Spectral Sensitivity of X-ray Vidicons

A. P. Shpagin

(Presented by the scientific seminar of the sector for defectoscopy of building materials, Scientific Research Institute EI)

When choosing the energy of a radiation source in introscopes, it is necessary to know the spectral characteristic of the radiation detector. In particular, the correct choice of radiation energy is of great importance for introscopes using X-ray vidicons. Experimental determination of the spectral characteristic of an X-ray vidicon requires the availability of a whole set of monoenergetic radiation sources and will apparently be rather labor-intensive; therefore, in the present work a method is proposed for calculating the functions of the spectral sensitivity of X-ray vidicons. The sensitivity of X-ray vidicons to ionizing radiation is determined by the change in the conductivity of the target under irradiation. The more strongly the conductivity of the irradiated target changes in comparison with the dark (unirradiated) conductivity, the higher the sensitivity. The dark conductivity of the target is determined by the concentration of free electrons and holes, their mobility, and their lifetime. The concentration of free charge carriers, their mobility, and lifetime depend on the temperature, chemical composition, structure, and sometimes the method of obtaining the semiconductor. The effect of gamma radiation on conductivity is reduced mainly to an increase in the concentration of electrons and holes as a result of ionization of the semiconductor atoms and to a decrease in their lifetime due to an increase in the probability of recombination.

The second process depends on the radiation intensity and will be noticeably reflected in the conductivity only when the concentration of nonequilibrium charge carriers formed by irradiation of the target is greater than the concentration of equilibrium carriers, i.e., at rather high irradiation levels. This process will mainly manifest itself in the nonlinearity of the amplitude characteristic of the X-ray vidicon in the region of higher intensities. Since the physical processes determining the accumulation of the potential relief and its readout proceed identically at all radiation energies, the cause of the nonuniformity of the spectral sensitivity of an X-ray vidicon may be either a nonlinear dependence of the quantum yield of the target on the energy of the quanta, or nonuniformity of the absorbing ability of the target over the energy range. As experimental studies have shown [1], the quantum yield in germanium and silicon, beginning with several electron volts, changes proportionally to the energy. This gives grounds to assume that for selenium and other semiconductors a linear dependence between quantum yield and energy will hold, at least in the energy region from several electron volts and higher. If this is so, then the spect-

the actual sensitivity is determined in the low-energy region by the transparency of the face glass of the tube,* and in the high-energy region by absorption in the semiconductor layer of the target

\[ \Phi(E)=\frac{\Pi(E)}{E}e^{-\mu_c(E)h_c}, \tag{1} \]

where \(\Phi(E)\) is the spectral-sensitivity function of the X-ray vidicon; \(\mu_c(E)\) is the attenuation coefficient of monoenergetic radiation with energy \(E\) in the face glass of the X-ray-vidicon tube; \(h_c\) is the thickness of the face glass of the X-ray vidicon; \(\Pi(E)\) is the mean energy absorbed in the target at normal incidence on the target of one quantum with energy \(E\).

Earlier, as applied to a thin single-crystal screen, we [2] obtained a formula making it possible to calculate the function \(\Pi(E)\) with accuracy up to the first collision. For energies below 1 MeV it has the form:

\[ \Pi(E)=\frac{1}{\mu(E)}\left[1-e^{-\mu(E)h}\right]\left[\tau(E)E+\sigma(E)E_z\right], \tag{2} \]

where \(h\) is the screen thickness, \(\tau(E)\) and \(\sigma(E)\) are the coefficients of the photoelectric effect and Compton scattering, respectively, and \(E_z\) is the mean energy transferred to a recoil electron in Compton scattering of a quantum with energy \(E\). Formulas defining \(E_z\) are given in the literature [2, 3].

The energy range in which formula (2) can be used is determined by the following conditions:

\[ \mu(E)h<1, \tag{3} \]

\[ r_0<h, \tag{4} \]

where \(r_0\) is the range of photoelectrons in the screen material.

Real X-ray vidicons have a selenium or lead-oxide target with thickness \((0.05 \div 0.25)\ \mathrm{g/cm^2}\); for such a target thickness condition [3] is satisfied for energies greater than 70 keV, but since at energies below 70 keV the interaction of radiation with the target material occurs almost entirely by the photoelectric effect, the use of formula [2] in this energy range is possible even when \(\mu(E)h>1\), i.e., condition [3], as applied to X-ray-vidicon targets, does not restrict the region of legitimate application of formulas [1] and [2].

Using data available in the literature [4–6] on the relation between the range of electrons and their energies, one can establish that condition (4) is satisfied, for the semiconductor-layer thicknesses indicated above, for electron energies below \(200 \div 400\) keV.

Figure 1 presents the spectral-sensitivity functions of X-ray vidicons with different selenium-target thicknesses calculated from formula (1). The calculation was carried out for an X-ray vidicon with face glass of thickness \(h_c=2\) mm, consisting of 34% silicon, 7.2% calcium, 10.8% sodium, and 48% oxygen, whose target consists of selenium with density \(4.8\ \mathrm{g/cm^3}\) and has thicknesses of 0.1 mm, 0.5 mm, 2 mm (curves 1, 2, 3, 4 in Fig. 1 correspond to these target thicknesses).

As is seen from Fig. 1, the maximum of the spectral-sensitivity function of an X-ray vidicon with a target thickness of 0.1 mm (approximately this corresponds to the target thickness in ordinary domestic X-ray vidicons—

* We do not take into account the influence of the signal plate, assuming that it is a thin layer of aluminum \(\approx 0.01\) mm. Since the absorption coefficients of glass and aluminum are approximately equal, even replacing the glass faceplate by an entirely aluminum one does not noticeably distort the spectral sensitivity.

no) is at an energy of 30 keV. In this connection the question may arise why, despite this, X-ray vidicons are often successfully used with X-ray installations at 150–200 kilovolts; moreover, when the voltage is raised from 70 kilovolts to 150–200, the sensitivity in some cases increases substantially. There is, however, nothing here that contradicts the spectral characteristics obtained. The point is that X-ray tubes generate a bremsstrahlung spectrum described by the formula [7]

\[ I(E)=ciZ(\nu_0-\nu)=ki(E_0-E), \tag{5} \]

where \(I(E)\) is the spectral intensity density, \(c\) and \(k\) are constant coefficients, \(Z\) is the atomic number of the material of the tube anode, \(i\) is the tube current, and \(E_0\) is the maximum quantum energy in the spectrum, approximately equal to the voltage on the tube.

As is evident from formula (5), when the voltage on the tube is increased, the intensity density in the low-energy region increases in proportion to the voltage; in addition, in most tubes the current also increases in proportion to the voltage and, consequently, the intensity density grows in proportion to the square of the voltage on the tube. Therefore, even if the X-ray vidicon were completely insensitive in the high-energy region, nevertheless, solely by increasing the intensity in the low-energy region, the sensitivity of an introscope with such an X-ray vidicon can increase. The situation will be different when monoenergetic radiation is used. In this case, increasing the radiation energy beyond the maximum will lead to a sharp decrease in sensitivity, because the signal will decrease with increasing energy, since it is formed only by primary quanta, while the background and noise will increase owing to the higher sensitivity of the X-ray vidicon to scattered quanta.

Therefore, when a monoenergetic radiation source is used, the best relative sensitivity of an introscope with an X-ray vidicon will be achieved when its energy corresponds to the maximum of the spectral-sensitivity function of the X-ray vidicon.

Fig. 1. Spectral-sensitivity functions of X-ray vidicons with a selenium target of thickness 2 mm; 1 mm; 0.5 mm; 0.1 mm, respectively curves 1, 2, 3, and 4.

As is evident from Fig. 1, with an increase in target thickness the maximum of the spectral-sensitivity function shifts toward higher energies and, at the same time, as the target thickness increases the absolute value of the spectral-sensitivity function at the maximum also increases*.

Formula (1) also makes it possible to determine the spectral-sensitivity function of an X-ray vidicon for quanta incident on the target

* It should be noted that the dependence obtained for the absolute value of the spectral sensitivity at the maximum on the target thickness characterizes only the absorbing capacity of the target, but not the entire X-ray vidicon, because the processes of charge accumulation and readout of the potential relief depend on the target thickness, since as the target thickness increases its capacitance decreases and the relation between the target thickness and the free-electron range changes.

nonperpendicularly. In this case, in formulas (1) and (2) it is necessary to substitute, instead of the thickness of the faceplate glass and the thickness of the target, the effective thicknesses of the faceplate glass and target, determined by the formulas:

\[ h_c' = h_c/\cos \Theta, \tag{6} \]

\[ h_i' = h_i\cos \Theta, \tag{7} \]

where \(\Theta\) is the angle of incidence of the quanta.

The spectral-sensitivity functions calculated by the indicated method for a target thickness of \(0.01\ \text{cm}\) and a glass thickness of \(0.2\ \text{cm}\) and for different angles of incidence are shown in Fig. 2. It is evident from the figure that the sensitivity of the X-ray vidicon is substantially higher with respect to quanta incident on the target at an angle, and, in particular, to scattered quanta.

Fig. 2. Spectral-sensitivity functions of an X-ray vidicon for quanta incident at an angle to the plane of the target: 1 — \(\Theta=60^\circ\), 2 — \(\Theta=45^\circ\), 3 — \(\Theta=0^\circ\)

The error in calculating the function \(\Phi(E)\) by formula (1) arises because part of the energy transferred to electrons near the boundary of the target is carried by them beyond the limits of the target; on the other hand, some fraction of the energy not taken into account in the calculation is transferred into the target by electrons emitted from the faceplate of the X-ray vidicon. However, in the case of a glass or aluminum faceplate, the energy transferred from the faceplate is much less than the energy carried out of the target, and it may be neglected. For the energies considered above, the main contribution to the error is made by photoelectrons, since Compton recoil electrons have low energy and a short range. In calculating the error it was assumed that the energy is carried out only by photoelectrons, and that all photoelectrons fly perpendicular to the plane of the target and lose their kinetic energy over a path equal to the maximum penetration depth (the extrapolated range [4]). It is obvious that all these assumptions lead to an overestimate of the error; consequently, the calculated error will be greater than the true one. Taking the indicated assumptions into account,

the relative error of calculation by formula (1) will be determined by the formula

\[ \delta=\frac{\tau l(E_e)\cdot 100\%}{2\Phi(E)}e^{-\mu_c(E)h_c}, \tag{8} \]

where \(l(E_e)\) is the maximum penetration depth of an electron with energy \(E_e\) in the target material, \(E_e=E-E_{\text{b}}\), where \(E_{\text{b}}\) is the electron binding energy; in the calculation it was assumed that all photoelectrons are ejected from the K shell, then \(E_{\text{b}}\approx 13\ \text{keV}\). The maximum penetration depth was determined by interpolation of the data given in the literature [6] for copper and tin. Calculation by formula (8) gave the following values of the relative error for a target \(0.1\ \text{mm}\) thick: respectively \(20\%\), \(16\%\), and \(9\%\) for quantum energies of \(200\ \text{keV}\), \(150\ \text{keV}\), and \(100\ \text{keV}\). With increasing screen thickness the relative error decreases inversely proportionally to the absorbed energy (the absolute error does not change with a change in the target thickness), i.e., approximately inversely proportionally to the target thickness.

Conclusions

The spectral sensitivity of x-ray vidicons is determined by the density and atomic number of the material of the target and of the end glass of the x-ray vidicon bulb, and changes considerably with changes in the thickness of the target and of the bulb end glass.

X-ray vidicons produced by domestic industry with a target thickness of \(0.1 \div 0.15\ \text{mm}\) have a maximum of spectral sensitivity in the energy region \(40 \div 60\ \text{keV}\), and, consequently, the best results with such x-ray vidicons can be obtained precisely at this energy of a monoenergetic source.

LITERATURE

1. V. S. Vavilov. The Action of Radiation on Semiconductors. Moscow, Fizmatgiz, 1963.
2. A. P. Shpagin. Candidate’s dissertation, Tomsk, 1967.
3. S. V. Starodubtsev, A. M. Romanov. Interaction of Gamma Radiation with Matter. Part I, Tashkent, “Nauka” Publishing House, Uzbek SSR, 1964.
4. A. A. Vorob’ev, B. A. Kononov. Passage of Electrons through Matter, Tomsk, TSU Publishing House, 1966.
5. L. V. Spenser. Phys. Rev. 98, 1597 (1955).
6. L. V. Spenser. Energy Dissipation by Fast Electrons. Nat. Bur. St. (US), 1959.
7. F. N. Kharadzha. General Course of X-ray Engineering. Moscow–Leningrad, “Energiya,” 1966.