infrared Phys. Vol. 29, No. 24, pp. 693-700, 1989 Printed in Great Britain. All rights reserved

0020-0891/89 $3.00 + 0.00 Copyright 0 1989 Pergamon Press plc

THERMAL EMISSION OF SEMICONDUCTORS UNDER NONEQUILIBRIUM CONDITIONS

V. K. MALYUTENKO, A. I. LIPTUGA, G. I. TESLENKO and V. A. BOTTE Institute of Semiconductors, Academy of Sciences of the Ukrainian S.S.R., Kiev-252650, pr. Nauki 45,

U.S.S.R.

(Received 26 August 1988)

Abstract-The thermal emission of semiconductors under the fundamental absorption edge at excitation of nonequilibrium charge carriers in them has been investigated. A broad spectrum of various actions upon a semiconductor-photoexcitation, contact injection, magnetoconcentration effect-has been used for the first time for modulation of the emissivity of crystals under isothermal conditions. Spectral, field, temperature and coordinate dependencies of the thermal emission as well as its transient characteristics at a pulsed excitation have been measured. It is shown that a considerable modulation of the thermal emission in a semiconductor can be obtained without a temperature change, through changing its emissivity alone. A number of features of the thermal emission in the region under consideration has been revealed: a spectral maximum which position depends on the optical thickness of the crystal, a kinetics delay effect, etc. It has been established that the thermal emission of an excited semiconductor can be used as a means for determining various parameters of a material. Experiments were carried out on Ge, Si plates and Ge diode structures at 310 $ T Q 350 K.

INTRODUCTION

The thermal emission is one of fundamental physical phenomena. However, while the laws of the thermal emission of ideal black bodies have been well studied, the thermal emission of real bodies is far from being studied completely. This fully applies to semiconductors. A particular attention is deserved by examining the possibility of a dynamic control of the thermal emission of semiconductors. As little as two studies on this subject have been known so far: studies of emission of IR radiation by Ge at a photoexcitation of the semiconductor were reported in Ref. (l), and at an injection of charge carriers, in Ref. (2).

In the present study the thermal emission of semiconductors under conditions of a strong excitation of the crystal’s electronic subsystem has been investigated in detail. Thermal emission characteristics and their features caused by a variation over a wide range of the free carrier concentration at an optical excitation, contact injection, as well as with the aid of the magneto- concentration effect have been studied.

At the above actions, the lattice and free carrier temperatures remained unchanged. The thermal emission was studied under the fundamental absorption edge, the band-to-band transition region having been excluded.

BASIC RELATIONS

In the spectral region under the fundamental absorption edge (o < E,/h; Eg is the forbidden band gap), thermal emission is governed by interaction of free carriers with the surrounding Plank’s background (we do not consider lattice vibrations). The power of the emission within a unit frequency range in the volume of semiconductor can be calculated if free carrier absorption coefficient K, is known?’

p,=$J[exp(z)- I]-‘, (1)

black-body emission and n, is the refractive index of where pW is the volume spectral density of the material.

693

694 V. K. MALYUTENKO CJI ul

The power emitted from a unit surface of a semiconductor plate of thickness d through one of its faces is:

pJ,(B)=~~~[l -exp(-%I](1 -R,,,)sinHcostidH. (3)

This expression takes into account that the radiation emitting from the sample is attenuated due to absorption at length y/cos 8, is partly reflected by the surface (R,., is the reflectivity) into the crystal bulk (multiple reflections are neglected), and emits to the outside within the incidence angles less than the total internal reflection angle. 0 < 8,, = arc sin YZ,., ‘.

In the selected spectral range, the free carrier absorption coefficient is connected with free carrier concentration N by the relation: K,., = Q,,, N (Q,,, is the absorption cross-section of a quantum of a given frequency). Thus, external actions which change N in a crystal change. in the general case, the emissive characteristics of semiconductor materials. An analysis of expression (2) readily distinguishes two versions governing the crystal response to an external excitation. If the initial optical thickness of the crystal is large (K,.,d >> I ) and remains such in the process of excitation. then the thermal emission power is independent of the carrier concentration change and, accurate to within the correction for reflectivity (1 - R,,), is equal to the power of emission of a black body which temperature does not differ from that of the semiconductor. But if the crystal is optically thin (K,d<< l), the emission follows in time with the carrier concentration change, increasing or decreasing relative to the initial value, and is linearly dependent on the absorption coefficient and the plate thickness.

Consider a time behavior of the power of thermal emission of an optically thin semiconductor plate where after the excitation removal at time moment t = 0 the carrier concentration decreases exponentially due to recombination: N, = N,e -” (r is the effective lifetime of carriers in the plate). From the analysis of (2) it follows that, depending on the excitation level (concentration N,). two relaxation curve types are possible:

(1) the excitation level is low and concentration N,, is such that at t = 0 the relation K,,,d/cos 0 << 1 is valid. In this case:

Pm(e) = 4 “, - const.e-“. (1 - K)p,c e N,d e_,Z _

Thus, the kinetics of thermal emission power decay is determined by lifetime r; (2) the excitation level is so high that at t = 0 the relation K,,,d/cos 0 >> I holds. Here, after the

excitation removal, the thermal emission power within time interval [0, t,] remains unchanged at the level of its maximum value:

and then at t > t, decreases exponentially. The duration of interval [0, t,] is governed by the

excitation level and, as shown by estimates, may many times exceed the lifetime.

EXPERIMENTAL

(4)

In the present study, as mentioned above, the free carrier concentration in a crystal was modulated by means of a contact injection, laser emission, and action of crossed electric (E) and magnetic (H) fields. The effect of carrier injection on semiconductor thermal emission character- istics was studied with the use of Ge diode structures operating in a forward bias mode. They were prepared in the form of rectangular parallelepipeds sizing 5 x 5 x 8 mm. A p-n junction was created on one of wide faces, and an Ohmic contact on the second face. Emission was observed from a 5 x 5 mm face. In studying the thermal emission kinetics, the diode functioned with a pulsed bias, the recording of spectra being accomplished by applying a fixed bias to the diode structure. In the latter case a standard IR spectrometer with a modified emitter unit where the diode was arranged, enclosed in a special holder which maintained the crystal temperature, was used.

Photocarriers in the semiconductor were produced by acting on the sample with pulses of a Nd-laser operating in a free oscillation mode. Si samples with a resistivity p - 250 R.cm were

Thermal emission of semiconductors 695

I 1 1 I

5 15 25 h,y

Fig. 1. Thermal emission spectra of black body (1) and Ge (24) at injection at T = 330 K. Forward bias voltage (V): 2 = I .4: 3 = 0.7; 4 = 0. Arrows indicate positions of spectral characteristic maxima.

used in the studies. The laser emission power was varied with the aid of calibrated attenuators, the maximum photoexcitation power being of the order of lo4 W cm-‘.

The thermal emission under magnetoconcentration effect conditions was studied using Ge with an intrinsic conductivity. The sample thickness was comparable with the diffusion length of carriers in Ge, which stemmed from the requirements for crystal dimensions needed to attain the carrier concentration control effect.(4) Samples for this part of the studies were prepared according to the standard procedure for the magnetoconcentration effect. They were placed in a static magnetic field of several kOe; the electric field was applied in the form of pulses with a duration of - 100 /AS.

In all cases, except for spectra measurements, the variable component of emission,

AP = Pe,,,act - PJP,,,, act, P,, are respectively the sample thermal emission power at external actions and the thermal emission power at the preset temperature at absence of external actions) was

Fig. 2. Thermal emission spectra of black body (1) and Ge plates of various thicknesses and doping levels (24) at T = 320 K. N,-N,(cm-3): 2 = 1.5 x 1018; 3, 4 = 1.2 x 10”; d(cm): 2 = 0.5; 3 = 0.1; 4 = 0.022.

Arrows indicate positions of spectral dependence maxima.

696 V. K. MALYUTENKO el ul.

recorded. Cooled photoresistors for a range of 5-10 pm were used as photodetectors. Narrow-band optical filters and limiting diaphragms were used where required.

Naturally, the studies were carried out at the presence of a background caused by the thermal emission of surrounding bodies; apart from the condition of inequality of sample and emission detector temperatures, inequality of sample (r,) and background (T,,) temperatures was therefore a necessary condition for experiments. Measurements were made both at T, > T,, and at T, < T,, the former version being used more often. As a rule, the sample temperature was within 3 lo-350 K and the background temperature was about 293 K. The initial thermal emission of nonexcited samples was weak since relation K,d 5 0.03 held for them in the spectral region under investigation.

RESULTS AND DISCUSSION

Spectral dependencies of the emission power of injected free carriers at various diode biases are presented in Fig. 1; curve 1 represents the black body emission spectrum, and curve 4, the emission spectrum of an undisturbed Ge crystal. In the initial state the emission of studied samples is formed by several processes: on the background of an emission associated with the free carrier absorption and steadily increasing with the wavelength there exists an emission due to transitions between subbands of the valence band of Ge and to multiphonon processes. Lattice absorption bands with characteristic peaks make an appreciable contribution in a region of 15-25 pm. In the S-~15 pm region the emission is mainly due to transition of holes from one to another subband of the valence band of Ge (V, + Vz transitions).

An increase in the hole concentration at the base of the p-n junction at a forward bias results in changing the emissive characteristics of a semiconductor plate. The greatest modulation of the thermal emission signal is attained in the short-wavelength part of the spectrum, where the crystal exhibits the highest initial transparence. The thermal emission power rises with increasing density of the current through the p-n junction. Increasing the thermal emission flux power to the maximum value, corresponding to the emission of a semiinfinite plate (K,,,d > l), calls for an insignificant control voltage (- 1 V). In this case, the semiconductor, with a correction for the reflection at faces (I - R,,), repeats the Planck’s spectrum (cf. curves 2 and 1, Fig. 1). In the course of generation of carriers, not only the emission spectrum shape changes, but also the position of

- \ cmel

\

\ \

3 \ 100 \ --lo@ \ \ \ \ \ \ \ \

o 1 2 3 4 5 6

t/“i

Fig. 3. Kinetics of power of thermal emission (I-3) and of relaxation of charge carriers cl’-3’) of semiconductor plate at photoexcitation.

Thermal emission of semiconductors 69-t

Fig. 4. Oscillograms of silicon plate thermal emission pulses at photoexcitation I, < I, < I3 < 14.

the maximum in the thermal emission spectrum shifts. The shift of the maximum at the experiment was of the order of 1 pm: from 9.68.8 pm (curve 2, Fig. 1) at T = 330 K. The shift of the maximum (as well as the emission power modulation depth) can be increased, e.g. by reducing the initial thickness of the sample. This is well seen from Fig. 2, where emission spectra of Ge samples of various thicknesses and doping levels are presented.‘5’

Consider next the kinetics of the thermal emission of a semiconductor at excitation of photocarriers in it. Figure 3 shows calculated dependences of relaxation of the relative power of emission (curves l-3):

P* = 4P”1(0)

0J CP, ( 1 - &) (5)

and the nonequilibrium concentration (l’-3’) of a semiconductor plate at various photoexcitation levels. Increasing numbers of the curves correspond to increasing power of the exciting emission. The calculation was conducted for a sample with parameters typical for silicon: d = 0.3 cm, r=50~s,~,=3.5xlO~‘“cm’,n=3.4atcosB=1.

An unusual trend of the thermal emission relaxation curves (delay) is accounted for by transition of the crystal in the course of recombination of carriers from the state of an optically thick to the state of optically thin one. At the initial period of time [0, t,] (great N value, K,d > l), the thermal emission power is the maximum, is independent of K,, and hence does not follow the change in the concentration of carriers in the course of their recombination. On expiration of this period, N decreases to such an extent that relation K,d < 1 starts being valid. Under such conditions, P, is determined by absorption coefficient K, and hence also by the carrier concentration. Because of this, time dependences N(t) and P,(r) at t > t, coincide.

Figure 4 presents oscillograms of thermal emission pulses, corresponding to various excitation levels. As would be expected, at a low excitation level (curve 1) the shape of the emission pulse is identical to that of the laser pulse (the laser pulse duration exceeded r). As the excitation intensity increased, the duration of emission pulses increased as well and a plateau which amplitude remained unchanged arose on relaxation curves 2-4. At a laser pulse decay time of 200~s (at a level of 0.7 of the maximum amplitude) the emission pulse delay time reached 800 ps.

The above-described effect of thermal emission delay is also possible at other semiconductor excitation methods, such as at injection of carriers through the p-n junction.

Figure 5(a) shows oscillograms of thermal emission pulses, corresponding to various injection levels. For comparison, Fig. 5(b) presents oscillograms of pulses of the recombination emission (luminescence) near the edge of the fundamental absorption of the material (2 N 2pm). As seen, at a low injection level (curves 1) the kinetics of both the thermal and the recombination emission has the usual form determined by the lifetime of nonequilibrium charge carriers. The situation at a high injection level is different (curves 2). Luminescence, as it should be, decays just after the end of an injecting pulse, whereas the thermal emission reaches its maximum value and remains constant during some time which exceeds by several times the exciting voltage duration, i.e. a situation corresponding to an optically thick crystal is observed.

This is also confirmed by the dependence of the maximum thermal emission signal at the moment of the injection pulse end on the magnitude of current, shown in Fig. 6. The parameter of curves is here a distance x from the injecting contact to the emitting layer limited by a slit diaphragm. It is seen that with increasing current all the curves tend to a common level, which determines the emission of a semiinfinite opaque Ge plate. The emission of the contact-adjoining region (curve 1) is, beginning from some current value, well stabilized with respect to current and voltage fluctuations.

698 V. K. MALYUTENKO et al

a

t- b

Ii_li_LUU-__LL 40 ps/div t --

Fig. 5. Oscillograms of pulses of thermal emiwon (a), lummescence (h) and voltage on Ge diode structure (cross-hatched) at T = 350 K. Bias current (A): I = 0.7; 2 = 20.

Similar oscillograms with flat-topped pulses, but of a negative polarity, are observed at T, < T,, For sample temperatures T, = T, i IO K the temperature dependence of the modulated thermal emission signal amplitude was found to be linear.

The plateau duration made it possible to evaluate the injection level. Evaluation from the data of Fig. 6, neglecting nonlinear mechanisms of recombination, yielded N z IO” cm ’ at a density of the current through the junction of 40 A cm ‘. The carrier lifetime was determined from the exponential decay of emission after the end of an injection pulse; the determined lifetime was in a good agreement with literature data.

Another interesting method for excitating a semiconductor is the magnetoconcentration effect. Its distinguishing feature is the possibility of changing the concentration both towards its increase (accumulation) and towards its decrease (exhaustion) from the equilibrium value. As known from the magnetoconcentration effect theory, 14) the total number of carriers in a crystal is dependent on many parameters: state of crystal surfaces, recombination of current carriers in the semiconductor volume, direction of removal of the carriers. Under practically realized conditions (Fig. 7; T z 350 K, intrinsic concentration of carriers of the order of 2.8 x 10” cme3), as is well seen from comparison of current-voltage characteristics in a magnetic field (curves 2-5) and at E x H = 0 (curve 1) it becomes possible to change rather considerably the total number of carriers in a crystal: to increase it to 3.3 x 10” cm ~’ (curve 2) at a drift of carriers to face s,,, (accumulation) and to reduce it (curve 5) practically to the level of a noncompensated impurity at their emergence at the opposite surface (exhaustion). The sample thermal emission power as well changes correspondingly [Fig. 7(b)]. Under conditions of depletion, AP’ P, decreases steadily (curves 4’, 5’); in a stronger

I (A,

Fig. 6. Thermal emission power vs bias current for various distances x from injection contact to emitting layer of diode structure. I (mm): I = 0.25: 2 = 0.55; 3 = 2; 4 = 3. T = 330 K.

Thermal emission of semiconductors

1,A

699

0

-0,5

-1.0

Fig. 7. Current-voltage characteristics (a) and field dependencies of thermal emission (b) of Ge in crossed electric and magnetic fields at T = 350 K. H(kOe): 1 = 0; 2,2’,4,4’ = 5; 3,3’,5,5’ = 10.

Accumulation = 2,2’,3,3’; exhaustion = 4,4’,5,5’.

magnetic field (curve 5’) the decrease is sharper, but no distinctions were observed: the emission power decrease curves correspond to the modulation of N on curves of current-voltage character- istics (dependencies 4, 5). In the case of accumulation the situation is different: in a weak magnetic field (curves 2, 2’), over the entire electric field variation range, the total number of carriers in a crystal remains above the equilibrium value (curve 2 lies above curve 1); accordingly, the signal of the relative change of the emission power has a positive sign (curve 2’). With increasing magnetic (or electric) field strength the effect of nonlinear mechanisms of carrier recombination and a finite value of s,,, results in that the rate of increase of the total number of carriers in the crystal slows down and N in the semicondutor volume becomes eventually less than in the equilibrium case (which is well seen from comparing dependences 1 and 3). As a result of this feature, a modulated signal of the thermal emission of a semiconductor crystal (curve 3’), rising initially with increasing E, then decreases, passes through the point corresponding to the emission of an unexcited sample, and reverses its sign. As seen, there exists a qualitative correspondence between the behavior of dependences 3 and 3’, but, due to the effect of the magnetoresistance, the intersection points of curve 3’ and straight line APIP,, = 0 (point c’) and of curves 1 and 3 (point c) are not coinciding.

Thus, acting on a semiconductor by crossed electric and magnetic fields provides a means for controlling its thermal emission power easily and, above all, over a broad range. The possibility of both increasing and decreasing the sample thermal emission power with respect to its initial value may be regarded as an essential feature of such a control.

CONCLUSIONS

The thermal emission of semiconductors in the long-wavelength region under the fundamental absorption edge at excitation of nonequilibrium charge carriers in them has been studied under

700 V. K. MALYUTENKO et al

isothermal conditions. A broad spectrum of actions on a semiconductor with the aim of modulating its emissivity has been used for the first time. Spectral, field, temperature and coordinate dependencies of thermal emission have been studied under conditions of action of crossed electric and magnetic fields, photoexcitation and contact injection on a crystal. The possibilities for controlling the thermal emission power and spectrum shape over a broad range have been demonstrated. It has been shown that studies of the kinetics of the thermal emission of a semiconductor can be used to determine parameters of the material. An advantage of the proposed approach lies in that, in contrast to luminescence, the thermal emission is independent of the quantum yield of the radiative recombination.

REFERENCES

1. V. F. R. Kessler, Zs. Naturforsch. 132, 295 (1958) 2. E. A. Ulmer and D. R. Frankl, Proc. IX Inrern. Cony. Semicond. PhJ8.c Nauka, Lenmgrad. p. 179 (1968) 3. T. S. Moss, G. J. Burrell and B. Ellis, Semiconducror Op/o-Eleclronics. Butterworths, London (1973). 4. V. K. Malyutenko, K. Yu. Guga and Yu. M. Malozovsky. Phys. Status Solid (a) 65, 131 (1981). 5. V. K. Malyutenko, V. A. Botte and V. I. Chernyakhovsky. Infrared Phys. 29, 155 (1989).