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CRYSTAL COUNTERS
In article ¹, which is a continuation of the review devoted to crystal counters ² published in Uspekhi Fizicheskikh Nauk, questions connected with the experimental investigation of their most important characteristics are considered.
The determination of the mobility of electrons in a crystal by experiment is based on measuring the rise time of a pulse caused by the incidence of an ionizing particle on the crystal. This time is equal to the “transport” time, i.e., the time taken by the electrons to pass from the negative
to the positive electrode. Reliable results are obtained under the condition that the secondary electrons are produced at the negative electrode and that the greater part of the electrons is not captured by traps uniformly distributed in the crystal. For this, the ionizing particle must have a short range.
The mobility \(v\) is determined from the rise time of the pulse
\[ \tau=\frac{d}{vE}, \]
where \(d\) is the thickness of the crystal and \(E\) is the electric-field strength. If the time \(T\) during which the electron remains free is small in comparison with \(\tau\), then
\[ \tau=\frac{\bar{x}}{E\cdot v}=T\left(1-e^{-\frac{d}{vET}}\right), \]
where \(\bar{x}\) is the average distance traversed by a group of electrons in one pulse. On irradiating diamond with electrons, the value
Fig. 1. Experimental investigation of the rise time of the pulse in a crystalline (AgCl) counter. The measurements were made at an absolute temperature of \(77^\circ\).
Fig. 2. Experimental investigation of the rise time of the pulse in a crystalline (AgBr) counter. The measurements were made at an absolute temperature of \(77^\circ\).
\(\tau=0.04\ \mu\text{sec}\) was obtained, agreeing with the value of the mobility calculated by Zeitz (\(156\ \text{cm}^2/\text{V sec}\)). According to Platt’s data, in a CdS crystal \(0.2\ \text{mm}\) thick it is less than \(0.2\ \mu\text{sec}\) (the ionization source is \(\alpha\)-particles). The mobility of electrons in liquid argon, measured at \(E=10\,000\ \text{V/cm}\), is approximately \(40\ \text{cm}^2/\text{V sec}\). According to Mil’ton and the author, the mobility of electrons in an AgCl crystal \(0.4\ \text{cm}\) thick is practically independent of the magnitude of the electric field (Fig. 1). The difference in the values obtained (\(114\) and \(163\ \text{cm}^2/\text{V sec}\)) was explained by the authors as being due to the strong dependence of the mobility on the stresses in the crystal and on its temperature. Analogous dependences were obtained by Yamakawa, who studied AgBr crystals (Fig. 2).
If the energy of the ionizing particle and the input capacitance of the circuit are known, then the energy \(\varepsilon\) expended in forming an ion pair in a crystal can be found by measuring the magnitude of the voltage pulse.
Fig. 3. Polarization effect in a crystalline (AgBr) counter when it is irradiated with electrons from P\(^ {32}\).
Finding from
\[ V_{\mathrm{eff}}=\frac{n_0 e}{C}\,F\left(\frac{\delta}{d}\right) \]
the number of secondary electrons \(n_0\), one determines the value \(\varepsilon\) from the expression
\[ \varepsilon=\frac{H}{n_0}. \]
Here the trapping of part of the electrons by traps is not taken into account; as a result, the mobility values obtained in this way will be overestimated. According to data from a number of experimenters, the energy for forming an ion pair in diamond and CdS is about 10 eV. For liquid argon a value of \(\varepsilon\) of about 25 eV was obtained. In crystals of silver halide counters, free from impurities, the value of \(\varepsilon\) is 7.6 eV (AgCl) and 5.8 eV (AgCl).
A number of authors have observed polarization effects in crystal counters. Thus, for example, the polarization effect in solid argon was manifested in the fact that pulses continued to arise after the electric field was removed from the crystal. A study of polarization caused by irradiating an AgBr crystal with electrons showed that the number of registered pulses and their magnitude decrease with increasing irradiation time (Fig. 3). The abscissa axis gives the numbers of the channels counting pulses of a definite amplitude.
Fig. 4. Distribution of pulses caused by monoenergetic electrons (\(E = 0.4\) MeV). The tail on the left is explained by scattering of the electrons. The dashed line shows the theoretical distribution.
decrease with increasing irradiation time (Fig. 3). Along the abscissa axis are plotted the numbers of the channels counting pulses of a definite amplitude.
It has been established that the efficiency of a diamond counter increases rapidly with the growth of the voltage gradient, with saturation occurring at about
$E = 4000\ \text{V/cm}$.
According to observations, the maximum efficiency of a diamond counter is 60%. When an AgCl crystal 4 mm thick was irradiated with radium $\gamma$-rays, an efficiency value of 13% was obtained.
A crystal counter is a linear device. This is confirmed by experiments with fast electrons (Fig. 4). The spread in pulse magnitudes is the result of nonmonoenergetic electrons, statistical deviations, amplifier noise, etc.
In the registration of $\gamma$-rays, linearity is naturally absent, since the magnitude of the pulses depends on the place where the secondary electrons are formed and on the energy they impart. The most valuable property of crystal counters is their strong stopping power, many times greater than the stopping power of gas. This property makes the use of crystals effective for the registration of high-energy $\gamma$-quanta.
B. Ratner
CITED LITERATURE
- R. Hofstadter, “Crystal Counters” (II), Nucleonics 4, No. 5, 29 (1949).
- R. Hofstadter, “Crystal Counters,” Uspekhi Fizicheskikh Nauk 39 (1949).