Efficiency of XR-100T-CZT Detectors
Application Note (ANCZT-1 Rev. 1)

Users are often interested in the detection efficiency of the XR-100T-CZT detectors. Due to charge transport effects, defining the detection efficiency is somewhat subtle. The purpose of this note is to provide general information on efficiency, for estimating system performance, and to recommend procedures for measuring the actual efficiency of a given detector.

Introduction

As is well known¹, when a beam of energetic photons, X-rays or g-rays, passes through a material the result is a simple exponential attenuation of the primary beam. Each of the possible interaction processes can be characterized by a probability of occurrence per unit path length in the absorber. The sum of the probabilities for the individual processes is the total probability per unit length that the photon is removed from the beam. This is termed the linear attenuation coefficient, is denoted µ, and has units of inverse length (cm-1). The number of primary photons transmitted through a thickness t is

where I₀ is the flux of incident photons, t is the thickness of the attenuator, µ is the linear attenuation coefficient, and Itrans is the flux of transmitted primary photons. The number of primary photons interacting in a thickness t is obviously

The linear attenuation coefficient obviously depends strongly on energy, since the interaction mechanisms are energy dependent. The attenuation is often described using the mass attenuation coefficient, µ_m=µ/p where p is the density of the medium. This can be written in units of cm²/g, with the density in g/cm³, or in units of barns (1 barn = 10^-24 cm²) with the density in atoms per cm³.

There are several different processes by which photons interact. In the energy range most often measured with the XR-100T-CZT, the most important processes are the photoelectric interaction and Compton scattering. In a photoelectric interaction, the entire incident energy of the interacting photon is deposited in the detector, while in Compton scattering, only a portion of the incident energy will generally be deposited in the detector. Photoelectric interactions contribute to the full energy, which is usually of primary interest. The probability of a photoelectric interaction is usually of primary interest.

Application to the XR-100T-CZT

Amptek's standard XR-100T-CZT consists of a 2 mm thick Cd_1-xZn_xTe (CZT) detector located behind a 10 mil (250µm) Be window. The Zn fraction of the CZT is typically 0.1. The probability of a photon interaction somewhere in the 2 mm CZT thickness is the product of (1) the probability of transmission through Be and (2) the probability of interaction in CZT,

The attenuation coefficients can be obtained through a variety of tables or through commercially available software². Table 1 lists attenuation coefficients at roughly log-spaced energy intervals from 1 keV to 10 MeV. It also lists the probability of an interaction occurring in the 2 mm physical thickness of CZT. The probability calculation includes the effects of transmission through the Be window and of stopping in the CZT, but neglect the effects of trapping and hole tailing. Both total and photoelectric probabilities are given. Plots of the interaction probabilities are shown in Figure 1 and Figure 2. A linear interpolation between the tabulated values is generally valid at low energies, with a log-log interpolation more accurate at high energies.

Table 1. Table of linear attenuation coefficients for CZT, along with interaction probabilities for the 2 mm CZT thickness. This table does not reflect the effective depth due to hole tailing, as discussed in the text.

Figure 1. Linear plot of interaction probability over the lower energy range (Be window responsible for low energy response).

Figure 2. Log-log plot of interaction probability between 1 keV and 1 MeV (Be window responsible for low energy response).

Consequences of Trapping and Hole Tailing

CZT is a wide bandgap, high-Z, compound semiconductor material. It is used for X-ray and g-ray spectroscopy because it has a very high linear attenuation coefficient, permitting high efficiency in a small volume, and low leakage currents, permitting low electronic noise without cryogenic cooling³. However, like other compound semiconductors, it exhibits significant spectral distortions due to hole trapping. As is discussed elsewhere⁴, the trapping length of holes in CZT is much smaller than the linear dimensions of the detector. For interaction occurring near the anode, virtually all of the signal is due to electrons and so the full charge is collected. For interactions occurring near the cathode, virtually all of the signal is due to holes and so a much smaller charge is collected.

The result is that the measured signal, the measured "energy", depends upon the depth of the interaction on the detector, decreasing with increasing depth. In the output spectrum, one observes a tail of counts towards lower amplitudes, an effect known as "hole tailing". Figure 3 is a plot of the pulse height as a function of depth in the detector, computed from the Hecht relation⁵ for two different values for the hole lifetime. Figure 4 is a plot of a measured spectrum demonstrating hole tailing. This was a measurement of a ⁵⁷Co source, which emits primarily at 122 keV. The blue trace in Figure 4 is the raw spectrum. The tail of counts extending to low values is due to hole tailing.

Figure 3. Plot showing the induced signal size as a function of depth, computed for two different values of the hole lifetime.

Figure 4. Measured ⁵⁷Co spectra, obtained with an Amptek's XR-100T-CZT. The blue trace shows the raw data, with hole tailing down to low amplitudes. The red and black traces show the result of applying risetime discrimination. The resolution is improved, but the efficiency is lower than that expected from the physical dimensions of the detector.

Note that in Figure 3, for the blue curve, about 40% of the depth of the detector produces a full signal. The rest of the depth produces a smaller signal. The effective volume of the detector, which contributes to the primary, full energy peak, is only 40% of the physical volume of the detector. For the red curve, about 20% of the detector volume contributes to the full energy peak.

For CZT, it is critical to distinguish between the total geometric efficiency and the efficiency of the full energy peak. The total geometric efficiency, which is due to the total physical volume of the detector, can be used to compute the total rate of counts in the detector. The efficiency of the full energy peak, which is due to the volume of the detector leading to "full charge collection", can be used to compute the total rate of counts in the primary peak. The phrase "full charge collection" is in quotation marks because it is not well defined. The charge collection efficiency decreases smoothly with increasing depth. Different users may define the full energy peak differently, depending on the specific application.

In Amptek's XR-100T-CZT, risetime discrimination (RTD) is used to minimize spectral distortions due to hole tailing. Figure 3 showed that the induced signal size is correlated with depth in the detector. The risetime of the pulse from the preamp is also well correlated with depth in the detector. Therefore, Amptek's PX2T-CZT measures the risetime of the pulses and rejects those with a long risetime. This leads to a significant improvement in the quality of the spectrum, as can be seen in Figure 4. The red and black traces show the effects of two different RTD thresholds. The black trace provides the very highest resolution, while the red trace shows somewhat poorer resolution but higher efficiency. The RTD setting for the red trace was set to maximize the efficiency for a given definition of the ⁵⁷Co photopeak region⁶.

When RTD is used with the XR-100T-CZT, the detection efficiency is significantly lower than would be anticipated from the physical dimensions of the detector. The effective depth depends upon the charge transport properties of the material. These are not well controlled by the manufacturer, so significant variations exist from one detector to the next. The effective depth also depends upon the RTD setting. The effective depth of Amptek's XR-100T-CZT detectors is commonly in the range of 0.5 to 1 mm, so is one quarter to one half of the physical depth.

Measuring the Efficiency

In many applications it is important to know the detection efficiency at a particular energy. Because there exists a wide variation in the effective depth of Amptek's XR-100T-CZT detectors, if a user requires precise knowledge, the best solution is to measure the actual efficiency at the energy of interest from some well-known standard. Since this can be difficult, another approach is to measure the effective depth of the particular detector. There are two approaches to this measurement.

If one has a calibrated source, with a very well known strength and an energy high enough to only be partially absorbed in the CZT, then the effective depth can be readily computed by inverting the relation above:

For example, from Figure 1 the 122 keV line from ⁵⁷Co should be detected with 70% efficiency and from Table 1 that the linear attenuation coefficient is 6.22 cm-1. Assume that a lab measurement shows that this line is detected with 35% efficiency. This gives t=0.7 mm. This effective depth can be used to computed the efficiency at any other energy (above the energy where attenuation in the Be window is significant).

In the absence of a calibrated source, then a single source which emits g-rays at two distinct lines with a well known ratio can be used, if at least one of the lines is high enough in energy to be detected with <100% efficiency and both are above the energy where the Be window is significant. The source must not attenuate either line significantly. For example, ⁵⁷Co emits at 14.4 keV with 9.8% efficiency and 122 keV with 85.6% efficiency. We define P1 and P2 as the probabilities of emission of the two lines, N1 and N2 and the measured counts of the two lines, and m1 and m2 are the linear attenuation coefficients of the two lines. The ratio of the measured counts will obviously be

Applying some algebra, this implies

ANCZT-1 Rev. 1 Application Note written by Bob Redus

Footnotes