Abstract
The effect of a quartz plate (window) on the silicon wafer temperature is studied in the conditions of the combined thermal transfer in a lamp-based chamber for the rapid thermal treatment (RTP) set up. The chamber for RTP is simulated by a radiative-closed thermal system including the influence of quartz window as a spectral filter of lamp emission and a source of emitted thermal radiation. Energy equations for thermal fluxes involved in the heat input and output from the working wafer and quartz window are solved in spectral approximation. The transfer characteristics that are defined by the temperature dependencies of the silicon wafer and the quartz window on the temperature of the heater are accounted. It is shown that temperature bistability in the silicon wafer initiates an induced bistability into the quartz window that does not reveal bistable behavior because of the linear temperature dependence of its total optical characteristics. A possibility for simulation of the quartz window by spectral restriction of the heater radiation is confirmed. The availability of the weak bistable effect in the mode of zero effective heat exchange coefficient of a non-radiative component of the thermal flux removed from the working wafer has been obtained.
Highlights
The processes of thermal treatment are an integral part of the micro- and nanoelectronics technology
The numerical solutions of equations were received for the description of the combined heat transfer in the radiative-closed thermal system composed of four plates, two interior of them are semitransparent for thermal radiation and outer ones possess the optical properties of blackbody
The transfer characteristics of the silicon wafer and quartz window are simulated in the thermal system modeling the lamp-based chamber for the different values of the heat exchange coefficients defining non-radiative components of thermal fluxes removed from the silicon wafer and quartz plate
Summary
The processes of thermal treatment are an integral part of the micro- and nanoelectronics technology. The bistable behavior of the wafer proposes that in its thermal treatment process there is an interval of a controlling parameter (a heater temperature, as a rule) in which the wafer temperature takes different values according to whether the controlling parameter increases or decreases. The theoretical transfer characteristic of the working wafer (i.e., its temperature dependence on the temperature of the heater) has an S-like shape and is experimentally observed as a hysteresis loop [12]. The object of the present investigation is analysis and comparison of different ways of simulating the lamp-based chamber and their impact on the shape of transfer characteristics that describe silicon wafer temperature dependence on the temperature of the heater modeling a lamp block of the thermal chamber. Particular attention has been given to the quartz window as a filter of radiation incident from the heater to the silicon wafer and as a source of emitted radiation
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