Recent studies on dynamic temperature profiling and lithographic performance modeling of the post-exposure bake (PEB) process have demonstrated that the rate of heating and cooling may have an important influence on resist lithographic response. Generally, wafers undergoing PEB processing are transferred on and off a plate maintained at a steady-state temperature. Using commercial test wafers with resistance-type sensors, wafer temperature measurements may be correlated with the plate temperature with a reported uncertainty (k =1) of 20 mK in the range 15 C to 230 C. Such tight temperature control is required in order to meet CD budgets. Measuring the transient surface temperature during the heating or cooling process with such accuracy can only be assured if the sensors embedded in or attached to the test wafer do not affect the temperature distribution in the bare wafer. For a typical heating process, heat transfer analysis predicts that at early times, the difference between the lower and upper wafer surface temperatures may be close to 100 mK, while the difference at steady-state conditions is close to 5 mK. The time-varying temperature gradient across the wafer thickness, combined with the disturbance caused by the thermal mass of an imbedded sensor can contribute significantly to the error in measuring transient surface temperatures.In this paper we report on an experimental and analytical study to compare the transient response of imbedded platinum resistance thermometer (PRT) sensors with a surface-deposited, thin-film thermocouple (TFTC). The TFTCs on silicon wafers have been developed at NIST to measure wafer temperatures in other semiconductor thermal processes. Experiments are performed on a test bed built from a commercial, fab-qualified track system with hot and chill plates using wafers that have been instrumented with calibrated type-E (NiCr/CuNi) TFTCs and commercial PRTs. Time constants were determined from an energy-balance analysis fitting the temperature-time derivative to the wafer temperature during the heating and cooling processes. The time constants for instrumented wafers ranged from 4.6 s to 5.0 s on heating for both the TFTC and PRT sensors, with an average difference less than 0.1 s. The time constants measured on cooling ranged from 5.6 s to 6.4 s and the RTDs averaged between 0.3 s and 0.4 s longer. For a given sensor undergoing multiple cycles, the repeatability of the measured time constant was approximately 0.3 s. The experimental value for the TFTC sensor is in agreement with heat transfer modeling of the bare wafer. A further purpose of the paper is to provide a detailed description of the measurement and analysis methods, with associated uncertainties. The study should contribute to an understanding of transient temperature measurement methods and limits of error. Such information should be useful to track system operators, sensor designers and lithographic simulators.
Data Analysis and Modeling for Process Control, Technical Conference | | Data Analysis and Modeling for Process Control | SPIE
February 26-27, 2004
Proceedings of SPIE--the International Society for Optical Engineering
post exposure bake, resistive-type temperature sensors, temperature measurements, thin-film thermocouples