The non equilibrium band model of silicon in TMAH and in anisotropic electrochemical alkaline etching solutions

Abstract

This study presents the energy band diagram of silicon in contact with an aqueous solution of tetra-methyl ammonium hydroxide (TMAH) during the anisotropic electrochemical etch process. The band diagram is constructed from the measured open circuit potential (OCP) and the measured total band bending of the silicon at the OCP which is determined by impedance measurements. Current–voltage as well as capacitance–voltage characteristics of silicon in contact with TMAH solutions are presented. The present study emphasizes the non-equilibrium operation of the electrochemical cell even at the open circuit potential (OCP). In previous studies of the band diagram of silicon in alkaline anisotropic etch solutions, the Fermi levels of the silicon and the electrolyte are aligned at OCP. In contrast, in the present study the Fermi levels are not aligned since steady state rather than equilibrium prevails at this operation point. The value of the measured OCP is used to determine the separation between the two quasi Fermi levels. The assumptions leading to the construction of the band diagram are elaborated. The relationships between OCP, flat band voltage, passivation potentials and Fermi potentials are discussed. The predictions of the model and the effect of conductivity type, doping level, temperature and illumination are compared with experiments. The new model and methodology presented in this study is applicable to additional anisotropic alkaline etch solutions such as KOH and EDP. It is very useful for the appropriate design of the process required for electrochemical etch stop for the fabrication of membranes and controlled micromachining of silicon.