# Temperature Measurement

## Hot Enough For You?

Accurate measurement of temperatures, particularly of wafers in process without undue disturbance of reactor conditions, is by no means trivial. How does one measure the temperature of an object? Let's look at some of the techniques available...

Thermometer: temperature measured based on expansion of a liquid or solid.

• liquid: volume expansion from bulb to narrow tube; 0-100°C
• solid: differential thermal expansion, bimetallic couple 0-300°C

Thermometers are inexpensive and readily available. It is often difficult to get good thermal contact between the thermometer and the object whose temperature you're trying to measure.

Thermocouples: these are made by joining wires with different responses of the electrochemical potential to temperature gradients. The gradient of electron chemical potential integrated over the length of the wire between junctions creates a small voltage which indicats the temperature of the junction relative to the contacts.

• up to 1500°C available
• junction temperature must equal the temperature of the object to be measured: use very fine gage wire or insert the junction deep into a hole in the object
• since the signal is generated along the length of the wires, their properties must be uniform anywhere a temperature gradient exists, and you can't switch to another metal (e.g. copper) until you're sure the temperature is constant at ambient
• Si wafers with embedded thermocouples are commercially available

Pyrometer: here one measures temperature by looking at infrared radiation emitted from an object.

• fast, non-contact, usable in vacuum and remote from sample
• single-wavelength measurement requires knowing the emissivity of the sample
• multiple wavelength techniques are available which are self-compensating; if you measure emission at two wavelengths and two temperatures you have four equations for the four unknowns (emissivity and temperature)
• one can also use the reflectance of the surface at the same wavelength as a measure of its emittance (from Kirchoff's law)

Diffuse reflectance / IR absorption: look for the absorption edge related to the semiconductor bandgap; from its energy (if the semiconductor is known) one can derive temperature.

• only applicable to semiconductors
• best for direct-bandgap [GaAs, InP], less effective for Si and Ge
• limited to about 500 °C (Si), 650°C (GaAs), due to generation of intrinsic carriers
• requires low-doped wafers for thru-wafer method

Acoustic propagation: Lamb waves (bending waves) have a propagation velocity with a well-defined temperature dependence. If you launch a wave at one point on a material with known mechanical properties (such as a Si wafer) you can time its arrive elsewhere and thus obtain the temperature.

• requires ability to contact the wafer (e.g. with lift pins)
• fast and potentially accurate; applicable over a wide temperature range
• wafer must be free to flex
• no simple way to create temperature maps across the wafer

All direct-contact methods rely on good thermal contact with the object being measured, which is not always easy to achieve. Pyrometric methods are vulnerable to calibration errors, especially with silicon wafers, whose properties in the infrared depend on just about everything (doping, deposited layers, thickness, back surface preparation). Accurate temperature measurement takes care; it is a good idea to confirm any single measurement with a complementary method.

Some references:

"Wafer Temperature Measurement in a Tungsten Deposition System Using 'Optical Fiber Pyrometry" D. Cammenga [SEMATECH] and "Temperature Measurement during implantation at elevated temperatures (300-500°C)" Peter Vandenabeele and Karen Maex [IMEC] J Vac Sci Technol B9 2784 (1991)

"Silicon Temperature Measurement by IR Absorbtion..." J. Sturm and C. Reaves IEEE Tr El Dev 39 81 (1992)

"Two-Wavelength Pyrometry with Self-Calibration", Daniel Ng, NASA Lewis, NASA tech briefs (1998?)

"Resolution of Silicon Wafer Temperature Measurement by In Situ Ellipsometry in a Rapid Thermal Processor" R. Sampson and H. Massoud [Duke U] J. Electrochem. Soc. 140 2673 (1993)

"Heat transfer in a microelectronics plasma reactor" J. Daviet, L. Peccoud and F. Mondon J. Appl. Phys. 73 1471 (1993)