Thesis Erik van Veenendaal


In this thesis the development of a full-fledged continuum description of crystal growth/etching is presented. Attention is focused to one specific application: wet chemical anisotropic etching of silicon, an important, technologically relevant process used in micro systems technology. The thesis can roughly be divided in three parts.

The first part of the thesis (chapters I-VI) introduces new concepts that are essential to come to a continuum description of crystal growth/etching. In chapters I and II, a method is presented for the construction of analytical expressions of the growth/etch rate as a function of crystal orientation. These network functions contain only a limited number of, physically meaningful, variables. In chapter III a network etch rate function is formulated for wet chemical etching of silicon in KOH, which is confronted with measurements of the etch rate as a function of orientation, using hemispherical specimen. In chapter IV the continuum theory of crystal growth and etching is generalised to imperfect crystals. The influence on the crystal shape of the presence of imperfections like dislocations, stacking faults, foreign particles adhering to the surface, or boundaries with a vessel wall, can all be described by introducing a point or line velocity source. In chapters V and VI, the surface morphology of wet chemically etched silicon surfaces on the hemisperical specimen is investigated. In chapter V the surface morphology is correlated with features of the corresponding network etch rate function. In chapter VI, the different instances of velocity source behaviour encountered on silicon surfaces etched in KOH are identified and treated in detail.

The second part of the thesis (chapters VII-XII) studies crystal growth/etching from an atomistic point of view, using Monte Carlo simulation. Chapter VII explains the occurrence of protrusions on etched Si{100} and Si{110} surfaces, starting from the hypothesis that small permeable particles are present on the surface that locally slow down etching. In chapter VIII, the possible influence of the presence of a mask junction on the etch rate and the surface morphology is clarified. Chapter IX studies the different criteria used in literature to detect the onset of kinetic roughening, which confirms that kinetic roughening is no sharp transition. Chapter X presents a study of spiral growth/etching, focusing on the interaction of the different growth/etching mechanisms. Chapter XI studies the equilibrium properties of the Si{111} surface; the usual flat and rough phases, but no DOF phase, are found. The first part of chapter XII shows that crystal dissolution is not simply the opposite of crystal growth. Etching of a crystal will produce an atomically flat surface if the bonds in this surface are sufficiently strong, despite a very high driving force for dissolution, an effect we have coined kinetic smoothing. The second part of chapter XII presents an analytical model of anisotropic etching of exact and vicinal Si{111} surfaces.

In the third part of the thesis (chapters XIII-XVI) two different tools for continuum simulation of crystal shape evolution are presented and applied. The first simulation tool deals with crystal shape evolution in two dimensions in the case that the advance rate of the surface solely depends on the surface orientation, i.e. in the case that volume diffusion is very fast and therefore not important. In chapter XIII, the detailed algorithms built into this tool are explained. In this chapter the simulation program is also applied to double-sided wet chemical etching of masked Si{100} wafers in KOH, which reveals that in this case the central assumption that the etch rate is constant and depends solely on the surface orientation is not valid everywhere on the surface all the time, because of the formation of zigzag patterns on emerging Si{110} surfaces. In chapter XIV, the simulation program is used to successfully reproduce the step patterns occurring on natural diamond {111} surfaces, which are due to slight etching during the ascent to the earth’s surface via vulcanic eruption. The second simulation tool deals with crystal shape evolution in two dimensions combined with volume diffusion. In chapter XV, the detailed simulation algorithms built into this tool are explained. In chapter XVI the simulation tool is used to study the transition of polyhedral to hopper crystal growth. Also, the influence of spiral growth on this transition is shown.