Operation of Crystal Triodes in the Frequency Range 5–25 MHz

The main obstacles to the wide use of semiconductor triodes at the present stage of their development are the high noise level, as compared with vacuum radio tubes, and the insufficiently wide range of operating frequencies. Below we shall consider the causes which, in the usual case, limit the frequency range to 7–10 megacycles, and describe a new method that makes it possible to extend this range to 23–25 MHz.

The drop in the amplification factor of a crystal triode with frequency \(^{1,2}\) is explained mainly by the transit time of the current pulse in the semiconductor and by the difference in the path lengths of individual charge carriers passing through the body of the semiconductor from the emitter to the collector.

The amplification of a signal by a transistor, in a first approximation, may be reduced to the following: the collector is at a negative potential of 10–50 volts; owing to the very small contact area, the field gradient near it reaches large values. From the emitter contact, whose role is to some extent analogous to that of the grid of a vacuum triode during passage of the signal pulse, “holes”—positive charge carriers—enter the body of germanium and are drawn by the field of the collector. Near the collector the “holes,” neutralizing the space charge at the surface of the crystal, lower the height of the potential barrier between the metal of the collector point and the germanium; this leads to an increase in the current through the contact and to the appearance of a voltage pulse across the load connected in series with the collector.

It is obvious that the transit time from emitter to collector depends on the field strength inside the germanium. Since the collector current is usually greater than the emitter current in a first approximation, the field strength in the semiconductor is determined by the collector current and by the resistivity of the germanium. According to the theoretical conclusions of Bardeen \(^{1}\), the “flight time” \(T\) is expressed as

\[ T=\frac{2\pi s^{3}}{3u_h \rho I_c}, \]

where \(s\) is the distance between emitter and collector, \(u_h\) is the mobility of the “holes,” \(\rho\) is the resistivity, and \(I_c\) is the collector current. From the geometry of an ordinary crystal triode it is evident that not all the “holes” traverse paths of equal length in the semiconductor. This smears the phase of the amplified signal, which is manifested in a decrease in the depth of modulation of the barrier height at the collector and, at sufficiently high frequencies, leads to the impossibility of signal amplification. In accordance with Bardeen’s expression, the parameter primarily determining the frequency characteristic of a crystal triode should be regarded as the distance between contacts \(s\). In modern transistor designs the distance \(s\) is not less than 0.06 mm. In addition, the limit of the operating-frequency range depends on the collector current \(I_c\), the maximum value of which does not exceed 5 mA. At higher currents the triode readily fails as a result of overheating of the contact. Finally, as is clear from the expression for \(T\) and from Fig. 1, the amplification factor \(\alpha\) depends strongly on the resistivity of germanium \(\rho\).

Thus, for maximum amplification in the radio-frequency range of about 5–10 MHz, a crystal triode must have a small distance between emitter and collector, a small contact area-

Fig. 1. Current amplification coefficient
\[ \alpha=\frac{\partial I_c}{\partial I_e} \]

Visible graph annotations: MHz; \(S=0.01\) mm; \(S=0.05\) mm; \(S=0.1\) mm; current values in mA.

Fig. 2. Schematic of the specimen in a magnetic field.

Visible labels: magnetic field; \(0.05\) mm; \(c\); \(e\).

Fig. 3. Current amplification coefficient \(\alpha\).

Visible graph annotations: MHz; field; 6000 oerst.; 1200 oerst. minimum; 400 oerst.

..., the high resistivity of germanium, and operation in the regime of the maximum permissible collector current.

The recently proposed method of magnetic focusing\(^{4,5}\), which makes it possible to extend the range of operating frequencies of germanium triodes to \(23\text{–}25\) MHz, consists in placing the triode crystal in a transverse magnetic field of the required direction (Fig. 2). In this case the emitter and collector currents are concentrated, the signal phase is blurred less, and the transit time \(T\) is reduced.

The current gain coefficient \(\alpha\), corresponding to the given frequency, increases considerably (Fig. 3).

The greater the intercontact distance \(s\) and the smaller the contact area, the greater the influence of the magnetic field. It is interesting to note

Fig. 4.

that this circumstance considerably equalizes the parameters of transistors, which normally vary sharply from specimen to specimen.

In conclusion we give the circuit of a single-stage resonant amplifier constructed by Brown (Fig. 4). Magnetic focusing by a field of the order of 7000 oersteds from a permanent magnet made it possible to obtain an eightfold voltage gain in a frequency band 8.8 MHz wide, with a maximum at 23.5 MHz of about 30.

V. S. Vavilov

CITED LITERATURE

1. J. Bardeen, Phys. Rev. 75, 1225 (1949).
2. V. S. Vavilov, UFN (1949) (review).
3. C. Bradner Brown, Phys. Rev. 76, 1736 (1949).
4. C. Bradner Brown, Electronics, July 1950, p. 81.