Thermal detectors as X-ray spectrometers

TL;DR: In this paper, the limits to the energy resolution of thermal detectors are derived and used to find the resolution to be expected for a detector suitable for X-ray spectroscopy in the 100 eV to 10,000 eV range.

Abstract: Sensitive thermal detectors should be useful for measuring very small energy pulses, such as those produced by the absorption of X-ray photons. The measurement uncertainty can be very small, making the technique promising for high resolution nondispersive X-ray spectroscopy. The limits to the energy resolution of such thermal detectors are derived and used to find the resolution to be expected for a detector suitable for X-ray spectroscopy in the 100 eV to 10,000 eV range. If there is no noise in the thermalization of the X-ray, resolution better than 1 eV full width at half maximum is possible for detectors operating at 0.1 K. Energy loss in the conversion of the photon energy to heat is a potential problem. The loss mechanisms may include emission of photons or electrons, or the trapping of energy in long lived metastable states. Fluctuations in the phonon spectrum could also limit the resolution if phonon relaxation times are very long. Conceptual solutions are given for each of these possible problems.

Summary

I. Introduction

• An ultimate goal for any spectrometer is to offer high resolving power and throughput simultaneously over a wide energy range.
• A thermal detector operating at cryogenic temperatures can offer the high efficiency of the solid state detector and resolution comparable to that of dispersive spectrometers.
• An operating temperature of 0.1 K has been chosen as the design temperature because it permits the desired resolution, and it can easily be achieved with an adiabatic demagnetization refrigerator operating with a 2 K heat sink.
• This will degrade the resolution of the spectrometer.
• The authors will discuss potential loss mechanisms and techniques for combatting them.

II. Theory of Operation

• A typical bolometer detector has three parts: an energy absorber, a semiconducting thermometer, and a support structure to carry away the applied heat and establish electrical contact to the thermometer.
• In this instructive example the authors will devise a solution for a white noise spectrum.
• For practical detectors using ser: iconducting thermistors, the assumption of white noise is quite good; the phonon noise and Johnson noise powers have substantial frequency 1 dependence, but their quadrature sum' does not.
• The estimates of U in each interval will be averaged with weights proportional to the squares of their signal to noise ratios.
• This analysis implicitly assumes that the moment of arrival of the pulse is known.

Optimization

• The authors will now give detailed formulas, for the NEP in the ideal bolometr, proceed to the energy resolution, and finally compute the optimum bias conditions and ultimate energy resolution of the detector.
• This work is based directly on Ref. b and parallels similar optimization calculations for infrared detectors.
• Note the very important fact that the thermal conductance G and the time constants T and ie have disappeared entirely from the equation.
• Values of A from 2 to 10 are typical for semiconducting thermomaters, although A w -100 to -1000 can be achieved for superconducting transitionedge detectors.

Y

• The value of input resistor for which the ratio of total amplifier noise to resistor Johnson noise is a minimum can be shown to be Rn e n/in .
• The corresponding total amplifier noise is EQUATION ) Added in quadrature, it proauces less than a 3% increase in system noise.
• If the authors are forced to choose a resistance near 10 MA for the device, the amplifier noise voltage is 67% of the detector noise, resulting in a 20% increase in system noise.
• Load resistor noise cannot be avoided, but can be made negligible by choosing the !resistance much larger than the detector resistance.

IV. Ste' e Detector Design

• The authors have calculated the characteristics of a complete detector desir n as an example of the performance which might be obtained in practice.
• Rather than trying to achieve the ultimate in resolution, the authors have chosen a design which uses established integrated circuit fabrication and silicon etching techniques at tolerances well within their routine capabilities.
• All materials used have well-known thermal properties, with measured values near the proposed operating temperature available from the literature.
• The thickness of the absorber is chosen to have reasonable stopping efficiency for x-rays up to q ke V, and the 0.5 mm x 0.5 mm size is suitable for use with many focussing instrtments.
• For an effective Y equal to 2.4 and 6 = 3, the results of the previous section give an energy resolution of 1.1 eV FWMO where the authors have assuned a conservative value of 4.0 for A (the logarithmic temperature sensitivity of the thermistor).

V. Detector Efficiency Variations and Resolving Power Limits

• At least five processes may modulate the responsivity of the detector.
• 'Random variations of these factors can limit the resoj , '-ing power (U/DU) of the detector.
• 1. The x-ray energy may be r,..arried by a photoelectron which escapes from the detector before depositing its full energy, also known as These factors are.
• Energy may be held in metastable states that are long-lived with respect to the readout process.
• The deposited energy may not be uniformly converted into a thermal spectrum o ^h'iOns before the phonons leak out through the support legs.

Photoelectron Escape

• A few photoelectrons produced near the detector surface will escape through that surface without depositing their full energy.
• Choices are limited by heat capacities at low temperatures .
• Most excitons decay by channels which give rise to rapid thermalization, but some small fraction may decay radiatively.
• Si is quite transparent to those photons and they can escape from the detector.
• Some solutions to this potential radiative loss problem are to 1) produce material without radiatively efficient traps, 2) put a sufficient number of neutral donors in the crystal to dominate undesirable traps, or 3) metallize the external surface of the detector with aluminum to prevent loss of photons created by radiative decays.

Nonthermal Phonon Spectrum

• A fourth potential problem is the fact that the spectrum of phonons in the detector following the incidence of an x-ray may be highly nonthermal.
• The spectrum changes little more for times as long as 2 ps. 10 Therefore, it is possible that the spectrum in their detectors might also remain nonthermal for a time scale on the order of 100 µs.
• It will be difficult to Provide sufficiently fast amplifier input*:= risetimes for detector time constants much shorter than 100 us, however,".
• The authors have one concept for measuring the energy deposited in the detector, with a constant responsivity regardless of the location of the x-ray.
• The detector in Fig. 1 would be modified to have four matched thermometers located at the corners of the silicon absorber and connected in series.

VI. Summary

• The authors propose a thermal detector as an efficient high resolution x-ray spectrometer.
• A theory for the resolution of the detector as a function of its physical parameters has been presented.
• For a given detector design and cryostat temperature, the detector temperature, controlled by its bias power, is the only free parameter.
• The authors derive the maximum resolution of a given detector for the optimal value of this parameter.

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NASA

-1WOMWEAMor-
Technical Memorandum 80092
THERMAL DETECTORS AS
X-RAY SPECTROMETERS
(NASA;-TM-86092) THERMAL DETECTORS AS X-RAY

N84-23866
SPECTROMETERS (NASA) 27 p HC A03/MF A01
CSC.L 14B
Unclas
G3/35 191:9
9
S.H. Moseley, J.C. Mather, and
D. McCammon
APRIL 1984
National Aeronautics and
Space Administration
Goddard Space Flight Center
Greenbelt, Maryland 20771
f
r
d

thermal Detectors as
X
-Ray
Spectrometers
S. H. Moseley
J. C. Mather
Goddard Space Flight Center
Greenbelt,, MD
20771
D. Mc Camnmon
Department of Physics
University of Wisconsin
Madison, WI 53706
Abstract
We show that sensitive thermal detectors should be useful for
measuring very small energy pulses, such as those produced by the
absorption of x-ray photons.

The measurement uncertainty can be very
small , making the technique promising for high resolution nondispersive
x-ray spectroscopy.
We derive the limits to the energy resolution of such thermal
detector
,
5
.

We use these to find the resolution to be expected for a
detector suitable for x-ray spectroscopy in the 100-10,000 eV range.

If
there is no noise in the thermalization of the x-ray, resolution better
than 1 eV full width at half maximum (FWM) is possible for detectors
operating at 0.1 K.
Energy .loss in the conversion of the photon energy to heat is a
potential problem.

Statistical fluctuations of lost energy would reduce
the energy resolution of the detector.

The loss mechanisms may include
emission if photons or electrons, or the trapping of energy in long-lived
metastable states. Fluctuations in the phonon spectrum could also limit
the resolution if phonon relaxation times are very long.

We give
conceptual solut. ons for each of these possible problems.
a
E
M yr

I. Introduction
An ultimate goal for any spectrometer is to offer high resolving power
and throughput simultaneously over a wide energy range.

Silicon solid
state diode detectors used as x-ray spectrometers have good efficiency but
their resolution is only 100-200 eV. Wavelength dispersive spectrometers
offer resolution < 10 eV, but have low throughputs.

A thermal detector
operating at cryogenic temperatures can offer the high efficiency of the
solid state detector and resolution comparable to that of dispersive
spectrometers.
Bolometers have been used for many years as infrared detectors (Low,
1961) . Recent work
102,3
shows that at temperatures as low as 0.32 K, the
dominant noise in properly constructed devices is due to the thermodynamic
fluctuations in the device itself'.
The energy sensitivity of a thermal detector scales as T/T where T is
the operating temperature and C the detector heat capacity.

Practical
designs for detectors can be made using the substantial body of low temper-
ature data existing in the literature. An operating temperature of 0.1 K
has been chosen as the design temperature because it permits the desired
resolution, and it can easily be achieved with an adiabatic demagnetization
refrigerator operating with a 2 K heat sink. Also, experimental data show
that the heat capacities of many of our candidate materials decline quite
slowly or actually increase below 0. 1 K.
2
-4

t-

4
1
t1l
r
i
We will demonstrate that the noise
in
the front end
amplifier junction
field effect transistor
CJFET)
and load resistor
need not seriously affect
the resolution.
The performance of a bolometer as an x-ray spectrometer depends on the
noiseless conversion of the x-ray to heat. If some fraction of
the energy
is
lost,
that fraction need not be exactly constant from photon to photon.
This will degrade the resolution of the spectrometer.
We will discuss
potential loss mechanisms and techniques for combatting them.
II. Theory of Operation
r
A typical bolometer detector has three parts: an energy absorber, a
semiconducting thermometer, and a support structure to carry away the
i
applied heat and establish electrical contact to the thermometer. A design
f
for such a detector is given in Figure 1 and discussed in Section TV. The
detector temperature is measured by applying a DC bias voltage to the
series combination of the thermometer and a load resistor. 9nall varia-
tions in the thermistor voltage are measured using a low noise amplifier,
whose first stage is usually a JFET source follower mounted near the
detector but operating at about 80 K.
The basic Theory
of
these detectors has been summarized.
4,5
A more
complete theory has been given by Mather,
6
and optimization for their use
as power detectors has been carried out.7
Ii
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r
3