NEW INSTRUMENTS AND METHODS OF MEASUREMENT

AMPLIFICATION OF HIGH-FREQUENCY CURRENTS BY CRYSTALLINE GERMANIUM TRIODES

V. S. Vavilov

1. INTRODUCTION

The crystalline germanium triode, known as the “transistor,” undoubtedly deserves great attention and will be the subject of systematic study and improvement. The first reports on the possibility of amplifying alternating currents with the aid of this device appeared at the beginning of 1948.¹˒² The idea of generating and amplifying radio signals in a device in many respects resembling the widely known crystal detectors is not new. As early as the 1920s, that is, before the beginning of the mass use of vacuum triodes, the Soviet physicist O. V. Losev succeeded in constructing an amplifier circuit, which he called a “crystadyne,” and which made it possible to generate radio-frequency oscillations (see, for example, ³˒⁴˒⁵).

However, in connection with the transition to tube circuits, this idea did not receive proper dissemination.

The development of radar and the transition to centimeter waves forced researchers once again to take up the study and improvement of crystal detectors, which are not characterized by limitations imposed by the electron transit time and whose capacitance is very small. At the present time the crystal detector is an almost indispensable element of a microwave receiver.

The technical successes achieved⁶ in the design of such detectors are very great. To a large extent this is due to the development of the theory of semiconductors, in which, by right, the leading place should be assigned to Soviet physics, to which we owe much to the works of A. F. Ioffe and his school (see, for example,⁷).

The possibility of applying the circuit shown in Fig. 1 for the amplification of signals was discovered in studying the action of an electric field in an electrolyte on the volt-ampere characteristic of a germanium detector immersed in the electrolyte and having a high reverse voltage. As will be indicated below, besides the circuit of Fig. 1, other methods of connecting the crystal triode may also be used for signal amplification.

Soon after the properties of the crystal triode were discovered, it proved possible to give it a form sufficiently convenient for practical application. The chief advantages of the crystal triode are the absence of a vacuum and of the need for an energy source for the cathode-heating filament. The weight of the amplifying “unit” (Figs. 2 and 5), together with the protective holder, is about 1.3 g. Significant shortcomings at its present stage of development are a noise level higher than in radio tubes, the small power (5–20 mW) at the output*) and the inconvenience of matching several elements in a multistage amplifier because of the large difference between the optimum input and output resistances. The range of operating frequencies, evidently, cannot be extended beyond approximately 10 Mc because of limitations imposed by the mobility of the conductivity carriers in the semiconductor.

Fig. 1. Circuit for connecting a crystal triode.
Fig. 2. Construction of a transistor.

Before proceeding to a more detailed exposition, it seems expedient to give a brief summary of the most characteristic features of germanium, in view of the fact that, until very recently, this element had not had any wide application in technology and had not been studied in detail (see Tables I and II).

The necessary information from the theory of electrical conductivity of semiconductors may be found, for example, in the review by F. F. Volkenstein in UFN⁸. The band theory has been developed more fully in ⁹, ¹⁰.

*) According to ⁸⁹, by modifying the design it has been possible to increase the useful power by at least 5–10 times.

2. ON THE PROPERTIES OF GERMANIUM

The existence of germanium was predicted by D. I. Mendeleev, who indicated the properties that this element, named by him ekasilicon, should possess.

In many respects germanium closely resembles carbon, silicon, and tin. This is evident from Table 1 below.

Table 1

Comparison of some properties of carbon, silicon, germanium, and tin

Chemically germanium is very close to carbon and silicon and, like these elements, can form long chains of hydrides and other compounds analogous to organic ones.^11

The method of isolating germanium usually consists in reducing its oxide in hydrogen at a temperature of about \(600^\circ\) C. Germanium oxide is obtained from the residues of zinc ores. In small quantities germanium has also been obtained by decomposing certain volatile compounds, for example \(\mathrm{GeCl}_4\). The germanium powder obtained by reduction of the oxide is fused into an ingot. The properties of crystalline germanium prepared in this way depend strongly on the atmosphere in which the germanium was melted, and on the heat treatment. Usually the melting is carried out in dry nitrogen, hydrogen, helium, or in vacuum. In all cases the presence of water vapor increases the resistance of germanium, which is disadvantageous for the construction of transistors \(^{12}\).

The specific resistance of germanium at room temperature ranges from \(50\ \mathrm{ohm\cdot cm}\) to \(0.001\ \mathrm{ohm\cdot cm}\), depending on the concentration and type of impurities. The sensitivity of germanium to impurities is such that one impurity atom per \(10^8\)—\(10^9\) Ge atoms noticeably affects the electrical properties. Aluminum, tin, arsenic, and gallium are evidently capable of substantially lowering the resistance of germanium.

One of the interesting features of germanium is its high reflection coefficient—in this respect germanium resembles a metal. The reflection reaches 50%. This property is anomalous. As is known, “metallic luster” is usually associated with the presence of free electrons and high electrical conductivity.

Germanium, having a density of free electrons approximately a million times smaller than aluminum or silver, reflects light almost as well as these metals. Evidently, a significant fraction of the electrons of germanium, bound so strongly that it is not a conductor, is nevertheless excited by the incident light and participates in reflection.

Mechanically, germanium is very hard and brittle.

In addition to the considerable dependence of conductivity on impurities mentioned above, germanium, unlike many other semiconductors, has appreciable conductivity at ordinary temperature not associated with the presence of impurities. This intrinsic conductivity can be separated out in the course of the temperature dependence of the total conductivity and corresponds to approximately \(100\ \mathrm{ohm\cdot cm}\) \(^{10}\).

Intrinsic semiconductivity of a substance occurs when the energy “gap” between the upper filled band and the lower part of the higher-lying free band is small. At absolute zero such a substance would be a dielectric, but at higher temperatures a certain number of electrons is “thrown” into the free band, which leads to the appearance of conductivity. For the properties of germanium as a detector, this conductivity is apparently not significant.

The introduced “impurity” semiconductivity arises as a consequence of the presence of additional energy levels, resulting from imperfections (disturbances) of the lattice or from the presence of impurity atoms. These levels lie in the normally forbidden region between the filled and the free band and may be “donors” or “acceptors.” The former give up an electron that goes into the free

Table II

Basic properties of germanium^10

band. The latter can capture an electron from the nearby upper edge of the filled band, leaving in it an unoccupied level.

In germanium, impurities are usually donors, giving rise to \(n\)-conductivity. The width of the forbidden region is of the order of \(0.75\ \text{eV}\), the impurity levels lying very close to the edge of the filled band \((\Delta E < 0.1\ \text{eV})\).

The energy-level diagram, indicating the permissible levels of valence electrons in a semiconductor such as germanium, is shown in Fig. 3. The continuous lower band is normally filled with bound electrons. In the interval \(E_G\) there are no levels corresponding to the lattice of an ideal crystal. The upper band—the conduction band—is normally unoccupied. The number of levels in the filled band is just sufficient for the placement of the valence electrons. Local impurity levels—acceptors, lying near and above the filled band, and levels—donors, lying below the conduction band—

conductivity, near it, correspond to electrons localized at impurity atoms. Donors are normally neutral, but when their electron is transferred (excited) into the conduction band they acquire a positive charge. Energy \(\Delta E\) is expended on this. Normally neutral acceptors are ionized negatively when an electron is excited from the neutral band. In germanium \(\Delta E_D\) and \(\Delta E_A\) are so small that practically all donors and acceptors are ionized at “room” temperature.

Fig. 3.

Just as “extrinsic” conductivity, the intrinsic conductivity of germanium depends on temperature. At low \((<300^\circ\mathrm{K})\) temperatures it constitutes only a small fraction of the total conductivity. At sufficiently high temperatures, in well-purified germanium (\(\rho = 10\ \Omega\cdot\mathrm{cm}\) or higher), intrinsic conductivity predominates, increasing with temperature. The combination of the two types of conductivity leads to a curve of the type shown in Fig. 4.

Fig. 4. Dependence of certain properties of germanium on temperature.

Study of the Hall effect shows that the change in resistivity \(\rho\) at low temperatures is caused by a change in the mean free path of the current carriers; the “intrinsic” conductivity, however, changes mainly as a result of thermal excitation of atomic electrons.

As is known, the Hall effect consists in the appearance of a “transverse” potential difference on a conductor carrying current, provided that the conductor is in a magnetic field perpendicular to the direction of the current and to the “front” side of the conductor.

The potential difference \(U\) is determined from the equation

\[ U = R\frac{HI}{t}, \tag{1} \]

where \(R\) is the Hall coefficient of the given substance, \(I\) is the current strength, \(H\) is the magnetic-field intensity, and \(t\) is the thickness of the specimen under investigation in the direction of the magnetic field. By studying the Hall effect, it is possible to determine the type and number of conductivity carriers; if the resistance of the substance is known, the mobility of the conductivity carriers and the mean free path can also be calculated. The dependence of the Hall coefficient on \(T\) is shown in Fig. 4. Where it does not change, the number of free electrons is constant, as occurs in the region of “impurity” conduction (see, for example, \({}^{7}\)). In the region of intrinsic conduction, \(R\) changes in the same way as the specific resistance \(\rho\). Speaking of Hall-effect measurements, it should be noted that unambiguous conclusions from them (for example, the number of conductivity carriers) can be obtained only if all conduction (impurity conduction) is due either solely to electrons or solely to “holes” \({}^{13}\).

Measurements of the mobility of conductivity carriers in germanium \(\left(\dfrac{R}{\rho}\right)\) have shown that electrons (\(n\)-conduction) are more mobile than “holes” (\(p\)-conduction). The mobility of electrons in germanium is higher than in all other solid conductors, except, perhaps, bismuth \({}^{11,12}\). The mobility of electrons at ordinary—of the order of \(300^\circ\) K—temperatures reaches \(3000\ \mathrm{cm^2/(V\,sec)}\), whereas for other semiconductors and metals mobilities of the order of \(20\)–\(100\ \mathrm{cm^2/(V\,sec)}\) occur \({}^{14,28}\).

Studies of the Hall effect in germanium show that, depending on the specimen taken, either electronic or hole conduction may occur in it.

Figure 4 also displays another interesting property of germanium—the strong dependence of the specific resistance on the magnetic-field intensity. This effect is the stronger, the lower the conductivity of the germanium. The curve shows the change of this effect at \(H = 12\,600\) oersteds with temperature (on the ordinate the quantity \(\dfrac{\Delta \rho}{\rho_0}\) is plotted on a logarithmic scale).

3. STRUCTURE AND PRINCIPLE OF OPERATION OF THE CRYSTAL TRIODE

In Fig. 1 the transistor is shown schematically in the form in which it was realized by Bardeen and Brattain. Two point contacts—the sharp ends of wires—touch the upper plane of a small germanium plate. The distance between them is very small (\(\simeq 0.005\)–\(0.025\ \mathrm{cm}\)). One of the contacts,

to which a small positive voltage is applied, is called by the authors the “emitter” and, in its function, corresponds to the control grid of a triode. The second contact, analogous to the “anode” of a triode (we recall that here there is only a formal analogy), is called the collector. The lower surface of the germanium plate is metallized. Thus, on this side the contact has a large area and, correspondingly, a small resistance[^14]. Figure 5 shows a model of a “coaxial” transistor[^15], which is at present being manufactured in series.

Germanium, used for crystal triodes, belongs to the semiconductors with electronic impurity conduction and has a resistivity of the order of \(10\ \Omega\cdot\text{cm}\). The surface

Fig. 5. Coaxial transistor.

of the plate, cut from an ingot with a diamond milling cutter, is prepared in the same way as for the manufacture of detectors with a high reverse voltage, i.e. it is polished and etched[^12].

The points of the contacts are in most cases made of phosphor bronze; the ends of the wires are ground in the form of a wedge, after which they are subjected to electrolytic polishing. The collector contact was sometimes formed by passing a current of the order of \(250\ \text{mA}\), which gave it greater stability in operation.

As has already been said, the emitter is at a positive potential relative to the base. This is the forward direction of the detector. A current \(I_e\) of the order of \(1\ \text{mA}\) flows into the plate. The collector is at a negative potential relative to the base, with \(|U_c| > U_e\); the direction of the current is opposite to the forward direction of the detector. The magnitude \(I_c\) reaches several milliamperes. The current in the collector circuit can be controlled by changing the emitter current. In particular, if \(I_e\) is changed by changing \(U_e\) at constant \(U_c\), then changes in the collector current \(I_c\) may considerably exceed the change in \(I_e\). Since the emitter is a detector operating in the forward-conduction regime, a small alternating voltage (and a small input power) is sufficient

for changing the current. The collector, however, being a reverse-biased crystal detector with a high reverse voltage, can be matched to a sufficiently large load resistance \(R_L\). The alternating voltage and the power in the load circuit considerably exceed the input values. The power gain in the most favorable cases reaches 100 (i.e., 20 db).

Below (Fig. 6) will be given the characteristics of an experimental transistor, showing how the current-voltage characteristic of the collector diode changes as a function of the emitter current.

The action of the transistor may be connected with the nature of the current passing in the germanium from the emitter. The germanium of the transistor has about \(10^{14}\) conduction electrons per \(1\ \text{cm}^3\), or about one electron per \(10^8\) atoms. The amplification of the crystal triode is evidently explained by the fact that the emitter current flows mainly by virtue of \(p\)-conductivity, i.e., it is carried by charge carriers of opposite sign relative to the electrons usually present in excess in germanium. A considerable negative potential is applied to the collector. The current flowing in the plate toward the collector point produces an electric field attracting the “holes” moving into the germanium from the emitter. If the emitter and collector are located very close to one another, a considerable part of the “hole” current of the emitter will go into the collector and its circuit. The collector contact is a high-resistance barrier for electrons leaving the metal for the semiconductor, but offers little hindrance to “holes” entering the contact from the semiconductor.

However, this concept makes it possible to explain only a change in the collector current of the order of \(I_e\), and does not explain the more considerable changes observed. The more considerable changes in \(I_c\) are probably the result of changes in the space charge of the blocking layer in the germanium at the collector contact due to the “hole” current.

It may be considered that the hole current of the emitter changes the form of the current-voltage characteristic of the collector (see below, Fig. 6).

Bardeen believes that the rectifying properties of the germanium detector are due to an internal blocking barrier arising at the free surface and not dependent on the metallic contact\({}^{16}\). This barrier near the surface includes a very thin region of \(p\)-conductivity, of the order of \(10^{-5}\ \text{cm}\). In connection with the above assumptions about the mechanism of transistor action, it would be very important to determine whether the density of “holes” in this region is sufficient for appreciable surface conductivity.

The first experiments with transistors in which the germanium surface was preliminarily oxidized (then the oxide layer was washed off and played no role in the operation of the triode) indicated the presence, though slight, of surface conductivity of the order of \(0.0005\)–\(0.002\ \Omega^{-1}\).

However, surfaces that had not been subjected to oxidation and that did not exhibit noticeable surface conductivity proved to be quite suitable for a transistor.

Further experiments showed that amplification can also be obtained, for example, in a coaxial device (Fig. 5), where there can be no doubt that the “holes” pass through the germanium layer of type “\(n\)” from the emitter to the collector\(^{15,17}\). One of the convincing experiments showing that the “holes” are transported directly through the bulk of the germanium was carried out by Haynes\(^{18}\). A thin, fairly long germanium plate was prepared, at both ends of which large-area electrodes were deposited electrolytically. The emitter and collector could be placed at different distances from one another on the “front” side of the plate.

The electric field between these electrodes could be varied by passing currents along the plate. A pulse signal applied to the emitter was detected in the collector circuit after a certain small interval of time. From the dependence of this time interval on the field, the mobility and the sign of the charge carriers were determined. It was thereby found that they are positively charged and that their mobility coincides with the mobility of “holes” in the bulk of germanium \((1000\ \text{cm}^{2}/\text{V sec})\).

This and other similar experiments will probably help to clarify the causes of the high conductivity of germanium detectors (diodes) in the forward direction (see, for example,\(^{19}\) and \(^{20}\)). Usually this conductivity was attributed to the influence of the strong electric field near the point contact. The authors of the transistor believe that this conductivity is a consequence of the injection of “holes” from the contact into germanium, and that this phenomenon is caused not by the large field strength at the contact, but by the nature of the blocking layer. An experiment confirming these ideas was performed by Shockley and Ryder\(^{21}\). A thin germanium plate had the shape of a wedge, on the narrow and wide ends of which electrodes were deposited. When current was passed through such a wedge, the field strength was greater at the narrow end. If a positive potential was applied to the narrow end, increased conductivity of the germanium was observed; when a positive potential was applied to the wide end, it was absent. The “holes” entering the germanium from the narrow end of the wedge reduced the resistance in the part that accounted for the largest share of the resistance. When the current passed in the reverse direction, the “holes” entering the germanium fell into a region of weak field, and their lifetime was insufficient for them to reach the narrow end and appreciably change the resistance.

The discussion of the mechanism of operation of the crystal triode will be continued below, after the introduction of certain quantities, partly similar to those characterizing electron tubes, and after a description of the characteristics.

4. TRANSISTOR CHARACTERISTICS

The static characteristics of a transistor can be obtained by considering four variables, which may be taken to be the emitter and collector currents \(I_e\) and \(I_c\), and the corresponding voltages \(U_e\) and \(U_c\). The directions of the currents in germanium are taken as positive. Potential differences are measured from the base of the transistor (see Fig. 1). Thus, \(I_e\) and \(U_e\) are positive for connection according to the first circuit, while \(I_c\) and \(U_c\) are negative.

Fig. 6. Characteristics of a germanium transistor.

There is a functional dependence among the four variables. Any pair of them may be taken as independent variables. Since the processes in germanium are associated with the passage and interaction of currents, it is more convenient to take precisely the currents \(I_e\) and \(I_c\) as the independent variables.

All fields in the semiconductor, outside the space-charge region, directly at the contact tips, are determined by the currents flowing through them. The emitter current changes the current-voltage characteristic of the collector diode. The potential differences are single-valued functions of the currents; however, owing to the presence of feedback, the currents may be double-valued functions of the voltages.

The characteristics shown in Fig. 6 are typical for experimental samples of crystalline triodes studied by Bardeen and Brattain (Fig. 2). The collector contact was formed by passing strong currents in the reverse direction, which lowered its reverse (blocking) resistance. This treatment, which worsens its באַ?

properties of the contact as a detector led to a significant improvement in the operation of the transistor.\(^{14}\)

The characteristics shown in Fig. 6 clearly demonstrate the influence of the emitter current on the volt-ampere characteristic of the collector. The curve corresponding to \(I_e = 0\) is the ordinary reverse characteristic of a germanium detector. As the emitter current is increased, the curves shift to the right. The change in \(I_c\) at constant \(U_c\) exceeds the corresponding change in \(I_e\). The current amplification factor \(\alpha\), defined as

\[ \alpha = -\left(\frac{\partial I_c}{\partial I_e}\right)_{U_c=\mathrm{const}} \tag{2} \]

has a value from 2 to 3.

The dotted curves correspond to constant values of the emitter potential. In the right-hand part \(U_c\) falls as \(I_e\) increases, which indicates a negative input resistance. This is explained by the inverse influence of the collector current on the characteristic of the emitter contact.

The collector current \(I_c\) lowers the surface potential of the germanium near the emitter and changes the effective bias of the latter. It may be assumed that this potential drop is equal to \(R_F I_c\), where \(R_F\) is the feedback resistance, depending in turn on the currents. The effective bias of the emitter will be equal to \(U_e - R_F I_c\), and one may write that

\[ I_e = f(U_e - R_F I_c). \tag{3} \]

In some cases \(R_F\) decreases with increasing \(I_e\) owing to the growth of the conductivity of germanium near the contacts when currents pass in the forward direction. The change in \(I_e\) due to its dependence on \((U_e - R_F I_c)\) may lead to an even greater increase in \(I_c\), which, through feedback, will increase \(I_e\), i.e. the regime will become unstable. This is one of the causes limiting the permissible amplification of a crystal triode.

In Fig. 6 the load line is indicated, corresponding to a supply voltage in the collector circuit of \(100\ \mathrm{V}\) and a load \(R_L\) equal to \(40000\ \Omega\). The equation of this line is

\[ U_c = -100 - 40 \cdot 10^3 I_c. \tag{4} \]

The load \(R_L\) is approximately equal to the collector resistance, given by the slope of the rectilinear sections of the characteristic. If the working section of the load line lies between the points \(P_1\) and \(P_2\), the voltage amplitude at the output is of the order of \(8\ \mathrm{V}\), and the current amplitude is about \(0.20\ \mathrm{mA}\). The corresponding quantities at the transistor input are \(0.07\) and \(0.18\), so that the power gain is

\[ G \approx \frac{8 \cdot 0.20}{0.07 \cdot 0.18} \cong 125. \tag{5} \]

Let us pass to the dynamic characteristics.
In the case of small deviations from the operating point \(P_0\), one may write:

\[ \Delta U_e = R_{11}\Delta I_e + R_{12}\Delta I_c, \tag{6} \]

\[ \Delta U_c = R_{21}\Delta I_e + R_{22}\Delta I_c. \tag{7} \]

The currents are here taken as the independent variables. The increments correspond to small deviations, i.e., to a small-amplitude signal at the input. The coefficients \(R\) are positive, have the dimension of resistances, and are determined as follows:

\[ \begin{aligned} R_{11} &= \left(\frac{\partial U_e}{\partial I_e}\right)_{I_c=\mathrm{const}},\\ R_{12} &= \left(-\frac{\partial U_e}{\partial I_c}\right)_{I_e=\mathrm{const}},\\ R_{21} &= \left(-\frac{\partial U_c}{\partial I_e}\right)_{I_c=\mathrm{const}},\\ R_{22} &= \left(-\frac{\partial U_c}{\partial I_c}\right)_{I_e=\mathrm{const}}. \end{aligned} \tag{8} \]

For the transistor whose characteristics are given in Fig. 3, at \(I_e = 0.75\) ma and \(I_c = -2\) ma they have the following values: \(R_{11}=800\) ohms, \(R_{12}=300\) ohms, \(R_{21}=100\,000\) ohms, \(R_{22}=40\,000\) ohms.

The coefficient \(R_{11}\) represents the input resistance at a given \(I_c\). \(R_{12}\) corresponds to the feedback resistance. The ratio \(\dfrac{R_{21}}{R_{22}}\) is equal to the current gain coefficient \(\alpha\). \(R_{22}\) is the collector resistance at a given current \(I_e\) and is equal to \((10\text{–}50)\cdot 10^3\) ohms, changing comparatively little with variation of \(I_e\). The power gain of the circuit of Fig. 1 depends on the choice of the operating point and on the load in the collector circuit.

Positive feedback, characterized by \(R_{12}\), increases the gain and makes it possible to obtain a very large gain near the generation threshold. The maximum gain, without taking feedback into account, is attained when \(R_L\) is equal to the collector resistance \(R_{22}\), and the total resistance (impedance) of the generator is equal to the emitter resistance \(R_{11}\). In this case

\[ G_1=\alpha^2 \frac{R_{22}}{4R_{11}}. \tag{9} \]

This quantity is equal to the ratio of the power of the signal dissipated in \(R_L\) to the power of the signal at the input.

Substituting the coefficients \(R_i\) given above, we obtain for the transistor whose characteristics are shown in Fig. 4 an amplification of about 80 (19 dB); the difference from the value \(G = 125\) given above is explained by the influence of feedback.

5. INFLUENCE OF THE SIGNAL FREQUENCY, THE DISTANCE BETWEEN POINTS, AND TEMPERATURE ON THE OPERATION OF THE GERMANIUM TRIODE. NOISE LEVEL

The highest frequency of signals that can be amplified by a transistor reaches, according to the data presently available\(^{22}\), approximately \(10\) MHz. Fig. 7 shows the change of the amplification coefficient \(\alpha\) with frequency. It should be noted that amplification of the signal power occurs also for \(\alpha < 1\), owing to the difference between the characteristics of the emitter and collector diodes.

It is interesting that, unlike the electronic triode (the ordinary radio tube), the transistor does not change the phase of the amplified alternating voltage by \(180^\circ\). In amplifying audio frequencies the phase remains practically unchanged. In the radio-frequency region an increasing phase shift of the amplified signal relative to the input signal is observed with increasing frequency (lower curves in Fig. 7). This phenomenon is connected with the transit time of the conductivity carriers in germanium, which provide the interconnection of the emitter and collector currents. Measurements of the dependence of amplification and phase shift on frequency for coaxial triodes\(^{15}\) with different thicknesses of germanium between the contacts showed that, for greater thicknesses, \(\alpha\) begins to fall at lower frequencies. The phase shift at one and the same frequency also increases with increasing thickness of the germanium.

Fig. 7. Frequency characteristics of a transistor.

From the considerations given above it is clear that the distance between the points of the electrodes must have a strong influence on the operation of a crystal triode.

As was to be expected, the emitter current, as the latter is moved away from the collector, has an ever smaller influence. \(R_{21}\) and \(\alpha\) decrease with increasing distance \(s\) between the points. From Fig. 8 it is seen that \(\alpha\) decreases almost exponentially when \(s\) changes from 0.005

to 0.03 cm. Extrapolation to \(s = 0\) shows that further bringing together would not increase \(\alpha\) by more than 25%.

There are only very few data on the change of transistor characteristics with temperature[^14]. It is known that the reverse characteristic of a germanium diode changes rapidly with temperature, and the dependence is the stronger the higher the reverse resistance. In a transistor, the forming of the collector contact leads to a considerable reduction of this resistance, and the influence of temperature is not so strong. The feedback resistance \(R_{12}\) depends comparatively little on temperature. The current amplification factor \(\alpha\) increases with temperature. The increase of \(\alpha\) with temperature may be compensated by a decrease in the ratio \(\dfrac{R_{22}}{R_{11}}\), which will lead to a negative temperature coefficient of the total amplification of the signal by the transistor.

Fig. 8. Dependence of the amplification factor on the distance between the tips.

In order to characterize the quality of a transistor as an amplifier from the point of view of the noises that arise, it is convenient to use the equivalent circuit (Fig. 9), introduced by Becker[^22] and analogous to equivalent circuits widely used in radio engineering. Noises in an amplifier are usually characterized by a number equal to the ratio of the noise power at the output to that noise power which would be measured if the “noise generators” \(N_e\) and \(N_c\) of the equivalent circuit were absent and all the noise were determined by the thermal noise of the signal generator at the input. For the transistor samples investigated by Becker, when operating at a frequency of about 1000 cps, this number (the noise factor) ranged from 55 to 70 db. This is much higher than the noise of vacuum triodes. However, experience

Fig. 9. Equivalent circuit for estimating noise.

...the struggle against noise in crystal detectors, which has led to good results, gives reason to think that it will be possible to suppress transistor noise, bringing it close in quality to electronic tubes. It is interesting that, as follows from the curve in Fig. 10, obtained by Becker, transistor noise falls sharply on entering the radio-frequency region.

Fig. 10. Frequency dependence of the noise level.

6. ON TRANSISTOR CONNECTION CIRCUITS. THE CRYSTAL TETRODE

Figure 11 shows the three principal possible circuits for connecting transistors. The circuit A considered above is analogous to the connection of a triode with a grounded grid \(^{23,25}\). The circuit with a grounded emitter is analogous to the connection of a triode with a grounded cathode. The collector is analogous to the anode, and the amplifying cascade, unlike circuit A, changes the phase of the signal by \(180^\circ\). At small values of \(R_L\) the circuit can generate oscillations (usually in the audio-frequency range).

The circuit with a grounded collector can be used to amplify a signal “in both directions”; moreover, when amplifying “from left to right” it does not change the phase of the signal, while when operating “from right to left” it changes it by \(180^\circ\). The gain is about \(15\ \mathrm{db}\). Increasing \(R_g\) leads to lower stability of operation; increasing \(R_L\) increases the stability.

The use of a number of transistors in successive cascades is disadvantageous, since their output impedance is large and their input impedance small. The maximum gain per cascade, in view of this, does not exce—

Fig. 11. Connection of a transistor as an amplifying element of a circuit.

has 5 db. With matching resistances by interstage transformers, however, it can be brought up to 15 db. Cascading transistors with grounded emitters is more difficult because of the lower stability, but the gain per stage can be greater. An amplifier was built that gave a gain of 55 db over three stages[^23].

In addition to germanium triodes, a tetrode has also now been designed, having three detector contacts. Two of them are emitters. The contacts are arranged in a triangle at equal distances of 0.005 cm from one another. A tetrode of this type has been successfully used in a frequency-conversion circuit (Fig. 12). It was found that \(f_1\) and \(f_2\) can be raised at least to 200 Mc/s, while the intermediate frequency \(f_1 - f_2\) remains within the operating range of an ordinary transistor, i.e., does not exceed several megacycles[^24].

Fig. 12. Frequency converter using a germanium triode.

Because of the comparatively high noise level, the use of crystal triodes for high-quality amplification of audio frequencies is still difficult. However, the obvious advantages of the transistor have already attracted attention to it in special fields. Thus, for example, an audio-frequency generator was used in a rocket radio altimeter[^25], where, owing to its small size and mechanical ruggedness, the crystal triode was preferred to the vacuum tube. It is likely that the transistor will first find application also, for example, in calculating machines, where many hundreds of amplifying units are used, and in switching telemechanical devices.

The lifetime of the transistor is at least of the same order as that of modern radio tubes. The mechanical strength of experimental production samples is evidently higher than that of vacuum tubes. During the electrical “forming” of the collector, what occurs is essentially spot welding, which makes this contact very stable[^12]. The emitter contact is more delicate.

Encapsulation of the finished transistor with insulating amorphous “fillers” leads to greater stability. There are data indicating that crystal triodes can also be made of silicon[^14].

7. ADDITIONAL INFORMATION ON THE OPERATING PRINCIPLE OF THE CRYSTAL TRIODE

In the present section a quantitative estimate is given for a number of quantities connected with the action of the transistor, namely:

1) the fields produced in germanium by the collector current;
2) the transfer times of “holes” from the emitter to the collector;
3) the current gain in the collector;
4) the feedback resistance.

It may be assumed that the collector current is due mainly to conduction electrons spreading radially from a point contact. This assumption is especially close to the truth if the collector current is considerably greater than the emitter current. The field at a distance \(r\) from the collector is equal to

\[ E=\frac{\rho I_c}{2\pi r^3}. \tag{10} \]

For example, if \(\rho=10\ \Omega\text{ cm}\), \(I_c=0.001\ a\), \(r=0.005\ \text{cm}\),

\[ E \simeq 100\ \frac{v}{\text{cm}}. \]

The transfer velocity of a “hole” in the field \(E\) is equal to \(\mu_h E\), where \(\mu_h\) is the mobility of the “holes.”

The transfer time

\[ T=\int_r \frac{dr}{\mu_h E} =\frac{2\pi}{\mu_h \rho I_c}\int_0^s r^2\,dr, \tag{11} \]

where \(s\) is the distance between the collector and the emitter. Integration gives

\[ T=2\pi s^3 \frac{1}{3\mu_h I_c}. \tag{12} \]

For \(s=0.005\ \text{cm}\), \(\mu_h=1000\ \frac{\text{cm}^2}{v\,\text{sec}}\), \(\rho=10\ \Omega\text{ cm}\), and \(I_c=0.001\ a\), the transfer time is approximately equal to \(0.25\cdot 10^{-7}\ \text{sec}\). This agrees with conclusions from the measurement of the phase shift with increasing signal frequency. The current \(I_h\) is in fact, of course, somewhat reduced by recombination on the way from the emitter to the collector.

Let us now consider the influence of the space charge of the “holes” on the blocking barrier at the collector. An estimate of the hole concentration may be obtained as follows. The field in the blocking barrier reaches a value of \(10^4\ \frac{v}{\text{cm}}\). Multiplication by the mobility gives a transfer velocity of “holes” \(v_h\) of about \(10^7\ \text{cm/sec}\). The “hole” current \(I_h\) is equal to

\[ I_h=n_h e v_h A_c, \tag{13} \]

where \(A_c\) is the area of the collector contact, and \(n_h\) is the concentration of “holes” in the barrier.

From the last equality this concentration can be expressed as

\[ n_h=\frac{I_h}{e v_h A_c}. \tag{14} \]

For \(I_h=0.001\,a\), \(v_h=10^7\ \mathrm{cm/sec}\), and \(A_c=10^{-6}\ \mathrm{cm}\), \(n_h\) is approximately equal to \(0.6\cdot 10^8\), which is of the same order of magnitude as the concentration of “donors” in the barrier. It is therefore natural to assume that the “hole” current can change the space charge of the barrier, and consequently also the electron flux from the collector, to a considerable degree. It is probably precisely this effect that explains values of \(\alpha\) greater than 1.

As was said earlier, the collector current exerts on the emitter current an influence having the character of positive feedback. The collector current lowers the surface potential near the emitter by the amount

\[ U=\frac{\rho I_c}{2\pi s}. \tag{15} \]

The feedback resistance introduced into equation (3) is expressed as

\[ R_F=\frac{\rho}{2\pi s}. \tag{16} \]

For \(\rho=10\ \mathrm{ohm\,cm}\) and \(s=0.005\ \mathrm{cm}\), \(R_F\) proves to be equal to 300 ohms, which is close to the observed values.

The estimate of the quantities given here agrees with the general physical picture of the operation of the transistor.

LITERATURE

A. Principal

1. Bardeen and Brattain, Phys. Rev. 74, 230 (1948).
2. Brattain and Bardeen, Phys. Rev. 74, 231 (1948).
3. O. Losev, Telef. i Telegr. b. Pr., No. 14, p. 375 (1922).
4. O. Losev, Telef. i Telegr. b. Pr., No. 53, 1929.
5. G. Ostroumov, Telef. i Telegr. b. Pr., No. 24, p. 204 (1924).
6. B. A. Dobrokhotov, Radio Engineering Measurements at Centimeter Wavelengths, Sovetskoe Radio Publishing House (1948).
7. B. I. Davydov, UFN 33, 157 (1947).
8. F. F. Vol’kenshtein, UFN 28, 389 (1946).
9. F. F. Vol’kenshtein, Electrical Conductivity of Semiconductors, Gostekhizdat, 1947.
10. Wilson, Quantum Theory of Metals, State Publishing House of Technical-Theoretical Literature, 1941.
11. Dunlap, General Electric Review 52, 9 (1949).
12. Torrey and Whitmer, Crystal Rectifiers, Mac Graw Hill, 1948.
13. Lark-Horovitz et al., Phys. Rev. 69, 258 (1946).

1. Bardeen and Brattain, Phys. Rev. 75, 1208 (1949).
2. Kock and Wallace, Electrical Engineering 68, 222 (1949).
3. Bardeen, Phys. Rev. 71, 717 (1947).
4. Shive, Phys. Rev. 75, 689 (1949).
5. Haynes and Shockley, Phys. Rev. 75, 691 (1949).
6. Bray, Lark-Horovitz and Smith, Phys. Rev. 72, 530 (1948).
7. Bray, Phys. Rev. 74, 1218 (1948).
8. Ryder and Shockley, Phys. Rev. 75, 310 (1949).
9. Becker and Shive, Electrical Engineering 68, 215 (1949).
10. Electronics, Apr. 1949, p. 120.
11. F. Lehan, Electronics, Aug. 1949, p. 90.
12. Haegele, Electronics, Oct. 1949, p. 80.
13. Krasyukov, Information Bulletin, Soviet Radio Publishing House, No. 17 (61), Sept. 15, 1949.

B. Additional literature and literature on related questions

1. Isenberg, Russell and Greene, Phys. Rev. 74, 1235 (1948), “Measurement of the Hall Effect in Semiconductors.”
2. F. Seitz, Phys. Rev. 73, 549 (1948), “Mean Free Path in Si and Ge.”
3. Conwell and Weisskopf, Phys. Rev. 69, 258 (1946), “Theory of Scattering in Semiconductors.”
4. Pearson and Bardeen, Phys. Rev. 73, 1265 (1948), “Electrical Properties of Pure Silicon and Its Alloys.”
5. Wireless World, Oct. 1948, No. 10, p. 358, “Amplifying Crystal.”
6. Power Generation 52, No. 10, 83 (1948), “The Transistor—A Crystal Triode.”
7. Atkins, Radio and Television News, Oct. 1948, p. 39, “Amplifying Crystal.”
8. Devis, Johnson, Lark-Horovitz and Siegel, Phys. Rev. 74, 1235 (1948), “Neutron Bombardment of Germanium Semiconductors.”
9. Electrical Times 114, 415 (1948), “Theory of the Transistor.”
10. Le Duc, Radio-Craft, July 1948, p. 20, “High-Frequency Crystal Diodes.”
11. McQuay, Radio-Craft, July 1948, p. 20; August 1948, p. 20, “Crystal Detectors.”
12. Scaff and Ohl, Bell System Techn. Journal 26, January 1947, “Development of Silicon Crystal Detectors for Radar.”
13. McQuay, Radio-Craft, September 1948, p. 26, “Crystal Detectors (III).”
14. Lark-Horovitz and Johnson, Phys. Rev. 69, 858 (1946), “Theory of the Specific Resistance of Germanium Alloys.”
15. Johnson and Lark-Horovitz, Phys. Rev. 69, 259 (1946), “Theory of Thermo-EMF in Germanium.”
16. M. Telkes, J. Appl. Phys. 18, 1116 (1947), “Germanium Thermocouples.”
17. Benzer, Phys. Rev. 72, 531 (1947), “Spontaneous Electric Oscillations in Germanium Crystals.”
18. Benzer, Phys. Rev. 73, 1256 (1948), “Photoelectric Effect and Its Relation to Rectification by a Metal–Semiconductor Contact.”
19. Brown, Phys. Rev. 73, 1257 (1948), “Relation of Temperature, Pressure, and Conductivity in Semiconductors.”
20. Radio-Craft, September 1948, “Sunset for Radio Tubes.”

1. Johnson and Lark-Horovitz, Phys. Rev. 73, 1257 (1948), “Theory of the Nernst and Ettingshausen effects in semiconductors at high temperatures.”

2. Sein, Phys. Rev. 70, 104 (1946), “Energy of impurity levels of semiconductors.”

3. Benzer, Phys. Rev. 70, 105 (1946), “Photodiffusion and photovoltaic characteristics in germanium.”

4. Meyerhof, Phys. Rev. 70, 106 (1946), “Contact potential difference in crystalline detectors.”

5. Benzer, Phys. Rev. 71, 141 (1947), “Germanium—germanium contact.”

6. Bray and Lark-Horovitz, Phys. Rev. 71, 141 (1947), “Photo- and thermoelectric effects in \(p\)-type Ge detectors.”

7. Pearson and Shockley, Phys. Rev. 71, 142 (1947), “Measurement of the Hall effect and of the resistivity of Ge and Si in the temperature range \(10—600^\circ K\).”

8. Meyerhof, Phys. Rev. 71, 727 (1947), “Contact potential difference in silicon crystalline detectors.”

9. Brattain and Shockley, Phys. Rev. 72, 846 (1947), “Density of surface states of silicon, obtained from measurements of contact potentials.”

10. Brattain, Phys. Rev. 72, 345 (1947), “Proof of the existence of surface states of a semiconductor from the change of contact potential under illumination.”

11. Estermann et al., Phys. Rev. 72, 530 (1947), “Resistivity and Hall constant of germanium samples at low temperatures.”

12. Estermann et al., Phys. Rev. 71, 484 (1947), “Resistivity of germanium at low temperatures and the influence of impurities.”

13. Goodman, Lawson and Shiff, Phys. Rev. 71, 191 (1947), “Thermal ionization of impurity levels in semiconductors.”

14. Benzer, Phys. Rev. 72, 1267 (1947), “Excess-defect germanium contacts.”

15. Dunlap and Hennely, Phys. Rev. 74, 976 (1948), “Non-rectifying germanium.”

16. Lehovec, Phys. Rev. 75, 1100 (1949), “On hole current in a germanium transistor.”

17. Pearson, Phys. Rev. 76, 179 (1949), “Mobility of electrons and holes in single-crystal germanium.”

18. Shockley and Pearson, Phys. Rev. 76, 180 (1949), “Current flow through an \(n—p\) boundary.”

19. Bray, Phys. Rev. 76, 458 (1949), “Injection of electrons into \(p\)-type germanium.”

20. Fan and Bray, Phys. Rev. 76, 458 (1949), “Blocking layer in \(p\)-type germanium.”

21. Pfann and Scaff, Phys. Rev. 76, 459 (1949), “A transistor made of \(p\)-type germanium.”

22. Pearson, Phys. Rev. 76, 459 (1949), “Electrical properties of the boundaries of crystalline grains in germanium.”

23. Shockley, Pearson, Sparks and Brattain, Phys. Rev. 76, 459 (1949), “Change in the resistance of a germanium filament by the injection of conduction holes.”

24. Radiotechnik 25, 375 (1949), “Coaxial transistor.”

25. Shockley and Pearson, Phys. Rev. 74, 232 (1948), “Modulation of the conductivity of a thin semiconductor film by a surface charge.”

26. Reich, Rev. of Sci. Instr. 20, 586 (1946), “Trigger circuit with a transistor.”

1. Brattain and Briggs, Phys. Rev. 75, 1705 (1949), “Optical constants of germanium in visible and infrared light.”

2. Smith, Phys. Rev. 73, 953 (1949), “Temperature dependence of the work function of semiconductors.”

3. Markham and Miller, Phys. Rev. 75, 959 (1949), “Influence of the surface condition on temperature changes of the work function of semiconductors.”

4. Suhl and Shockley, Phys. Rev. 75, 1617 (1949), “Concentration of electrons and holes by a magnetic field.”

5. Webster et al., RCA Rev. 10, No. 1, 5 (1949), “Some new circuits for a three-electrode crystal amplifier.”

6. Bray, Phys. Rev. 76, 152 (1949), “Dependence of the specific resistance of germanium on the electric field.”

7. Benzer, Phys. Rev. 76, 150 (1949), “Hall effect in metal–semiconductor point contacts.”

8. Benzer, J. of Appl. Phys. 20, 804 (1949), “Germanium detectors with high reverse voltage.”

9. Pearson and Bardeen, Phys. Rev. 75, 865 (1949), “Electrical properties of pure silicon and alloys of silicon with boron and phosphorus.”

10. Aisberg, Toute la Radio 16, 218 (1949).

11. Electronics, Nov. 1949, p. 120, “Amplification and frequency conversion by means of a transistor.”

12. Putley, Proc. Phys. Soc. 62, 284 (1949), “On the electrical conductivity of germanium.”

13. Lehovec, Electronics 22, 89 (1949), “Methods of testing transistors.”

14. Electrical Engineering 68, 937 (1949), “Photoeffect in germanium.”

15. Shockley, Pearson and Haynes, Bell System Techn. Journal 28, 314 (1949), “Injection of conductivity holes in germanium. Quantitative data and the filament transistor.”

16. Ryder D., Fischer, ibid., p. 367, “Some prospects of circuits with transistors.”

17. C. Herring, ibid., p. 401, “Theory of transition processes in the transfer of ‘holes’ in excess semiconductors.”

18. Bardeen, ibid., p. 428, “On the theory of the impedance of contact detectors.”

19. Shockley, ibid., p. 435, “On the theory of \(n\)—\(p\) boundaries in semiconductors. Transistors with an \(n\)—\(p\) junction.”

20. Matt, PIEE 96, I, p. 253 (1949), “Semiconductors and detectors.”