A.c. hopping conduction in Mn-Co-Ni-Cu complex oxide semiconductors with spinel structure

1. Phys. Chtm. Solids Vol. 41. pp. 1253-1260 Pqamoa Press Lid., 1980. Printed in Great Britain

A.c. HOPPING CONDUCTION IN Mn-Co-Ni-Cu COMPLEX OXIDE SEMICONDUCTORS WITH SPINEL STRUCTURE MINORU Ibaraki Electrical

Communication

Laboratory,

SUZUKI

Nippon Telegraph and Telephone Public Corporation, Ibaraki, 319-l I, Japan

(Received 20 July 1979; accepted 8 February

162 Tokai,

1980)

Abstract-The radio-frequency (RF) conductivities of spinel-type Mn-Co-Ni-Cu complex oxide semiconductors were investigated at low temperatures for ceramic samples with various Cu contents. The a.c. conductivities show large frequency dependences, which are ascribed to hopping of localized carriers between Mn ions at oxygen octahedral sites. When the Cu content is increased, the conductivity increases markedly and its frequency dependence is weakened. The hopping is considered to be a random walk process because the hopping sites are randomly distributed at the spine1 oxygen octahedral sites. In this situation, the random walk theory in disordered systems developed by Scher and Lax is applicable, and the experimental results agree with this theory very well. The reduced frequency dependence is also successfully explained in this way. The Cu ions in these complex oxides lead to an increase in the localized carrier transition probability, and consequently lead to an increase in conductivity and a reduction in the frequency dependence of the a.c. conductivity.

INTRODUCTION

Transition metal oxide semiconductors with the spine1 structure are known to be low mobility materials. Their electrical conduction is usually considered to be due to charge transfer between octahedral cations by hopping. Complex oxides of M&o-Ni-Cu form a cubic spine1 lattice structure in a certain composition range, and are characterized by this conduction mechanism. Although they are quite useful as materials for therm&em or sensors, the mechanism of electrical conduction has been investigated by only a few workers [ l-41, and discussion has been confined to the valency distribution of the several sorts of cations which occupy the oxygen octahedral sites. In the present paper, we attempt to explain the conduction mechanism of these materials by regarding the spine1 oxygen octahedral sites as hopping sites. In Mn-Co-Ni complex oxide semiconductors with the cubic spinel-type lattice structure, the octahedral sites (B sites) are predominantly occupied by Mn and Ni ions, and the tetrahedral sites (A sites) by the other ions. At low temperatures, Ni ions at B sites are not available as hopping sites, so carriers are mainly localized to the Mn ions, which act as hopping sites. The localized carriers hop between randomly distributed Mn ions, since Ni ions are distributed randomly at B sites. In this situation, the a.c. conductivity of these materials shows a typical dependence upon frequency and temperature, which is recently described by Scher and Lax[S] (hereafter SL) in their stochastic theory of the random hopping process. Therefore, in order to consider the hopping process in these materials, the temperature and frequency dependence of the a.c. conductivities were measured, and the results were successfully fitted to the SL theory. Copper ions in these oxide semiconductors increase the conductivity by a factor of more than 102, and this implies variations in hopping site concentration, hopping distance and hopping probability. Several samples with different electrical conductivities were prepared with varying Cu content. The frequency and temperature

dependence of the a.c. conductivity in each sample showed fairly good agreement with the SL theory.

EXPERIMENTAL

The Mn-Co-Ni complex oxide samples were prepared by prefiring an intimate mixture of 99.9% pure Mns04, NiO and Co0 at 950°C for 2 hr in air. After milling the products obtained, they were pressed into pellets about I mm thick and 12 mm in diameter. The pellets were fired at 1200°C for 4 hr in air, and then cooled in a furnace. The samples containing Cu were prepared by the same method as above with the addition of 99.9% pure CuO to the mixture. The Cu containing samples were sintered at 1050-l25o”C, and annealed at 950°C in order to give completely single phase material, following the method of Azaroff [l2]. The sintering conditions and the compositions are listed in Table I. The sintered samples were confirmed to have the cubic spine1 structure by X-ray diffraction. The density of the samples was about 8693% of the X-ray density. Samples used for measurements were disks about I I mm in diameter and 0.2-l mm thick. The electricalcontacts were Au films or Pd-Ag paste. For thin samples, Au was evaporated on to both sides; for thick ones, Pd-Ag electrodes were formed by heating at 850°C in air for 30 min. Good ohmic contacts were obtained in both cases. The dc.. conductivity was measured by the van der Pauw method. Samples for these measurements were cut into a four-leaf-clover shape. The RF conductivity was obtained by measuring the RF impedance of samples using a vector impedance meter (YHP 4815A) in the frequency range 500 kHz to IOOMHz. Samples were loaded into a coaxial type sample holder with a SOohm characteristic impedance similar to those described elsewhere[6,7]. This sample holder was embedded in a liquid nitrogen cryostat and the sample temperature controlled from I40 K up to room temperature. The sample

1253

1254

MINORU

Table

1. Compositions

and sintering

conditions

cu content

Sample NEllW

complex

oxide semiconductors Sintering Conditions

(at.0)

1-11-2

0

Cul-S-3

1

cuz-9-1

3

cu3-10-l

5

Cu4-10-2

10

cua-8-l

15

cu9-7-1

20

?

. SC00 . tTNiO. 6

C"0.09(""1 . SC00 . gNiO . 6)O . 97 '4 CU0.15(M"1.8C00.6Ni0

'4

CU0.45(M"1 .SC00 .gNiO .6)O .85 '4 C"0.6("nl .8'0 .gNiO .6)O .8 '4

I

I

. 6)O . 95

C"0.3(Mnl . SC00 . gNiO . 6)O . 90 '4

The d.c. conductivities of Mn-Co-Ni-Cu complex oxide semiconductors containing various amounts of Cu are shown in Fig. 1. In order to achieve the largest conductivity and to obtain a single spine1 phase. the sintering temperature was varied according to the Cu content as shown in Table 1. The color of specimens was black, becoming tinged with brown with increasing Cu content. The d.c. conductivity increases up to about 10-l mholcm when the Cu content reaches 25% of the total cation concentration. This value is larger by a factor of 102than that of samples without Cu. Specimens with a Cu content of more than 25% were also sintered at 1050°C in air, but a single spine1 phase could not be obtained, and the conductivity was reduced. The conduction type of this series of oxide semiconductors was determined to be p-type from the polarity of the thermoelectric force.

2

12oooc

'4

CU0.03'M"1 .SC00 .gNiO .6)O .99 '4

RESULTS

I

4h

1250°C lh

950°C 12h

125O'C lh

95OT

1250°C lh

950°C 12h

12OO'C lh

95O'C 12h

115OOC lh

950-C 12h

llOO°C lh

950°C 12h

12h

In Fig. 2, the RF conductivity vs 1000/T is shown at various frequencies for sample l-1 l-2 (Cu = 0%). The frequency dispersion of the RF conductivity in Fig. 2 can obviously be attributed to the a.c. hopping conduction of the localized carriers, namely positive holes. This behavior of the RF conductivity is analogous to that observed in a single crystal of NiO by Aiken and Jordan[8], in n-type Si by Pollak and Geballe[9], in Ge by Gollin[ 101and in VO, by Palmier et al. [ I I]. Generally in ceramic materials, the difference in dielectric constant and conductivity between grains and grain boundaries also causes RF conductivity frequency dispersion. However, in our experiments, dispersion due to grain boundaries was not observed. In other speci-

I

I

IO’t1

1

Slntered

(It

i 512

Cu I. D.c. various

conductivities Cu contents

I

I

I

012

Fig. with

for Mn-C&Ni-Cu

Composition

holder was connected to the measuring equipment by a semi-rigid 50 ohm coaxial cable.

I

SUZUKI

5102

5

Mm%)

of M&o-Ni-Cu complex oxides (at room temperature, Mn-Co-Ni = 60:20:20).

4

5

6

IOW/T(K~‘)

Fig. 2. Temperature dependence of a.c. conductivity Ni complex oxide (sample l-l I-2).

for Mn-Co-

As. hopping conduction in h&Co-Ni-Cu

complex oxide semiconductors

1255

with spine1 structure

1

.

‘1 :’

0.5MH2

IO”

I

1

> I 6

5

4

1000/T

(K-l)

Fig. 3. Temperature dependence of a.c. conductivity for Mn-CoNi-Cu (Cu = 5%) complex oxide (sample CL&I&I).

mens whose grain boundaries were forced to have moderately higher resistivity than the bulk grains, such an effect was observed as well as dispersion due to a.c. hopping conduction, but the frequency and temperature dependence were quite different in their behavior. In Figs. 3-5, RF conductivities vs 1000/T are shown for samples with Cu contents of 5, 10 and 15%, respectively. The frequency dispersion is reduced with increasing Cu content. In Fig. 6, RF conductivities at 100MHz vs IO/T are shown for samples with various Cu con-

Fig. 5. Temperature dependence of a.c. conductivity for Mn-CoNi-Cu (Cu = 15%) complex oxide (sampleCUE&~).

tents. For samples with a Cu content of no more than 5%, the effective activation energies of the 100MHz conductivities at temperatures below 180K are very small (O.O23eV),but those of the high Cu content samples are rather large (about 0.18 eV), and hence nearly equal to the activation energies of the d.c. conductivities. The RF conductivities of all samples range roughly between lOa and IO-‘mholcm at room temperature, but they have a tendency to have similar values at low temperatures. DISCUSSION

In order to discuss the hopping conduction or the hopping process, it is necessary to know the cation

1 Cu4-IO-2

I 4

5

6

7

4

a

II/I,.,,, 5

,, 6

!

7

IOOO/T(K.‘)

Fig. 4. Temperature dependence of a.c. conductivity for Mn-CoNi-Cu (Cu = 10%) complex oxide (sample Cub10-2).

Fig. 6. Temperature dependence of IOOMHz conductivity for Mn-Co-Ni-Cu complex oxide with various Cu contents.

MINORUSUZUKI

1256 distributions.

From the work of Azaroff [ 121on the cation and valency distribution of the Mn-Co-Ni complex oxide system, the following cation distribution is derived for sample l-l l-2 (Cu = 0%). Co~‘jMn~;[Mn:;Ni~“sMn~+21042-

where the B site cations are indicated by square brackets. When Mn2+ ions are included in small amounts, the cation distribution is Co~~Mn~+sMn,Z’[Ni~+sMn:+2_ZSMn~:’2+s]0,Zand when y at % Cu is included in the composition, the cation and valency distribution is considered to be Cu:,,-,,Co~+,,-,,Mn~~,-~,+~~ [Ni~ZI-,,Cu::Mn:I;,,-~,-2xyMn~~,,-~,+~~10~2from the work of Dreiling[l3] and Brabers[l4], where x (0 < x < I) is the fraction of B site Cu ions. For this complex oxide with the spine1 structure, hopping sites are considered to be cations in octahedral coordination, from analogy to ferrites. Figure 7 shows the hopping sites (B sites) in the spine1 structure, which form a path of charge transfer. Carriers (holes) are localized at Mn ions at B sites and charge transfer is executed between the nearest neighbour Mn ions by the process Mn” t Mri” e Mn4’ t Mn”. When Cu is included, the process also includes Mn3’ + Cu2+ t Mn”+ 2 Mn4’ t Cu’ t Mn4’ Z? Mn4+t Cu*’ t Mn3+.

checked by the ws rule. With regard to ra.,.(Rea(w)ud.C ), s was in the range 0.75-0.85 for sample l-l t-2 at low temperature, and no more than 0.8 for samples with up to 5% Cu. For samples containing more than 5% Cu, Redo) and 0d.c. were almost equal, and a,, could not be discriminated clearly. The behavior of a,., , which follows the w’ rule, may be explained by the pair model, but only for the samples without Cu at low temperatures. For samples containing Cu, the frequency dependence of U(O) cannot be explained by the pair model. The condition for adopting the pair model is that only hopping site pairs are available, and that a carrier is confined to a pair and cannot hop among three or more hopping sites. For this reason, the pair model cannot be used for these results because at any arbitrary hopping site (Mn ions at B sites), there is a large probability (more than 0.5) of a neighboring 19 site also being a hopping site. A similar situation was found in NiO single crystals[b]. Since the B sites are occupied mainly by Mn, Ni and Cu ions and the carriers are localized at Mn ions, the hopping sites are considered to be distributed randomly at the B sites. In such cases, when the carriers are hopping between randomly distributed sites, the a.c. electrical conduction (and d.c. conduction) can be treated by the random walk theory in disordered systems developed by SL, and the frequency dependence of u(w) of these materials can be interpreted in terms of the SL theory. In the SL theory, a generalized dimensionless diffusion constant D(R) and dimensionless frequency 0, which are defined by the following equations, are shown to lie on a universal curve. This curve represents both the frequency and the temperature dependence of the a.c. hopping conductivities. The defining equations are D(R) = ATa(

W exp (-A/kT)

R = w/W exp (-AlkT) The Cu ions participate in the transfer process in the form of instantaneous Cu’ quasi-stable state at the B site. Therefore, Mn and Cu ions at these sites function as hopping sites, while Ni ions interrupt the chain of hopping sites, since the third ionization energy of Ni is relatively high. Experimental data on a.c. conductivity were first

0-O

ion

0-B

site

ion l:r:~-A site ion

Fig. 7. B sites in spinel-typestructure, showing chains of hopping sites.

(1) (2)

where W is the transition probability, A is the activation energy of impurity conduction and A is a constant. The D(n) - 0 plots for samples with various Cu contents are shown in Figs. 8(a)-(d). It is found that the D(n)- fl plots lie on a universal curve for all samples at every temperature and every frequency. This is an essential of the SL theory and it follows that a.c. hopping conduction in Mn-Co-Ni-Cu complex oxide semiconductors is in good agreement with the SL theory, especially at high Cu content. With low Cu content, there is a deviation from the universal curve calculated by SL for n-type Si. For this reason, it is supposed that the localized electrons hop only between nearest neighbour B sites when the Cu content is low, but in silicon electrons can hop over a rather long range. In n-type Si at high impurity concentration, the activation energy A is dependent on the spatial separation of donors and this causes deviations at high w as discussed by SL. However, in complex oxide systems, the separation between hopping sites is almost equal, and the activation energy A is nearly constant. Therefore, the SL theory works very well in this complex oxide, especially at high Cu contents.

complex oxide semiconductors

AX. hopping conduction in Mn-Co-Ni-Cu

with spine1 structure

a A = 0 28

c' 2

0

221

+

23,

K

:

"

257

K

0

271

K

-

n231K

16'F

s 5 5

K

la”

c^

i

0'

l"

ILT’ DIMENSIONLESS

ILT’

-5 FREQ”E&

.

1‘4K

0

155K

~~o15~~17,~~05F~057~~

I

165K

A = 0 22 l "

.

175K

cu3-loId

t

#m1sm

to*

;,u‘-

llul

,,,d

I

1,1,,

I

IO-” I@’ 10’ IO+ DIMENSIONLESS FR.EQUENCY 5-2

0152K 1

I

I

b

0

E

I 6’

R

Cuo,5Mn,,53Nio51 Coo5&

1

1

,L,,,,

,

IO-’

d

A'O2OeV

l 161K

Fig. 8. D(R)-fl plots for Mn-Co-Ni-Cu complex oxides: (a) sample I-1 l-2, (b) sample Cu3-IO-l, (c) sample Cu4-10-2 (d) sample C&8-l. A’s were calculated from the d.c. conductivities at about WK. The broken curve in (c) is the theoretical curve calculated by SL for n-type silicon (1) = 4 x IO-‘). In each plot, w’s were chosen so as to fit the theoretical curve. A typical value of W is 2.8 x IP set-’ for C&IO-Z.

1257

1258

MIN~RUSUZUKI

ILI,C50NTEN:qat cu

X)

15

Fig. 9. Variation of transition frequency 0, and transition probability W of localized carriers with Cu content.

When the hopping site concentration is almost equal for all samples, and changes in the effective Bohr radius of the localized electrons are small, one universal curve is obtained for the series of Mn-Co-Ni-Cu complex oxide samples. Thus, if we substitute an appropriate value into W for each sample, the D(n) - 0 curves can be fitted to one universal curve for all samples. Under these conditions, the transition probability of the localized carriers can be estimated by choosing an appropriate value for W in eqns (I) and (2) so as to fit the D(R)- 0 plots to the universal curve. The variation in transition probabilities of these oxide semiconductors compared with that of the sample without Cu ions is shown in Fig. 9. The transition probability increases with the Cu content, and this implies that the carriers can hop over rather long ranges in these oxide semiconductors because of the Cu ions.

However in actual fact, Cu incorporation at B sites increases the hopping site density ND to a small extent equivalent to the decrease amount in Ni ions, since Mn and Ni ions are both substituted by Cu ions. Also, the effective Bohr radius of electrons at hopping sites varies according to the fraction of Cu ions at B sites, because electrons can hop between Mn3+ levels and/or Cu’ levels, and the Bohr radius of electrons at each level may be different. In the case of complex oxides where electrons are localized around each cation core, the effective Bohr radius can be approximated by a cation ionic radius multiplied by a factor less than unity. This factor means that the Bohr radius is less than the ionic radius because there are almost no electrons outside a sphere with the ionic radius. We tentatively take a value of 0.75 for the factor; this does not affect the relative behavior of D(n) among samples with different compositions as a whole. The Ionic radii of Cu’ and Mn3+ are O.%A and 0.65& respectively[ltI], and therefore the average ionic radius of the hopping sites increases substantially by Cu incorporation. Regarding an ensemble average for the ionic radius multiplied by a factor (0.75) as an effective Bohr radius (=2&), and assuming that the hopping site density ND is the sum for Mn and Cu ions at B sites, we can estimate 71= 4nNr,Rd3, which uniquely defines the universal curve D(n)-flby the SL theory. Calculated values for ND, Rd and 77are listed in Table 2 for various Cu contents. The universal curves calculated with the t)‘s in Table 2 are shown in Fig. IO, together with the experimental data for all samples with fixed W. The frequency R,( = exp (-T-“~)) characterizing the transition of D(R)to d.c. (R = 0) in the SL theory is also indicated in Fig. IO for each value of 17.Small increases of 9 depress the Rdependence of D(n),and consequently the o-depen-

Table 2. Calculated values for q and Q

sample name

l-11-2

lattice,conStant (A)

averaged ion radius 2Rd/f

cu3-10-Z

Cu4-10-2

Cu4-10-2

8.39

8.37

8.35

8.33

0.650

0.671

0.692

0.712

70.1

71.6

73.1

74.6

3.46~10-~

3.90x10-3

4.41x10-3

4.95x1o-3

4.12~10~~

1.12x10-7

2.91x10-7

6.73X1O-7

(A, Fraction of B site Mn and CU ion (%) effective hoppin site density ND (m-3)

q=4nNDRd

Rc

3

A.c. hopping conduction in M&o-Ni-Cu

complexoxide semiconductors with spine1 structure

Fig. 10. Calculated universal curves for the n’s in Table 2. The corresponding transition frequencies indicated. Experimental data are replotted from Fig. 8 with W = 2.3 x 1020 set-‘.

1259

are also

dence of a(o) is markedly depressed. Reduction of A enhances this tendency. Thus, the markedly depressed o-dependence of u(o) caused by Cu incorporation can be successfully explained by the SL theory. For the samples with Cu contents of more than IO%, the experimental results and theoretical curves from the SL theory show good agreement, while there is a deviation for samples with less than 5%. This deviation from the theoretical curve at low Cu contents is attributed to the localization of carriers around a few hopping sites. On the other hand, at high Cu contents (IO%), hops can occur over large distances; this can be adequately fitted to the random walk model of SL. When 71is fixed, the transition probability W must be chosen for each sample. Therefore, W is found to increase with Cu content (Fig. 9). For fixed W,q changes slowly with Cu content, and accordingly the transition frequency 0, increases markedly. The change of R, is shown in Fig. 9 together with that of W; both behave quite similarly as a function of Cu content. Thus in either case SL theory is consistent with Cu substitution acting to facilitate electron hopping. The mobility of the ferrites is no more than lo-’ cm2/V sec[lS], and that of NiO is several times IO-’ cm2/Vsec[16]. On the other hand, the mobility of

Cu20 is 50-100 cm’/V set [ 171,very large compared with other transition metal oxides. This indicates that electron transfer may occur frequently. The Cu ions substituted at spine1 B sites may also have similar effects. The electron wavefunction of the Cu ion may expand more broadly than those of the other transition metal ions so that electron transfer between Cu and Mn ions may occur more frequently. The potential change due to Cu incorporation is schematically represented based on the above discussion in Fig. I 1, where the solid line indicates the potential without Cu, and the broken line that with Cu incorporation. The barrier height for electron transfer is lowered because of the extended electron wavefunction at the Cu’ level. This reflects the slight decrease in activation energy of the d.c. conductivity when Cu is incorporated. Consequently, the hopping probability of the charge transfer increases with increasing Cu content. Transfers involving two or more Cu ions may also occur, and carriers can hop larger distances at a time.

Fig. I I. Schematic representation of Mn site and Cu site potential, where the solid line indicates the potential in the absence of Cu and the broken line indicates the potential due to Cu in-

Acknorvledgemenfs-The author wishes to express his gratitude to Drs. S. Fushimi, A. Yamaji and K. Koga for their continued encouragement, and the Drs. T. Inamura and T. Murakami for their valuable comments.

corporation. PC.9 Vol.41.No. II-C

CONCLUSION

In Mn-Co-Ni-Cu complex oxide semiconductors with the cubic spine1 structure, hopping conduction of positive holes localized at Mn ions is dominant at temperatures below 250K. This hopping process causes a strong frequency dependence of the ac. conductivity at frequencies higher than about 10 MHz. When the Cu content increases, the frequency dependence is substantially reduced. The frequency and temperature dependence of the ac. conductivity agrees with the SL theory, and the markedly depressed o-dependence of u(o) following Cu incorporation can also be successfully explained by the SL theory. It is concluded that the addition of Cu ions increases the transition probability of localized carriers and that hops can occur larger distances as the Cu content increases.

1260

MINORUSUZUKI REFERENCES

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