Mechanisms of absolute negative photoconductivity in solids

Volume 112A, number 5

MECHANISMS

PHYSICS LETTERS

OF ABSOLUTE NEGATIVE PHOTOCONDUCTIVITY

28 October 1985

IN SOLIDS

V.K. M A L I N O V S K Y , V.N. N O V I K O V a n d B.I. S T U R M A N

Institute of Automation and Electrometry, USSR Academy of Sciences, Siberian Branch, Novosibirsk 630090, USSR Received 15 March 1985; revised manuscript received 5 August 1985; accepted for publication 19 August 1985

The microscopic mechanisms governing the absolute negative photoconductivity in solids (Jph = %h E, %h < O) discovered recently in concentrated ruby crystals are described. It is shown that in hopping models of photoconductivity the contribution to the current, connected with the field-induced asymmetry of processes of electron photoexcitation and recombination, dominates. It is predicted that the sign of Oph(C0) changes as a transition over an absorption resonance is performed.

A new bright effect has been discovered recently in concentrated ruby crystals: an absolute negative photoconductivity [ 1 - 3 ] . This effect consists o f the fact that light generates a current directed opposite to the field, iph = °phE,

Oph < 0.

(1)

The absolute negative photoconductivity (ANP) leads to dielectric instability, growth o f electrostatic field fluctuations (up to E 0 = 10 6 V/era in ruby). Presently the observed data have been interpreted only at the level o f a phenomenological model [3]. The microscopic mechanisms o f ANP as well as the conditions o f its appearance are still unknown. This paper is devoted to a search for them. We associate the negative contribution to the photocurrent with the field-induced asymmetry o f the processes o f electron photoexcitation and recombination. As will be seen below the contribution is most effective in case o f hopping-like charge transfer. We consider the following rather general problem. Let electrons in the absence o f light be localized on deep centers and possess negligibly low mobility. The photoexcited electrons have a larger localization radius r0, so that a small overlap o f wave functions o f the neighbouring centers appears. The excited states can conform, for example, to impurity energy levels with uniform or nonuniform broadening, to a narrow polaron zone. We denote b y g ± ( R , 60, E ) the mean rate o f photogeneration on the centers which are at a

3 Fig. 1. The resonance mechanism of asymmetry. Energy levels of impurities 1, 2 and 3 axe shifted by the external electric field E. The short arrows show the energy level shifts of the centers 1 and 3 relative to the center 2; the long axrows, possible channels of photogeneration. The wave arrows correspond to the intracenter recombination. The absorption line shape is shown beside the excited energy level The case is shown when to > too ; the transition to the left is resonant and the one to the right is nonresonant, so g_ > g~. If to < too theng_
= (g+ - g - ) / ( g o +g+ + g - ) "

(2)

Here K is the light absorption coefficient, J is its intensity; ~ is an asymmetry parameter. Recombination 237

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contribution to the current is not taken into account in (2). This is justified for symmetrical, particularly for intracenter recombination. Let us consider the main mechanisms of the origin of the asymmetry. Firstly, it is evident that the field E shifts energy levels of the different centers relative to one another. For neighbours at a distance R the shift is Ae = eER, fig. 1. Variation in positions of the levels manifest itself in a frequency dependence of the photoexcitation rates,

g+(R, co, E ) = gl(R, co + e E R I ~ - I ) .

(3)

Therefore, for small E,

,~ [2eER/l~(g o + 2gl)] bgl(R, co)/~co.

(4)

It should be emphasized that in the given case the asymmetry has a resonance character, the sign of the current/a s is defined by detuning co - coO from the center of the line, and its magnitude by the width of the line P. The asymmetry is especially great when the intracenter excitation is suppressed, go -+ 0 (although this condition is not necessary for observation of ANP). In this case the magnitude ~ is evaluated by the width of the absorption line,

~ eER/hP.

(5)

Smallness o f g 0 could be the consequence of selection rules for electron transitions or energetic forbiddenness. Note that the smallness o f g 0 does not mean weakness of the intracenter recombination. The latter can run through intermediate energy levels or can have a multiphonon character. In a model with occupied low-lying levels (low compensation k) intra- and intercenter transitions conform to different light frequencies, since they lead to configurations different in their charge state and energy ,1. In the two-electron configuration the recombination can happen only due to the transition of the excited electron to the ground state of the neighbouring empty center. Because of the low compensation this empty centeris as a rule just the same as the one from which the electron has been excited. Thus the photogeneration contribution to /'as and the recombination one cancel each other (if k = 0). If k 4 : 0 there are situations when the electron is excited beside the empty center. In this case recombination can happen both on this center and on #1 Inter-center transition photoconductivity of this kind was observed.in Ge:Zn [4]. 238

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Fig. 2. The nonresonant mechanism of asymmetry. The ellipses are localization regions of the excited electrons~ For simpficity the localization radius in the ground state is assumed negligible. The excited state has no center of symmetry because of wave function polarization caused by the external electric field. The excited state of the left center and the ground state of the right center are closer to each other than the excited state of the right center and the ground state of the left center. This leads to the asymmetry of photogeneration: g_ > g+. W(R) is the probability of a jump between the excited states of the neighbouring centers On the left: the scheme of energy levels: 3-2, the resonance transition; the states 1 and 2 of opposite parity are mixed by the electric field.

that from which the electron has been excited. As a result the cancellation of the contributions becomes not complete andJas is proportional to the degree of compensation k. The second mechanism of asymmetry is related to the distortion of the electron wave functions by the external electric field. The field mixes wave functions of opposite parity (see fig. 2):

~2 = ~2 + [(t~lleErlOd2)/(e2 - el)] ffl" This mixing leads to the loss of the center of symmetry. It is natural to think that an excited state is polarized by a field stronger than the ground one due to a large localization radius. Spatial shift of the electron wave function leads to a difference between the generation ratesg_ and g+, see fig. 2. An estimate of can be obtained by assuming that the field E adds to the wave function of the excited state a suitably syrrimetric function which corresponds to a nonresonance energy level, fig. 2. If we denote by A the corresponding energy distance then

~ eroE//X.

(6)

The sign of ~ depends on the sign of A. Positive polarizability corresponds to a current/as directed opposite to the field, fig. 2. The nonresonance mechanism of the asymmetry is rather similar in its sense to mechanisms of the photovoltaic effect (PVE) in polar crystals [5]. It has no resonance character and leads as a

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rule to lower values of the asymmetry parameter as compared to the resonance mechanism. For ANP to exist a negative sign of Oas = d/as/dE is not sufficient. The fact is that there is a usual positive contribution to the photoconductivity o+ caused by motion o f photoexcited electrons in the electric field. The specific character o f the above model o f hopping charge transfer consists in the fact that it leads to small yalues of o + ' 2 . In order to determine o+ we need to introduce two additional parameters: the lifetime of an excited electron with respect to intracenter recombination r e and the typical probability o f a jump between excited states W. The value W(R) can be related both to uniform and nonuniform broadening o f levels [6,7]. Usually it drops exponentially as R increases and activationally depends on temperature. Assuming r e >> ~'vib ~ 10-14_ 10-12 s, where 7"vib is the time of vibrational relaxation, we can use the Einstein relation and evaluate the electron mobility as eWR2T - 1. Correspondingly,

8+ ~ e2(KJ/h~o) WreR2T-1.

(7)

A characteristic feature o f ( 7 ) is the presence of the kinetic parameter Wr e. Due to the smallness o f the wave function overlap integral this parameter has no lower limit. Let us write out the condition o f ANP realization in an explicit form. Using (2), (5), (7) we obtain:

Wr e < TffiF.

(8)

Inequality (8) or similar relations do not set rigid limitations on the hopping model parameters. ANP is expected to be realized in a rather wide range o f dielectrics with little hopping photoconductivity. We present finally the simplest evaluation of the field resulting from the development o f electric instability. Assuming that getting out o f the system from the resonance is a mechanism o f instability stabilization, we get

E 0 ~ (hF/e) N 1/3 ,

(9)

where N O is the impurity concentration. In addition to a more detailed development o f the theory, experiments on discovering the predicted ,2 In zone mechanisms the case is opposite. Using representations developed in the study of PVE mechanisms [5] one can show that the condition a+ < oas leads to um-eal limitation on the lifetime of the photoelectron, r e ,~ 10-1 s _ 10-17 s,

28 October 1985

resonant ANP would be of great interest. Among promising objects of investigation we can point out semiconductors with low impurity levels and highly doped laser crystals. In well-studied semiconductor crystals, such as Ge and Si, one can control in a wide range the concentration of defects, the degree o f compensation, and the binding energy. On the other hand, in these semiconductors the methods o f description o f the hopping transfer o f a charge are well developed [6,8]. Let us evaluate/as by the parameters of a shallow center. Under detuning fi6o "~ F and T ~ 7~6o, /as ~ 4rr(e2 /~ic)(e2~/h2F2) N1/3

X exp(-2C/ro N1/3) JE.

(10)

The current is strongly dependent on the impurity concentration and the binding energy. However, with reasonable values of the parameters (10) leads to quantities Of/a s that can be easily discovered. For example, for r 0 = 50 A, N O = 1017 cm -3, F = 1013 s -1, C = 1 , J = 1 W/cm2,/as[A/cm 2] ~ 1 0 - 8 E [V/cm], E 0 ~ 102 V/cm. In laser crystals due to strong impurity localization ANP must appear under high doping levels and lead to large values o f saturating fields. For F = 1013 s-1, N O = 1020 cm - 3 we have E 0 ~ 105 V/cm. From the viewpoint of description o f the effect laser crystals are probably more complicated objects than semiconductors. [1] P.E. Liao, A.M. Glass and L.M. Humphrey, Phys, Rev. B22 (1980) 2276. [2] S.A. Basun, A.A. Kaplyansky and S.P. Feof'flov, Pis'ma Zh. Eksp. Teor. Fiz. 37 (1983) 492; Zh. Eksp. Teor. Fiz. 87 (1984) 2047; S.A. Basun, A.A. Kaplyansky, S.P. Feofilov and A.S. Furman, Pis'ma Zh. Eksp. Teor. Fiz. 39 (1984) 161. [3] M.I. Djakonov, Pis'ma Zh. Eksp. Teor. Fiz. 39 (1984) 158; M.I. Djakonov and A.S. Furman, Zh. Eksp. Teor. Fiz. 87 (1984) 2063. [4] S.M. Kogan, T.M. Lifshits and V.I. Sidorov, Zh. Eksp. Teor. Fiz. 46 (1964) 395. [5] V.I. Belinicher and B.I. Sturman, Soy. Phys, Usp. 23 (1980) 199. [6] N.F. Mott and E.A. Davis, Electron processes in noncrystalline materials (Clarendon, Oxford, 1979). [7] Yu.A. Firsev, ed., Polarons (Nauka, Moscow, 1975) (in Russian). [8] B.I. Shklovsky and D.L. Efros, The electronic properties of doped semiconductors (Nauka, Moscow, 1979) (in Russian). 239