3. Thermal X-Ray Detectors

Moseley et al. (1984) proposed X-ray microcalorimeters as a means of simultaneously attaining high spectral resolution and throughput. In contrast to a bolometer which measures an integrated radiant flux, a calorimeter measures the energy of individual X-ray photons by the temperature rise they cause when absorbed in a small sensing element. The concept of a calorimeter is similar to that of a bolometer. However it is subject to more stringent design constraints due to the necessity of thermalizing individual photons rapidly. Figure 3 is a schematic of an X-ray microcalorimeter. An X-ray photon hits an absorber which converts its energy into heat. In its simplest form ( $\Delta$T $\ll$ T) the resulting temperature rise is $\Delta$T = ${E\over C}$ where E is the energy of the photon and C is the heat capacity of the calorimeter. This is sensed by a thermometer, typically consisting of a doped semiconductor. A thermal link to a heat bath conducts heat away from the calorimeter so that the temperature decays exponentially to the baseline value with a thermal time constant $\tau$ = ${C\over G}$ where G is the thermal conductance of the link.

Figure 4: Concept of a microcalorimeter.

For this device to be useful several conditions must be met. The heat capacity C must be small enough to produce a significant temperature rise. Because the heat capacities of most of the materials used to construct calorimeters vary as T³ as T$\to$ 0 this may be achieved by operating the device at low temperatures, typically below 100 mK. For applications over the 1-10 keV band, the absorber is a significant contributor to the total heat capacity. The main contributor to the heat capacity of the calorimeter is the absorber. Normal metals such as gold and silver are excellent absorbers and thermalizers of X-ray photons but their large electron heat capacities render them unsuitable for practical devices. Alternative choices for absorbers are semimetals such as HgTe or superconductors such as tin (e.g. Moseley et al. (1992)).

The absorber must have a high X-ray opacity and a low heat capacity, and must convert the photon's energy into phonons in a time much less than $\tau$. Superconductors have lower heat capacities than normal metals. However, in a superconductor much of the energy of a deposited X-ray goes towards breaking Cooper pairs into quasiparticles. When these recombine into Cooper pairs this energy is converted into phonons. One problem is that the quasiparticles can take a long time to recombine which degrades the resolution. Raising the normal electron concentration can reduce this effect. Thus heat capacity and recombination time must be traded off to obtain optimum performance (Stahle et al. (1993)).