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Localized States in Narrow-Gap Ferroelectric-Semiconductor PbSnTe:

Injection Currents, IR and THz Photosensitivity, Magnetic Field Effects

549

traps, the charging processes of the various traps will proceed simultaneously without

emergence of notable current oscillations. The latter situation refers to the case of high

voltages at which a reduction of the current oscillation amplitude and, then, complete

vanishing of oscillations were observed in the experiment.

Thus, involvement of the mechanism of current decrease due to trapping-induced reduction

of free-electron concentration, on the one hand, and involvement of the mechanism of

current increase owing to recharging-induced change of trap polarizability, on the other

hand, can result in an oscillating dynamics of the current decay to a steady-state value of the

current.

7. Conclusions

The object under study being solid solution Pb-Sn-Te with a substantial (up to a few atomic

per cents) In content, this object has to be considered as a disordered system presenting a

solid without long-range ordering, with the potential energy of charge carriers no longer

being a periodic function of coordinates. The violation of long-range ordering is related to

the fact that any chosen site of the metal sublattice may contain, with certain probability,

any of the three components. Electronic processes in such systems, namely, in amorphous

germanium and silicon, and also in chalcogenide glasses, were considered in (Mott & Davis,

1979). Such properties of PbSnTe:In as the Fermi-level pinning, the absence of an EPR

signal, and deviations from linearity in the temperature dependence

(

)

log 1

= are

similar to chalcogenide properties. J. Marshall and A.E. Owen (Marshall & Owen, 1976)

considered a state density model assuming that the forbidden band of PbSnTe contains deep

donors with energy levels below the acceptor energy (see Figure 18).

Fig. 18. Density of states in a non-crystalline semiconductor. VB – valence band; CB –

conduction band; E

- Fermi level; D – donors; A – acceptors; E

, E

– mobility edges; E

–

valence-band ceiling; E

– conduction-band bottom. Shaded are localized states.

The states in the forbidden band of PbSnTe pin the Fermi level at the middle of the energy

gap, thus leading to decreased conductivity. If the deep acceptor and donor states do not

overlap, then unpaired electrons, normally causing an EPR signal, are lacking, except for

those due to magnetic impurities. Without going into details, we can state that the model by

I.A. Drabkin and B.Ya. Moizhes

(Drabkin & Moizhes, 1981) mentioned in Section 1 closely

follows the theory by P.W. Anderson (Anderson, 1975).

The unique possibility of creating injecting contacts to PbSnTe:In has allowed researchers to

examine charge transport processes related to the recharging phenomena of localized states

Ferroelectrics – Physical Effects

550

in PbSnTe:In both under conditions with screened background radiation and under sample

illumination in a broad spectral range, from IR to THz radiation.

The fact that PbSnTe:In is a ferroelectric has widened available possibilities in studying the

effect of magnetic field on the charge transport due to electrons.

Of course, the data described in the present publication present no final results; yet, we

believe that space-charge-controlled limitation of the electric current, and also capture of

electrons into localized traps and their emission from those traps, which affect sample

polarizability, are factors that need to be taken into account in developing theoretical

models.

8. Acknowledgments

This work was supported by the Programs of Russian Academy of Sciences No. 5.4, 21.20

and, 21.34.

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Piezo-optic and Dielectric Behavior of the

Ferroelectric Lithium Heptagermanate Crystals

A. K. Bain

, Prem Chand

and K. Veerabhadra Rao

Department of Physics, Indian Institute of Technology Kanpur

Advanced Center for Materials Science, Indian Institute of Technology Kanpur

India

1. Introduction

It is well known that piezo-optic and electro-optic effects in crystals find wide ranging

applications in laser devices. The photoelastic behavior of crystals forms a necessary prelude

to study the electro-optical effect of ferroelectric crystals. Lithium heptagermanate Li

(LGO) is regarded as a weak ferroelectric and its curie point T

is 283.5K (Wada et al., 1981,

1983). Due to its intermediate behaviour between order-disorder and displacive types in a

conventional grouping of ferroelectric materials LGO remains a subject of interest from both

the theoretical and the application point of view. The paraelectric phase above T

orthorhombic

~ pbcn and below T

the ferroelectric phase is

C ~ pbc2

with four

formula units in a unit cell in both the phases. Below T

LGO shows dielectric hysteresis

loop and the permittivity shows a sharp peak at T

(Preu, 1982; Wada et al., 1981, 1983). The

Raman scattering spectrum shows a shoft mode whose frequency tends to zero as T

approached from below (Wada & Ishibashi, 1983). Below T

the spontaneous polarization

appears along the c-axis. The nature of the second order phase transition is not simple

because according to Raman spectra the transition is suggested to be a displacive phase

transition. But the temperature dependence of the permittivity ε is indicative of the order

disorder character of the phase transition (Preu, 1982; Wada et al., 1981, 1983) and does not

agree with the behaviour expected of a displacive phase transition.

Many interesting physical properties of LGO such as birefringence (Kaminsky & HaussÜhl,

1990), elastic (Hauss

Ühl et al., 1980), thermal expansion (Wada & Ishibashi, 1983), dielectric

susceptibility (Preu, 1982; Kudzin, 1994a, 1995b), electron paramagnetic resonance (EPR) of

doped ions Mn

and Cr

(Trubitsyn et al., 1992; Bain, 1994) and photoluminescence

(Bain, 1994) exhibit strong anomalies around T

. However, the optical properties vary

only to such a small degree that the transition could not be detected with the aid of a

standard polarization microscope (Kaminsky & Hauss

Ühl, 1990). Interestingly with the

help of a high resolution polarization device, Kaminsky and Hauss

Ühl (Kaminsky &

HaussÜhl, 1990) studied the birefringence in LGO near T

and observed anomalies at the

phase transition.

The study of piezo-optic dispersion of LGO (un-irradiated and irradiated) in the visible

region of the spectrum of light at room temperature (RT=298 K) shows an optical

zone/window in between 5400Å and 6200Å with an enhanced piezo-optical behavior (Bain

et al., 2008). The temperature dependence of the photoelastic coefficients of the ferroelectric

Ferroelectrics – Physical Effects

554

crystals Li

(both un-irradiated and x-irradiated) in a cooling and a heating cycle

between room temperature and 273K shows an interesting observation including the

lowering of the T

under uniaxial stress contrary to the increase of T

under hydrostatic

pressure and observation of thermal photoelastic hysteresis similar to dielectric behavior

(Bain et al., 2009). The study of a.c. electrical impedance (Z) along the c-axis of the crystals

LGO in the temperature range 283.5 K to 573 K at the frequency range 10kHz – 10,000 kHz

shows a sharply decrease of the magnitude of ǀZǀ with increasing frequency and tends to

zero value at about the frequency 10,000kHz.

This chapter will include basic properties of the ferroelectric Lithium heptagermanate

(Li

) crystals, related experimental studies on this crystal including growth of single

crystals, agreement and disagreement between the results of different experimental

investigations. The brief description on the theory of photoelasticity, fabrication process of

the ferroelectric Li

crystals, experimental methods of the photoelastic coefficients of

LGO (un-irradiated and irradiated) at different wave length and temperatures around the

phase transition temperature T

and also the practical applications of the LGO crystals in the

opto-electronic devices will be discussed.

1.1 Growth and structure of Li

crystals

Single crystals of Li

are grown in an ambient atmosphere by Czochralski method

from stoichiometric melt, employing a resistance heated furnace. Stoichiometric mixture of

powdered Li

and GeO

in the ratio of 1.03 and 7.0 respectively was heated at 1100 K for

24 hours to complete the solid state reaction for the raw material for the crystal growth. The

crystals were grown by rotating the seed at the rate of 50 rpm with a pulling rate of 1.2

mm/hour. The cooling rate of temperature in the process of growth was 0.8-1.2 K/hour. The

crystals grown were colorless, fully transparent and of optical quality. The crystal axes were

determined by x-ray and optical methods.

The desired impurities such as Cr

, Mn

, Bi

and Eu

etc are also introduced in desired

concentration by mixing the appropriate amount of the desired anion salt in the growth

mixture. The crystal structure of LGO above T

is orthorhombic (psedohexagonal) with the

space group

(Pbcn). The cell parameters are a: 7.406 Å, b: 16.696 Å, c: 9.610 Å, Z = 4

and b~√3c. Below T

a small value of spontaneous polarization occurs along c-axis and the

ferro-phase belongs to

C (Pbc2

) space group. The crystal structure contains strongly

packed layers of GeO

tetrahedra linked by GeO

-octahedra to form a three dimensionally

bridged frame work in which Li atoms occupy the positions in the vacant channels

extending three dimensionally (Hauss

Ühl et al., 1980; Wada et al., 1984, 1988; Iwata et al.,

1987). The size of the unit cell (Z = 4) does not change at the phase transition and

ferroelectric phase transition is associated with a relaxational mode as well as the soft

phonon (Wada, 1988).

1.2 Theory of photoelasticity

If a rectangular parallelepiped with edges parallel to x[100], y[010] and z[001] axes is

stressed along z-axis and observation is made along y-axis, as shown in Fig.1, then the path

retardation δ

introduced per unit length due the stress introduced birefringence is given

= (Δn

– Δn

) = C

(1)

Piezo-optic and Dielectric Behavior of the Ferroelectric Lithium Heptagermanate Crystals

555

where Δn

and

Δn

are the changes in the corresponding refractive indices, (Δn

– Δn

) is

the corresponding stress induced birefringence, P

is the stress along z-axis and C

is a

constant called the Brewster constant or the relative photoelastic coefficient. In general the

Brewster constant is related to the stress optical and strain optical tensors of forth rank

(Narasimhamurty, 1981) and is a measure of the stress induced (piezo-optic) birefringence.

It is conveniently expressed in the unit of 10

-13

/dyne per cm thickness along the

direction of observation is called a Brewster (Narasimhamurty, 1981).

Fig. 1. A solid under a linear stress of stress-optical measurements (P

is the applied stress

and LL is the direction of light propagation and observation).

1.3 Experimental method of determining the photoelastic constants

To study the piezo-optical birefringence the experimental set up consists of a source of light

(S), a lens (L) to render the rays parallel, a polarizer (P), an analyzer Polaroid (A), a Babinet

compensator (B) and a detector (D), as shown in Fig.2. The P and A combination are

adjusted for optimal rejection of light. The sample with stressing arrangement and a Babinet

compensator are placed between P and A. A monochromator and a gas flow temperature

controlling device are used to obtain the piezo-optic coefficients (C

) at different wavelengths

and temperature. The subscript λ in the symbol C

denotes that the piezo-optic coefficient

depends on the wavelength of light used to measure it. The experiments are carried out for

different wavelengths using white light and a monochromator and the monochromatic

sodium yellow light. An appropriate stress along a desired direction of the sample is applied

with the help of a stressing apparatus comprising a mechanical lever and load.

Fig. 2. A schematic diagram of the experimental setup for the measurement of photoelastic

constants of the crystals at room temperature. Source of light (S), Lense (L), Polarizer (P),

Crystals (C) under stress, Babinet Compensator (B), Analyzer (A) and Detector (D).

Ferroelectrics – Physical Effects

556

To start with, the Babinet compensator is calibrated and the fringe width is determined for

different wavelengths of light in the visible region. The crystal specimen is placed on the

stressing system so that the stress could be applied along vertical axis and observation made

along horizontal axis. A load on the crystal shifts the fringe in the Babinet compensator and

this shift is a measure of the piezo-optic behavior. The piezo-optic coefficients (C



) are now

calculated using the calibration of the Babinet compensator. The experiment is repeated for

other orientations of the crystals and the results are obtained.

1.4 Piezo-optic dispersion of Li

crystals

The experimental procedure for the piezo-optic measurements is described in section 1.3. The

polished optical quality samples worked out to dimensions i) 5.9 mm, 9.4 mm and 5.0 mm; ii)

3.17 mm, 5.88 mm and 6.7 mm, along the crystallographic a, b and c axes respectively. The

stress was applied with an effective load of ~23 kg in each case (Bain et al., 2008).

The values of C

thus obtained at different wavelengths are given in Table 1 and the results

are plotted in Fig. 3. Here C

is the piezo-optic coefficient with the stress direction being p

and observation direction being q. The results show an interesting piezo-optic behavior. A

survey of literature indicates that the piezo-optic behavior of materials studied till now

shows a reduction of C

with increasing wavelength in the visible region (Narasimhamurty,

1981). In the present case, C

decreases with wavelength up to a certain wavelength as in

other normal materials and then suddenly shows a peak and later on the usual behavior of

reduction in the values of piezo-optic coefficients is observed.

Wavelenghts

Obs. C

4358Å 4880Å 5390Å 5890Å 6140Å

1 C

4.024 3.819 3.722 4.328 3.677

2 C

5.243 4.895 4.770 5.552 4.451

3 C

4.084 3.525 3.092 3.562 2.913

4 C

4.353 4.118 3.946 4.261 3.866

5 C

4.179 2.814 3.177 3.713 3.172

6 C

3.312 2.991 2.650 4.190 2.618

Table 1. Stress optical coefficients c

(in Brewster) for Li

at different wave lenghts.

To the best knowledge of the authors this behavior is unique to the LGO crystals. For the

sake of convenience we denote C

measured at λ = 5890 Å as C

5890

and so on. The results

show that sometimes the value of C

5890

is even higher than that at C

4400

, the value of piezo-

optic coefficient obtained at the lowest wavelength studied here. This is the case with C

and C

. For other orientations the value is lower than that at 4400 Å. Further, C

found to have increased to more than 50% in the case of stress along [001] and observation

along [100]. Also, it is interesting to note that the value of C

6140

, is less than that of C

5390

, in

tune with usual observation of piezo-optic dispersion. Thus one can see an “optical

window” in between 5400 Å and 6200 Å. The height of this optical window is different for

various orientations, though the width seems approximately the same. The maximum

height of about 1.5 Brewster was found for C

followed by C

with about 0.9 Brewster. It

should be noted here that Z-axis is the ferroelectric axis for LGO. It is also interesting to note

that the change in height is more in the former while the actual value of C

, is less compared

to that of the latter. The percentage dispersion also is different for various orientations. It is

very high, as high as 25% for C

, while it is just 10% for C

Piezo-optic and Dielectric Behavior of the Ferroelectric Lithium Heptagermanate Crystals

557

Fig. 3. Stress optical dispersion of Li

crystals with wavelength at room temperature

(298 K).

Figure 4 shows the variation of C

(λ) at the temperatures ranging from 298K to 283K on

cooling process of the sample LGO. It is clear from the figure that the distinct peak of C

(λ)

appears only at the sodium yellow wavelength of 5890 Å for the whole range of

temperatures (298 K–283 K) investigated. It is also interesting to note that a temperature

anomaly is also observed around 283 K. LGO undergoes a second order phase transition at

283.5 K from the high temperature paraelectric phase to the low temperature ferroelectric

phase. So this anomaly is related to this phase transition of the LGO crystal.

The observed peculiarity of piezo-optic behavior could be due to many factors, viz., i)

anomalous behavior of refractive index or birefringence ii) anomalous ferroelastic

transformation at some stage of loading iii) shift of absorption edge due to loading. The

following have been done to identify the reasons for this peculiar behaviour.

Birefringence dispersion has been investigated in the visible region and no anomalies in its

behavior has been observed. This rules out the first of the reasons mentioned. The reason

due to ferroelastic behavior also is ruled out since the effect would be uniform over all the

wavelengths investigated. It was not possible to investigate the effect of load on the

absorption edge. Hence an indirect experiment has been performed. If there is a shift in the

absorption edge due to loading the sample, the peak observed now at sodium yellow light

would shift with load. No clear shift of the peak could be observed within the experimental

limits. Another interesting experiment was done to identify the source of the anomaly. It is

well known that T

of LGO changes under uniaxial stress. The measurements were made

near T

under different stress (loads). Although T

was found to shift a little with load the

Ferroelectrics – Physical Effects

558

dispersion peak did not show any discernible shift. No particular reason could be

established as to why a dispersion peak appears around sodium yellow region. Another

interesting work in this direction is on Gd

(Mo0

)

— where an anomalous peak was

recorded in spontaneous birefringence at 334.7 nm (Saito et al., 1994), an observation made

for the first time.

Fig. 4. The variation of C

(λ) at the temperatures ranging from 298 K to 283 K on cooling

process of the sample Li

It is well known that the photoelasticity in crystals arises due to change in number of

oscillators, effective electric field due to strain and the polarisability of the ions. In the

present case, as the wavelength approaches around 5400 Å , the ionic polarisability seems to

be changing enormously. There is no optical dispersion data available on LGO. We

haveconducted an experiment on transmission spectra of LGO along x, y and z-axes, which

shows a strong absorption around 5400 Å . The observed anomaly in the piezo-optic

dispersion may be attributed to the absorption edge falling in this region. This explanation

needs further investigation in this direction. It is also known that the strain optical

dispersion arises due to the shift in absorption frequencies and a change in the oscillator

strength caused by the physical strain in the crystal.

1.5 Irradiation effect on Piezo-optic dispersion of Li

crystals

The ferroelectric single crystals Li

was irradiated by x-ray for one hour and the

experimental processes described in section 1.4 were repeated for the crystal (irradiated)

LGO in order to understand the radiation effect on piezo-optical birefringence

dispersion(Bain et al., 2008). The values of C



of the crystal (irradiated) LGO thus obtained

at different wavelengths are given in Table 2 and the results are plotted in Fig. 5.

Lallart M. (ed.) Ferroelectrics - Physical Effects

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