Transition Edge Sensors
One technique used for measuring energy is calorimetry. The energy absorbed by a physical system with heat capacity C (the calorimeter) causes an increase in temperature according to the following equation
Since the energies of interest in the Dark Matter and x-ray detection fields are on the order of 10 keV (~ 1fJ), using of calorimeters with C as low as ~ 1 pJ/K, results in a temperature change of ~ 1 mK. This illustrates the need for highly sensitive thermometers.
An accurate method of measuring temperature involves using resistive thermometer to transform the temperature change into a voltage signal, based on the following circuit.
By applying a voltage bias across a temperature sensitive resistor and measuring the current flowing through the circuit we can detect any temperature changes. In order to be sensitive to truly minute temperature variation, however, the dependence of the resistance on temperature, R(T) must be quite large. This dependence is quantified by the variable alpha, which is defined as
Superconductors are well known for having zero resistance below a certain "critical temperature" (Tc), while above this temperature they have a normal state resistance that is characteristic of the metals of which they're made.
Within the span of ~ 1 mK around the Tc, the resistance rises from zero to its normal value, resulting in a large value of alpha, and thus a strong dependence of R on T, as shown in this figure. When some energy is absorbed in the device, the temperature and resistance quickly increase,
eventually the device cools back down to the ambient temperature, accompanied by a decrease in resistance. This produces a pulse whose amplitude is a good measure of the absorbed energy.
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