RADIATION NOISE IN TRANSISTOR AMPLIFIERS

D. I. Sviryakin

(Presented by the scientific seminar of the Research Institute of Electron Introscopy)

In the receiver unit of any radiation television introscope, provision is made for connecting a preamplifier that provides the initial amplification of the electrical signals taken from the output of the transducer. Owing to its immediate proximity to the transducer, the preamplifier, as a rule, is subjected to the same radiation exposure as the transducer. Fluctuations of the output current or voltage of the preamplifier caused by radiation exposure and due to its statistical nature, as well as to temporal and spatial variations of the radiation flux, increase the noise power in the introscope channel and lead to a reduction in the signal-to-noise ratio, that is, to a decrease in the sensitivity of the introscope. Therefore, in order to approach correctly the problem of selecting active elements for introscope preamplifiers, it is necessary to have a realistic understanding of the radiation effects that accompany irradiation of these elements, and it is especially important to know how radiation affects their noise parameters. In view of the widespread introduction of transistors and integrated circuits into amplifier technology, it is expedient to estimate the degree to which fluxes of penetrating radiation affect noise in semiconductor devices, especially since, among the large number of works that have investigated the radiation resistance of semiconductor devices, there are almost no systematized data on the influence of radiation on their noise characteristics.

However, in the field of semiconductor detectors of nuclear particles there is a considerable number of literary sources on the relationship between radiation and noise. In addition, many researchers have used radiation as a means of studying the noise mechanism. At the same time, experimental data are available only for a few device models, while the majority of the data are only approximate and have been obtained by relating known radiation effects to known noise mechanisms.

Proceeding from the problem posed, it is necessary to consider only those interrelations that are important for estimating the change in noise in irradiated or irradiated devices; therefore, in the table below only those varieties of transistor noise are listed that are sensitive to radiation effects and defects (that is, to reversible and irreversible phenomena).

Table

The noise factor of a bipolar transistor is expressed by the formula [1]

\[ F = 1 + \frac{kT}{R_c \cdot 2 \cdot I_k} + \frac{R_c \cdot I_k}{2kT} \left[ \frac{1}{h_{\mathrm{ct}}} + \left(\frac{f}{\Delta f}\right)^2 \right], \tag{1} \]

where \(k\) is Boltzmann’s constant;
\(T\) is the absolute temperature;
\(R_c\) is the output resistance of the signal source;
\(e\) is the electron charge;
\(I_k\) is the dc collector current;
\(h_{\mathrm{ct}}\) is the static current gain;
\(f\) is the frequency;
\(\Delta f\) is the passband width.

Formula (1) shows that no parameter except \(h_{\mathrm{ct}}\) depends on radiation damage and effects. With the appearance of radiation-induced bulk and surface damage (and consequently with a decrease in the lifetime of carriers, with the accumulation of carrier recombination centers), the coefficient \(h_{\mathrm{ct}}\) decreases. But the change in \(h_{\mathrm{ct}}\) has a noticeable effect on the value of \(F\) only under the condition \(R_c \ne R_{c\mathrm{opt}}\), where

\[ R_{c\mathrm{opt}} = \frac{kT}{I_k} \left[ \frac{1}{h_{\mathrm{ct}}} + \left(\frac{f}{\Delta f}\right)^2 \right]^{1/2}. \tag{2} \]

In this case

\[ F_{\mathrm{opt}} = 1 + \frac{1}{(h_{\mathrm{ct}})^{1/2}} . \tag{3} \]

Formula (1) was derived under the condition \(R_c > r_b\) (\(r_b\) is the base resistance), when the high-frequency thermal noise associated with the base resistance does not play an essential role in comparison with shot noise and may be omitted.

A convenient formula for the high-frequency noise factor of a junction field-effect transistor with a controlled \(p\)-\(n\) junction and for a MOS transistor is given in [2]:

\[ F = 1 + \frac{g_{\mathrm{zi}}}{G_c} + \frac{R_{\mathrm{sh}}}{G_c}\left(G_c + g_{\mathrm{zi}}\right)^2, \tag{4} \]

where \(g_{\mathrm{zi}}\) is the input conductance of the field-effect transistor;

\[ G_c \]

is the conductance of the signal source

\[ \left(G_c = \frac{1}{R_c}\right); \]

\[ R_{\mathrm{sh}}=\frac{1}{S} \]
— noise resistance;

\(S\) — transconductance of the transistor.

In field-effect transistors, the predominant high-frequency noise is thermal noise in the conducting channel, while the predominant radiation effect is carrier recombination at defects. Therefore, radiation has only a slight influence on the noise characteristic of such transistors until \(S\) and \(g_{zi}\) begin to change, i.e., until the devices themselves begin to be damaged. In addition, in MOS transistors, surface radiation effects are of great importance; their occurrence is associated with the appearance of fast surface states, leading to a decrease in transconductance and, consequently, to an increase in the noise factor.

Low-frequency noise in field-effect transistors with a p-n junction is called generation noise, since it arises from fluctuations of charges at generation centers in the depleted region [3]. This process can be expressed as an additional component of the noise resistance \(R_{\mathrm{sh}}\), and then

\[ R_{\mathrm{sh}}=\frac{1}{S}+BN_t, \tag{5} \]

where \(N_t\) is the density of generation-recombination centers, increasing in proportion to the number of bulk radiation damages;

\(B\) is a constant coefficient determined by the geometry of the device, as well as by the position of the energy levels and the capture coefficient of the generation centers.

Substituting (5) into formula (4), we obtain the complete noise factor of a field-effect transistor with a p-n junction.

Low-frequency noise in MOS transistors is usually associated with surface effects caused by the distribution of very slow surface states in the oxide near the silicon-oxide interface. Despite advances in studying the nature of flicker noise (or \(1/f\)), a quantitative prediction of the effect of radiation on this noise source is still impossible [4]. In bipolar transistors, the influence of radiation on flicker noise is even more complex.

Burst noise is generated at the moment when the current through a radiation defect is modulated by the charge in a generation-recombination center adjacent to the defect. The influence of radiation on this noise mechanism has likewise not been studied.

Photocurrent (quantum) noise is caused by the creation of excess current carriers under the action of gamma quanta or electrons and may significantly exceed shot noise. The number of carriers generated by a gamma quantum can be very large, and from the statistical point of view these carriers are generated together, not independently, as occurs in ordinary shot noise. The mean-square noise current \(\overline{i_{\mathrm{sh}}^{2}}\) is equal to

\[ \overline{i_{\mathrm{sh}}^{2}}=2MeJ_{\mathrm{ph}}\Delta f, \tag{6} \]

where \(M\) is the mean number of carriers generated by each incident quantum interacting in the collection volume of the transistor;

\(J_{\mathrm{ph}}\) is the primary photocurrent.

The factor \(M\) can be estimated by the formula

\[ M=\frac{E_{\gamma}}{\Delta E}\cdot n_{\gamma}\cdot n_e. \tag{7} \]

where \(E_\gamma\) is the energy of the gamma quantum;

\(\Delta E\) is the energy required to generate each electron–hole pair (for silicon \(\Delta E=3.5\) eV);

\(\eta_\gamma\) is the fraction of the energy transferred by the gamma quantum to the initial electron;

\(\eta_e\) is the efficiency of the initial electron in generating further electron–hole pairs within the active volume of the transistor.

One may take \(\eta_\gamma=1/3\) and \(\eta_e=0.1\). Then, for \(E_\gamma=1\) MeV, using formula (7), we obtain \(M=10^4\) electron–hole pairs per gamma quantum. Photocurrent noise plays an important role under the condition

\[ 2eMI_{\phi} > \frac{4kT}{R_C}. \tag{8} \]

If \(R_C=5\ \text{k}\Omega\) and \(M=10^4\), then a photocurrent of only \(1\) nA is needed in order to increase the noise by 3 dB.

Thus, when transistors are irradiated it is necessary to take quantum noise into account, since it may be the predominant noise in the amplifier circuit. In those cases when pulsed radiation sources are used in introscopes, and the bandwidth of the video channel is limited, a background component may appear in the output video signal, distorting the transmission of halftone images. The background component is caused by the integration of short electrical pulses that arise when particles or gamma quanta pass through the crystals of the semiconductor devices used in amplifiers. In almost all practical cases, the flux density of the radiation is sufficient for the pulses from individual quanta to overlap one another and to provide, at the output, a parasitic signal that is an envelope repeating the shape of the radiation pulse. Thus, for example, Fig. 1 shows oscillograms of the currents of the collector (upper) and emitter (lower) junctions,

Fig. 1.

of the GT-402 transistor, caused by X-ray radiation from an RUP-120-5 apparatus at an anode voltage of 120 kV and an anode current of 4 mA (distance to the tube focus 20 cm). In the selected operating mode of the irradiated GT-402 transistor (emitter–base voltage 0.1 V, emitter–collector 3 V), and with no signal at the input, a signal appeared across the collector load (2.2 kΩ) that repeated in shape the half-wave of the vo...

voltage on the x-ray tube. This, of course, does not mean that, when sources with a radiation flux constant in time are used, the quantum noise in the circuits of transistor amplifiers will decrease. As follows from the formulas given above, the rms noise current will remain the same, but the noise spectrum, like the radiation spectrum, will change, while the background component (in essence, radiation pickup) will disappear.

REFERENCES

1. Thornton R. D. and atts. Characteristics and Limitations of Transistors. Chapt. 4. J. Wiley, 1966.

2. Bruncke W. C. and Van der Ziel. IEEE. Trans. Electron. Dev., Vol. E. D.-13, pp. 323—329, March, 1966.

3. Lauritzen P. O. Solid-State Electron, Vol. 8., pp. 41—58, Jan. 1965.

4. Lauritzen P. O. IEEE Trans on Nucl. Sci., Vol. NS-19, N 2. pp. 321—325, Apr. 1972.