Thermistor temperature sensitivity

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SUMMARY

The discussion focuses on the temperature sensitivity of thermistors, highlighting their superiority over traditional thermocouples for high-precision temperature measurements. The key equation presented is σ=σ_0e^(-E_g/2kT), which relates conductivity to temperature. The user attempts to derive the temperature sensitivity by integrating the conductivity equation, resulting in dσ/dT = [σ_0(E_g/2k)e^(-E_g/2kT)]/T^2. However, the challenge lies in connecting resistance sensitivity to temperature sensitivity, which remains unresolved.

PREREQUISITES
  • Understanding of semiconductor physics, specifically intrinsic silicon properties
  • Familiarity with the concepts of conductivity and resistance
  • Knowledge of thermistors and their applications in temperature measurement
  • Basic calculus for integration and differentiation of equations
NEXT STEPS
  • Research the relationship between resistance and temperature sensitivity in thermistors
  • Explore advanced semiconductor physics, focusing on temperature dependence of conductivity
  • Learn about the practical applications of thermistors in high-precision temperature measurements
  • Investigate the impact of material properties on thermistor performance
USEFUL FOR

Students studying semiconductor physics, engineers designing temperature measurement systems, and researchers interested in high-precision thermistor applications.

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Homework Statement


. (a) It was pointed out in Section 15.3 that the temperature sensitivity of conductivity in semiconductors make them superior to traditional thermocouples for certain high-precision temperature measurements. Such devices are referred to as thermistors. As a simple example, consider a wire of 0.5 mm in diameter × 10 mm long made of intrinsic silicon. If the resistance of the wire can be measured to within 10^-3 Ω, calculate the temperature sensitivity of this device at 300 K. (hint: The very small differences here may make you want to develop an expression for dσ/dT.)

Homework Equations


The Attempt at a Solution


I know the equation relating temperature and conductivity is

σ=σ_0e^(-E_g/2kT)

So I integrate the formula to get dσ/dT = [σ_0(E_g/2k)e^(-E_g/2kT)]/T^2

and I know the formula for conductivity
σ=l/RA
where l is the length, R resistance, and A area.

My problem is that I don't know how to relate resistance sensitivity to temperature sensitivity
 
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