Transient model of wafer temperature in a furnace for semiconductor fabrication process

Abstract

The nonuniform temperatures that develop over silicon wafers on insertion and removal from the furnaces used in the oxidation and diffusion processes of semiconductor fabrication are one factor in reduced yields. For example, because of temperature differences in the oxidation process there are thermal stresses and differing thermal hystereses over the wafer surface which degrade the uniformity of the oxide layer formed. The most pronounced temperature differences, occurring when the wafers are inserted into the furnace, develop mainly because of the effect of the boat jig which supports the wafers. Since the heat capacity of the boat is much greater than that of the wafers, during the slower rise in the boat temperature radiant heat exchange with the wafer bottoms keeps the temperature of the bottoms lower than the temperature of the wafer tops, which are almost unaffected by the boat. This transient in the wafer temperature depends on such process parameters as the boat insertion speed, the ratio between the wafer and furnace reactor tube diameters, and the wafer spacing. In order to analyze this temperature characteristic the process is modelled and the results of numerical simulation are compared with experiment. The model for the wafer temperatures inside the furnace is a system of coupled partial differential equations for the mostly radiant heat fluxes of the boat and wafers. With an insertion speed of 2 m/sec, both the experimental data and the model give a maximum temperature difference over the wafer surface of 230°C near the end of insertion, thus confirming the model.

Nonempirical Design of Rapid Thermal Processing System

“…For the analysis and the optimization of the entire heat transport from the radiation heat source to the substrate in the RTP system, many researchers have studied the theoretical calculation models. 7,9,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] The next step is providing the technology to design the RTP system.…”

Design of a Rapid Thermal Processing System Using a Reflection-Resolved Ray Tracing Method

“…Further improvement in the RTP system for various aspects, 15 such as uniformity, reproducibility, and the ramp rate of the substrate temperature, requires advanced and appropriate theoretical calculation models 19,20 which can optimize the entire heat radiation from the heat source accounting for entirely and exactly the complicated three-dimensional geometry of the RTP system. Since the rays from tungsten/halogen filament lamps to a mirror-polished silicon substrate surface surrounded by reflectors have extremely complicated paths, the usual theoretical models 16,17,19,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] are insufficient to describe the RTP system. Therefore, the direct approach model using ray trace simulation ͑DARTS͒ [36][37][38] has been developed and evaluated as an extension of the ray tracing method.…”

Thermal Conditions in Rapid Thermal Processing System Using Circular Infrared Lamp

“…It is noted here that the rays from the tungsten/halogen filament lamps heat a mirror polished silicon substrate surface surrounded by reflectors. Since extremely complicated paths of the rays emitted from the tungsten/ halogen filament lamps must be taken into account, the application of the usual theoretical models 8,10,19,[21][22][23][24][25][26][27][28][29][30] to the RTP system is considered to be difficult. This has been the catalyst for development of the direct approach ray trace simulation model (DARTS), 31 which is an application of the ray tracing method.…”