SEMICONDUCTOR BOLOMETERS

I. D. Konozhenko

1. INTRODUCTION

At the present time there exist several types of receivers of infrared radiation (IRR), whose operation is based on entirely different physical phenomena. Among them are bolometers, in which the action of IRR is reduced to heating of the sensitive element, as a result of which its resistance changes.

Since heating can occur not only through absorption of IRR, instruments of the bolometer type are also used for measuring the power of the current passing through them, and also as resistance thermometers.

Among the various receivers of IRR, bolometers, together with thermoelements, possess the greatest merits. Let us recall that the broad development of infrared spectroscopy first became possible precisely as a result of the use of bolometers (1880).

However, the problem of creating a high-quality IRR receiver still cannot be regarded as solved. Existing radiation receivers, in their characteristics, are far from satisfying all the requirements of modern spectroscopy. Attempts to solve this problem by creating a metallic bolometer have so far not yielded fully satisfactory results. Therefore at present, in the literature, one can increasingly often find works devoted to semiconductor receivers of IRR and aimed at solving the problem of creating high-quality receivers from semiconductor materials possessing a high temperature coefficient of resistance. It should be noted that work is simultaneously being conducted on the creation of dielectric bolometers[^1].

In contrast to photoresistances, which possess sharply expressed selectivity, bolometers retain their sensitivity over a broad range of wavelengths of electromagnetic radiation; there is no red limit of sensitivity for them, and this constitutes one of their essential advantages over other radiation receivers.

The quality of a modern bolometer is determined by its sensitivity, the magnitude of its sensitivity threshold, the rapidity of its response to the action of IRR, and the rapidity with which the initial temperature is restored. The last property of bolometers is characterized by a quantity called the “time constant,” or the “temperature-relaxation time.”

The intensity of the radiation incident on the radiation receiver in a spectrometer with sufficiently high resolving power ranges from \(5—10^{-7}\) to \(5—10^{-9}\) W. It is therefore important that the sensitivity threshold of the IRR receiver lie within the indicated range of powers.

The sensitivity of bolometers \(Z\) depends, in the main, on three quantities\(^{1,2,3}\): the thermal coefficient of resistance (t.c.r.) \(\alpha\) of the material from which the sensitive element of the bolometer is made, the voltage \(V\) applied to the bolometer, and the surface area \(S\) of the sensitive element of the receiver, namely:

\[ Z \sim \frac{\alpha V}{S}. \tag{1} \]

With a decrease in the thickness of the layer \(d\) forming the sensitive element, the sensitivity of the bolometer increases and its inertia decreases. For both metallic and semiconductor bolometers, the value of \(S\) may be the same. As for \(\alpha\) and \(V\), for semiconductor bolometers they are almost an order of magnitude larger than for metals. Theoretically, therefore, semiconductor bolometers should possess a sensitivity exceeding the sensitivity of metallic bolometers by two orders of magnitude. At present this possibility has been fully realized\(^{5,8}\). In some cases semiconductor bolometers have a sensitivity of more than \(100\ \mathrm{V/W}\), whereas the sensitivity of metallic bolometers is equal to \(\sim 1\ \mathrm{V/W}\).

This, however, does not mean that semiconductor bolometers are displacing metallic ones. Every infrared-radiation receiver has its own noise level, on which the minimum detectable power of the IRR flux depends, i.e., the sensitivity threshold of the receiver. Since semiconductor bolometers have a resistance exceeding \(10^{6}\ \Omega\), their intrinsic-noise level, as a rule, is not lower than \(10^{-7}\) V, and for the most part it is equal to \(10^{-6}\) V. As a result, their sensitivity threshold is usually higher than that of metallic bolometers, for which it is \(10^{-8}—5\cdot 10^{-9}\) W. At the same time, in individual cases it proves possible to create samples of semiconductor bolometers\(^{2}\) that have a sensitivity threshold reaching \(5—10^{-10}\) W. In the case of metallic bolometers, such a sensitivity threshold has not yet been achieved.

Since semiconductor bolometers have high resistance, it is possible to use amplifier tubes. This eliminates the need to use exclusively galvanometers as signal recorders; other instruments may also be used: a cathode voltmeter, a cathode oscilloscope, etc. A disadvantage of semiconductor bolometers is their lower stability than that of metallic bolometers, the result of which is instability of the indicator zero point. However, if one abandons the use of the Wheatstone-bridge circuit and, using a tube amplifier, employs an ordinary circuit with a load resistance (see Fig. 4 below), then this defect of semiconductor bolometers can be reduced to a minimum.

At present, semiconductor bolometers make it possible to record a change in the temperature of the sensitive element of \(10^{-6}—10^{-7\circ} \mathrm{C}\). Such a change in temperature gives rise to a signal of \(\sim 1\) \(\mu\mathrm{V}\), which can readily be recorded.

The construction of receivers with a solid substrate and without a substrate is sufficiently robust and eliminates the possibility of a microphonic effect. Below, various designs of semiconductor bolometers, their features and characteristics, will be described.

2. PRINCIPLE OF OPERATION OF THE BOLOMETER AND CIRCUITS FOR ITS CONNECTION

The most widely used circuit for connecting a bolometer is the Wheatstone-bridge circuit, one of whose arms is the sensitive element of the bolometer (Fig. 1). Infrared radiation absorbed by the sensitive layer of the bolometer heats it and thereby changes its resistance, disturbing the equilibrium of the bridge. For a direct-current bridge in which all four arms have equal resistances, the change in the voltage drop on the bridge diagonal \(AB\) in the case of semiconductor bolometers is equal to

\[ \Delta V = -\frac{1}{4}\frac{B}{T^{2}} V \Delta T, \tag{2} \]

Fig. 1.

where \(-\dfrac{B}{T^{2}}=\alpha\), \(\Delta T\) is the change in temperature of the sensitive surface of the bolometer under the action of an infrared-radiation flux of power \(W\). With a temperature law of resistance linear in first approximation, the change in temperature \(\Delta T\) can be determined from

by means of the following relation:

\[ \Delta T=\frac{\chi W}{4\sigma S\varepsilon T^3+P_0}, \tag{3} \]

where \(\chi\) is the IR absorption coefficient, \(\varepsilon=\varepsilon_1+\varepsilon_2\), \(\varepsilon_1\) and \(\varepsilon_2\) are the emissivities of the front and rear surfaces of the receiver, \(P_0\) is the heat loss through thermal conductivity, \(T\) is the temperature of the sensitive element, and \(\sigma\) is a constant.

Fig. 2.

In bridge circuits with high \((10^6—10^3\ \Omega)\) ohmic resistance of the arms, the choice of galvanometer is of great importance. In practice, conditions must be satisfied under which the critical

Fig. 3.

resistance of the galvanometer \(R_{\mathrm{cr}}\) is considerably greater than the resistance of the bolometer, which is not always easy to achieve. For this purpose Bauer1

used the connection of the bridge with an amplifying circuit (Fig. 2). This is a kind of two-stage tube voltmeter, by means of which it was easy to record voltage changes arising across the diagonal of the bridge. In the case of high-resistance bolometers \((R \sim 10^6\ \Omega)\), circuits of an alternating-current bridge are often used (Fig. 3)\(^{6}\).

For measurements, a compensation circuit is usually used. Since it is difficult to make two perfectly identical sensitive elements of a bolometer, rheostats are connected in series with them. The bridge is powered by means of an audio-frequency generator with a frequency of 500–800 cps, which considerably reduces temperature oscillations in the circuit over the course of one period.

Fig. 4.

Instead of Bauer’s circuit, a more convenient circuit, shown in Fig. 4, is often used. For this circuit the change in the voltage drop across the resistance \(R_1\) is determined by the following relation:

\[ \Delta V = -\frac{B}{T^2}\, \frac{R_1 R_x V}{\left(R_1 + R_x + \dfrac{B R_x \Delta T}{T^2}\right)(R_x + R_1)} . \tag{4} \]

Examination of this equation shows that, under the condition \(R_1 = R_x\), we obtain the maximum value of the signal \(\Delta V\). In this case formula (4) takes the form

\[ \Delta V = -\frac{B}{T^2}\, \frac{V}{4 + \dfrac{2B\Delta T}{T^2}} . \tag{5} \]

The bolometer connection circuit presented in Fig. 4 is convenient under conditions of radiation modulation with subsequent resonant amplification of the signal. At the same time, the bridge circuit is also suitable in the case when radiation modulation is not used, and the signal is recorded directly by means of a galvanometer or with the use of B. P. Kozyrev’s amplifier\(^{16}\).

From formulas (2) and (5) it is seen that, when the temperature of the sensitive element is raised under the action of infrared radiation, its resistance

in the case of semiconductor bolometers, will decrease (consequently, the potential difference \(\Delta V\) will also decrease), and not increase, as is the case for metallic bolometers, which have a positive value of the t.c.r.

3. ON THE SENSITIVITY AND TIME OF TEMPERATURE RELAXATION OF SEMICONDUCTOR BOLOMETERS

By the sensitivity of a receiver one usually understands the ratio of the output voltage to the power of the radiation absorbed by the receiver, and expresses it in volts per watt. It is easy to see that combining formulas (2) and (3) gives us an equation for determining the sensitivity of a semiconductor receiver under the action of unmodulated radiation:

\[ Z=\frac{\Delta V}{xW}=-\frac{B}{T^{2}}\frac{V}{16\sigma S\varepsilon T^{3}+P_{0}}. \tag{6} \]

An analogous formula was obtained by Bauer\(^5\) for calculating the sensitivity of a bolometer made of copper oxide. For equation (6) two cases are characteristic: if \(R_x=R_3\) (see Fig. 1) and \(R_3\) does not depend on temperature, then the sensitivity does not depend on the correction term \((P_0)\). When \(R_3\) depends on temperature, the correction term is equal to

\[ P_{0}=-\frac{B}{T^{2}}\frac{V^{2}}{R_xS}. \tag{7} \]

Expression (7) in Bauer’s formula characterizes the thermal effect of the current. At small voltages this correction term is small and may be neglected. At large voltages it is also necessary to distinguish two cases: a) if the t.c.r. is positive, then the denominator will be smaller and the sensitivity greater; b) with a negative t.c.r. the denominator will be greater and the sensitivity smaller. Therefore, for bolometers with a negative t.c.r. the first condition \(P_0=0\) is more advantageous, and for bolometers with a positive t.c.r.—the second condition \((P_0\ne0)\).

In Fig. 5, borrowed from Bauer’s work\(^5\), results are presented for a study of the sensitivity of bolometers made of copper oxide as a function of \(V\) and \(T\) of the sensitive element of the bolometer. At high voltage, owing to heating by the current, the sensitivity of the bolometer falls markedly (the t.c.r. decreases).

Formula (6) and its brief analysis given above are valid for the sensitivity of a receiver operating under an unmodulated IR flux. In the case of a modulated flux, the sensitivity of a semiconductor bolometer can be calculated with the aid of the approximate formula proposed by Brattain

and Becker^8. However, from a practical point of view it is of little use. A more acceptable formula for the case of symmetry of the resistances of the bridge arms (taking into account heat losses to the substrate, the surrounding medium, and the metallic electrodes) was obtained by Worsmer:

\[ Z=\frac{1}{2}\alpha xV\left[ \frac{1}{c_1}\left(1-e^{-\frac{t}{\tau_1}}\right) +\frac{1}{c_2}\left(1-e^{-\frac{t}{\tau_2}}\right) +\frac{1}{c_3}\left(1-e^{-\frac{t}{\tau_3}}\right) \right], \tag{8} \]

where \(c_1\), \(c_2\), and \(c_3\) are the constants of heat losses through the substrate, electrodes, and surrounding medium, respectively; \(t\) is the time of action of the radiation; \(\tau_1\), \(\tau_2\), \(\tau_3\) are the time constants of the heat flows.

Fig. 5. Sensitivity of a copper-oxide receiver as a function of the temperature of the sensitive layer and the applied voltage. Curve \(S_a\)—uncompensated receiver, but with \(R_x=R_3\). Curve \(S_b\)—compensation receiver. Curve \(V\)—applied voltage.

Expressing the time constants \(\tau_1\), \(\tau_2\), \(\tau_3\) through the effective time constant \(\tau\), formula (8) can be represented in a practically acceptable form:

\[ Z=\frac{\alpha xV}{2}\left[ \frac{1}{c}\left(1-e^{-\frac{t}{\tau}}\right) \right], \tag{9} \]

where \(c\) is the total heat loss. It should be noted that formula (9) is valid provided that the thermal effect of the current does not have a substantial influence. Formula (9) indicates that which is common to

semiconductor bolometers have the property that their sensitivity to modulated radiation increases according to the law

\[ Z \approx Z_0 \left( 1 - e^{-\frac{t}{\tau}} \right), \tag{10} \]

and decreases according to the law

\[ Z \approx Z_0 e^{-\frac{t}{\tau}} . \tag{11} \]

These regularities can be illustrated graphically by the curve shown in Fig. 6. It is easy to see that the time during

Fig. 6.

which \(\tau\) reaches 63% of its maximum value, or decreases by 63% from its maximum value, will correspond to the time constant of the bolometer. As shown by V. P. Zhuze and S. M. Ryvkin\(^7\), \(Z\) is related to \(Z_0\), i.e., to the sensitivity at modulation frequency \(f = 0\), to the light modulation frequency, and to the time constant \(\tau\) by the following relation:

\[ Z = Z_0 \operatorname{th} \frac{1}{4 \tau f}. \tag{12} \]

This formula is valid in the case of rectangular IR modulation with equal durations of the light pulses and the intervals between them.

On the basis of (12) it follows that the temperature relaxation time of a semiconductor bolometer can be determined by means of the following formula:

\[ \tau = \frac{1}{ 2 + \ln \frac{Z_0 + Z}{Z_0 - Z} }. \tag{13} \]

In the case of unmodulated IR, the question must be treated in a more general form.

To calculate the time constant of the bolometer, it is necessary to solve the heat-conduction equation for a thin strip, which is usually used as the sensitive element of a receiving-

...conductivity. This equation, taking into account the sudden action of IR and the thermal effect of the electric current passing through this strip, has the form

\[ \frac{dq}{dt} - \frac{\lambda}{C_0}\frac{\partial^2 q}{\partial x^2} + \left[ \frac{4T^3\varepsilon\sigma}{C_0d} - \frac{I^2\alpha\rho}{C_0a^2} \right] = \frac{W}{C_0d} + \frac{I^2\rho}{C_0a^2}, \tag{14} \]

where \(q=T-T_v\), \(\lambda\) is the thermal conductivity of the strip, \(C_0\) is its specific heat capacity, \(d\) is the cross section of the strip, \(x\) is the distance from the middle of the strip, \(\rho\) is the specific resistance, and \(W\) is the IR power.

From the solution of equation (14), the following approximate formula for determining \(\tau\) is obtained:

\[ \tau=\frac{4l^2 C_0}{\lambda\pi^2}, \tag{15} \]

where \(l\) is half the length of the strip.

The sensitivity of semiconductor bolometers was investigated over a wide range of IR powers—from a level equal to the Johnson-noise level to a level exceeding it by a factor of 1000. In the work of Wormser \(^{9}\) it is indicated that over this entire range the sensitivity remains constant. The sensitivity was also measured for different portions of the sensitive surface of the bolometer with the aid of a thin beam of infrared radiation (with a cross section of \(0.01\) mm). It was found that the sensitivity increases at the edges of the sensitive surface. This phenomenon is apparently explained by the fact that a sharper temperature gradient occurs at the edges. The numerical value of the sensitivity of semiconductor bolometers varies over a wide interval, from tens to hundreds of volts per watt.

4. ELECTRICAL NOISES AND THE SENSITIVITY THRESHOLD OF BOLOMETERS

Different authors approach the question of the sensitivity threshold of radiation receivers in different ways \(^{2, 3, 15, 17, 19, 20, 21}\) and, because of this, obtain contradictory data. Both in theoretical studies of this question and in the practical determination of this physical quantity there is much that is unclear and confused.

The sensitivity threshold of receivers, when the applied voltage is sufficiently constant, is determined by a number of causes, namely: a) fluctuations of the temperature of the sensitive element of the radiation receiver as a result of changes in the temperature of the surrounding medium; b) fluctuations of the current and voltage in the bolometer circuit; c) interference in the input tube of the amplifier.

In the work of Dahlke and Hettner \(^{37}\) it is shown that the mean fluctuation of the temperature \(\Delta T\) of the sensitive element, located at a tem-

temperature \(T\) and having heat capacity \(C\), under the condition that the heat exchange with the medium is equal to

\[ \Delta T = T \sqrt{\frac{k}{C}}, \tag{16} \]

where \(k\) is Boltzmann’s constant.

As a result of these temperature fluctuations, which affect the resistance of the sensitive element, voltage fluctuations arise in the electrical circuit of the bolometer. The magnitude of the fluctuation changes in voltage can be determined by means of the following formula\(^5\):

\[ \Delta T_{\phi} = \frac{\alpha T}{4} \left[ \frac{4 R \delta k \varepsilon}{C_0} \sqrt{T^4 - T_0^4} \right]. \tag{17} \]

The second essential factor influencing the magnitude of the bolometer noise is the electrical fluctuations in the closed circuit of the bolometer. Their mean value can be determined by means of the well-known formula\({}^{38,39}\):

\[ \Delta I'_{\phi} = \left( \frac{\pi k T}{R t} \right)^{1/2}, \tag{18} \]

and

\[ \Delta V_{\phi} = \left( \frac{\pi k T R}{t} \right)^{1/2}, \tag{19} \]

where \(t\) is the measurement time.

Further, owing to fluctuations of the filament voltage of the amplifier tubes and the shot effect in the input tube, the voltage fluctuations may amount to a value of \(\sim 10^{-8}\) V.

The first two factors are especially important to take into account when designing non-vacuum semiconductor bolometers. However, in most cases the receiver’s own noise level is higher than the total noise level of the entire electrical measuring system, and it is this that limits the sensitivity threshold of the radiation receiver.

K. S. Vul’fson\(^3\) asserts that the theoretical sensitivity threshold of a radiation receiver of any type is limited by a power of \(7 \cdot 10^{-9}\) W. One cannot agree with this conclusion, if only because at present there are receivers that have a sensitivity threshold of \(\sim 10^{-9}\) W. A simple calculation may be made which confirms this value of the sensitivity threshold. As indicated above, with the aid of a bolometer one can detect a temperature change of the order of \(3 \cdot 10^{-7}\,^{\circ}\mathrm{C}\). We shall regard the bolometer as a heat engine (although the bolometer acts as a relay that controls the energy of the current source) and, applying the second law of thermodynamics, calculate its efficiency by means of the formula

\[ \eta = \frac{T - T_0}{T}. \tag{20} \]

Taking \(T = 300^\circ\) K and \(T - T_0 = 3 \cdot 10^{-7^\circ}\) K, it is easy to see that \(\eta = 10^{-9}\). If one takes into account that the minimum current power detectable by means of a galvanometer is of the order of \(2 \cdot 10^{-12}\) erg/sec, then the minimum power that can be detected by a bolometer will be equal to

\[ \Delta W = 2 \cdot 10^{-3}\ \text{erg/sec} = 2 \cdot 10^{-10}\ \text{W}. \]

A detailed analysis of the theoretical studies of K. S. Vul’fson\(^3\) shows that the sensitivity threshold of metallic bolometers, on the basis of his formula, is equal to

\[ \Delta W = \frac{0.694 n (1.5 T_0)^{1/2}}{\chi} \left(\frac{4 \pi k \omega \lambda S}{t}\right)^{1/2} \left(\frac{\rho}{\alpha}\right)^{1/2}, \tag{21} \]

which amounts to \(4.8 \cdot 10^{-11}\) W under the condition that \(S = 0.1\ \text{cm}^2\), \(T_0 = 290^\circ\) K, \(\chi = 0.9\), \(n = 100\), and with the values of \(\rho\) and \(\alpha\) for nickel respectively equal to \(1.2 \cdot 10^{-6}\ \Omega \cdot \text{cm}\) and \(6.2 \cdot 10^{-3}\ 1/\text{degree}\).

Formula (21) was derived under the assumption of bridge equilibrium, taking into account heat losses through the lead wires to the sensitive layer, which is in vacuum. However, the influence of the change in current passing through the sensitive layer during its irradiation is not taken into account here.

Six years after K. S. Vul’fson’s work, Givens\(^ {21}\), on the basis of his own studies, likewise came to the conclusion that the theoretical sensitivity threshold of radiation receivers of any type should be a power of the order of \(3 \cdot 10^{-11}\) W.

Baur, for determining the sensitivity threshold of semiconductor bolometers, gives the following formula:

\[ \Delta W = 8 \left[ 200 k \varepsilon \frac{T \tau}{\Delta T^4} \right] \frac{T^2}{\lg \sqrt{S}} . \tag{22} \]

Taking \(T = 300^\circ\) K, \(S = 0.1\ \text{cm}^2\), and \(\varepsilon = 1\), we obtain \(\Delta W \simeq 2 \cdot 10^{-10}\) W.

Table I presents theoretical data on the sensitivity threshold obtained in the works of a number of authors. These data have been recalculated for the value \(S = 0.1\ \text{cm}^2\). In addition, in Joules’ formula\(^ {18}\) certain additional losses have been taken into account. From these data it may be concluded that the theoretical sensitivity threshold of bolometers is a power of \(5 \cdot 10^{-11}\) W.

The considerations given above concerning the sensitivity threshold are insufficient if we pass to the case of a modulated flux of heat rays. Here, as Cherny\(^ {22}\) has shown, the sensitivity threshold is determined by means of the following formula:

\[ \Delta W = \frac{4 n V}{\chi T R_x \alpha S} \left\{ k T R_x \Delta f \left[ 1 + 3 \left(\frac{\omega}{\omega_{1/2}}\right)^{1/2} \right] \right\}^{1/2}, \tag{23} \]

where \(\omega\) is the angular frequency of the modulation and \(\Delta f\) is the width of the frequency interval passed by the amplifier. It is clear that, in the case of infrared modulation, the sensitivity threshold of bolometers will differ somewhat from the threshold for unmodulated radiation. But even in this case some specimens of semiconductor bolometers have a sensitivity threshold reaching \(5\cdot 10^{-10}\) W.

Table I

5. SELECTION OF SEMICONDUCTORS FOR BOLOMETERS

The formulas (2) and (5) given above clearly indicate that the magnitude \(\Delta V\) is proportional to the T.C.R. of the semiconductor from which the sensitive element of the bolometer is made, and to the applied potential difference. From this one can draw a conclusion as to which semiconductors should be used for making bolometers. It is known from the literature \(^{2,5,8,9}\) that the principal semiconductors used for making bolometers are oxides of manganese, cobalt, and nickel, as well as cuprous oxide. Table II gives data for a number of semiconductors, from which it follows that oxides in layers \(10^{-4}\) cm thick have a T.C.R. close to 3% per \(1^\circ\)C. From this point of view they are certainly suitable. But the quality of a semiconductor for a bolometer is determined not only by the magnitude of the T.C.R. It is necessary to take into account its other properties as well.

As was indicated above, in view of the high resistance of a semiconductor bolometer it is necessary to apply a high voltage as well, which, it would seem, should not be embarrassing, since the sensitivity is proportional to the voltage. However, here it is necessary

*) \(5\cdot 10^{-11}\) W was obtained by us with the aid of K. S. Vul'fson’s formula.

SEMICONDUCTOR BOLOMETERS

Table II

attention to the following circumstance. In studying the dependence of the current strength on the voltage applied to the semiconductor, it was found that violation of Ohm’s law for different semiconductors is observed at different voltages.

Fig. 7. Dependence \(V=f(I)\) for a bolometer made of oxides of MnCo and Ni.

In the case of such semiconductors as the oxides of manganese, cobalt, and nickel, the picture observed is that presented in Fig. 7, borrowed from the work of Worsmer \(^{9}\). The peak voltage is determined with the aid of the following relation, obtained on the basis of Newton’s law of cooling:

\[ V_{\mathrm{p}} = C_T R_x (T - T_0)^{1/2}, \tag{24} \]

where \(C_T\) is the steady rate of heat dissipation in W/deg, \(T\) is the bolometer temperature, \(T_0\) is the ambient temperature, and \(R_x\) is the resistance of the bolometer. It turns out that in this case the permissible voltage at which the bolometer will operate normally is \(0.6\) of the peak voltage.

Jones\(^{14}\) investigated the heating effect of semiconductor bolometric layers when an electric current passes through them and established the conditions for obtaining load curves for the case of the steady state of semiconductor bolometers.

The exponential law of variation of the resistance of a semiconductor with temperature may be represented in the form\(^{4}\)

\[ R = R_0 e^{\left(\frac{B}{T} - \frac{B}{T_0}\right)} . \tag{25} \]

Denoting \(\frac{T_0}{B}=a,\ \frac{R_0}{R}=b\), Jones obtained an expression for determining the relative changes in current and voltage when the resistance of the semiconductor changes as a result of the thermal action of the current.

Fig. 8.

If at the voltage \(V_{\mathrm{p}}\) the resistance was \(R_0\) and the current \(I_0\), and at \(V\), respectively, \(R\) and \(I\), then for various values of \(a\) \((0;\ 1/8;\ 1/4;\ 1/2)\) the dependence of \(\frac{V}{V_{\mathrm{p}}}\) on \(\frac{I}{I_0}\) will be as shown in Fig. 8. (The graph is plotted on a logarithmic scale.) From these curves it is seen that the maximum current is obtained at a certain voltage \(V_{\max}\). The dependence between \(\frac{V}{V_{\max}}\) and \(\frac{I}{I_{\max}}\) for two values \(a=0\) and \(a=0.085\) is presented in Fig. 9. If the resistance of the sensitive element of the bolometer did not change, we would have obtained a straight line.

In the general case, the dependence between the current passing through a bolometer with a negative or positive value of tempera-

Fig. 9.

Fig. 10. Possible dependence \(I_t=f(V)\) for a bolometer with positive \((+a)\) and negative \((-a)\) TCR.

Fig. 11. Dependence of the receiver resistance \(R\) on the voltage across the receiver \(V\).

of the temperature coefficient of resistance and the applied voltage can be illustrated by the curves presented in Fig. 10, a and b[^23]. The arrow on the curve indicates the course of the change in the dependence \(I\) on \(V\) when the temperature of the bolometer’s sensitive layer is raised.

The correctness of these conclusions can be illustrated on a particular semiconductor, such as cuprous oxide. Bauer[^5] carried out calculations of the dependences \(R=f(V)\) and \(I=f(V)\) for bolometric layers of cuprous oxide \(17\,\mu\) thick, whose surface was \(F=0.1\ \text{cm}^2\) and whose layer resistance was \(R=10^8\ \Omega\) at \(T=293^\circ\text{K}\) \((B=3000^\circ\text{C};\ e_1+e_2=1)\). The layer was in a high vacuum.

Fig. 12. Dependence of the power of the current passing through the receiver layer on the voltage at the receiver, \(V\). In the case of high-vacuum bolometers the receiver is in a high vacuum. \(T^\circ=293^\circ\text{K}\), \(R_{293}=10^8\ \Omega\), \(B=3000^\circ\), \(S=0.1\ \text{cm}^2\), \(e_1+e_2=1\).

The results of these investigations are presented in Figs. 11 and 12. As the resistance decreases, the corresponding voltage increases, reaches a maximum, then falls to a minimum, and again increases (see Fig. 10). As the current increases, the voltage first increases, reaches a maximum, falls to a minimum, and then again increases. Thus, in a certain region a falling characteristic takes place. Therefore the voltage that can be applied to the bolometer is limited by certain conditions \((V_{\text{п}})\). It is desirable to have sensitive layers whose resistance would not exceed \(1{,}000{,}000\ \Omega\). In this case, as experience shows, the noise of the first stage of the amplifier will be less than Johnson noise.

6. SEMICONDUCTOR BOLOMETERS

Information on semiconductor bolometers began to appear in the literature in 1942, although their development had been begun considerably earlier. During this time a small number of works have been published \(^{2,5,8,9,12,14,15}\); we shall briefly discuss some of them.

The difficulties in fabricating semiconductor bolometers lie in the complexity of obtaining thin \((5\text{–}15\,\mu)\) oxide semiconductor layers with good electrical properties. In some cases the authors indicate that the oxides were deposited on a substrate—a thin quartz plate; in other cases layers without a substrate were prepared.

Brettain and Becker \(^{8}\) made a bolometer from the oxides of manganese, cobalt, and nickel. The ratio of the components was such that the resulting layers had a temperature coefficient of resistance of \(4\%\) per \(1^\circ\mathrm{C}\). The layers were deposited on extremely thin quartz substrates measuring \(3\,\mathrm{mm}\times0.2\,\mathrm{mm}\times10\,\mu\). The resistance of the layers was \(4\cdot10^{6}\ \Omega\). At a voltage of \(400\ \mathrm{V}\) and an infrared-modulation frequency of \(300\ \mathrm{Hz}\), the threshold sensitivity of the vacuum bolometer proved to be \(2\cdot10^{-8}\ \mathrm{W}\), and the time constant was \(3\cdot10^{-3}\ \mathrm{s}\). A temperature increase of \(2\cdot10^{-6}\,^\circ\mathrm{C}\) caused a decrease in the resistance of the sensitive layer by \(0.3\ \Omega\).

Becker and Moore \(^{2}\) achieved better results. The bolometer they made from the oxides of Mn, Co, and Ni had, according to the authors, a sensitivity threshold of \(5\cdot10^{-10}\ \mathrm{W}\), despite the fact that the resistance of this bolometer was \(6\cdot10^{6}\ \Omega\). The bolometer of these authors had sensitive-element dimensions from \(1\) to \(5\ \mathrm{mm}\) in length and from \(0.1\) to \(1\ \mathrm{mm}\) in width. The layer thickness ranged from \(2\cdot10^{-2}\) to \(10^{-2}\ \mathrm{mm}\).

The contact electrodes were deposited by evaporation in vacuum, and lead wires were soldered to them. In some cases such an element was placed in an evacuated metal bulb with a TBI-5 window for infrared radiation; in other cases the bolometer operated in air. The bridge was supplied with alternating current, the signal was amplified, and at the amplifier output it was recorded by a recording device. A bolometer with a resistance of \(4\cdot10^{6}\ \Omega\) had a time constant of \(3\cdot10^{-3}\ \mathrm{s}\) and a sensitivity threshold of \(10^{-8}\ \mathrm{W}\) at a radiation modulation frequency of \(30\ \mathrm{Hz}\), which is of substantial significance.

At the same time, a bolometer with a resistance of \(2\cdot10^{6}\ \Omega\) had a time constant of \(5\cdot10^{-3}\ \mathrm{s}\) and a sensitivity threshold of \(5\cdot10^{-10}\ \mathrm{W}\) at a modulation frequency of \(14\ \mathrm{Hz}\). The sensitivity of such bolometers is from \(300\) to \(700\ \mathrm{V/W}\), depending on the applied voltage.

As was stated above, Bauer \(^{5}\) used cuprous oxide for fabricating a bolometer. The specific resistance of \(\mathrm{Cu_2O}\) is \(3.3\cdot10^{4}\ \Omega\cdot\mathrm{cm}\), the temperature coefficient of resistance is \(\alpha=3.3\cdot10^{-2}\ 1/\mathrm{degree}\), and the specific heat—

capacity \(4.9 \cdot 10^{-3}\ \mathrm{W \cdot sec/deg \cdot cm^{2}}\). To make the sensitive element of the bolometer, copper foil \(0.001\ \mathrm{cm}\) thick was taken and thermally converted into cuprous oxide, its thickness thereby becoming \(0.0017\ \mathrm{cm}\). The ends of the \(\mathrm{Cu}_{2}\mathrm{O}\) strip were reduced to copper, which ensured reliable contact between the layer and the lead conductors. Two such strips made it possible to create a compensation bolometer. These strips were mounted on a quartz plate into which four metal electrodes had been introduced, as shown in Fig. 13, \(b\). The strips were arranged parallel to one another at a distance of \(0.8\ \mathrm{cm}\), one of them being shielded from irradiation by a screen. The vacuum part of the bolometer, in which both strips—the sensitive and the compensation strip—were mounted, was placed in a metal housing having a slot for admitting radiation. In addition, for better thermal insulation the bolometer was placed in a tube made of pertinax with a wall thickness of \(0.6\ \mathrm{cm}\). Since a high voltage was supplied to the bolometer, the base was made of amber. The general appearance of the bolometer is shown in Fig. 13, \(a\). No blackening was used, since no blackening adhered to the layer. The measurements were made while the bolometer bulb was being systematically evacuated.

Fig. 13. \(a\)—external appearance of the bolometer; \(b\)—internal vacuum part of the bolometer, where two arms of a bridge made of \(\mathrm{Cu}_{2}\mathrm{O}\) are mounted, one of which is subjected to irradiation.

The bolometer produced had a total resistance of \(10^{8}\ \Omega\). With a voltage of \(1200\ \mathrm{V}\) across the bridge, it was possible to record a sensitivity, for an area of \(0.5\ \mathrm{mm}^{2}\), equal to \(16700\ \mathrm{V/W}\) at a temperature of the sensitive surface of \(313^\circ\mathrm{K}\). The sensitivity threshold proved to be \(6 \cdot 10^{-8}\ \mathrm{W}\), and the time constant \(2.2\ \mathrm{sec}\).

From a practical point of view, the above characteristics of the cuprous-oxide bolometer are not of particular value, even with such high sensitivity. It is known that selective absorption of light is characteristic of semiconductors \(^{24,25,12}\). In particular, cuprous oxide in the wavelength region from 1 to \(13\ \mu\) possesses sharply pronounced selectivity \(^{25}\), as is seen from Fig. 14. Bauer’s bolometer is thus a selective receiver and, consequently, is no longer a bolometer. In addition, it is known \(^{4}\) that cuprous oxide possesses photoelectric sensitivity (internal photoeffect) in the visible region of the spectrum. The maximum photoelectric sensitivity

SEMICONDUCTOR BOLOMETERS

is located in the wavelength region of approximately 0.6 μ. Baur carried out his experiments by acting on the receiver with visible radiation; therefore, in general the question arises: what did the author measure—the photoelectric or the bolometric effect?

Fig. 14.

Fig. 15. Spectral characteristics for a Cu\(_2\)O layer of thickness 12 μ.
I — frequency \(f_1 \simeq 100\) cps; II — frequency \(f_2 \simeq 200\) cps; III — frequency \(f_3 \simeq 400\) cps. The resistance of the specimen is \(7 \cdot 10^7\) ohm.

The spectral photosensitivity of thin cuprous-oxide layers in the visible region of the spectrum, according to the data of our investigations, is presented in Fig. 15. The calculation of the photosensitivity of the specimens we investigated

samples shows approximately the same order of magnitude as that indicated in Bauer’s work. It is quite clear that, with such a character of the selective photosensitivity, it is impossible to make a cuprous-oxide bolometer without blackening the sensitive elements.

Table III

Of great interest is the work of Wormser\(^9\) on the development of a semiconductor bolometer from combinations of Mn and Co oxides, as well as from Mn, Co, and Ni. To achieve low inertia of the

Fig. 16. Frequency response of the sensitivity of a semiconductor bolometer on a quartz substrate.

bolometer, the author deposited a layer of a mixture of semiconductor oxides on a cut of a quartz crystal perpendicular to the optical axis \(Z\), whereby a good combination of thermal conductivity and high insulation resistance was achieved. In other cases substrate layers were used, but on the rear side of the active part of the layer a metal plate was placed. There was a gap between the plate and the layer.

Data that were obtained for bolometers with various layer arrangements are presented in Table III. These data were obtained for bolometers with a sensitive-surface area \(S = 0.5\ \mathrm{mm}^2\) and resistance \(R_x = 3 \cdot 10^6\ \Omega\) at \(t^\circ = 25^\circ\mathrm{C}\). Although the data in this table were obtained at different voltages and bandwidths of the frequency band passed by the amplifier, they nevertheless give an idea of the possibilities that open up to experimenters in the manufacture of bolometers.

For a more complete evaluation of the quality of a modern semiconductor bolometer, we shall present the frequency characteristic of sensitivity obtained by Worsmer (Fig. 16). Despite the fact that these bolometers have a relatively large total heat capacity, their inertia is small, and the sensitivity falls to zero only at frequencies above 300 cps.

Fig. 17. Spectral sensitivity of a blackened bolometer \((0.6 \times 0.75\ \mathrm{mm})\) and a blackened thermoelement \((0.75 \times 0.75\ \mathrm{mm})\).
\(1\) — black body at \(1183^\circ\mathrm{K}\); \(2\) — thermoelement with a KBr window;
\(3\) — bolometer with a KBr window.

Since the semiconductors used by Worsmer possess selectivity, blackening was applied. Figure 17 presents curves of spectral sensitivity in the wavelength range from 2 to \(19\ \mu\) (black-body radiation) for a blackened semiconductor bolometer (size \(0.6 \times 0.75\ \mathrm{mm}\)) and a blackened gold vacuum thermoelement (size \(0.74 \times 0.75\ \mathrm{mm}\)). For comparison of the detectors, the signal level is normalized by division by the Johnson noise. The general course of the dependence of the decrease in sensitivity with increasing wavelength is as follows: in the interval of wavelengths

Table IV

bolometers

bolometers

bolometers

bolometers

in the wavelength region from 2 to 7 µ the sensitivity of the bolometer amounts to from 60 to 80% of the sensitivity of the thermocouple. In the region 8–10.5 µ the sensitivities of both receivers are equal, whereas in the interval 10.5–19 µ the sensitivity of the bolometer is 1.5–2 times higher than the sensitivity of the thermocouple. As can be seen, in this wavelength range the receiver has no sharply expressed selectivity. Thus, with the proper use of blackening it is possible to avoid the manifestation of a selective effect in semiconductor bolometers.

It follows from what has been said above that, along with the further development and improvement of metal bolometers as infrared receivers, work on semiconductor bolometers must also be developed. At present they are still in the initial stage of their development; however, fairly encouraging results have already been obtained.

In order to judge the place that semiconductor radiation bolometers already occupy among other types of bolometers, we give summary Table IV.

The data presented in Table IV have been borrowed from various literature sources without the corresponding recalculations to common conditions. An attempt at such recalculations did not yield positive results. The designs of the receivers and the conditions under which the characteristics were taken are so different that it is difficult to make an absolute comparison between them. In this connection we have tried to collect, as far as possible, all the data available in the literature on all types of bolometers. From these data one can, to some extent, form a judgment about the quality of one or another type of bolometer.

In bolometric technique, standard criteria have not yet been developed for measuring one or another quantity for estimating the quality of a bolometer. Data on sensitivity as a function of the frequency of the radiation are almost absent. It seems to us that, for a correct assessment of the quality of a radiation receiver, the following information is necessary:

1. Relative sensitivity and threshold of sensitivity. These data must be obtained using a standard infrared source, for example a black body at a temperature of 200° C.
2. The size of the sensitive element and its thickness.
3. The specific resistance and the temperature coefficient of resistance of the sensitive layer.
4. The operating voltage or the supply-current strength of the electrical circuit of the bolometer.
5. The frequency characteristic of the sensitivity of the bolometer acted upon by modulated infrared radiation.
6. The time of thermal relaxation.
7. The dependence of sensitivity on wavelength.
8. The type of blackening, vacuum or gas-filled.

Only if all the above data, obtained under identical experimental conditions, are available will it be possible to more accurately

...to make it possible to compare with one another individual receivers of the same type and then of different types, and consequently to give an assessment of the quality of infrared receivers.

7. CONCLUSIONS

1. Investigations of the electrical properties of semiconductors show that oxide-type semiconductors, with appropriate temperature conditioning, have a temperature coefficient of resistance of about \(3\text{--}4\%\) per \(1^\circ\mathrm{C}\). In terms of their electrical properties, they are therefore quite suitable for the manufacture of infrared receivers.

2. The sensitivity of semiconductor bolometers considerably exceeds that of metallic ones, which makes it possible to manufacture them with a low sensitivity threshold, despite the fact that they have high resistance and noise level. Their inertia is also small, and this makes it possible to employ modulation of infrared radiation.

3. Semiconductor bolometers, along with metallic ones, are finding ever wider application in various fields of science and technology. Experience in the use of semiconductor bolometers shows \(^{1,2,9,41}\) that, in quality, they not only are not inferior to metallic bolometers, but sometimes surpass them. The technique of using them is simpler, and the possibilities of application are broader.

4. Semiconductor bolometers can be recommended not only for spectroscopic investigations, but also for solving a number of problems in the introduction of automation and telemechanics into production, for temperature control, and for solving other problems.

In terms of inertia and sensitivity threshold, superconducting bolometers have the best objective data, whereas dielectric bolometers have the least satisfactory characteristics.

It should be noted that, among metallic bolometers, gas-filled bolometers and bolometers in which the metallic layers are deposited on thin celluloid films have satisfactory frequency characteristics. In this case the thin layers have a relatively high resistance (\(100\text{--}200\ \Omega\)), which makes it possible to use tube amplifiers. On the other hand, they have a small total heat capacity and are therefore of low inertia.

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1. As visible on the page, the reference marker appears after “Bauer”; the corresponding reference text is not present on this page. ↩