Temperature and Doping Dependency of Piezoresistivity in p-type Silicon
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Temperature and Doping Dependency of Piezoresistivity in p-type Silicon Eivind Lund and Terje G. Finstad Dept. of Physics, University of Oslo 0314 Oslo, Norway ABSTRACT We have performed new measurements of the temperature and doping dependency of the piezoresistive effect in p-type silicon. Piezoresistivity is one of the most common sensing principles of micro-electro-mechanical-systems (MEMS). Our measurements are performed in a specially designed setup based on the well-known 4 point bending technique. The samples are beams of full wafer thickness. To minimize leakage currents and to obtain uniform doping profiles, we have used SIMOX (Separation by IMplantation of OXygen) substrates with resistors defined in an epitaxial layer. Spreading resistance measurements show that the doping profiles are uniform with depth, while measurements of leakage current versus temperature indicate low leakage current. In this paper we present results for the doping concentration range from 1x1017 – 1x1020 cm-3 and the temperature range from –30 to 150 degrees Celsius. The results show a doping dependency of piezoresistivity well described by the current models. The measurements of the temperature dependency of the coefficients of piezoresistivity are compared to a linear model with a negative temperature coefficient whose absolute value decreases with increasing doping. INTRODUCTION Smith [1] first described piezoresistivity (PR) in silicon and germanium in 1954. Since then, PR has been used in stress sensors for a wide range of applications and devices. PR is described as the ability of a material to change its electric conductivity when a mechanical stress is applied. PR is currently one of the major sensing principles of MEMS. Silicon has become the most common material for MEMS manufacturing due to heritage of process technology from the IC industry and due to its favorable material properties. Silicon has ideal mechanical properties with linear behavior until fracture. It is of vital importance for manufacturers of MEMS to know the dependency of PR on physical parameters such as temperature and doping. Doping dependency of PR is important for optimization of the manufacturing process, while temperature dependency of PR is important to optimize operation and readout electronics. Observed deviations from the current models for doping and temperature dependency of PR have motivated our measurements. Temperature and doping dependency of PR have been measured before, but the advantage of our measurements are the low leakage currents obtained by using SIMOX Silicon On Isolator (SOI) substrates and the possibility to achieve uniform doping profiles. The low leakage current and the uniform doping profile are verified by measurements. THEORY PR originates from mechanical stress changing the electronic band structure, resulting in a change of resistance. As can be shown from tensor theory, we need to measure the resistance in EE5.13.1
three specific directions to fully determine the three PR coefficients. One suitable set of direction
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