J . PRAXASH: Photo-Induced Polarization and Photo-Induced Depolarization 747

phys. stat. 801. (a) 70, 747 (1982)

Subject classification: 10.2 and 14.4; 22.5.2

Department of Physics, University of Gorakhpurl)

On the Occurrence of Photo-Induced Polarization and Photo-Induced Depolarization

BY J. PRAKASH

The phenomena of photo-induced polarization (PIP) and photo-induced depolarization (PID) take place via electronic excited states (ees). It is assumed that the activation energy for the orientation of impurity-vacancy (IV) dipoles in ees is less than that required in the electronic ground state (egs). Expressions for dielectric polarization/depolarization of IV dipoles during PIP/PID are established following a bistable model. It is observed that the dielectric polarization increases during PIP whereas the polarization of frozen-in polarized dipoles decreases during PID.

Die Erscheinungen der photoinduzierten Polarisation (PIP) und der photoinduzierten Depolarisa- tion (PID) finden iiber angeregte elektronische Zustande (ees) statt. Es wird angenommen, daB die Aktivierungsenergie fur die Orientierung der Storstellen-Leerstellen (1V)-Dipole in ees geringer ist als die fur den elektronischen Grundzustand (egs) geforderte. Ausdriicke fur die dielektrische Polari- sation/Depolarisation von IV-Dipolen wahrend PIP/PID werden entsprechend einem bistabilen Model1 aufgestellt. Es wird beobachtet, daO die dielektrische Polarisation wahrend der PIP zu- nimmt, die Polarisation von eingefrorenen polarisierten Dipolen dagegen wahrend PID ab- nimmt.

1. Introduction

The presence of impurity-vacancy (IV) dipoles in alkali halides is generally detected through dielectric dispersion and absorption studies. IV dipoles in alkali halides are created by introducing divalent cation or anion impurity centres substitutionally. With respect to the impurity ion, the IV dipole lies along one of the twelve equivalent orientations (110). In the absence of the electric field these orientations have equal probability to be occupied by IV dipoles. In the presence of an electric field, IV dipoles try to align along the electric field direction and the system is thus polarized. The extent of polarization can be evaluated quantitatively following the bistable model [l]. It has been observed [2 to 51 that selective irradiation in the presence of an electric field creates a situation in which more dipoles are aligned along the electric field direction, whereas such an irradiation in the absence of the electric field destroys the preferred orientation of the frozen-in polarized dipoles. These phenomena are known as photo-induced polarization (PIP) and photo-induced depolarization (PID), respectively. It has been suggested that PIP and PID take place via electronic excited state (ees) where the activation energy for the orientation of I V dipoles is less than that required in the electronic ground state (egs). PIP and PID have also been observed for the Suzuki phase in Pbf*-doped KC1 by Benci et al. [6]. The disorientation of IV dipoles via ees has been found [7] to be the responsible mechanism for PID in Pb++- doped KC1. It has been proposed by Fischer [8] that the activation energy in the ees (EL) should be sufficiently smaller than that required in the egs (Ea). However, EL < < E, seems to be a sufficient condition for the occurrence of PIP and PID as establish-

l) Gorakhpur 273001: India.

748 J. PRAKASK

ed here. Expressions for dielectric polarization/depolarization of IV dipoles corre- sponding to PIPjPID are established according to the bistable model. It has been observed that the dielectric polarization increases during PIP, whereas the polarization of frozen-in polarized dipoles decreases during PID.

2. Bistable Model

Let us choose for simplicity only two equivalent orientations in the bistable mode1 along which an IV dipole can lie. Consequently, there are two potential energy minima which are separated by a potential energy barrier of height E, as shown in Pig. 1. The distance between the two minima is cl such that the dipole moment ( p ) of the IV dipole is given by p = ed/2, where e is the electronic charge. Orientations 1 and 2 correspond to the preferred and unpreferred directions, respectively. Expressions for dielectric polarization/depolarization in different conditions are established in the following paragraphs.

2.1 Dielectric polarization in egs

The potential energy curve in egs is modified in the presence of an electric field as shown in Pig. 1. Consequently, the jump probabilities per second in going from orien- tation 1 to 2 (v12) and 2 to 1 (v2,) differ which were same in the absence of the electric field. The rate of increase of IV dipoles in orientation 1 after the application of the electric field is given by [l]

n, = n2vZl - nlv12 ,

vZ1 = v,exp [ - { E , - (1/2) AE,} /kT] . where

n, and n2 represent the number of IV dipoles per unit volume in orientations 1 and 2, respectively, such that nl = n2 = n/2 in absence of the electric field, and n is the total number of IV dipoles per unit volume. The extent of splitting by an amount AE, as a result of application of the electric field ( E ) is given by (1/2) AE, = pE. However, for small fields AEJ2kT < 1 and hence

I 2 orientation

Vig. 1. Activation energy for the orientation of IV di- poles in electronic ground and excited states before (solid curve) and after (dashed curve) the application of the electric field in the bistable model

Occurrence of Photo-Induced Polarization and Photo-Induced Depolarization 749

where v is the jump probability in the absence of the electric field and v, is the fre- quency factor. Similarly v12 is represented by

v12 = v [1 - g]. (3)

Equation (1) with the help of (2) and (3) can be rearranged as n1 = -2v[n, - El] (4)

which suggests that n, will increase exponentially with a time constant of 1/2v. i& represents the equilibrium value of IV dipoles per unit volume in orientation 1 and is given by

Zl = (1/2)n L-1 + (pE/kT)I . (5) The equilibrium value of IV dipoles per unit volume in orientation 2 will similarly be represented by

(6) - n2 = (1/2)n [1 - (pE /kT) ] .

It is apparent from (5) and (6) that Zl = Z2 = n/2 in the absence of E. Also, 121 + E2 gives the total number of dipoles in egs. Since Zl is greater than n2, the system will polarize under the influence of an applied electric field. The magnitude of the polari- zation will be given by

nEp2 P = (n, - Z2) p = ____ kT *

(7)

It is obvious that P does not depend upon E,. The relaxation time (t) in egs is con- trolled by E, through

z = zo exp ( E J k T ) , (8) where z = l / v andz, = l/v,. If t is not large and I V dipoles are thermally able to cross over the potential energy barrier, the extent of polarization will not be affected by E,. This situation prevails in the case of polar liquids and liquid mixtures a t moderate temperatures. However, in the case of solid, where z is large, IV dipoles a t a particular temperature become unable to cross over the potential energy barrier. E,, thus determines through (8) the lower temperature limit up to which I V dipoles can be polarized. The smaller the value of E,, the lower will be the temperature limit. At experimental temperatures below the temperature limit, the system ceases to be polariz- ed by the application of the electric field as shown in Fig. 2. For KI:S-- the corre- sponding temperature limit in egs is m 170 K [5]. I n Fig. 2, the dashed curve represents P versus T for a hypothetical system in accordance with (7) and the solid curves 1 and

Fig. 2. Polarization (P) versus temperature curve for a hypo- thetical system normalized with respect to the polarization at 220 K (P,,,). - - - theoretical curve, - experimental curves in egs (1) and in ees (2)

750 J. PRAKASH

2 represent the experimentally expected polarization. It is apparent from the figure that T , is the temperature limit in the egs and the system will be polarized along curve 1. This argument is supported by the experimentally observed curve represented in Fig. 6 of [5].

2.2 Dielkctric polarization via ees When the system is irradiated in the presencelabsence of an electric field, i t gets a chance to be polarized/depolarized via ees. I n the ees there are two potential energy minima similar to egs as shown in Fig. 1. These minima in the ees are separated by a potential energy barrier of height EI such that EL < E,. The distance between poten- tial energy minima and the dipole moment of IV dipole in the ees are assumed to be d and p respectively, i.e. independent of the electronic state. Let n; and nd represent the number of IV dipoles per unit volume in the ees in orientations 1 and 2, respec- tively. n' represents the total number of IV dipoles per unit volume in ees such that

n' = n; + ni = EIW, + E2W,, (9) where W , is the transition probability for optical excitation. It depends upon the intensity of irradiating wavelength and upon the nature of the IV dipoles through

W , = as, where u is the absorption cross-section of the IV dipole and S the number of incident photons per unit area per unit time [8 ] . It is apparent from (9) that with increasing irradiation time, more and more dipoles will be excited to ees.

Just after optical excitation and before thermal readjustment, the difference in I V dipoles in the two orientations in ees is

N' = n; - n2 = (nl - Tiz) W , (10) or the corresponding polarization will be N ' p = (121 - Ti2) pW, = PW,. Thus, optical excitation transfers polarization P W , to ees from egs. Now, such an optically excited dipole thermally readjusts in ees in the presence/absence of an electric field corre- sponding to PIP/PID, respectively.

, -

2.2.1 P I P Due to an initial difference N' in ees obtained just after optical excitation, the number of IV dipoles which will be thermally readjusted in the presence of an electric field is n' - N' = 2ni. Rate equations expressing the way n; increases or ni decreases in the presence of an electric field can be represented similarly as in the case of egs discussed in Section 2.1. The change in EL in the presence of E is given by (1/2)AE; = pE. It can be seen that n; increases exponentially with a time constant of 1/2v' where v' is the jump probability in ees in the absence of the electric field such that

where vi represents the frequency factor in ees.

thermal readjustment in orientation 1 in ees will be

v' = v i exp ( -Ei /kT) , (11)

It can be established that the equilibrium value of IV dipoles per unit volume after

The equilibrium value of IV dipoles per unit volume after thermal readjustment in orientation 2 in ees will similarly be represented by

-, n2 = ni (1 - g).

Occurrence of Photo-Induced Polarization and Photo-Induced Depolarization 761

The validity of (12) and (13) can be justified since they lead to 2; + fii = n'. Further, it can also be seen that in the absence of the electric field and before the thermal readjustment n; = n; and ?ii = ni.

Thus, the polarization established in the ees in the presence of an electric field after optical excitation and thermal readjustment is

, p2E kT

These oriented dipoles return back to egs by spontaneous emission of radiation and contribute to the polarization already present in egs. Thus, the net polarization during PIP will be given by

P, = polarization in egs - polarization transferred to ees during irradiation

(14) P' = (?i; - ?id) p = P W a + 2nz -.

+ polarization returned back from ees

= P l + W , l + - . [ ( 31 However, for small fields ( p E / k T ) < 1, and hence

nEp2 kT P, = ___ [1 + Wal

It is apparent that if there is no optical excitation during PIP, there will be no increase in the polarization. Furthermore, with increasing irradiation time, Pi will increase in agreement with the experimental observations.

It is evident from equation (15) that the magnitude of polarization observed during PIP does not depend upon EI. The relaxation time in ees (t') is controlled by EL through the relation

where t' = l/v' and ti = l /v& It is obvious that EL should be smaller than E , for the occurrence of PIP. A higher value of EL in comparison to E , will lead to a large relaxation time which will consequently restrict thermal readjustments in the ess. As discussed in Section 2.1, EL determines the lower temperature limit up to which IV dipoles can be polarized via ees. Obviously, the corresponding temperature limit in ees will be lower than that observed in egs since EL < E,. Thus, the system will be polarized via ees along curve 2 with T, as the temperature limit as shown in Fig. 2. I n PIP measurements [3, 51, the system is polarized in egs by applying an electric field. With the electric field still on, the system is rapidly cooled down to the irradiation temperature where it is irradiated in the presence of an electric field. During irradiation procedure it gets a chance to be polarized via ees resulting in an increase in the net polarization. For example, the K1:S-- system ceases to be polarized below 170 K in egs whereas it can be polarized up to 130 K via ees during PIP [3, 51.

t' = 7; exp (E;/kT) ,

2.2.2 PID The frozen-in polarization ( P F ) is given by

nEp2 P - F-l and can be derived similarly as (7). It is apparent that the magnitude of P, depends upon the initial polarization conditions. These frozen-in polarized dipoles, when being irradiated in the absence of the electric field during PID, get a chance to thermally

752 J. PRAKASH

readjust vide ees. Just after irradiation and before thermal readjustment, an initial difference N' in the number of IV dipoles is established in ees. It can be seen that n; decreases and consequently ni increases exponentially with a time constant of 1/2v' provided E; < E,. Equilibrium values of IV dipoles per unit volume in ees after thermal readjustments in the absence of the electric field during PID will be

(16) -, -, nl = n2 = + n' .

Thus, the polarization established in the ees in the absence of the electric field after optical excitation and thermal readjustment is

P' = (n; - n;) p = 0 . (17) These reoriented dipoles when returning back to egs, contribute to the frozen-in polarization already present in egs. Thus, the net polarization during PID will be given by

P, = frozen-in polarization in egs - polarization transferred to ees during irradiation + polarization returned back from ees

= P, [l - W,] . (18) It is apparent that if there is no optical excitation during PID, there will be no

change in the polarization. Furthermore, with increasing irradiation time, P , will decrease in agreement with the experimental observations.

I n PID measurements [2, 3,5], the system is polarized in egs by applying an electric field. With the electric field still on, the system is rapidly cooled down to LNT where the electric field is switched off. Thus, a system with frozen-in polarized dipoles is obtained. Such dipoles are then irradiated in the absence of the electric field. During irradiation, frozen-in polarized dipoles get a chance to thermally readjust in ees leading to a decrease in the net polarization. It has been observed in K1:S--, that the thermal readjustment ceases below 170 K in egs, whereas it is found to be active up to 130 K in ees during PID [2, 3, 51.

3. Discussion

Polarizations attained during PIP and PID are represented quantitatively by (15) and (18), respectively, according to the bistable model. Experimental data of PIP and PID recorded in KI:S-- [3,5], KI:Se-- [9], and KBr:S-- [lo] can thus be explained with the help of these equations. The bistable model suggests, however, that below a certain temperature the system ceases to be polarized by the application of the electric field. Subsequently, the corresponding lower temperature limits in ees and in egs are T , and T,, respectively, such that T, < T, provided E; < E,. This suggests, therefore, that thermal readjustment ceases below T, in ees even during PIP or PID. The increment observed during PIP a t temperatures lower than T , can be explained with the help of the mechanism of electrooptically stimulated exchange between divalent anion impurity ion and anion vacancy [ll]. The latter mechanism takes place when the system is irradiated in the presence of an electric field and consequently is inactive during PID. The details of the mechanism are discussed elsewhere [ll, 121. It has been observed experimentally [3, 5, 9, 101 that PIP takes place in the tempera- ture range between LNT and room temperature, whereas PID starts to appear only a t Tfe when thermal disorientations in ees become active. Thus, the results of PIP and PID give an insight into the mechanisms involved in ees.

Acknowledgement

The author is thankful to Prof. Nitish K. Sanyel for his interest in the work.

Occurrence of Photo-Induced Polarization and Photo-Induced Depolarization 753

References [l] A. S. NOWICK, in: Point Defects in Solids, Ed. J. H. CRAWFORD, JR., and L. M. SLIFKIN,

[2] J. PRAKASH and F. FISCHER, J. Physique 37, (3-167 (1976). [3] J. PRAKASK and F. FISCHER, phys. stat. sol. (a) 39, 499 (1977). 141 J. &BASH, Indian 5. pure appl. Phys. 16, 995 (1978). [5] J. PRAKASH, phys. stat. sol. (a) 64, 681 (1979). [6] S. BENCI, R. CAPELLETTI, R. FERMI, and M. MANFREDI, J. Physique 37, C7-138 (1976). [7] R. CAPELLETTI, R. FIESCHI, and E. OKUNO, Internat. Conf. Color Centers in Ionic Crystals,

[8] F. FISCHER, phys. stat. sol. (a) 52, 189 (1979). [9] J. PRAKASH, to be published.

Plenum Press, New York 1972 (Chap. 3, p. 166).

Sendai (Japan) 1974 (p. Gl36).

1101 J. PBAKASR, unpublished. 311 J. PRAHASH, phys. stat. sol. (a) 67, 775 (1980). 1121 J. PRAKASH, Indian J. pure appl. Phys. 20 (1982).

(Received January 28,1982)