CONDUCTIVITY OP BaTiO3. PURE SINGLE CRYSTALS AND DOPED (Fe, OH) SINGLE CRYSTALS

HAL Id: jpa-00214975

https://hal.archives-ouvertes.fr/jpa-00214975

Submitted on 1 Jan 1972

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

CONDUCTIVITY OP BaTiO3. PURE SINGLE CRYSTALS AND DOPED (Fe, OH) SINGLE

CRYSTALS

G. Godefroy, M. Couson

To cite this version:

G. Godefroy, M. Couson. CONDUCTIVITY OP BaTiO3. PURE SINGLE CRYSTALS AND DOPED (Fe, OH) SINGLE CRYSTALS. Journal de Physique Colloques, 1972, 33 (C2), pp.C2-120-C2-122.

�10.1051/jphyscol:1972239�. �jpa-00214975�

M m e

GODEFROY

G.

AND

M.

COUSON

B.

CONDUCTIVITY OF BaTiO, . PURE SINGLE CRYSTALS AND DOPED (Fe, OH) SINGLE CRYSTALS

Abstract.

- When single crystals of barium titanate are placed under d. c. voltage, they are crossed by a constant and reproducible current after ageing (repeatedly applied voltages followed by earthing). Characteristics

i = f (V)

obtained with aged crystals are divided into

2

sections

:

for low voltages, ohmic law

;

for high voltages parabolic law. Constants

^y

and

a

which are deduced from these laws, increase exponentially with

1/T.

Activation energy

Wa

and injection energy

Wi

are calculated.

A

band scheme with two trap-levels may explain our experimental results

:

a shallow level traps some cathode-injected electrons while a deep level receives electrons from the valence band and ensures a hole-conductivity with low voltage. The shallow levels are more numerous than the deep levels

;

both are compensated by ionic impurities which in no way affect conduction.

Since the position of the trap-levels depends very little on dopage, the shallow levels are imputed to oxygen vacancies with a trapped electron

(F

centre) and deep levels to oxygen vacancies without electrons.

A great deal of research has been carried out on the cor:ductivity of single crystal barium titanate.

We only cite the most recent

:

that of Tredgold and his co-workers [I], [2], 131, [4], and that of Benguigui [5], [6],

[7],

[S]. T o understand better the role of the defects in electrical properties of barium titanate, we have resumed conductivity measurements and speci- fied conditions of current reproducibility, and the influence of doping material (Fe, OH) o n characte-

FIG. 1.

-Variation of current versus time (ohmic region) Pure single crystal Ti03Ba

: T = 27 OC, V = 75

V,

L = 2 x 10-4 m, S = 6 x 10-6 m2.

I Z

20 40 60 80 (hours)

FIG, 2.

-Variation of current versus time (injection region) Pure single crystal TiO3Ba

: T = 85 OC, V = 75 V,

L = 2 x 10-4 rn, S = 6 x 10-6

mz.

ristic curves

i =

f (V) at different temperatures. By adapting Lampert's theory of monoinjection [9] t o our particular case, it was possible to explain all our results.

I.

Technical

problems.

-

Single crystals are grown in accordance with Remeika's method (growth from meIted potassium fluoride)

;

they are doped with iron by adding ferrous oxide before growth

;

they are doped with oxhydrile by heating pure crystal in water vapour.

Conductivity measurements are classical but must be carried out in a primary vacuum to avoid the

FIG. 3.

- Characteristic current versus voltage

at

different temperatures. Single crystal, pure Ti03Ba

: L = 2 X 10-4

m,

S = 5

x

10-6

mz.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972239

CONDUCTIVITY OF BaTiO*. PURE SINGLE CRYSTALS AND DOPED

11. Experimental results. - 1 . CHARACTERISTICS

: ^{1 0 8} i =

f ( V ) .

-

Figure 3 shows characteristics for pure current increasing due to the presence of water. When a low voltage is applied t o a virgin crystal at a low

temperature, the current decreases to a limit current

i, _{l ~ b .}

(Fig. 1)

;

with a high voltage at high temperature, the

injection phenomenon becomes preponderant and the current presents a minimum, then reaches a limit value

i,

(Fig. 2). These limit currents increase when

^10'.

voltages and earthing are repeatedly applied. After many experiments, this limit current reaches a repro-

ducible

<(

super limit

B

current

i,.

The crystal is then 1c6.

said to be an <(aged crystal )>. Ageing is all the more rapid as temperature and voltage are increased, but a crystal aged under one particular set of temperature and voltage conditions remains aged under all other

^lo'

conditions. The results given below were obtained with aged crystals.

( T'C ) A % ( ~ . n i ' . ~ - ' )

'

FIG. 5.

-

Variation of constant ^cl versus temperature : curve 1 : pure Ti03Ba : W i = 0,76 eV ; curve 2 : Fe doped TiO3Ba : W i = 0,75 eV ; curve 3 : OH doped TiO3Ba : Wi = 0,71 eV.

barium titanate ; we obtain similar curves with Fe

1 0 ' ~ .

and OH doped crystals. With low voltage, the current

follows Ohm law and we are able to calculate conduc- tivity y. With high voltage, the current is proportional to V2 and we can calculate the constant

a =

J / V 2 where J is current density. The transition tension betwen these two laws is referred to as V,,.

10'" ^\

1

^{\ \ ,}

^{along 2.} TEMPERATURE with temperature

INFLUENCE.

for the - two Currents kinds increase of law (V and V2). Transition tension decreases as the tempe- rature increases. Figures 4 and

5

show that

y

and

a

TO-"

- vary exponentially with 1/T as follows

:

p

2,4 2,5 2,6 2,7 2,8 2,9 3,O 3,l 3 4

( + l o )

3 I

162 144

l i 7

liz 9'7 8'4 7'3 6'2

5b

^3'9

^y

^{= yo}

^exp -

^{- w a}

wi

kT a

=

a, exp -

-

( T°C)

kT

FIG. 4. - Variation of conductivity y versus temperature :

wa

⁼

activation energy w i

⁼

injection energy

curve 1 : pure Ti03Ba : W, = 0,81 eV ; Curve 2 : Fe doped

Ti03Ba : Wa = 0,81 eV; curve 3 : OH doped TiOBa : yo

and a, constants, characteristic of the material.

W, = 0,74 eV.

The following table gives our results : yo (ohm-', m-l)

a,

(A-2 T 2 )

- ^{w a}

(eV)

- Wi (ev)

- -

Pure Ti03Ba

Tc =

ll0OC Doped 0,2 % Fe

Ti03Ba

Tc =

88 OC Doped OH

Ti0,Ba

Tc

=

98 OC

C2-122 ^{M m e} GODEFROY G . AND M. COUSON B.

W, and W i are not identical and W i < W a

;

W, and Wi are virtually identical in pure Ti0,Ba and in Fe doped Ti0,Ba

;

we observe a slight decrease for W, and W i with OH doped crystal

;

this last-mentioned material is a better conductor than the two others.

111. Results

:

discussion. - Lampert presents cal- culations for monoinjection phenomena without traps, with deep traps, and with shallow traps. It is only in this last case that injected current with high voltages varies with temperature. If the impurity level, responsible for p conductivity under low vol- tage acts precisely as a shallow trap in injection pheno- mena, the transition tension does not vary with tempe- rature and W a

=

Wi.

We were consequently led to propose a model with two levels, one shallow E,,, and one deeper E,,.

We call

:

N,,

:

density traps for E,,, Nt2

: -

- El,,

N ,

:

- Ec (conduction band),

nt2

=

Ni,

1 + ^{exp E,,}

_kT

^{- EF}

We know the electrical charge of the crystal is due to injected electrons which have a mean density G i under voltage V

_:

- 3

&V

E

dielectric constant, q elementary charge, L thickness of sample.

Traps Ntl and N,, are compensated by ionic impu- rities

;

so we have the very simple equation (5)

:

n + ntl + ^{n,, -}

^{p =} -

^{ni .}

⁽⁵⁾

SO we may calculate exactly n, nil, n,,,

p,

E, for each T and V.

If we suppose N,, < N,,, we may find the following approximate formulas

:

-

ni - ^{0 p}

^%

ⁿ

^p

- N , N,, exp Ev - Et, 2 kT N"

:

- -

E, (valence band).

Y

= qPp N v

Nt2 exp E"

-

Et,

It is possible to know for each temperature T and 2 kT

voltage V

: -

ii

%

n n,, - ^{N,, n,, -- ni n} - ⁱⁱ

⁸

n

:

electron density in conduction band,

p

:

hole density in valence band, with

8-

Nc exp-- E l 1 - E c

n,, :

electron density on E,, level, Nt, kT

nti

:

electron density on level,

EF

:

quasi-Fermi level.

We have Fermi-Dirac equations

Nc Having compared this with our experimental results

n = ^-

(I) we are in a position to state that

:

E, - EF

1 + exp

----

k7' wa

⁼

^{E,, - Ev}

2 wi

⁼

Ec - E , , . P

=

Nv

(2) This enables us to construct a band scheme

;

we EF - Ev

1 + exp

----

note that it is affected very little by the type of doping kT material used, and so we are led to conclude that the trap-levels are those of the defects common to all ntl

=

- ^{Nt1 (3)} the materials

:

oxygen vacancies with a trapped

1 + exp

^{E 1 l}

- E~ electron, or F centre, for shallow trap E,,, oxygen

IcT

vacancies without electron for deep trap E,,.

References

[I]

Cox

(G. A.)

and

TREDGOLD (R. H.), Phys. Letter [5] BENGUIGUI (L.), C. R. Acad. Sci. Paris, 1966,262,642.

Netherl., 1963,4,4, 199.

[2]

Cox

(G. A.)

and

TREDGOLD (R. H.), Brit. J. Appl. [61 BENGUIGUI (L.1, Onde Electriq~le, 1969, 49, 10.

Phys., 1965, 16, 427.

131

cox

^{(G. A.)}

and

TREDG~LD (R. H.), Brit, J . ~ ~ [71 ~BENGUIGUI l . (L.), Phys Letters, 1967, 25, A 2,117.

Phys., 1967,18,37. [8] BENGUIGUI (L.), Sol. Stat. Comm., 1969, 7 , 1245.

[4] TREDGOLD (R.

H.), BRANWOOD (A.),

HUGHES (0.

H.),

HURD (J. D.), PWC. Phys. Soc., 1962, 79, 1161. [9] LAMPERT (M. A.),

Current Injection

in

Solids

(1970).