Crystal Counters

R. Hofstadter*)

Until the present time, the main body of experimental data in the field of nuclear physics has been obtained with the aid of gas-filled counters. It seemed that there was no need for other types of counters. However, the new branches of knowledge that have developed in recent years have required improved means for counting individual particles and photons.

Such areas as the interaction of γ-rays with matter, the measurement of decay times in the disintegration of elementary particles and nuclei, work with powerful installations such as, for example, synchrotrons and synchrocyclotrons, and the study of cosmic rays require a more perfect counting mechanism than that used up to now. The difficulties in using gas-filled counters for these purposes are explained by the long charge-collection time, the large dead time, and the low counting efficiency.

In this connection, the development of “solid” counters—the conducting-type crystal counter and the scintillation counter—appears very promising. These counters should in many ways contribute to obtaining new information in the enumerated areas of physics.

The purpose of the present review is to set forth a number of published facts concerning the operation of the first of these counters—the crystal counter.

Historical Review

The earliest investigations of the effects of ionizing radiation in crystals showed the presence of induced conductivity ³, ⁴, ⁵. However, the smallness of the observed effects, polarization effects, the unsuccessful choice of materials (mica, glass, quartz, rock salt), and the imperfection of the amplification and counting technique employed did not allow the authors of these works to create a crystal counter.

As a practical instrument for detecting individual particles, the crystal counter was first described by Heerden ⁶,¹, who used silver chloride crystals at low temperature. Soon after his discovery and, apparently, independently of him, Frerichs and Warmin—

*) R. Hofstadter, Nucleonics 4, No. 4, 2 (1949). Translated by B. R.

... showed that β-particles and γ-rays can be detected with the aid of crystals of pure cadmium sulfide.

In this case the ionization currents were produced by the simultaneous entry into the crystal of a large number of β-particles or γ-quanta. It was assumed that, with sufficient amplification, it would be possible to record also an individual particle entering a CdS crystal. Stetter^8 observed a single conducting pulse in a solid (diamond), but his experiments were not completed by the construction of a counter. In one of Herden’s papers^10 the counting effect of positive particles in diamond is described. Confirmation and further development of Herden’s work were carried out by Stritt^11 and Hofstadter^12,13.

BASIC PROPERTIES

Conductivity and counting

The use of a solid instead of a gas as a counter has a number of advantages, namely: a) the small dimensions of the counter (which ensures good geometry of the experiment), b) a large stopping power (which is useful for work with γ-rays and high-energy particles), c) a small resolving time (which ensures a high counting rate and the counting of coincidences), d) transfer of a greater energy to each ion pair than in a gas (which ensures a better signal-to-noise ratio).

Most of these advantages are inherent both in a counter of the conducting type and in a scintillation counter. The advantages of a solid counter of the conducting type are, to a certain extent, offset by a number of difficulties arising in working with it, described in detail below. These include: deformation of the crystal, polarization effects, variations in counting efficiency in different parts of a single crystal, the need for annealing and for operation at low temperatures*).

Fig. 1. Diagram of a crystal counter.

A brief description of the operation of a crystal counter may be given with the aid of Fig. 1. A particle, for example a β-particle of high energy, enters the crystal at point \(A\). Until it comes to rest it liberates secondary electrons from the crystal counter. A process occurs analogous to ionization in a gas, when along the track

) For some materials. (Translator’s note.*)

particles form positive and negative ions. In the crystal, a large number of free secondary electrons is concentrated along the track of the \(\beta\)-particle. At the same time, an equal number of positive “holes” is formed.

Holes may be immobile or mobile. If they are immobile, we have an obvious difference from the phenomena occurring in a gas. Let us suppose that the holes are immobile*).

Under these conditions, the cloud of liberated electrons is accelerated by the electric field in the crystal. The motion produced by the field is superposed on random thermal motion, which the electrons perform as a result of collisions with ions or atoms of the crystal lattice. The theory of the collision process was given by Fröhlich and Mott\({}^{20}\). The combined effect of these motions gives a displacement of the electrons in the direction toward the positive electrode.

On the way to the positive electrode, an individual electron may pass near a “capturing” center or “trap”**). Traps may be impurity atoms, voids, cracks, or any other defects of the lattice.

If an electron passes sufficiently slowly and close to a trap, it will be captured and thus become immobile. Electrons can sometimes be released from a trap by thermal quanta, but the probability of this process is small\({}^{22,23}\), and we shall not dwell on it. Owing to trapping phenomena in a weak field, a case is possible in which all electrons will be captured before reaching the positive electrode. In a stronger field the electrons will move with greater velocity and, consequently, will not remain for a long time near traps. Therefore they may cover the distance between the negative and positive plates without being captured and, apparently, will be completely retarded in the electrode. In this case the electrons will pass through the entire thickness of the crystal. It is clear that a further increase of the field will give no other result except an increase in the drift velocity of the secondary electrons***); the number of collected electrons will tend to a constant value.

In the given energy range, the process of formation of ionizing-particle secondary electrons in a nonconducting crystal may be described in the simplest way by means of the theory of the solid state. Such a description corresponds to the qualitative theory of photoconductivity in crystals\({}^{21,23,24}\).

*) For AgCl at low temperature this was shown by Lefeld in a delicate experiment on the study of photoconductivity\({}^{28}\).

) A discussion of traps in solids may be found in\({}^{31}\). The possibility of the existence of surfaces acting as traps was investigated by Tamm. I. Tamm, Phys. Zeits. d. Sowjetunion 1, 733 (1932). See also W. Shockley, Phys. Rev. 56**, 317 (1939).

***) We do not take into account here complex processes; they are considered in\({}^{40}\).

Let us suppose (Fig. 2) that under normal conditions in the insulator the quasi-stationary region \(A\) of possible energy states is completely filled in accordance with the Pauli exclusion principle. When a \(\beta\)-particle enters the lattice and approaches electrons in state \(A\), it transfers them to higher states of the normally unoccupied conduction region \(D\). In this region the electron is in a quasi-free state and can receive energy from the electric field \(E\), causing it to pass from level \(G\) to some unoccupied level \(H\).

It is highly probable that the electron will quickly descend to the base of the conduction region, before it has had time to move far from the place where it became free. Under these conditions \(G\) and \(H\) must be regarded as lying near the base of the conduction region.

Fig. 2. Energy-level diagram for a nonconducting crystal in which there are traps \((F)\) and impurity atoms \((BC)\).

Since the electron no longer occupies state \(H\), the released electron can again fall onto this level without violating the Pauli exclusion principle. In such a process the electron moves quasi-freely in the direction of the field, acquiring energy during its motion.

This process does not continue indefinitely because of the numerous collisions of the electron with ions or atoms of the lattice. In collisions the moving electron apparently gives up to the lattice the kinetic energy it had previously acquired.

Thus the electron is ready to repeat this process once again, and its motion may be represented as a series of jumps with a component of motion in each of them in the direction of the electric field.

It is assumed that during these jumps the electron remains in region \(D\). This will be the case if there are no other processes tending to remove the electron from this region. However, during one of the jumps the electron may pass very close to the center of a trap (for example, \(F\) in Fig. 2, or a local level \(C\) adjacent to an impurity atom).

In such cases the electron may be captured and held in \(F\) (or \(C\)). The length of time during which the electron remains in \(F\) depends on the depth of the energy well \(h\) and on the temperature\(^{22}\).

When an electron is captured in \(C\), at the moment of transition of the electron-impurity system into the ground state \(B\), a quantum of luminescence may be emitted\(^{23}\). In order for state \(B\) to be unoccupied, it must be assumed that the holes in region \(A\) formed after the transition of electrons (under the action of the \(\beta\)-particle) into state \(D\) rapidly move toward the ato-

impurities and that the electrons pass from state \(B\) into these holes.

Such a process can also be used to explain the properties of certain materials used for scintillation counting. In this case, however, the motion of holes is postulated, and there are no means of proving its existence in scintillating materials. In AgCl at low temperatures the holes apparently do not move.

It is, of course, also possible that the electron leaves the trap by thermal excitation, after which, owing to migration, it finds itself near another free level \(B\). The electron can fall onto this level, again emitting a light quantum \(^{23}\). Luminescence of this type may prove to be prolonged, since a considerable time is required for the electron to leave the trap \(F\).

Secondary electrons, torn out by light or by a \(\beta\)-particle, are captured according to the process phenomenologically described by Hecht \(^{25}\), who confirmed his analysis by experiments on the photoconductivity of AgCl. The essence of Hecht’s analysis is as follows. Suppose that an electron remains free for some average time \(T\), which does not depend on the magnitude of the field. Then, on average, during this time the electrons will not be captured by traps. The probability for an electron to be captured during a small interval of time \(dt\) is equal to \(\dfrac{dt}{T}\).

If there are \(n\) free electrons, then during the time \(dt\) of them

\[ dn = n\,\frac{dt}{T} \]

will fall into traps. The number of electrons remaining free after a time \(t\) will therefore be

\[ n = n_0 e^{-\frac{t}{T}}, \tag{1} \]

where \(n_0\) is their number at the instant \(t=0\). The mean path traversed by an electron before capture will obviously be

\[ \delta = vET, \tag{2} \]

where \(E\) is the field strength, and \(v\) is the mobility, or drift velocity at unit field strength*). Theoretical estimates of the mobility may be found in the works of Fröhlich and Mott \(^{30}\) for polarized crystals and of Seitz \(^{26}\) for nonpolarized crystals.

The quantity \(\delta\), sometimes called the “drift path,” is extremely important for investigations of crystal counters and photoconductivity. The electron increases the charge of the pulse only by an amount proportional to the path traversed in the direction of the field. Thus, the electron does not necessarily transfer its entire charge \(e\) to the grid \(G\) (Fig. 1). Indeed, from theoretical considerations \(^{27}\) one can

*) It is assumed that the drift velocity is small compared with the thermal velocity of the electrons.

CRYSTAL COUNTERS

one may expect that an electron traversing a path \(\Delta x\) in a crystal of thickness \(d\) creates on the grid \(G\) a charge

\[ q_{\mathrm{eff}}=\frac{e\Delta x}{d}. \tag{3} \]

This equation is confirmed by Hecht’s work. If the hole also moves, then the induced charge is

\[ q_{\mathrm{eff}}=e\frac{\Delta x_{-}+\Delta x_{+}}{d}, \tag{4} \]

where \(\Delta x_{-}\) and \(\Delta x_{+}\) are the distances traversed by the electron and the hole before the electron is captured by a trap. Accordingly, in the case when the holes are immobile, the signal voltage is

\[ V_{\mathrm{eff}}=\frac{e\Delta x}{Cd}, \tag{5} \]

where \(C\) is the capacitance to ground of the system formed by the grid, the crystal, and also the connections.

Simple calculations can be carried out for the case when the bombarding particle penetrates only a very small thickness of the crystal. For example, let an \(\alpha\)-particle enter the crystal at point \(A\) (Fig. 1) and penetrate into it to a distance of the order of \(10\,\mu\). Such penetration is negligibly small in comparison with the thickness of the crystal, amounting to one or several millimeters. In this case \(n_0\) secondary electrons are formed at a very small distance from the negative electrode \((x_0=0)\). Each secondary electron may, before being captured by a trap, travel a different distance \(x\). The number of electrons that have traveled distances from \(x\) to \(x+dx\) will be

\[ dn=\frac{n_0}{\delta}e^{-\frac{t}{\tau}}\,dx, \]

which follows from (1), (2), and the expression

\[ x=vEt. \tag{6} \]

Expressing in terms of \(x\), we obtain

\[ dn=\frac{n_0}{\delta}e^{-\frac{x}{\delta}}\,dx. \]

The electrons captured in the interval from \(x\) to \(x+dx\) will give an effective charge

\[ dq_{\mathrm{eff}}=\frac{ex}{d}\,dn=\frac{exn_0}{\delta d}e^{-\frac{x}{\delta}}\,dx, \]

and hence

\[ q_{\mathrm{eff}}=\frac{\delta n_0 e}{d}\int_{0}^{d}\frac{x}{\delta}e^{-\frac{x}{\delta}}\frac{dx}{\delta}, \]

after integration over all electrons traversing the distance from \(x=0\) to \(x=d\).

Electrons capable of traversing a distance exceeding \(d\) transfer the full charge \(e\). The charge transferred by them is added to \(q_{\mathrm{eff}}\), giving \(Q_{\mathrm{eff}}\). Consequently,

\[ Q_{\mathrm{eff}} = \frac{\delta n_0 e}{d} \left( \int_{0}^{d} \frac{x}{\delta} e^{-\frac{x}{\delta}} \frac{dx}{\delta} + \frac{d}{\delta}\int_{d}^{\infty} e^{-\frac{x}{\delta}} \frac{dx}{\delta} \right) \]

or

\[ \frac{Q_{\mathrm{eff}}}{n_0 e} = \frac{\delta}{d} \left(1-e^{-\frac{d}{\delta}}\right) = F\left(\frac{\delta}{d}\right) = \frac{\bar{x}}{d}. \tag{7} \]

The graph of this function is shown in Fig. 3 at the top. Hence the magnitude of the voltage pulse on grid \(G\) (Fig. 1), corresponding to the rapid formation of \(n_0\) electrons at the cathode of the crystal, will be

\[ V_{\mathrm{eff}}=\frac{n_0 e}{C}\,F\left(\frac{\delta}{d}\right). \tag{7a} \]

Fig. 3. Curves of the dependence of the pulse magnitude on \(\dfrac{\delta}{d}\); \(\delta\) is proportional to the electric field. Top: for weakly penetrating particles (according to (7)). Bottom: for particles penetrating into the crystal and ionizing throughout the entire volume (according to (7b)).

It is obvious that the dimensions of the pulse depend on the value of the function \(F\left(\dfrac{\delta}{d}\right)\), which has characteristic saturation properties. Often the curve is plotted as a function of the electric field, rather than of \(\delta\). Expression (2) shows that \(\delta\) is proportional to \(E\). Having obtained such a dependence from experimental data, one can in principle find the value of \(\delta\). This was done in the study of photoconductivity\({}^{28}\). Here, however, it is necessary to assume that the electrons, until they reach the positive electrode, are not delayed by a barrier (for example, by a crack). In other words, determination of \(\delta\) requires that the sole cause of electron retardation be traps sparsely distributed in the crystal (a homogeneous distribution of traps). If, for example, one assumes a barrier in the form of a plane separating

two crystals in contact, then the effective charge \(Q_{\mathrm{eff}}\) will be

\[ Q_{\mathrm{eff}}=n_0 e\,\frac{\delta}{d}\left(1-e^{-\frac{S}{\delta}}\right), \tag{8} \]

where \(S\) is the distance between the cathode and the barrier. The saturation value of \(Q_{\mathrm{eff}}\) in this case will be \(Q_{\mathrm{eff}}=\dfrac{n_0 e S}{d}\), whereas in the preceding case (absence of a barrier)

\[ Q_{\mathrm{eff}}=n_0 e. \tag{9} \]

Here it should be noted that the very fact of saturation by no means signifies that the electrons traverse the entire distance between the electrodes. Only saturation at the maximum value of the charge \(n_0 e\) definitely indicates that the electrons pass through the whole thickness of the crystal.

It is useful to give an expression for the magnitude of the pulse in the case when the bombarding particle is penetrating, as, for example, an electron, proton, or meson of high energy. In this case the secondary electrons will be formed along the track of the particle in the crystal. The track will be surrounded by a sheath of free electrons and holes.

If we assume that the particle ionizes uniformly along its entire path, then the magnitude of the resulting pulse can be obtained either directly from the calculations leading to formula (7), or from a somewhat modified formula of Mott and Gurney (see, \(^{21}\), p. 122). The charge is found to be equal to

\[ \frac{Q_{\mathrm{eff}}}{n_0 e}=\frac{\delta}{d}\left[1-\frac{\delta}{d}\left(1-e^{-\frac{d}{\delta}}\right)\right], \tag{7б} \]

where \(n_0\), as before, is the total number of secondary electrons released by the ionizing particle in the crystal. The form of this function is shown in Fig. 3 below. As \(\delta\to\infty\), the magnitude of the pulse tends to the value \(\dfrac{n_0 e}{2}\), if again the assumption is made that there are no other barriers except rarely situated traps. If the holes are also mobile, the magnitude of the pulse doubles.

Incidentally, it should be noted that the voltage producing saturation is proportional to the square of the crystal thickness. This follows from the fact that, in order to obtain a given fraction of the maximum pulse, the value of \(\delta\) must be proportional to \(d\). However, \(\delta\) itself is proportional to \(\dfrac{V_0}{d}\); consequently, \(V_0\) must be proportional to \(d^2\). Experimental confirmation of this is given in the work of Flechsig \(^{22}\).

Mean path of a secondary electron \(\delta\)

Let us consider the factors determining the magnitude of the path \(\delta\), since this characteristic is very important in deciding whether some material can be used as a crystalline counter. If \(\delta\) is small, then it seems very doubtful that the crystal, under normal conditions, would be an effective counter (at moderate voltage gradients). In this case the exponent in \({}^{(7)}\) may be neglected, and

\[ Q_{\mathrm{eff}}=n_0 e^{-\frac{\delta}{d}}, \tag{10} \]

i.e., for small \(\delta\), \(Q_{\mathrm{eff}}\) is also small. Another condition for the impossibility of using a crystal as an effective counter is the presence of barriers for which

\[ \frac{S}{d}\ll 1 \]

(see \({}^{9}\)). This condition is considered below.

The quantity \(\delta\), which is the mean free path with respect to trap centers, may be expressed as follows:

\[ \frac{\delta}{E}=\frac{e}{6kT}\,\frac{l}{P\sigma}, \tag{11} \]

where \(T\) is the absolute temperature, \(l\) is the mean free path length with respect to the lattice, associated with mobility, \(P\) is the number of uniformly scattered trap centers per unit volume, and \(\sigma\) is the cross section for capture of an electron by a trap center.

The value of \(P\) is not known for most crystals (\(P\) may depend on the prior treatment of the crystal). Values of \(l\) may be taken from theoretical works \({}^{20,26}\).

Table 1 presents these values, calculated from the formulas of Fröhlich and Mott \({}^{20}\) for various substances.

Table 1 may be used to obtain values of \(\delta\). For this it is necessary to choose the quantities \(\sigma\) and \(P\), which are difficult to determine. Mott and Gurney take \(\sigma \simeq 3\cdot 10^{-15}\ \mathrm{cm}^2\) for AgCl. We also use this value in our calculations, although it would be desirable to refine it.

The value of \(P\) for AgBr is taken from Lehert’s data for \(\delta/E\) and from calculations of the quantity \(l\), which agree well with experimental data. Let the values of \(P\) for AgBr and TlBr be equal to the value taken for AgBr. For AgCl and AgBr one can establish an upper limit in the estimate of \(P\), if one assumes that the effective mechanism of capture into a trap is an \(F\)-center*), i.e., a lattice in which an electron replaces a negative halide ion \({}^{30}\). To find—

*) We have assumed that the effective capture mechanism is an \(F\)-center, since the path varies inversely with the concentration of \(F\)-centers (see \({}^{21}\), p. 127).

CRYSTALLINE COUNTERS

Table I*)

*) Fröhlich–Mott:

\[ v=2\sqrt{\frac{3}{\pi m k\theta}}\, e a_0\left(e^{-\frac{\theta}{T}}-1\right) \left(\frac{\varepsilon-\varepsilon_0+1}{\varepsilon-\varepsilon_0}\right) \]

\((a_0\)—radius of the first Bohr orbit);

\[ \theta=\frac{hc}{k\lambda}\,(\varepsilon-\varepsilon_0+1)^{\frac12};\qquad l=\frac{1}{e}\sqrt{3mkTv}; \]

\(\lambda\)—absorption wavelength, \(T\)—absolute temperature.

The effective mass of the electron in the conduction band is taken equal to the mass of a free electron.

**) By order of magnitude.

For the determination of \(P\), the calculation of \(^{31}\)*) was used. Here an expression is given for the optical absorption coefficient as a function of the density of capture centers, the oscillator strength, and the width of the absorption band of \(F\)-centers in crystals of the KCl and KBr type. By investigating the absorption in pure LiF, KCl, KBr, and NaCl crystals, one can establish an upper limit for the values of \(P\) for these samples. Table II presents the values of \(\delta\), calculated from these data and from (11). In this calculation the amplitude of oscillation is taken equal to 0,75, except in the case where it was measured experimentally (KCl).

From Table II it is seen that at low temperatures the values of \(\delta\) for the majority of crystals are large \((0,2\div10,0\ cm)\). Crystals of the KCl and KBr type with low \(\delta\) have not yet been used as counters.

*) See also \(^{30}\), p. 386.

Table II*)

*) The trapping capture cross section is taken to be:

\[ \sigma = 3\cdot 10^{-15}\ \mathrm{cm}^{2}. \]

Number of secondary electrons \(n_0\)

In addition to the two quantities \(\delta\) and \(l\), the number of secondary electrons \(n_0\) is also very important for crystalline counters. The magnitude of the pulse is directly proportional to \(n_0\), as is evident from (7), (7a), and (7b). The question of the magnitude of \(n_0\) is directly connected with the question of the distribution of the energy of the bombarding particle between the crystal lattice and the quasi-free electrons moving in the conduction band. Apparently, the ionizing particle first produces a very large number of electrons. The number of such electrons corresponds, in order of magnitude, to the energy of the particle divided by the energy interval \(\rho\) in Fig. 2. The duration of the ionization process is about \(10^{-12}\) sec. After this time has elapsed, the electrons may recombine with holes, forming a Frenkel exciton\(^{32}\), or give up their energy to the lattice in another way, for example as a result of several collisions\(^{6}\). In any case, the free electrons leave the conduction band, and their energy is transferred to the lattice.

As a result, the electrons remain free for too short a time (of the order of magnitude of about a microsecond) to be drawn into the conduction process. These considerations may be summarized as follows: if a significant fraction of the energy of the bombarding particle is expended on thermal excitation of the lattice, then little energy remains for the creation of free electrons, and comparatively few of them are formed.

The measurement of the efficiency of formation of conduction electrons is reduced to determining the “energy per ion pair” or the “energy per free electron.” It is known that for a gas the corresponding quantity is about 30 eV. For an AgCl crystal an analogous value has been found, equal to 7.6 eV, i.e., considerably smaller than for a gas. There are no theoretical calculations for polarized and nonpolarized crystals that would make it possible to compare the experimental and theoretical data. Therefore at present one must rely only on experimental results.

The number of secondary electrons released by an ionizing particle that loses all its energy in the crystal may be represented by the coefficient \(\psi\), multiplied by the ratio of the particle energy to the smallest value of the energy per ion pair \(\rho\), or to the energy interval between the filled and conducting regions. Under these conditions the number of secondary electrons is

\[ n_0=\frac{H}{\rho}\psi, \tag{12} \]

where \(H\) is the initial energy of the particle.

If \(\psi=1\), then no energy is lost in thermal processes. Hearden’s results give, for AgCl, a value of \(\psi\) of about 0.6. Values of \(\psi\) for other materials are given in the second part of the review.

Polarization Effects

A number of investigators\(^{33,34,35}\) have observed that, when an electric current passes through a crystal, polarization phenomena are observed. It was to be expected that similar phenomena should occur also in crystals used as counters\(^{6}\). In the first experimental works\(^{14,16}\) these effects were indeed observed. At present the mechanism of polarization processes is still not fully understood. Here a very simple theory of a number of polarization phenomena is presented, which may help to explain some of the observed phenomena.

The polarization effect in crystalline counters is usually revealed by a gradual decrease in the amplitude of pulses as their number increases. This fact is explained by the displacement of charge caused by the electric field, which creates a field directed opposite to the initial one. As a result, the electrons travel a shorter distance before being captured; i.e., \(\delta\), which depends on the magnitude of the true field, decreases as the number of counted events increases. It is assumed here that the captured electrons and holes are immobile.

Polarization effects can also be found for the case in which the holes move (as, for example, in diamond) and are subsequently captured by traps. We shall, however, consider only the simplest case:

which applies, for example, to AgCl, in which only the electrons move before being captured by traps, while the holes remain immobile.

Let us suppose that the process of ionization and the subsequent displacement of electrons in the crystal cause a separation of positive and negative charges, as shown in Fig. 4. The model presented in this figure, of course, simplifies the actual picture of the charge distribution, since the positive charge formed by immobile holes and the negative charge of the captured electrons are here assumed to be concentrated in planes parallel to the surfaces of the crystal (or electrodes). A closer approximation to the actual distribution of charge produced by monoenergetic $\beta$- or $\alpha$-particles entering the crystal from the negative electrode is given by the following model: a uniform distribution of positive charge in region $B$ (Fig. 4) and an exponential decrease for the distribution of negative charge in the remaining part of the crystal. Our treatment also includes the possibility of the existence of a crack or of a disruption of the crystal bond between regions $A$ and $C$. The distance $b$ is of the order of half the range of the $\beta$- or $\alpha$-particle in the crystal. Here it is assumed that the positive charge is concentrated on a positively charged surface with density $\sigma$*) at a distance $b = R/2$ from the negative electrode, where $R$ is the mean range of monoenergetic $\alpha$- or $\beta$-particles. A layer of equal negative charge, separating regions $A$ and $C$, will be formed independently of the magnitude of the electric field and of whether a region of electron traps exists.

Fig. 4. Model of polarization in a crystal. The positive holes in the hatched region are replaced by a positively charged plane (I), having surface charge density $+\sigma$. The electrons are captured in the barrier plane (II), where the surface charge density is $-\sigma$. $R$ is the mean range of the incident particle.

In the particular case of an ideal crystal without traps and barriers, the charged layer will arise at the positive elec-

) In what follows, $\sigma$, in contrast to the preceding section, denotes the surface charge density. (Translator’s note.)*

trode \((a=d-b)\). In an ordinary crystal (for example, an AgCl crystal with traps) this will occur only in a strong electric field.

It is further evident that in the particular case of \(\alpha\)-particles and fission fragments, for which the penetration into the crystal is very small (10 μ or less), the layer of positive charge is situated practically at the negative electrode. The phenomenon under consideration resembles the polarization of a dielectric between the plates of a capacitor. If the voltage on the capacitor is maintained by a battery (i.e., \(e=V_0\)), then the electric field in the capacitor is

\[ E=\frac{V_0}{d}, \tag{13} \]

i.e., it remains the same as in the absence of the dielectric. The charges appearing on the electrodes as a consequence of the polarization of the atoms and molecules of the dielectric are neutralized by charges coming from the battery and reaching the plates of the capacitor.

In exactly the same way, in a crystal under ionization caused by \(\alpha\)-particles and fission fragments, the charged layers I and II are situated at the electrodes, and the polarization, owing to the accumulation of charges on the electrodes, proves to be insignificant. The field \(E\) in the crystal remains equal to \(\dfrac{V_0}{d}\), on the assumption that \(\dfrac{b}{d}\) is small*). As a result, in a small counter a very large number of heavy particles (\(10^8\) or more) may be counted before a decrease in the magnitude of the pulse becomes noticeable. In a real crystal containing barriers, polarization may begin earlier.

Polarization by β-particles

If a particle penetrates deeply into the crystal, as, for example, the \(\beta\)-particle in Fig. 4, then the polarization of the crystal becomes appreciable, and the electric field no longer corresponds to (13). A simple electrostatic calculation, made without taking edge effects into account,

*) If it is assumed that region \(B\) is filled with positive charges and if \(\dfrac{b}{d}\ll 1\), then it can be shown that the secondary electrons formed in this region by the ionizing particles will give an additional polarization field coinciding in direction with the main field. In \(B\) there is a narrow subregion of width \(\dfrac{b^2}{2d}\), adjoining boundary plane I, where the additional field is directed opposite to the main one and is of the same order as in region \(A\). Therefore region \(A\) may be represented as a somewhat broader effective region.

shows that the field in regions \(a, b, c\) is determined by the equations

\[ E_a=\frac{V_0}{d}+\frac{4\pi\sigma}{\varepsilon}\left(1-\frac{a}{d}\right), \tag{14} \]

\[ E_b=\frac{V_0}{d}-\frac{4\pi\sigma}{\varepsilon}\frac{a}{d}, \tag{15} \]

\[ E_c=\frac{V_0}{d}-\frac{4\pi\sigma}{\varepsilon}\frac{a}{d}=E_b, \tag{16} \]

where \(\sigma\) is the charge per unit area and \(\varepsilon\) is the static dielectric constant of the crystal. From these equations it is evident that additional fields exist, caused by polarization. In regions \(b\) and \(c\) the additional field coincides with the main one; in region \(a\) it is directed opposite to the main one. Let us calculate the reduction in the size of the pulse due to these polarization fields.

The surface charge density \(\sigma\) in the above formulas can be expressed in terms of the number of ionization events and the energy associated with each event. If \(N\) particles, each with energy \(H\), enter the crystal uniformly through its surface \(S\), and if, furthermore, the energy required to form an ion pair is denoted by \(p\), then the density of positive charge will be

\[ \sigma=\frac{NH}{pS}e, \tag{17} \]

where \(e\) is the absolute value of the electron charge. Substituting this expression for \(\sigma\) in (14) and solving it, we obtain for the case when the initial field \(\frac{V_0}{d}\) is reduced to the fraction \(f\frac{V_0}{d}\),

\[ N_f=\frac{V_0p\varepsilon S}{4\pi dHe}\,\frac{f-1}{1-\frac{a}{d}} =\frac{n(1-f)}{1-\frac{a}{d}}, \tag{18} \]

where

\[ n=-\frac{V_0p\varepsilon S}{4\pi dHe}. \tag{19} \]

In these equations \(V_0\) is a negative potential and, consequently, \(N_f\) is a positive quantity equal to the number of pulses reducing the field to its fraction \(f\cdot \frac{V_0}{d}\). Thus, if the electric field is reduced to \(1/2\), \(1/5\), and \(1/10\) of its initial value, then \(N_f\), respectively, will take the values

\[ 0.5\,\frac{n}{1-\frac{a}{d}};\qquad 0.8\,\frac{n}{1-\frac{a}{d}};\qquad 0.9\,\frac{n}{1-\frac{a}{d}}. \tag{18a} \]

Equation (7) gives the magnitude of the pulse as a function of the field \(E_a\), since \(\delta\), according to (2), is directly proportional to \(E_a\). Hence it is clear that the amplitude of the pulse obtained from (2) and (7) decreases with increasing \(N\).

In many applications of crystal counters it is desirable to use strong fields, in order to operate reliably in the saturation region for pulse amplitudes. Then, owing to saturation (see (7) or Fig. 3), decreasing the field by a factor of two will lead only to an insignificant reduction in the pulse size. Decreasing the field by a factor of five will cause a noticeable reduction in the pulse magnitude. Moreover, from (18a) it is clear that even small increments in the number of counted events are sufficient to obtain relatively large changes in the effective field strength in the region \(a\).

Let us give a numerical example: suppose that our source of \(\beta\)-particles is \(P^{32}\); then the mean particle energy is \(660\ \mathrm{KeV}\). The range of such a particle in silver chloride is about \(0.05\ \mathrm{cm}\). Thus, \(b\) may be taken equal to \(0.025\ \mathrm{cm}\). If it is assumed that there are no barriers and cracks in the crystal (a uniform distribution of traps), i.e. \(a=d-b\) or \(c=0\), then the negative layer is formed at the positive electrode*). Further, for a crystal of thickness \(0.5\ \mathrm{cm}\), \(a=0.475\ \mathrm{cm}\). Let us take \(V_0/d\) equal to \(5000\ \mathrm{V/cm}\) and \(\varepsilon=12\) (for AgCl). With \(S=1.0\ \mathrm{cm}^2\) and \(p=7.6\ \mathrm{eV}\) per ion pair, we find \(N_{0.5}\), \(N_{0.2}\), and \(N_{0.1}\) equal respectively to \(3.8\cdot 10^6\), \(6.1\cdot 10^6\), and \(6.8\cdot 10^6\) particles. A noticeable decrease in the pulse magnitude will occur in the interval between 3.8 and 6.1 million pulses.

In comparison with Geiger–Müller counters (whose lifetime is \(10^8\)—\(10^{10}\) pulses), these numbers are small. Although means have been found for reducing the polarization effect, the short lifetime poses serious obstacles to the use of such counters for rapid counting. It is true that heating the crystal removes the polarized charges, and after cooling the crystal is fit for use. It is possible that irradiation of the crystal with visible and infrared light can achieve the same effect.

Polarization caused by penetrating radiation

If polarization occurs throughout the entire volume of the crystal, for example when it is bombarded by \(\gamma\)-rays, then, when secondary electrons are removed from the positive electrode, a spatial positive charge is formed in the crystal. A saturation field again arises. Let \(N\) be the number of \(\gamma\)-quanta counted by a crystal of volume \(\tau\). It is assumed**) that each \(\gamma\)-quantum creates on average \(H/p\)

*) We do not consider the case in which the electron is captured in the region between layer I and the positive electrode. Such capture can undoubtedly occur, but its consideration lies outside the scope of our approximate calculation.

) Very approximately. (Translator’s note.)

secondary electrons. The positive space charge per unit volume will be

\[ \rho_0=\frac{NH}{p\tau}e. \tag{20} \]

In so doing we assume that the absorption of radiation in a crystal of the size under consideration (thickness \(0.5\ \text{cm}\)) is small. For the case of a uniform space charge one can show that the effective field is

\[ E=\frac{V_0}{d}-\frac{2\pi\rho_0}{\varepsilon}(d-2x), \tag{21} \]

where \(x\) is the distance from the negative electrode. This dependence is shown in Fig. 5. It should be noted that the effective field is numerically greater than the applied field for values \(x<\dfrac{d}{2}\), less than it in the region \(x>\dfrac{d}{2}\), and equal to the applied field at \(x=\dfrac{d}{2}\). Consequently, polarization effects first of all arise in the region \(x>\dfrac{d}{2}\). In this region the reverse field will gradually increase, so that with increasing \(\rho_0\), i.e., with an increase in the number of counted pulses, the number of captures will also increase. As an example one may take the following values. Let \(\dfrac{V_0}{d}=5000\ \text{V/cm}\), \(\tau=0.5\ \text{cm}^3\), \(d=0.5\ \text{cm}\), \(\varepsilon=12\), \(p=7.6\ \text{eV}\) per ion pair, \(H=0.5\ \text{MeV}\). The number of pulses necessary to reduce the field to one fifth of its initial value at the point \(x=\dfrac{3}{4}d\) will be \(1.6\cdot 10^6\). This case is difficult to consider in more detail, since the magnitude of the pulse depends on the energy transferred in the Compton effect, and on the place of origin of the secondary electrons after formation of the polarization field.

Fig. 5. Diagram of the electric field in the crystal. The inclined line characterizes the field when the crystal is irradiated with penetrating, for example \(\gamma\)-rays. A positive space charge of volume density \(+\rho_0\) is formed in the crystal. Electrons are displaced toward the plate \((x=d)\) and do not create a polarization field; \(\varepsilon\) is the dielectric constant. The horizontal line represents the initial electric field

\[ E=\frac{V_0}{d}. \]

Further remarks on polarization effects

a) It sometimes appears possible to use small electric fields, insufficient to displace most of the secondary electrons toward the positive electrode. Such a situation may arise when fast protons or mesons are used, losing in the crystal a considerable fraction of their energy and accordingly producing a large number of secondary electrons. In this case a signal is obtained that greatly exceeds the noise level, although the electrons do not move far. Before being captured by traps, the secondary electrons traverse only small distances. The holes are again assumed to be immobile, forming a polarization field in the crystal.

The polarization effect produced by such a displacement of charges can be compensated by moving an equal number of elementary charges in the opposite direction. This displacement can be achieved by changing the direction of the applied field for the time during which the number of counted pulses is equal to the number of pulses that caused the polarization. Such a repeated change of the field direction was described in ^14 and gave the desired result. It is unclear, however, how many times such a reversal can be applied without producing new effects.

It is obvious that such an operation should be effective for ionization occurring throughout the whole volume of the crystal, and not so effective in counting β-particles, when the incident particles have lower energy and pass through only a small part of the crystal near the negative electrode, and when saturating fields are usually required. Secondary electrons moving in the reverse direction when the sign of the field is changed do not go beyond the boundary determined by the range of the β-particles.

b) It should also be noted that the effective field in region \(B\) of Fig. 4 (or in the region \(x < \frac{d}{2}\) for the case of a space charge) is greater than the applied field. The field may increase so much that the entry of electrons into the crystal from the negative electrode becomes probable.^28 A number of specific properties of the crystal counter, noted by Waitemore and Streit,^16 can apparently be explained by such polarization effects.

Lefeldt^28 observed the conductivity of a silver chloride crystal at low temperatures after irradiating it with a large amount of light. This conductivity, obtained in the photoelectric effect, was explained^26 by the penetration of electrons into the crystal from the electrode due to the double charged layer located near the negative electrode.

Waitemore and Streit observed very large and nonperiodic pulses appearing after prolonged irradiation of the crystal

γ-rays. Their presence can be explained by fluctuations in the direct current from the negative electrode. False pulses in some crystals were observed at high voltages and, apparently, are not caused by polarization effects. Such false pulses were noted in TlBr—TlJ \(^{36}\) and, it is believed, are caused by inhomogeneities in the crystal specimens. When working with pure artificially grown crystalline specimens, false pulses were obtained rarely, apart from cases involving the use of very high gradients or long exposures of the crystals to ionizing radiation.

c) If our picture is correct, then after removal of the applied field (the high-voltage electrode is grounded), the following may be expected as a result of polarization:

1. When working with β-particles, large pulses of the opposite sign should not appear. If, after β-particles, one works with γ-rays, the appearance of such pulses is probable.

2. If γ-rays are used in the experiment, then pulses of both signs may be expected from Compton or other electrons arising in one or the other half of the crystal. The polarization field is equal to zero at the center of the crystal and has opposite signs in the two halves of the crystal. In practice, after removal of the applied field, pulses of opposite signs were observed. The author also observed such inverted pulses in AgCl when working with γ-rays. Experiments with solid argon \(^{42}\) are related to these problems, although here the mechanism of the phenomenon is apparently still more complicated.

d) We have considered effects caused by immobile positive regions. In reality, there also occurs (as was already noted) capture of negative space charge. In the first stages of polarization, the negative charges are almost entirely captured near the positive electrode and, consequently, have a very weak effect on the observed phenomena. Later, when the applied field decreases, capture of negative charges occurs throughout the whole crystal, and the calculation for such an arrangement of charge is no longer valid. But, after the initial polarization properties have been obtained, the influence of the negative space charge may be neglected.

TECHNIQUE AND APPARATUS

Materials

The materials used as indicators of individual ionization processes are AgCl \(^{6}\), AgBr \(^{37}\), C (diamond) \(^{8,10,15}\), ZnS \(^{38}\), TlBr—TlJ \(^{36}\), CdS \(^{39,40}\), and argon in the solid and liquid states \(^{41,42}\). Crystals of diamond, zinc sulfide, and cadmium sulfide can operate at room temperature; AgCl, AgBr, and TlBr—TlJ require the creation of a low temperature, since at room temperature they possess ionic conductivity.

Preparation of Crystals

Crystals operating at room temperature (diamond, ZnS, and CdS) require no preliminary treatment, apart from the necessary cleaning before use. Diamond and ZnS were used in the form of natural crystals. The CdS specimen was artificially prepared by Frerichs, and very high demands were placed on its purity.

Fluctuations of room temperature apparently do not affect the counting efficiency. Crystals of AgCl, AgBr, and TlBr—TlJ require careful preliminary heat treatment and very cautious storage. In a number of cases^36 no counting is observed at all before heat treatment.

The necessity of heat treatment for AgCl crystals was first demonstrated by Herden. He established that, after exposure to air, colloidal grains of silver appear in AgCl crystals and act as electron traps. These grains give the crystal a characteristic bluish tint, which can be completely removed by keeping the crystal for several hours at a temperature of 400° C.

In Heins’s work^43 with individual AgCl crystals, the suggestion is made that a very probable cause of electron trapping is their entry into regions of mechanical stresses. It is therefore quite possible that an additional result of heat treatment of an AgCl crystal is its release, during annealing, from stresses. Complete proof that regions of stress act at low temperatures as traps has not yet been obtained, although such properties seem very plausible.

Heins described in detail a process by which large AgCl crystals free from stresses can be obtained. As far as the author knows, these crystals were not intended to be used for counting purposes. In this connection it should be pointed out that even after preparing a stress-free crystal, touching it with the fingers is sufficient to produce stresses (as a consequence of a change in the temperature of the crystal). Such stresses are detected by examination in polarized light. To eliminate the appearance of stresses during touching and mounting of the crystal, a new technique was employed (see below), in which the crystal is not touched after it has been placed in the holder.

In any case, heat treatment of AgCl, AgBr, and TlBr—TlJ crystals clearly improves the properties of these materials as crystalline counters.

Below are given some data on the apparatus and annealing technique successfully used for the preparation of AgCl and AgBr crystals.

R. HOFSTADTER

Crystal Samples

Crystals used in work with solid conducting counters are selected from among natural crystals (diamond, ZnS) or grown artificially (AgCl, AgBr, TlBr—TlJ).

Diamond. Not all diamonds possess the ability to count. Up to the present time there is no physical criterion for selecting “counting” diamonds, apart from the counting property itself. An attempt was made to correlate data on the ultraviolet irradiation of samples with the property of counting γ-rays44. The results of this study show that diamonds that count γ-quanta belong to the variety possessing transparency in the ultraviolet (type II). An explanation of this property was proposed by the author45. However, the experimental observations have not yet been completed, and at present no final conclusion can be drawn. A study of the registration of γ-rays by diamonds46 indicated a better counting ability in diamonds of good quality, pure and white. This result is not in agreement with other investigations2, which did not establish such a correlation. It is much easier to find a diamond that counts α-particles. Unfortunately, no tests have been carried out to establish the connection between diamonds that count α-particles and γ-rays. It was pointed out, however, that in small crystals the observation of pulses from α-particles is far more probable than from γ-rays45,47. The reason for this is that an α-particle can lose all its energy in a small crystal, whereas the Compton electron liberated by a γ-quantum loses only a small part.

ZnS. The considerably smaller pulse magnitude than in diamond makes it difficult to study the counting properties of ZnS. Synthetic ZnS crystals have been obtained, but nothing is known about their counting qualities. It has been established that the presence of a small amount of impurities (up to 0.1%), chiefly germanium, does not impair the counting properties of the crystals.

CdS. The properties of non-luminescent and luminescent CdS crystals were investigated48. In the first case (an ordinary crystalline counter) the properties were studied at room temperature, and the pulse magnitudes from α-particles and electrons corresponded to the assumption that the liberated electrons are displaced in the direction of the anode without multiplication. In crystals of the luminescent type, a pulse amplification of the order of \(10^5\) was obtained, and the pulses from a single α-particle had an amplitude of about two volts. In the latter case the pulse lasted 0.05 sec. It is evident that in this counter the main role is played by secondary effects, whereas in the first type of counter only primary effects are significant. Crystals previously irradiated with infrared light lose all multiplying properties. Irradiation with visible light (a volume effect) restores the multiplication properties. The luminescence of the cry-

crystals giving secondary effects lies in the red and infrared regions.

Interesting experiments were also carried out with β-particles and γ-rays, confirming the results obtained earlier for AgCl.

Halide compounds of silver and thallium. All halide-containing crystals are prepared synthetically. For this purpose the methods of Kyropoulos^49 and Bridgman^12,10,16,50,5 were used; by the latter method very pure and homogeneous AgCl and AgBr crystals were obtained.

According to Bridgman’s method, the powder of the halide compound is placed in a round Pyrex tube sealed at one end, as shown in Figs. 6 and 7. The tube is suspended on a nichrome or platinum wire connected to a holder mounted in the upper part of the tube. After melting has begun, powder is added to the tube until the desired volume of melt is obtained. The temperature in the upper part of the furnace is maintained 10° above the melting temperature. The tube is lowered into the furnace at a rate of 1–2 cm per day by means of a motor and gear transmission. When the melt is lowered, it passes through the temperature zone at which the liquid crystallizes (AgCl—455°C, AgBr—434°C). To maintain constancy of the temperature and of the temperature gradient in the furnace, the use of a transformer supplying stabilized voltage proved sufficient; it is possible that more careful temperature regulation will give still better results. After the crystal has been lowered below the zone

Fig. 6. Glass melts and artificially grown crystals of silver chloride (above). Specimens of crystal counters cut from melts and ingots (below).

Fig. 7. Furnace; gear transmission and melt shown in position before the melt is lowered into the furnace (Bridgman method).

during crystallization the temperature of the furnace is uniformly lowered to room temperature. In the case of AgBr, a pure yellow crystal with a granular top is formed. At the apex the color of the crystal is usually darker, and sometimes even black. This is the region of impurities. The lower part of the crystal can be remelted and recrystallized again. After this the color of the crystal, with the exception of the very top, becomes uniformly light yellow.

Excellent results were obtained with such twice- and thrice-crystallized specimens. It is not difficult to make a normally reading system in the form of a cylinder (see Fig. 6—the far-right specimen). The glass is cut with a carborundum saw and the specimen is pressed out of the glass ring. To facilitate the latter operation, hyposulfite is sometimes used.

To remove carborundum dust from the surface and to eliminate stresses, the specimen is etched with hyposulfite, which is then thoroughly washed off. In this form an electrode layer can be applied to the specimen. This operation is carried out by spraying, by the evaporation method, or with the aid of special developers1. A paper developer and aquadag were used successfully. Crystals grown slowly have a smooth surface at the point of contact with the Pyrex tube, in contrast to crystals that formed rapidly.

Recently a large AgCl crystal, 3.7 cm in diameter and 6 cm long, was grown in a furnace 10 cm in diameter. This furnace was heated by two coils, and the temperature above, below, and at the level of crystallization was monitored by three thermocouples. If it is desired to introduce into the crystal impurities that evaporate at high temperature, the crystals are grown in vacuum. Unfortunately, the counting properties of specimens grown in vacuum have not been described in the literature. An attempt was made to grow crystals in a square Pyrex tube in order to minimize subsequent processing of the specimen. As a result, instead of a single crystal a polycrystal with small crystals at the corners was formed.

Fig. 8. Etch figure of a rolled AgCl specimen. The surfaces of small crystals are visible. Specimen diameter—3.1 cm.

Etching of AgBr specimens prepared by Bridgman’s method showed that usually each of them consists of separate crystals. Etch figures are clearly visible on the round specimen shown in Fig. 8. Crystals grown by Yamakawa and Harrison show almost no structure upon etching, except for the regions of inhomogeneity at the apex of the specimens.

For the detection of stresses and crystal boundaries, specimens may also be examined in polarized light. Despite the simplicity of such tests, the distortions arising from stresses make it preferable, when determining crystal boundaries, to use the etching method. More complete indications regarding the counting properties of crystals will apparently be provided by X-ray photographs of the crystals.

Specimens grown and cut by the method described above are shown in Fig. 6. Such crystals do not exhibit electrolytic or electronic conductivity at low temperature, i.e., they are insulators. Specimens taken from the upper part of the crystal or prepared from inhomogeneous material show conductivity even at low temperatures and cannot be used as counters. Commercial AgCl specimens also possess such conductivity. Spurious pulses caused by such conductivity may appear at large voltage gradients in contaminated specimens. It is believed that at least part of the spurious pulses observed in crystal counters made from halide compounds is caused by these impurities.^36 An interesting circumstance is that pure AgCl and AgBr crystals prepared by recrystallization, after exposure to light at room temperature, darken more slowly than impure specimens, which indicates a connection between darkening and the presence of impurities in the specimen.

A crystal removed from the mold and freed from the glass must be annealed. Otherwise it will not count.

It is possible that other methods of preparing crystals exist; however, the absence of publications does not permit comparison of them with the present one. A eutectic was also tested: thallium iodide (60%)—thallium bromide (40%).

The advantages of this material are its high density (> 7.00) and the comparatively high temperature required for counting (−70°C). However, its dielectric constant is rather large (~30 as against 12 for AgCl), and therefore the capacitance of the crystal is also somewhat higher. The pulse sizes are smaller. The large dielectric constant diminishes the growth of polarization effects in these crystals.

Solid and liquid argon. Recently performed^41,42 highly interesting experiments have shown that argon in solid and liquid form can be used for recording ionizing radiation (α-particles and γ-rays were tested). The argon was carefully purified of oxygen impurities (1% dissolved oxygen is sufficient to destroy the entire counting effect). At the same time, considerable amounts of dissolved nitrogen do not change the pulse shape.

R. HOFSTADTER

Apparatus

A typical crystal holder, used in work with diamond crystals[^15], is shown in Fig. 9. To protect the specimen from the action of atmospheric moisture vapors, it is advisable to place the holder in a vacuum chamber. This chamber also protects against spurious pulses caused by ionization of the air between the electrodes. For work at low temperatures the chamber is necessary.

Fig. 9. Diamond holder.

In Fig. 10 one of such chambers, used by the author, is presented. Here the lower part of the Dewar vessel located inside it is also visible. The photograph also shows Micallite bushings, electrode clamps, the crystal, the round positive electrode (behind), and the square quartz plate serving as an insulator. The screen, shown lying separately, is usually placed over the crystal holder. The thermocouple is fastened to the outer part of the screen.

Fig. 10. Vacuum chamber, Dewar vessel, and crystal holder used for investigations of crystalline counters (silver chloride and thallous chloride) at low temperatures. The radioactive source and shutter are visible on the left on the chamber cover.

On the left, a radioactive preparation \(P^{32}\) is deposited on the plate, shown together with a brass shutter which, when rotated, is placed in the path of the electron beam or outside it. The construction of the crystal holder is shown in Fig. 11.

Fig. 11. Vacuum chamber, Dewar vessel, and crystal holder (schematic).
1 — liquid nitrogen or heater. 2 — stainless steel 0.46 mm. 3 — siphon. 4 — shutter. 5 — source. 6 — screen. 7 — side opening. 8 — coaxial leads to the amplifier and high-voltage source. 9 — thermocouple wire. 10 — copper. 11 — quartz. 12 — silver. 13 — silvered springs. 14 — thermocouple. 15 — opening for lead-in. 16 — mica inserts. 17 — mica.

The general appearance of the apparatus used in investigations with crystal counters is shown in Fig. 12. The camera serves for photographing the voltages arising in AgBr crystals at various temperatures. The side openings in the vacuum chamber make it possible to carry out investigations with illumination switched on. In the left part of the table there is a drive that moves the specimen.

A schematic diagram of the equipment is presented in Fig. 13. The positive electrode is connected to the amplifier. From the amplifier the pulse is fed in parallel: a) through the triggering circuit to the sweep of the oscillograph, and b) to the vertical plates of the oscillograph. The pulse in a crystal counter is larger than in an ionization chamber, owing to the smaller loss of energy in the formation of ion pairs. Nevertheless, for investigating the shape of the pulses and their number, considerable amplification of the initial signals, having an amplitude of the order of 1–2 mV, is required. In this connection the problem of noise arises. In a number of investigations\(^{6,56}\) it is pointed out that

the best signal-to-background ratio is obtained for certain frequency characteristics of the amplifier. Thus, for example, the minimum detectable pulse of 100 electrons on the grid of a 6AK5 tube

Fig. 12. General view of the apparatus for investigating crystalline counters operating at low temperatures. The heater used for annealing is inserted into the Dewar vessel; the water-cooled parts maintain room temperature outside the Dewar vessel; the camera serves for photographing stresses in the specimens.

Fig. 13. Diagram of the measuring apparatus shown in Fig. 12.

is observed in the case where the rise time and the RC of the amplifier are, respectively, 40 and 16 μsec. A pulse of 100 secondary electrons on the grid of the 6AK5 corresponds in AgCl to a β-particle with an energy of 760 eV.

It is quite probable that electrons with energies of 5–10 KeV can be recorded by a crystalline counter without any special difficulties. With such an amplifier one can count 160 pulses per second with less than 1% loss. This counting rate satisfies the requirements of a considerable number of problems, such as, for example, the study of new materials for crystalline counters, the energy expended in the formation of an ion pair, etc.

For other applications, such as, for example, coincidence counting, measurement of short time intervals, mobility measurements, etc., it is necessary to have a rise time much less than 40 μsec. Indeed, with a mobility of the order of 250 cm² per volt-second, one can obtain pulse rise times in the crystal of 0.5 μsec and less. In this case an amplifier with a large bandwidth is required. At Princeton all measurements were made with a type 501 amplifier (rise time 0.15 μsec and amplification \(3 \cdot 10^5\)). The noise level is equivalent to approximately 10 eV. For the study of γ-rays by means of diamond counters, “slower” amplifiers are more suitable. For photographing the pulse front, a delay line with a delay time of 4.8 μsec and a rise time of 0.15 μsec is used. In all investigations, as mentioned above, careful mounting of the crystal and its annealing are necessary. The following simple operation makes it possible to fulfill both of these requirements.

Before being installed in the vacuum chamber, the crystal is prepared with thin metallic electrodes. After this it is mounted in the vacuum chamber, as shown in Fig. 10. The crystal must be clean, and the pressure of the contacts must not be excessive. The vacuum chamber is closed and evacuated to a pressure of \(10^{-4}\)—\(10^{-5}\) mm Hg. A small heater is placed inside an ordinary Dewar vessel. The heater raises the temperature of the crystal holder to 400° for AgCl and 380° for AgBr. After holding at this temperature for several hours, the temperature is gradually lowered.

Although tests to determine the optimum duration of the heat treatment were not carried out, experience showed that seventeen hours is sufficient for complete annealing of a small crystal.

The Dewar vessel, cooled to room temperature, is gradually, over the course of several hours, filled with liquid nitrogen until the temperature drops to 77° K. Such treatment makes the crystal sensitive to ionizing radiation. There is no need to carry out the annealing operation before each use of the crystal.

If the crystal is kept in the dark, subsequent coolings to low temperatures are not reflected in the shape or dimensions of the pulse. Yamakawa’s investigations showed that several coolings of the crystal do not change the pattern of stresses in it in cases where the cooling lasted at least half an hour.

The apparatus described above can be improved by placing the heating coils directly in the crystal holder. Water cooling of the outer surface of the vacuum chamber also seems advisable, since, because of the heating of the metal walls, the rubber seals may become unusable. In addition, the device described above requires the use of temperature-resistant electrode holders (for example, micalex).

In conclusion, let us point out that the difficulties usually encountered can be avoided by observing the following precautions: one should not apply an electric field to an uncooled crystal; otherwise continuous changes will take place in the crystal. After voltage has been applied to the specimen, illumination in the vacuum chamber must be completely absent.

If necessary, the crystal may apparently be illuminated, after removal of the voltage, with orange or red light. During annealing, in order to avoid evaporation, the temperature of the crystal should not be raised above the prescribed value.

Only silver, platinum, and gold give good contact with crystals. Other metals react chemically with the crystals. To obtain the best signal-to-noise ratio, the capacitance of all connections must be minimal.

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