Defect Properties and the Photorefractive Effect in Barium Titanate

Chapter 26

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Defect Properties and the Photorefractive Effect in Barium Titanate Barry A. Wechsler, Daniel Rytz, Marvin B. Klein, and Robert N. Schwartz Hughes Research Laboratories, Malibu, CA 90265

Barium titanate (BaTiO) is a photorefractive material that exhibits high gain. However, significant improvements in performance can be achieved through proper control of defect properties. Our approach to optimizing these properties involves growth of pure and doped BaTiO crystals. Annealing under controlled atmospheres is used to control the valence state of the dopants. The effects of growth conditions on the defect and photorefractive properties are characterized by optical absorption, electron paramagnetic resonance, and two-beam coupling measurements. Theoretical modeling of defect equilibria aids in understanding the relation between processing conditions and photorefractive behavior. Substantial differences in behavior are observed for various dopants and annealing conditions. Thus far, cobalt-doped crystals are the most promising for visible and near-infrared applications. 3

3

The p h o t o r e f r a c t i v e e f f e c t i s a l i g h t - i n d u c e d change i n t h e i n d e x o f r e f r a c t i o n o f a c r y s t a l . A l t h o u g h r e f e r r e d t o as " o p t i c a l damage" when t h e e f f e c t was f i r s t d i s c o v e r e d (1,2) i t was soon r e a l i z e d t h a t r e f r a c t i v e i n d e x g r a t i n g s w r i t t e n and s t o r e d i n such c r y s t a l s c o u l d be used f o r a wide range o f o p t i c a l a p p l i c a t i o n s . P h o t o r e f r a c t i v e c r y s t a l s c a n be used t o make s i m p l e phase c o n j u g a t o r s w i t h a p p l i c a t i o n s i n d i s t o r t i o n c o r r e c t i o n , l a s e r power c o m b i n i n g , remote s e n s i n g , and t r a c k i n g systems. These m a t e r i a l s may a l s o p l a y an i m p o r t a n t r o l e i n v a r i o u s o p t i c a l computing and s i g n a l p r o c e s s i n g d e v i c e s such as r e c o n f i g u r a b l e o p t i c a l i n t e r c o n n e c t s , a s s o c i a t i v e memories, and p a s s i v e l i m i t e r s f o r s e n s o r p r o t e c t i o n . The most w i d e l y s t u d i e d p h o t o r e f r a c t i v e m a t e r i a l s c a n be d i v i d e d i n t o t h r e e c l a s s e s : f e r r o e l e c t r i c o x i d e s , i n c l u d i n g L i N b 0 , KNb0 , B a T i 0 , and v a r i o u s t u n g s t e n b r o n z e - t y p e c r y s t a l s such as S r _ B a N b 0 ; oxides of the s i l l e n i t e family, i n c l u d i n g B i S i O , B i G e O , and B i T i O ; and s e m i - i n s u l a t i n g compound 3

3

3

1

1 2

x

x

2

2 0

6

1 2

1 2

2 0

0097-6156/91/0455-0394$06.00/0 © 1991 American Chemical Society In Materials for Nonlinear Optics; Marder, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

2 0


26. WECHSLER ET Al»

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Barium Titanate

semiconductors, including GaAs, InP, and CdTe. The f e r r o e l e c t r i c oxides generally display the largest r e f r a c t i v e index changes due to t h e i r r e l a t i v e l y large e l e c t r o - o p t i c c o e f f i c i e n t s . On the other hand, they have small charge c a r r i e r m o b i l i t i e s and large d i e l e c t r i c constants, which r e s u l t i n long response times and low s e n s i t i v i t i e s . In contrast with the s i l l e n i t e s and compound semiconductors, measured time constants for the photorefractive e f f e c t i n the f e r r o e l e c t r i c oxides are t y p i c a l l y more than three orders of magnitude slower than the t h e o r e t i c a l l i m i t . E x i s t i n g c r y s t a l s display a great deal of v a r i a b i l i t y among d i f f e r e n t samples and are photosensitive only over a l i m i t e d wavelength range. For these reasons, e f f o r t s to optimize these materials through improved c r y s t a l growth and processing methods may prove worthwhile. Because the photorefractive e f f e c t involves photocarrier ionization, transport, and recombination, t h i s behavior i s l i k e l y related to the presence of defects such as s u b s t i t u t i o n a l impurities and/or cation and anion vacancies. Our approach to optimization of BaTi0 involves both a t h e o r e t i c a l understanding of the mechanisms involved i n the grating formation process and an experimental e f f o r t on the growth, processing, and characterization of pure and doped c r y s t a l s . In the following sections, we present some r e s u l t s of our recent studies aimed at probing the nature of the photorefractive centers i n BaTi0 and a l t e r i n g the photorefractive properties through doping and heat treatment. 3

3

Physics of the Photorefractive E f f e c t The e s s e n t i a l features of the photorefractive e f f e c t and the influence of defect centers on t h i s behavior can be understood i n terms of a band transport model (3,4). Consider a hypothetical species with two possible charge states having energy l e v e l s within the band gap (Figure 1). Illumination with photons of s u f f i c i e n t energy causes c a r r i e r s (holes and/or electrons) to be photoionized from f i l l e d s i t e s . These c a r r i e r s undergo transport by d r i f t and d i f f u s i o n and recombine at empty trapping centers. I f the illumination i s non-uniform, a space charge f i e l d i s produced that modulates the index of r e f r a c t i o n through the e l e c t r o - o p t i c e f f e c t . A useful method of characterizing t h i s behavior i s two-beam coupling. Two i n t e r f e r i n g laser beams produce a periodic irradiance pattern i n the c r y s t a l . A r e f r a c t i v e index grating develops which i s i n general out of phase with respect to the irradiance, leading to energy exchange (gain) between the incident beams. The gain and response time of t h i s grating can be measured as a function of the crossing angle of the beams ( i . e . , grating spacing or wave vector), intensity, wavelength, etc., and used to determine material properties r e l a t e d to the photorefractive e f f e c t . The gain c o e f f i c i e n t , which i s determined by measuring the r a t i o of transmitted i n t e n s i t i e s of a weak signal beam with and without a strong reference beam, i s given by Γ = (2*/X)n r 3

e f f

E

s c

,

where λ i s the wavelength, η i s the background r e f r a c t i v e index, r i s the e f f e c t i v e e l e c t r o - o p t i c c o e f f i c i e n t for the measuring geometry, and E i s the space charge f i e l d , given by: s c

In Materials for Nonlinear Optics; Marder, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

(1) e f f


396

MATERIALS FOR NONLINEAR OPTICS: CHEMICAL PERSPECTIVES

CONDUCTION BAND

-X/X+ ΔΕ

9

V A L E N C E BAND

Figure 1. Schematic energy-level model for a single species in two valence states. (Reproduced with permission from Ref. 11. Copyright 1988 Optical Society of America.)


26.

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Barium Titanate

WECHSLER E T AL.

kT

(0-1)

K

B

E

=

s e

Γ

·

(2)

e 1 (K/K ) (C l) Here, k i s Boltzmann's constant, Τ i s the absolute temperature, e i s the electron charge, and Κ i s the grating wave vector. K i s the Debye screening wave vector, defined by 2

+

S

+

B

s

K, = ( e ^ / e e ^ T ) '


1

,

2

(3)

where e i s the r e l a t i v e d i e l e c t r i c constant, e i s the p e r m i t t i v i t y of free space, and i s the e f f e c t i v e empty trap density, given by 0

N

= N N /(N N )

E

A

D

A+

(4)

.

D

N i s the concentration of photoactive centers f i l l e d with electrons (species X), and N i s the concentration of s i t e s f i l l e d with holes (species X*). The f a c t o r ξ = (C-1)/(C+1) accounts f o r the competing photoconductivity contributions due to electrons and holes, and has a value of -1 when electron photoconductivity dominates and +1 when hole conductivity dominates. Intermediate values occur when mixed conductivity i s present. C i s defined by 0

A

s

2

2

N

A

(K +K )

s. N

0

(K +K )

h

e

C =

(5)

, 2

2

h

where s and s are the photoionization cross sections for holes and electrons, respectively, and K and K are the inverse transport lengths f o r holes and electrons. The response time, r , i s t y p i c a l l y determined by measuring the grating build-up time or erasure rate. For large grating spacings, the response time i s the inverse d i e l e c t r i c relaxation rate: h

e

h

e

1 1+(K/K,) - = 7 = 7di« : τ 1 (Κ/Κ )

2

2

+

1+(K/K,) 7dih Γ 1 (K/K )

2

+

β

+

>

() β

2

h

where s /*e e l e

N

s /*

D

h

Tdie =

7

and 7·

"

0

N

d î h

el

N

ee

N

A

. 7

A

h

= h

0

(7)

D

7^ - and 7 \ are the d i e l e c t r i c relaxation rates f o r electrons and holes (neglecting the dark conductivity) , μ and / i are the c a r r i e r m o b i l i t i e s , 7 and 7 are the recombination rates, and I i s the incident i n t e n s i t y . The gain and response time of a c r y s t a l are subject to v a r i a t i o n through growth and processing techniques. In general terms, gain i s enhanced by a large empty trap density, N , and large (positive or negative) values of the r e l a t i v e conductivity factor, ξ. The response time i s made faster by higher absorption (s N +s N ) and longer c a r r i e r l i f e t i m e s (TR =l/7eNA> R h V 7 h N D ) Within the context of the model described here, the e f f e c t s of growth conditions on these properties can be understood. The r e f r a c t i v e index, e l e c t r o - o p t i c c o e f f i c i e n t , and d i e l e c t r i c constant are fundamental βx

d

h

Β

e

h

h

E

h

r

A

e

D

=

e



398


material properties that cannot generally be modified, although they may be s e n s i t i v e to temperature and, i n the case of mixed c r y s t a l s , composition. The photoionization and recombination rates depend on the energy l e v e l structure of the photoactive species, and are therefore s e n s i t i v e to the p a r t i c u l a r dopants, impurities, or other defects present. Although these can be altered by processing techniques, i t i s d i f f i c u l t to predict a p r i o r i the optimum species; therefore, various possible dopants must be t r i e d . The c a r r i e r m o b i l i t i e s are fundamental properties of the material, although they may vary somewhat depending on the nature of the defects. Carrier transport can be altered by varying the temperature as well as by applying an e l e c t r i c f i e l d . Since hole and electron m o b i l i t i e s are in general unequal, i t i s also possible to modify the e f f e c t i v e transport properties by s e l e c t i n g the dominant photocarrier through appropriate material preparation techniques. The properties most readily subject to control through growth and processing procedures are the concentrations of the f i l l e d and empty traps. The t o t a l concentration of photoactive species (N +N ) can be altered by doping and/or other changes i n growth conditions. Furthermore, the r e l a t i v e proportions of the two states (N /N ) can be controlled by i n - s i t u or post-growth oxidation-reduction treatments. I t must be understood, however, that defect e q u i l i b r i a are complex and i t i s therefore usually not possible to vary any single parameter without also a f f e c t i n g other material properties. D

D

Crystal Growth and

A

A

Processing

BaTi0 i s a perovskite-type c r y s t a l . At high temperature (between 1432 and 132°C), the structure i s cubic and consists of corner-linked T i 0 octahedra with the much larger Ba ions occupying the voids between these octahedra. At 132°C, a displacive phase t r a n s i t i o n occurs. The titanium ion moves s l i g h t l y off the central p o s i t i o n i n the oxygen octahedron, giving r i s e to an e l e c t r i c p o l a r i z a t i o n . This phase, which has tetragonal symmetry, i s f e r r o e l e c t r i c and f e r r o e l a s t i c : the d i r e c t i o n of the spontaneous p o l a r i z a t i o n can be reoriented by a p p l i c a t i o n of an e l e c t r i c f i e l d or a non-hydrostatic stress. Below room temperature, BaTi0 undergoes two additional phase t r a n s i t i o n s , from tetragonal to orthorhombic at about 10°C and from orthorhombic to rhombohedral at -90°C. Between 1432°C and the melting point (1625°C), the stable phase of BaTi0 has hexagonal symmetry and d i f f e r s s i g n i f i c a n t l y i n structure from that of the cubic perovskite. The hexagonal-cubic transformation i s reconstructive and would r e s u l t i n a serious degradation of the o p t i c a l and mechanical i n t e g r i t y of single c r y s t a l s grown from the pure melt and cooled through t h i s phase t r a n s i t i o n . For t h i s reason, BaTi0 c r y s t a l s have been grown by a variety of f l u x methods. Of these, the top-seeded solution growth (TSSG) approach developed by Linz and co-workers (5) i s the most successful for the production of large, high quality samples. This method uses an excess of T i 0 as the flux, which has the advantage of not introducing any foreign ions as impurities. A melt composition near 65 mol% T i 0 i n the system BaO-Ti0 i s t y p i c a l l y used, having a liquidus temperature near 1400°C. Growth i s i n i t i a t e d on a seed lowered into the melt from above and i s driven by cooling the melt at a rate of a few tenths of a degree per hour. The c r y s t a l i s usually 3

6

3

3

3

2

2

2


26.

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Barium Titanate

rotated at about 60 rpm and withdrawn from the melt at a rate of 0.Ι Ο. 2 mm/h during growth. The c r y s t a l i s removed from the melt at 1335°C and then cooled to room temperature. In order to optimize the photorefractive performance of BaTi0 , i t i s necessary to control the centers involved i n the i o n i z a t i o n and trapping of photocarriers. This may be accomplished i n part by i n t e n t i o n a l l y doping the c r y s t a l with various t r a n s i t i o n metal or rare earth ions, which may exist i n more than one valence state. These may be added to the melt during growth i n the form of oxide or carbonate compounds. In our work, we have surveyed most of the t r a n s i t i o n metals, using doping concentrations i n the melt of 50 to 200 ppm of dopant ions per BaTi0 formula unit. Although even undoped c r y s t a l s with no more than about 10 ppm of unintentional impurities present are s t i l l photorefractive, some studies (6,7) have suggested that the photorefractive gain can be enhanced by the addition of dopants (or by higher impurity concentrations). On the other hand, there does not appear to be any simple c o r r e l a t i o n between doping concentration and photorefractive gain; rather, the behavior i s more complex, being influenced by the inevitable presence of other i n t r i n s i c and e x t r i n s i c defects. T r a n s i t i o n metal dopants and impurities are probably incorporated s u b s t i t u t i o n a l ^ for T i i n BaTi0 . Emission spectrographic analyses indicate that the d i s t r i b u t i o n c o e f f i c i e n t s for Mn and Fe dopants are on the order of 1 to 2, i . e . , the c r y s t a l s are s l i g h t l y enriched r e l a t i v e to the melt. Cr and Ni may have d i s t r i b u t i o n c o e f f i c i e n t s s l i g h t l y less than 1. For Co, the measured concentrations i n the c r y s t a l s display considerable scatter; we estimate that the d i s t r i b u t i o n c o e f f i c i e n t i s on the order of 4. Fe i s the most prevalent t r a n s i t i o n metal impurity and i s t y p i c a l l y present at a concentration of 10-15 ppm by weight. S i , A l , Mg, and Cu are also t y p i c a l l y present at 5-50 ppmw. Fe and Cr impurities have also been observed by EPR spectroscopy, although Cr could not be detected by emission spectroscopy, with a detection l i m i t of 10 ppmw. The two most important i n t r i n s i c defects i n BaTi0 are oxygen and barium vacancies. Both of these can be modified to some extent by growth and processing conditions. Barium vacancies are introduced as a r e s u l t of the excess of T i 0 i n the TSSG melt. Phase equilibrium experiments show that as much as 1 or 2 mol% excess T i 0 may be incorporated i n BaTi0 at temperature above 1500°C (8,9). However, i n the temperature range over which BaTi0 i s normally grown, i . e . , below 1400°C, i t i s l i k e l y that the excess of T i 0 i s no more than about 100 ppm (10). Nevertheless, t h i s i s s i m i l a r to the dopant concentrations, and therefore i t would not be s u r p r i s i n g i f Ba vacancies play an important r o l e i n the photorefractive behavior, p a r t i c u l a r l y i n high purity undoped c r y s t a l s . Oxygen vacancies are the p r i n c i p a l charge compensating defects i n BaTi0 . Thus, t h e i r concentration i s determined by the o v e r a l l balance of donor and acceptor type species. In most BaTi0 c r y s t a l s , acceptor-type impurities predominate, which raises the concentration of oxygen vacancies. The oxygen vacancy concentration i s also dependent upon the oxygen pressure i n the surrounding atmosphere during growth and cooling. Because oxygen vacancies are highly mobile at elevated temperatures, t h e i r concentration can be changed by post-growth annealing. Each oxygen ion removed from the c r y s t a l by annealing under low P(0 ) conditions leaves behind two electrons.


3

3

3

3

2

2

3

3

2

3

3

2


400


These electrons are thermally ionized from the vacancy and may combine with an available acceptor, thus a l t e r i n g the charge state of the acceptor species. Experiments have shown that such a process can lead to a change i n sign of the dominant photocarrier as well as modified gain and response time of the photorefractive e f f e c t .


Thermodynamic Point Defect Model In order to obtain a better understanding of the e f f e c t s of doping and oxidation-reduction processing on the defect populations and photorefractive properties of BaTi0 , we have studied a thermodynamic point defect model (11). This model, o r i g i n a l l y developed for BaTi0 by Hagemann (12), can be used to calculate the concentrations of point defects as a function of temperature and oxygen pressure f o r various dopants. These populations determine the photorefractive trap densities (N and N ) and can therefore be used to predict the beam coupling gain and response time. Although t h i s model i s probably too s i m p l i s t i c to give accurate quantitative r e s u l t s , i t provides a useful q u a l i t a t i v e picture of the way i n which c r y s t a l growth and processing conditions can a l t e r the behavior. We assume that a single acceptor-type species i s present that acts as both the source and trap for photocarriers. This species has at l e a s t two possible stable charge states with energy l e v e l s i n the band gap. We consider the presence of eight defect species: oxygen vacancies i n neutral, s i n g l y - , and doubly-ionized states; acceptor s i t e s (e.g., t r a n s i t i o n metals s u b s t i t u t i n g for T i ) also i n neutral, singly-, and doubly-ionized forms; and free charge c a r r i e r s (electrons and holes). The oxygen vacancy concentrations are governed by the exchange of oxygen between the c r y s t a l and i t s surrounding atmosphere, and are given by: 3

3

D

[V„]

= KJ e - « / B

[VQ]

= 2 [V*] e (

E

k

T

r

A

1

P^ / -

E

^

k

B

2

(8) (9)

T

x

[V··] = [V ] ( E ' + E " - 2 E ) / k T e

n

F

B

(

1

0

)

n

where the superscript x indicates a defect that i s neutral, and the superscript dots indicate p o s i t i v e charges with respect to the i d e a l l a t t i c e . E£ i s the enthalpy of reduction, K£ i s a constant r e l a t e d to the entropy change of reduction, k i s Boltzmann's constant and Τ i s the absolute temperature. E and Ε** are the i o n i z a t i o n energies corresponding to the removal of electrons from the neutral oxygen vacancy, and E i s the Fermi l e v e l . The concentrations of the acceptor species are given by: B

+

F

[A] —

x

[A ] 1

E

+

E

k

1/2 e ( F " " ) / B

(11)

T +

e

(2E -E--E")/k T F

B

E

[Α'] = 1/2 [A ] ( F - E " ) / k T x

e

[A"]

= [A ] e x

( 2 E f :

B

E

E

" "" "

) / k B T


(

1

2

)

(13)

26.

WECHSLER ET AL.

401

Barium Titanate

where the superscript primes indicate negative charges r e l a t i v e to the i d e a l l a t t i c e and E~ and E~~ are the energies corresponding to the i o n i z a t i o n of holes from the neutral acceptor s i t e . The free c a r r i e r concentrations are determined by thermal i o n i z a t i o n across the band gap, and are given by: np = N


η = N

N

c

e"V B k

v

T

(14)

E

c

e

-( c-E )/k T F

(15)

B

where N and N are the densities of states i n the conduction and valence bands, respectively, E i s the energy of the conduction band edge, and E i s the band gap energy. One further equation i s established by the condition that o v e r a l l charge balance must be maintained: c

Y

c

g

[λ>]

+

2[A>>]

+

η = [V·]

+

2[V--]

+

ρ

.

(16)

Here, a l l the negatively charged species appear on the left-hand side of the equation and the p o s i t i v e l y charged species are on the r i g h t . These nine equations i n nine unknowns (eight defect concentrations plus E ) can be solved simultaneously for any temperature and oxygen pressure, given the values f o r the aforementioned energy parameters and densities of states. An example of such a c a l c u l a t i o n for BaTi0 :Co i s shown i n Figure 2a. We have used the data of Ref. 12, showing an i o n i z a t i o n l e v e l 1.45 eV above the top of the valence band, which involves the Co */Co * states. A second i o n i z a t i o n l e v e l at the valence band edge corresponds to the Co */Co * i o n i z a t i o n reaction. We assume that the t o t a l oxygen vacancy concentration i s established and "frozen i n " at the process temperature, but that the i n d i v i d u a l defect species are i n thermal equilibrium at room temperature. In Figure 2b, the corresponding model predictions f o r the photorefractive gain and response time are shown. These were calculated using Equations 1-7, where the concentrations of Co * and Co * were used for the parameters N and N , respectively. Because the values of s , /*,h> * 7e,h well known, i t i s necessary to make several assumptions to calculate the photorefractive properties (11). Therefore, these r e s u l t s should only be viewed as being q u a l i t a t i v e l y meaningful. A number of i n t e r e s t i n g observations can be made from model calculations such as these. Referring to Figure 2a, i t i s seen that under o x i d i z i n g conditions, Co * i s the predominant dopant species. Under reducing conditions, the cobalt valence state i s lowered to 2+. Doubly ionized oxygen vacancies are present at half the Co * concentration i n the oxidizing regime to provide charge compensation. At lower oxygen pressures, the oxygen vacancy concentration becomes equal to the Co * concentration. After a l l the cobalt has been converted to the divalent state, further reduction leads to an increasing population of electron-occupied oxygen vacancies. (Note that t h i s c a l c u l a t i o n does not allow for the presence of Co *, although Co * i s allowed at high oxygen pressures.) The photorefractive gain, shown i n Figure 2b, i s predominantly determined by two factors: the trap density, N , and the r e l a t i v e conductivity factor, ξ. The l a t t e r factor accounts for the minimum F

3

2

3

3

4

2

3

D

anc

A

e > h

a r e

e

3

3

2

1

4

E


n o t

402



τ—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—Γ

15

-10

-5

0

5

L O G O X Y G E N P R E S S U R E (bar)

Figure 2. (a) Point defect concentrations as a function of oxygen p a r t i a l pressure f o r BaTi0 :Co processed at 800°C. (b) Calculated gain and response time f o r the model shown i n (a). 3


26.

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403

Barium Titanate

i n the gain and associated sign change near the middle of the P(0 ) range. At t h i s point, which actually corresponds to a maximum i n the trap density, the photoconductivity contributions due to electrons and holes exactly cancel one another, r e s u l t i n g i n no net photorefractive e f f e c t . The gain also vanishes at higher and at lower oxygen pressures due to the absence of traps ( i . e . , the concentration of the minority species, which e f f e c t i v e l y determines the trap density, becomes n e g l i g i b l y small). The response time i s slowest where the trap density reaches a maximum, because c a r r i e r s are trapped more quickly and hence t h e i r transport lengths are shorter. With a smaller trap density, the response time i s f a s t e r . The model suggests that response times can vary by about 2 orders of magnitude within the high gain regime. Since the i o n i z a t i o n energies of various t r a n s i t i o n metals i n BaTi0 have been determined (12), t h i s model can be used to compare the expected behavior for d i f f e r e n t dopants. For example, the model indicates that Fe i s present predominantly as F e * throughout most of the accessible region of P(0 ) conditions. The minority species, F e * at high oxygen pressures and F e * at low oxygen pressures, are present at r e l a t i v e l y low concentrations throughout most of the available region of P ( 0 ) ; thus, one would expect to f i n d a smaller trap density i n Fe-doped BaTi0 than for the same concentration of cobalt. Also, because the conversion between Co * and Co * occurs under e a s i l y achievable conditions, the photorefractive behavior can i n p r i n c i p a l be more e a s i l y controlled for t h i s dopant. Calculations for Mn and Cr also predict valence changes under r e a d i l y accessible P(0 ) conditions. However, Ni i s present only i n the divalent state except under high oxygen pressures and therefore would not be expected to p a r t i c i p a t e i n the photorefractive e f f e c t . Model calculations also suggest that the photorefractive behavior becomes quite complex when two or more species can contribute to the e f f e c t . For example, with two ionizable species present, each with two l e v e l s i n the band gap, seven sign changes are predicted as a function of reduction. Even though one of these species may be present at low concentrations ( i . e . , as an impurity i n the background of a doped c r y s t a l ) , i t may nevertheless have a s i g n i f i c a n t impact on the expected behavior.


2

3

3

2

4

2

2

3

3

2

2

This model has a number of l i m i t a t i o n s , including the f a c t that only point defects are considered. As discussed below, there i s some evidence that more complex defect pairs or clusters may occur i n BaTi0 . In addition, the model requires that photocarriers are associated with only a single p a r t i a l l y f i l l e d l e v e l i n thermal equilibrium and cannot account for light-induced charge r e d i s t r i b u t i o n among multiple l e v e l s . Several studies (13-15) have suggested the possible importance of the l a t t e r e f f e c t , based on observations of intensity-dependent absorption and the sublinear intensity-dependence of the response time i n many c r y s t a l s . 3

Spectroscopic

and Photorefractive Characterization

Optical Absorption. Figure 3 compares the o p t i c a l absorption spectra of undoped, Co-, Μη-, and Fe-doped BaTi0 c r y s t a l s grown i n a i r . Transmission spectra were obtained on a Perkin-Elmer Lambda 9 spectrophotometer modified for use with polarized l i g h t and were reduced to absorption c o e f f i c i e n t s by correction for Fresnel 3



404


300

400

500

600

700

800

900

WAVELENGTH (nm)

Figure 3. Wavelength dependence of the absorption coefficient (measured with light polarized perpendicular to the c-axis) of undoped and doped BaTi0 crystals. Concentrations refer to dopant atoms per BaTi0 formula unit in the melt. 3

3


26.

WECHSLER ET A L

405

Barium Titanate

r e f l e c t i o n . In Co-doped BaTi0 a strong, broad absorption band i s centered near 550 nm; the t a i l of t h i s peak overlaps the i n t r i n s i c band edge near 400 nm. We assign t h i s absorption to a charge transfer t r a n s i t i o n between the valence band (made up of oxygen 2p o r b i t a l s ) and l e v e l s associated with cobalt. Theoretical calculations (16,17) suggest that neither Co nor C o i n a complete octahedral environment has energy levels appropriate f o r a t r a n s i t i o n at t h i s wavelength. However, a Co *-V pair does have unoccupied mid-gap energy levels that could be responsible for t h i s absorption. The peak absorption i n Mn-doped BaTi0 appears to l i e at shorter wavelengths than i n BaTi0 :Co. In BaTi0 :Fe, a weak, broad absorption band i s centered near 600 nm, and there i s an apparent s h i f t of the absorption edge from about 400 to 410 nm. Reduction at 800°C with a 99% C0 /1% CO gas mixture induces a color change from reddish-brown to yellow i n both BaTi0 :Co and BaTi0 :Cr. 3

2+

3 +

3


0

3

3

3

2

3

3

Electron Paramagnetic Resonance. Electron paramagnetic resonance (EPR) spectroscopy i s a powerful and extremely s e n s i t i v e technique for characterizing the charge state and s i t e symmetry of various defects i n c r y s t a l s . Unfortunately, i t i s d i f f i c u l t to perform EPR measurements on properly oriented, single domain samples of BaTi0 at low temperatures due to the phase t r a n s i t i o n s at 10 and -90°C. One way to avoid t h i s d i f f i c u l t y i s to use powder specimens. We have obtained spectra of BaTi0 powders doped with a l l the t r a n s i t i o n metals and annealed under a wide range of oxygen pressure conditions. We have also studied the spectra of doped BaTi0 c r y s t a l s that have been ground into powder form. Although some information i s inevitably l o s t as a r e s u l t of the powder averaging, t h i s technique provides a r e l a t i v e l y rapid means of i d e n t i f y i n g the valence state of the dopants and monitoring the changes induced by oxidationreduction processing. Powder EPR spectra of BaTi0 :Mn powders are shown i n Figure 4. The spectrum i n Figure 4a was taken on a powder that was synthesized i n a i r at 1400°C and then cooled r a p i d l y below 800°C. Three prominent features are observed: 1) a sextet at low magnetic f i e l d (g - 4) with a hyperfine s p l i t t i n g constant |A| = 78.8 G that i s attributed to Mn ; 2) a sextet centered at g = 2.0015 with hyperfine s p l i t t i n g |A| = 87.8 G that i s attributed to Mn ; and 3) a strong resonance l i n e at g - 2 due to F e * and C r * impurities. Upon mild reduction (800°C, C0 ), the Mn * spectrum disappears and the Mn spectrum grows s u b s t a n t i a l l y (Figure 4b). This r e s u l t reveals the ease with which a valence change can be induced i n t h i s material by annealing i n a mildly reducing atmosphere. Valence state changes i n mildly reduced samples have also been observed i n BaTi0 :Co and BaTi0 :Cr. However, the spectra on BaTi0 :Fe show that F e remains predominant except under very reducing conditions (1200°C, 99% CO). 3

3

3

3

4+

2+

3

3

4

2+

2

3

3 +

3

3

Photorefractive Measurements. Photorefractive gain and response time measurements have been carried out on a variety of samples using the two-beam coupling technique (18). D i f f e r e n t samples of 50 and 100 ppm Co-doped c r y s t a l s were processed at 800°C under oxygen and C0-C0 gas mixtures with various oxygen p a r t i a l pressures. Samples of each dopant concentration were found to have gain vs. grating spacing curves that agreed with one another to within experimental uncertainty p r i o r to the oxidation-reduction treatments. Theoretical 2




406

Figure 4. X-band EPR spectra of BaTi0 :Mn powders. processed i n a i r . (b) Sample processed i n C 0 . 3

(a) Sample

2


26.

WECHSLER ET AL.

407

Barium Titanate

f i t s to the gain data using Equations 1-5 y i e l d estimates f o r the trap density, r e l a t i v e conductivity factor, and transport lengths. Gain data at 515 nm f o r as-grown samples of undoped, Mn-doped, and Co-doped BaTi0 are shown i n Figure 5. As-grown Co-doped c r y s t a l s have consistently high gains comparable to or better than those of any BaTi0 c r y s t a l s previously reported. The high gains appear to be attributable both to a large trap density (N = 6 χ 1 0 cm" i n both cobalt-doped c r y s t a l s versus 9 χ 1 0 cm" i n the undoped c r y s t a l and 2 χ 1 0 cm" i n the Mn-doped crystal) and to r e l a t i v e l y l i t t l e electron-hole competition (ξ = 0.74 and 0.60 i n 100 ppm and 50 ppm c r y s t a l s , r e s p e c t i v e l y ) . Both oxidized and reduced Co-doped c r y s t a l s have lower gains than as-grown samples, due to smaller trap densities and increased electron-hole competition. The photoconductivity i n as-grown c r y s t a l s i s hole-dominated. Co-doped c r y s t a l s reduced i n C0 are also hole-dominated, whereas c r y s t a l s reduced i n a 99% C0 /1% CO atmosphere are electron-dominated. Preliminary measurements suggest that Cr doping also leads to enhanced gain r e l a t i v e to undoped c r y s t a l s . However, Fe-doped c r y s t a l s have gains s i m i l a r to that of undoped BaTi0 . Response times of undoped and Co-doped c r y s t a l s f o r an incident i n t e n s i t y of 1 W/cm and a grating spacing of 0.7 μτο. are shown i n Table 1. No systematic trend i s apparent from these data, at least p a r t i a l l y due to experimental uncertainties such as sample heating and variable r e f l e c t i o n and absorption losses. Response times of asgrown and reduced Fe-, Μη-, and Cr-doped BaTi0 (18) range from 200 to 1200 ms under the same experimental conditions. Thus, i t i s clear that response times can vary considerably for c r y s t a l s with d i f f e r e n t dopants and oxidation states. Additional experiments are needed to achieve better control over t h i s key property. 3

3

1β

E

3

15


1β

3

3

2

2

3

2

3

Table 1.

2

Response Times (ms) at 1 W/cm

(A

g

= 0.7 /un)

Atmosphere Dopant Undoped 50 ppm Co 100 ppm Co

0

2

170

Air

C0

420 1400 730

800

2

1% CO 55 610

Measurements of self-pumped phase conjugate r e f l e c t i v i t y i n BaTi0 :Co i n the wavelength range from 633 to 930 nm are i n d i c a t i v e of a strong photorefractive response i n the near infrared. Crystals doped with Co at concentrations above 25 ppm have high r e f l e c t i v i t i e s when operated as self-pumped phase conjugate mirrors i n the t o t a l i n t e r n a l r e f l e c t i o n geometry, without the use of index matching f l u i d s . This e f f e c t appears to be reproducible i n Co-doped c r y s t a l s , i n contrast with undoped c r y s t a l s , where a strong infrared response i s observed i n only a limited number of samples. 3



408


—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—Γ -"Ν

-

0

/ \" /

*

\"

1

I

I

• Co, 100 ppm

I

I 1

I

I

I I I I I I 2 GRATING SPACING, pm

I

I 3

I

I

I

I

4

Figure 5. Photorefractive two-beam coupling gain coefficient of undoped and doped BaTi0 crystals. Curves are theoretical fits to the data. Experimental conditions: λ = 515 nm, I = 3-5 W/cm , beam ratio > 200, s-polarization, grating wave vector parallel to c-axis Concentrations refer to dopant atoms per BaTi0 formula unit in the melt. 3

2

3


26. WECHSLER ET AL.

409

Barium Titanate

Conclusions Efforts to optimize the photorefractive performance of BaTi0 rely heavily on understanding and controlling the photosensitive defects. Theoretical modeling suggests that the behavior can most readily be influenced by doping crystals with aliovalent ions and through oxidation-reduction processing to control the valence state of the dopant. Undoped and transition metal doped crystals have been grown by the top-seeded solution growth method and characterizd by optical absorption, electron paramagnetic resonance, and photorefractive twobeam coupling. Of the crystals studied, cobalt doping gives the highest photorefractive gain in the visible wavelength region and appears very promising for applications in the near infrared as well. Co, Cr, and Mn in BaTi0 can have their valence state altered by oxidation-reduction processing and are therefore the most interesting dopants from the point of view of modifying the photorefractive response. Substantial progress has been made toward achieving reproducibly high-gain crystals. Based on our understanding of the importance of defect properties in this material, further improvements in response time are likely to be achieved.


3

3

Literature Cited 1. Ashkin, Α.; Boyd, G.D.; Dziedzic, J.M.; Smith, R.G.; Ballman, A.A. Appl. Phys. Lett. 1966, 9, 72. 2. Chen, F.S. J. Appl. Phys. 1967, 38, 3418. 3. Strohkendl, F.M.; Jonathan, J.M.C.; Hellwarth, R.W. Opt. Lett. 1986, 11, 312. 4. Valley, G.C. J. Appl. Phys. 1986, 59, 3363. 5. Belruss, V.; Kalnajs, J . ; Linz, Α.; Folweiler, R.C. Mat. Res. Bull. 1971, 6, 899. 6. Godefroy, G.; Ormancey, G.; Jullien, P.; Lompre, P.; Ousi, W.; Semanou, Y. In Digest of Topical Meeting on Photorefractive Materials, Effects, and Devices; Optical Society of America: Washington, DC, 1988; p. 159. 7. Schunemann, P.G.; Pollak, T.M.; Yang, Y.; Teng, Y.-Y.; Wong, C. J. Opt. Soc. Amer. Β 1988, 5, 1702. 8. Rase, D.E.; Roy, R. J. Am. Ceram. Soc. 1955, 38, 102. 9. Kirby, K.W. M.S. Thesis, U.C.L.A., Los Angeles, 1988. 10. Sharma, R.K.; Chan, N.-H.; Smyth, D.M. J. Am. Ceram. Soc. 1981, 64, 448. 11. Wechsler, B.A.; Klein, M.B. J. Opt. Soc. Amer. Β 1988, 5, 1711. 12. Hagemann, H.-J. Ph.D. Thesis, Rheinisch-Westfalische Technische Hochschule, Aachen, Federal Republic of Germany, 1980. 13. Brost, G.A.; Motes, R.A.; Rotge, J.R. J. Opt. Soc. Amer. Β 1988, 5, 1879. 14. Holtmann, L. Phys. Stat. Sol. (a) 1989, 113, K89. 15. Mahgerefteh, D.; Feinberg, J. Phys. Rev. Lett. 1990, 64, 2195. 16. Michel-Calendini, F.M.; Moretti, P.; Godefroy, G. Ferroelectrics Letters 1983, 44, 257. 17. Michel-Calendini, F.M.; Moretti, P. Phys. Rev. Β 1983, 27, 763. 18. Rytz, D.; Wechsler, B.; Garrett, M.H.; Nelson, C.C. In Digest of Topical Meeting on Photorefractive Materials, Effects, and Devices II; Optical Society of America: Washington, DC, 1990; p. 2. RECEIVED August 13, 1990 In Materials for Nonlinear Optics; Marder, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

Defect Properties and the Photorefractive Effect in Barium Titanate

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