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Single Photon Calorimeters

Perhaps the most intriguing advance in X-ray astronomy instrumentation in the 1990s has been the development of single photon calorimeters, spearheaded by work at NASA's Goddard Space Flight Center. These devices detect X-rays by the temperature pulses they generate in a small absorber which is cooled to a fraction of a Kelvin.

When an X-ray stops in a detector, it gives all of its energy to one electron. That electron can rattle around in the detector and give energy to other electrons. All these excited electrons would rather go back to their original energy. They want to return to what is called the 'ground state'. Through scattering with other electrons or with vibrations in the solid itself, they can lose that extra energy. But that energy has to go somewhere. What it does is heat the solid and increase its temperature. If you measure the change in temperature, you can measure how much energy the X-ray originally had.

How are heat and energy and temperature all related? Heat is a manifestation of energy. Heat and energy are measured in the same units (Joules). We usually think of energy as heat if we are thinking of the total energy of a large ensemble of objects that can exchange energy with each other and come into equilibrium. So, when an X-ray photon heats a solid, it gives its energy to the whole solid. On average, each atom is vibrating a little bit more than before the X-ray hit. Temperature is the way we relate the total energy of a system to its state of disorder (entropy). A physical property called "heat capacity" tells us how much the temperature rises in a material if we put in a certain amount of energy.

Suppose we wanted to measure the temperature increase due to an X-ray photon being absorbed. We'd want a very sensitive thermometer, something that had some physical property that changed a lot for a small change in temperature. And we'd want the detector to have a small heat capacity, so its temperature would change a lot for a small change in energy. And you'd want to do the whole thing at very low temperatures, because at room temperature there would already be too much thermal energy in your detector to see the very small change in energy from the X-ray. That is what an X-ray calorimeter does. It uses a silicon thermistor which has an electrical resistance which changes dramatically with small changes in temperature. It has a low heat capacity. And it operates at less than 0.1 K. That's Kelvin. Zero on the Kelvin scale is an absolute zero and represents the cessation of all thermal vibrations. Water freezes at 273 K. Nitrogen liquefies at 77 K. Helium liquefies at 4 K. and we operate calorimeters at less than 0.1 K! Calorimeters are able to get the best spectral resolution of any non-dispersive spectrometer.

Diagram of an X-ray single photon calorimeter
Diagram showing the
essential elements of
a calorimeter. Inset shows
temperature response to an
X-ray hit.

Energy Resolution

Single photon calorimeters work by the low-noise conversion of absorbed energy to heat. Such a device consists of an X-ray absorber and a thermistor that is linked through a load resistor to a low-noise amplifier. The temperature rise induced by the absorption of an X-ray produces a voltage pulse from which energy information can be extracted. The trick is to measure a small increase in temperature on top of a background noise of intrinsic thermal fluctuations and Johnson noise. Johnson noise is a fundamental noise associated with any resistance. The limiting energy resolution is given by the equation delta E = 2.36 x Eta x sqrt(k T0 2C) where C is the heat capacity (in joules per Kelvin) of the detector at a heat sink temperature T0, k is Boltzmann's constant, and Eta is a detector constant dependent primarily on the properties of the thermistor. Typically, Eta has a value in the range 1-3 for silicon thermistors. Non-ideal effects make the realized resolution somewhat worse than this. Other thermometer technologies, such as superconducting transition edge sensors, make lower values for Eta attainable.

Spatial Resolution

In order to keep the heat capacity low, yet use an absorber that is opaque to X-rays, individual calorimeters tend to be small. For example, the area of the calorimeter pixels on XRS, an instrument to be part of the Astro-E satellite, is 0.625 mm x 0.625 mm. If you want to have more area, we can pack a lot of calorimeters close together. This can be a bit tricky, because you need to find a way to get the signal connections out between the individual detectors and you need room for the connection to the heat sink. This is done on the XRS calorimeters by making the absorbers bigger than the thermometers to which they are attached. Thus, XRS has a 6 x 6 array of calorimeters (of which only 32 are actually read out) with a gap of only 0.015 mm between detectors. With X-ray optics with sufficiently good focusing capabilities, this would be an imaging array.
image of XRS calorimeter
View of the XRS calorimeter
under construction.

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