicon surfaces can be correlated with features of the etch rate as a function of surface orientation. The topics that are treated include: triangular and hexagonal shaped etch pits on Si{1 1 1}, spherical depressions and the occurrence of pyramidal protrusions on Si{1 0 0}, the occurrence of staircase or zigzag structures on Si{1 1 0} and the morphology of the transition regions between these three main silicon surfaces. Nowhere on any of the etched silicon hemispheres microscopically smooth surfaces can be observed.

Kinetic roughening of the Kossel (100) surface: comparison of classical criteria with Monte Carlo results

Kinetic roughening is not a phase transition and, as such, it lacks an exact definition. Many criteria are used to mark the onset of kinetic roughening. Criteria stemming from the classical two-dimensional nucleation theory are widely used. On the other hand, experimentalists observe a transition from flat to rounded crystal facets at certain driving forces. And measuring the growth rate as a function of driving force, a change from exponential to linear growth kinetics is frequently found. It is assumed that these experimental phenomena coincide with the onset of kinetic roughening. These experimental criteria, three classical criteria for kinetic roughening and statistical mechanical criteria based on the interface width and the surface roughness, are compared with each other by means of Monte Carlo simulations on a Kossel (100) SOS model. Surface diffusion is neglected, and only attachment/detachment kinetics is considered. The change from flat to rounded facets with increasing driving force turns out to be quite gradual. Nevertheless, this experimental criterion is made explicit by defining a critical driving force for which the curvature of a facet becomes visible by optical microscopy. The conditions for an experiment to detect kinetic roughening using this criterion are described. The different criteria for kinetic roughening yield different values for the critical driving force, although most of the criteria studied show a similar, almost linear, dependence of the critical driving force on the nearest neighbor bond strength. This again indicates that kinetic roughening is diffuse in nature, and shows that in discussions on kinetic roughening it is imperative to mention the criterion used. Some attention is also paid to the two-dimensional anisotropy of step motion on a Kossel (100) surface. An anisotropic step velocity is found far below thermal roughening. The anisotropy is reduced by increasing the driving force.

The construction of orientation-dependent crystal growth and etch rate functions II: Application to wet chemical etching of silicon in potassium hydroxide

In Part I we introduced a construction method for analytical orientation dependent growth and etch rate functions. In this article, this network construction principle is applied to wet chemical etching of silicon in concentrated aqueous potassium hydroxide. Detailed measurements of the etch rate as a function of crystal surface orientation are used to fit the phenomenological parameters in the network etch rate function. In this function, for each crystal facet, two surface processes are accounted for, etching through misorientation step flow and etching through nucleation of pits. The fitting procedure identifies additional mesoscopic, surface processes which influence the orientation dependence of the etch rate. These processes correspond to instabilities of the surface. In the {111} region step bunching occurs which evolves into microfaceting for larger inclination angles. Moreover, for certain experimental circumstances, the fast etching {110} region breaks up into a staircase structure of terraces. Additional network elements are defined to account for these instabilities. The step-bunching instability is treated using an ad hoc approach. With these amendments the experimental etch rate functions can be fitted to an accuracy of about 5% by a network function with nine parameters. This shows that it is possible to reproduce the essential features of an experimental growth or etch rate function using an analytical function with a limited number of physically meaningful parameters

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 crystal.

A Monte Carlo study of dislocation growth and etching of crystals

It is well known that screw dislocations are step sources that allow crystals to grow at low driving forces. Growth is accelerated at the outcrop of a screw dislocation generating a spiral hillock. This makes the intersection of a screw dislocation and a crystal surface a so-called velocity source. In this paper the interaction between dislocation growth, 2D-nucleation and misorientation step flow is investigated for a wide range of driving forces by means of Monte Carlo simulations of growth of the Kossel (1 0 0) surface. The interactions between the different growth mechanisms are shown to agree with a general model for velocity source behavior, which allows for a simple analytical expression of the growth rate. This expression can be used in a continuum description of crystal growth. Finally, dislocation etching is studied and compared with dislocation growth.

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 Image

The construction of orientation-dependent crystal growth and etch rate functions. Part I. Mathematical and physical aspects

For mathematical analysis and computer simulation of the shape evolution of crystals, we need a continuum description of crystal growth or etching, rather than the conventional atomistic description. This allows the mathematical integration of the interface process with other transport steps that are usually also described by continuum equations, like diffusion, viscous flow, and chemical reactions. For this reason we need a function R(n,T,C,p,…): the growth or etch rate as a function of the surface orientation n and of experimental variables such as temperature, composition, pressure, etc. of the parent phase. In this article we describe a logical construction method for such growth or etch rate functions. The virtue of our method is that the n variable covers the full unit sphere, i.e., all minima due to different crystal facets are expressed in the R function. The orientation dependence of the growth or etch rate of interfaces (three dimensional) and of steps on a facet (two dimensional) is described i...

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.

Influence of the angle between etched (near) Si{111} surfaces and the substrate orientation on the underetch rate during anisotropic wet-chemical etching of silicon

Anisotropic wet-chemical etching of silicon in alkaline solutions is a key technology in the fabrication of sensors and actuators. In earlier work it was found that not only the etchant and temperature determine the exact anisotropy of etched silicon; the angle between the silicon surface and the mask was also shown to play an important role. In this paper this phenomenon was quantified for several etching conditions. Also, the etch rates of Si{ 100} and Si{ 110} were determined under these conditions, together with the activation energies of these orientations. Finally, the anisotropy ratios (etch depth/underetch) of the etched samples were determined.