Oxidation of Metals, Vol. 39, Nos. 5/6, 1993

Oxidation of Copper and Electronic Transport in Copper Oxides*

J.-H. Parkt and K. Natesant

Received February 19, 1992, January 22, 1993

Oxidation of copper and electronic transport in thermally-grown large-grain poIycrystals of nonstoichiometric copper oxides were studied at elevated tem- peratures. Thermogravimetric copper oxidation was studied in air and oxygen at temperatures between 350 and IO00~ From the temperature dependence of the oxidation rates, three different processes can be identified for the oxida- tion of copper: bulk diffusion, grain-boundary diffusion, and smface control with whisker growth; these occur at high, intermediate, and low temperatures, respectively. Electrical-conductivity measurements as a function of tempera- ture (350-1134~ and oxygen partial pressure (lO-S-l.Oatm) indicate intrinsic electronic conduction in CuO over the entire range of conditions. Electronic behavior of nonstoichiometric Cu20 indicates that the charge defects are doubly-ionized oxygen interstitials and holes. The calculated enthalpy of formation of oxygen (AHo2) and hole-conduction energy (EH) at constant composition for nonstoichiometric Cu20 are 2.0:1:0.2 e V and O. 82 • 0.02 e V, respectively.

KEY WORDS: Cu oxidation; electrical conductivity; defect mechanism; defect mobility; nonstoichiometry; copper oxides.

INTRODUCTION

Defects and Transport in Copper Oxides

Two copper oxides, (Cu20 and CuO) are stable in the copper-oxygen sys- tem. Cuprous oxide, Cu20, is known to be a metal-deficient, p-type semicon-

*This work was supported by the U.S. Department of Energy, under Contract W-31-109-Eng- 38.

"~Materials and Components Technology Division, Argonne National Laboratory, Argonne, Illinois 60439.

411

0030-770X/93/0600-0411507.00/0 �9 1993 Plenum Publishing Corporation

412 Park and Natesan

ductor with cation vacancies and electron holes as the primary defects] The deviation from stoichiometry has been studied as a function of temperature and oxygen partial pressure by chemical analysis of quenched samples, 2 by thermogravimetry, 3-5 and by high-temperature solid-state coulometric titration. 6 The data are inconsistent. These studies generally conclude that Cu20 is metal-deficient and that the prevailing atomic defects are neutral copper vacancies. However, on the basis of previous studies, several different models were proposed for the defect structure of nonstoichiometric Cu20. These include neutral 3-5 (depicted in Eqs. (1) and (4) of Table I), singly- ionized copper vacancies z' 7 (Eq. 5), singly-ionized oxygen interstitials 8 (Eq. 2), and doubly-ionized oxygen interstitials (Eq. 3). Also shown in Table I is the oxygen-partial-pressure (pO2) dependence of the electrical conductivity of Cu20 with various defects.

The electrical conductivity (~r) of Cu20 has been measured over a wide range of temperatures and pO2 levels. 7'9-13 Maluenda et al. 14 measured electri- cal conductivity of Cu20 over the temperature range 700-1100~ at a pO2 corresponding to the Cu20 phase, down to 10 -6 atm. According to their results, the slope (dlog er/dlog pO2) is greater than 1/8, which is not expected if Vb, is the only charged atomic defect. To account for the observed pO2 dependence of ~, Maluenda et al.14 Suggest that a defect pair ' x (VcuVcu) may become important with increasing pO> However, Peterson and Wiley 13 developed the exact expression for electrical conductivity, which includes the coupling of singly-ionized copper vacancies, Vb,, and oxygen interstitials, O~. They made two assumptions in analyzing their data: the mobility of the hole,/-0,, was assumed to be independent of temperature; and the mobilities of Vbu and V~u were assumed to be equal. The enthalpy of formation values for the defects obtained from electrical-conductivity measurements appear to be a function of both temperature and partial pressure, 7 and the values are not consistent with those deduced fi'om thermogravimetric measurements. 3 5

Table I. Possible Defects in Nonstoichiometric Cu20

Expected Point defect Eq. Exponent defect Charge reaction no. n ~

Oio 0 1/202 (g) = Oio 1 0 0 i, -- I 1/202 ( g ) = O r + h " 2 1/4 0~,, - 2 1/202 (g) = Or, + 2h' 3 1/6 gcu" 0 1/202 (g) = 2 Vcu.~ + 0o~ 4 0 VCu, - 1 1/202 (g) - 2 VCu, + 0 o * + 2 h - 5 1/8

Vcu. - 2 1/202 (g) = Vcu,, + 0o~ + 2h" 6 1/6

Intrinsic e' and h- O = e ' + h �9 7 0

�9 lln aExponents, n, m ~ ~ pO 2 (pO2 dependence of electrical conductivity).

Copper Oxides 413

Because the deviation from stoichiometry in Cu20 is rather small, quan- titative agreement among different studies is only fair. Peterson and Wiley ~3 measured the temperature and pO2 dependence of cation-tracer diffusion in Cu20. The results suggested that both neutral and singly-charged copper vacancies contribute mainly to cation self-diffusion. However, a defect model 13 involving both neutral and singly-charged copper vacancies, holes, and singly-charged oxygen-interstitial ions was developed and compared with the tracer-diffusion data, the electrical-conductivity data obtained by Maluenda e t al . , ~4 and the stoichiometry data of O'Keefe et al. ~5 The model (see, for example, Eq. 5 in Table I) suggests that majority of the neutral species in Cu20 are neutral copper vacancies and therefore may not provide a good explanation for electronic transport.

Measurements of the chemical-diffusion coefficient in Cu20 by electrical conductivity were reported by Maluenda e t al. ~4 These authors interpret diffusion in terms of neutral copper vacancies that are very mobile. Tracer diffusion of the stable isotope ~SO has shown that interstitial oxygen ions are the predominant atomic defect in the oxygen sublattice. ~s However, the pO2 dependence of stoichiometries and electrical conductivity of nonstoichi- ometric Cu20 are not consistent unless one considers a partial ionization of an extremely minor portion of the cation vacancies. In the present study, the temperature and pO2 dependence of electrical conductivity have been reevaluated in terms of intrinsic and nonstoichiometric defects in Cu20. Thermodynamic measurements of Cu20 were conducted to establish the defect structures of nonstoichiometric Cu20.

Data on nonstoichiometry of CuO are not available. The conductivity of CuO is not dependent on oxygen activity at high temperature because of significant intrinsic-electronic excitation. Intrinsic ionization predominates, i.e., 0 = e'+ h., and if one neglects the temperature dependence of electronic charge carriers, the activation energy of 1.1 eV suggests a band gap of 2.2 eV in the temperature range of 700-900~ transport studies on CuO are incom- plete. Physical parameters for Cu20 and CuO are given in Table II. 16

Oxidation of Copper

Multiphase scales of Cu20 and CuO form on Cu oxidized in oxygen or air at high temperatures, depending on the thermodynamic stability of the oxides.3'~7'lS The parabolic rate constant, kp, for the oxidation of copper depends on pO~/4 when only Cu20 forms. Mass transport mainly involves neutral copper vacancies. 19-22 This implies that the majority of the copper vacancies in the outer layer of the scale have zero effective charges. The formation of neutral copper vacancies, V~u, was considered in Eq. (3). According to Mrowec and Stoklosa, studies on the oxidation of copper as

414 Park and Natesan

Table 1I, Physical Parameters of CuzO and CuO

Parameter CuO 2 Cue

Formula weight 143.08 79.54 Melting point (~ 1235 1326 Crystal system Cubic Monoclinic Space group Pn3m(224) C2/C Z ~ 2 4 Lattice parameters (A) ao=4.2696• ao=4.684•

bo = 3.425 • 0.005' Co = 5.129 4- 0.005 (flo = 99.47 4- 0.17 ~ )

Cell volume (10 24 cm 3) 77,8334-0.055 81.164-0.17 Molar volume (cm 3) 23.437 4- 0.016 12.02 4- 0.03 X-ray density (g/cm 3) 6.1047 • 0.0043 6,509 • 0.014

"Z=number of gram formula weight per unit cell (source: Ref. 16).

a function of oxygen partial pressures, at high pO2 the scale consists of Cu20 and CuO at the scale/gas interface, and the parabolic rate constant is independent of pO2. 22 However, to verify this pO2 independence of oxida- tion, high-purity specimens ( ~ 99.9999% Cu) are needed because impurities can have a significant effect on defect concentration in nonstoichiometric Cu20. The existence of even a very thin layer of a compound of a higher- metal-oxidation state on the scale surface can alter the dependence of the reaction rate on oxidant pressure. Recently, Onay and Rapp 23 per formed/n situ oxidation of copper at 10 -4 a tm and 300~ Their results indicate that the multiphase, multilayer scales form by dissociation of the Cu20 scale, which loses contact with the copper substrate upon thickening and also leads to microchannels and formation of oxygen-rich CuO in Cu20 scales. Kaufman and Hawkins 24 performed optical-luminescence measurements on thin films of Cu20 on copper. They suggest that the rate of copper oxidation is limited by the diffusion of copper vacancies.

Mechanisms whereby CuO whiskers form during oxidation of copper may involve chemical-vapor transport or condensat ion/evaporat ion, as well as short-circuit diffusion up the center of the whiskerY Rapp and Raynaud 26 have proposed that the growth mechanisms for pyramids and pits are related to those of whiskers.

EXPERIMENTAL PROCEDURES

Sample Preparation

Copper-foil samples (99.999% Cu) were used for the oxidation tests. Thin copper foil (2.0 • 10.0 • 0.10 or 0.01 ram) was used to grow copper-

Copper Oxides 415

oxide samples for electrical-conductivity measurements, and large-grain polycrystals of Cu20 (99.999%) with a size of 3.0 x 7.5 x 1.5 mm were used in four-probe electrical conductivity measurements, similar to our previous w o r k s Platinum wires were used as electrical leads.

Oxidation Tests

Oxidation tests were performed in oxygen or air with a CAHN electro- balance. Samples were suspended with a platinum wire, and the reaction gases flushed the system at room temperature. The samples were heated in the reaction gas to the desired test temperature, and weight change was monitored with time. All samples were completely oxidized. The oxidized samples were examined by scanning electron microscopy (SEM) and elec- tron-energy-dispersive spectroscopy (EDX); X-ray diffraction (XRD) was also conducted.

Electrical-Conductivity Measurements

A copper-foil sample was introduced into the conductivity-measuring apparatus, similar to that used by Maluenda et al., 7 to monitor the EMF. Air and several Ar/O2 gas mixtures were used for the outside reference gas, and various pO2 values were monitored with the YSZ oxygen sensor. Samples were oxidized in the furnace, and electrical conductivity was measured as a function of temperature and pO2. Initially, conductivity was determined as a function of pO2 at constant temperature by the standard four-probe method at a fixed dc current of 1 mA. The IR drop across the probe was monitored with a strip-chart recorder. Sensitivity of the measure- ments was adequate. No appreciable differences were observed because of polarization in the dc measurement at the temperatures of the present study. However, in the low-pO2 region, it was difficult to obtain a stable pO2; consequently, measurements were performed in flowing premixed Ar/O2 gas mixtures.

Conductivity was also measured by switching from inert gases (e.g., argon or helium) to gases of fixed compositions or by using the gas-tight sealing cell described in our previous publications. 27-29 Some simultaneous measurements of electrical conductivity and weight change were also made in the present study.

Thermodynamic Measurements

Thermodynamic measurements were performed, along with conductiv- ity measurements, on large-grain Cu20 polycrystals in the gas-tight electro- chemical cell described in Refs. 27-29.

416 Park and Natesan

RESULTS AND DISCUSSION

Oxidation of Copper

Figure 1 shows a typical weight-gain vs. time curve for the oxidation of pure Cu in flowing oxygen at temperatures between 350 and 1000~ Parabolic rate constants, Kp, were obtained from the initial oxidation period, which normally gives a straight line in a plot of (weight) 2 vs. time. Tempera- ture-dependent oxidation rates in pure oxygen are plotted in Fig. 2. Three different oxidation mechanisms can be inferred from the microstructures and fracture Surfaces of the thermally grown scales (Fig. 3) and from the temperature dependence of the oxidation rates. At high temperatures, the oxide grain size was large, and the calculated activation energy from the slope of log Kp vs. reciprocal-temperature plot was 1.79 eV. From this infor- mation, we infer that the kinetics involve mainly bulk diffusion at high tetr~peratures. At intermediate temperatures, grain-boundary transport or a short-circuiting process leads to an activation energy of 0.87 eV, and some small whiskers form on the oxide surface. At low temperatures, whisker formation on the surface is the rate-limiting process, with a high activation energy of 2.32 eV.

Some features of the bulk process were investigated by the moving Cu20/CuO phase boundary during oxidation. Figure 4 shows weight gain vs. time during oxidation at 1000~ in oxygen, corresponding to the forma- tion of the Cu20 and CuO phases. The initial increase in weight corresponds to oxidation of Cu to CuaO. The weight increase due to oxidation of Cu20 to CuO occurs over a longer time. Figure 5 represents the moving phase boundary of Cu20/CuO as Cu20 is converted to CuO. The moving-bound- ary constant, Kb, at 1000~ was 7.45 x I0 -13 cm2/s, which may be related to oxygen diffusion in the CuO phase. Cu20 has an open structure, but CuO does not have sites available for fast atomic transport (Table II). Multiphase

0.4- E T = 600~ 0.a . . . . . .

0.2-

0.1

0 , 0 v

o 7ioo 144oo 216oo Oxidation Time (s)

Fig. 1. Typical plot of weight gain vs. oxidation time.

Copper Oxides 417

E

E v

O

o , , : ' G , a , o b ; , , n d a ; y § (0.87 eV)

"Bulk

(1.79 eV) ~ " 1 ~ -4

-6 "Whisker or Surface" , " ~ ' ~ (2.32 eV)

-8 6 . . . . . ; . . . . . 12 1 ; i s

1 04/m (K)

Fig. 2. Log kp vs. lIT for oxidation of copper in oxygen.

scales formed when Cu is oxidized in oxygen or air at high temperatures (such as Cu20 and CuO). When the reaction proceeds at a pO2 below the dissociation pressure of CuO, a single-phase scale of pure Cu20 forms. In this case, there is an increase in the concentration gradient of lattice defects in the scale, as well as in the rate of scale growth, with an increase in pO2. However, at higher pO2 levels (greater than the dissociation pressure of CuO), a thin layer of CuO forms on the scale surface. The concentration gradient of lattice defects in the Cu20 layer, however, no longer depends on external oxygen pressure, 19 22 because the concentration of defects at the Cu20/CuO phase boundary is now determined by the dissociation pressure of CuO, which is constant at a given temperature. Consequently, a further increase in oxygen pressure affects only the concentration gradient of lattice defects in the CuO layer, but does not, however, influence the overall rate of reaction, because this rate depends only on the growth rate of the Cu20 layer.

At temperatures < 750~ whiskers grow on the oxide surface (Fig. 3). Chemical-vapor transport, condensation/evaporation, and short-circuit diffusion up the center of the whisker have been suggested as mechanisms for whisker growthY The X-ray diffraction pattern for whiskers correspond to CuO. Oxides grown at temperatures < 750~ yielded pure Cu20, which was verified by X-ray analysis.

Electronic States in Copper-Oxide Systems

EDX analyses were performed on copper with different valences, i.e., Cu metal (zero), Cu20 ( + 1), and CuO ( + 2). Figure 6 shows the intensity ratio of the Cu(1) to Cu(Ka) transition for the individual samples. To extend

oo

Fig

. 3.

F

ract

ure

sur

face

s an

d o

xide

mo

rph

olo

gy

at

seve

ral

tem

per

atu

res

bet

wee

n 3

50 a

nd

900

~

g~

ga,

Copper Oxides 419

g" E 0.2o E

E o.15 v

~3 t" 0.10

0 0.05

0.00 N o

f

T = 1000~

�9

I

�9 " - ' t "CuO"

" m a i n l y C u 2 0 "

L i

200 400 6 0 0 8 0 0

Oxidation Time (h)

Fig. 4. Weight gain vs. time curves at IO00~

the profile for higher copper valences, sequential tests were conducted on YBa2Cu306.98, which has an average copper valence of + 2.3, and on KCuO2 with a copper valence of + 3. This sequence alters the number of electron occupancies in 3d orbital for different copper valences. The electronic-transi- tion probabilities and selection rules are based on wave mechanics, 3~ for the Cu(l) transition, the selection rules are AI= +1 o r - 1 , and An=0, 1, 2, 3 . . . . i.e., the Cu(l) transition possible from the 3d to 3p and 2p. The electron configuration for Cu can be represented as shown in Table III. Figure 6 shows that the intensity ratio, R = Icu(t)/Icu(K~), for the transition of Cu(1) to C u ( Ka) decreases as the copper valence increases; the ratios for

E 12 . . . . . . . . . . . . . . -~. T o = 1000 C

1 0 Pure OYvn~n f O "~ 8 O

O 6

(t) o~ 4 e" " 2 ~ Mov'mg Boundary _ .o ~ Kb = 7.48 x 10 "13 cm2/s e-- D -

0 500 1000 1500

Square Root Time (s) 1/2

]Zig. 5. Thickness vs. square root of time for CuO phase at 1000~ in oxygen.

420 Park and Natesan

"-~ 0.5 l 0.4-"

o

0.3- n-

~ , o.2-

e- oA-

e,,

Atomic Valence

Fig. 6. Intensity ratio for Cu(1) to Cu(Ka) transition for various copper valences.

Cu metal and Cu20 do no t differ significantly. This indicates that the number o f electrons in 3d are the same for both, as shown in Table III .

E l e c t r i c a l C o n d u c t i v i t y

Electrical conduct ivi ty was measured as a function o f temperature and pO2, and the data are shown in Figs. 7 9. The C u 2 0 / C u O transit ion is evident in Fig. 7a. In Fig. 7b, linear extrapolat ion o f the conduct ivi ty o f the Cu20 phase to the CuO phase bounda ry yields a somewhat lower value than the value for CuO conductivity, but this trend varies with temperature. Figure 8 shows the activation energy for hole conduct ion (01628 eV) at pO2 = 10 -4 atm. Previous investigators reported activation energies for electrical conduct ivi ty o f 0.54 to 0.73 eV, ~4 depending on temperature and pO2.

N o pO2 dependence was observed over the CuO-phase-stabil i ty region; this indicates that the intrinsic electronic defect is dominant . This trend extends to temperatures as low as 300~ where impurities normal ly pre- dominate. N o evidence o f contr ibut ions f rom additional defects was detected in the electrical-conductivity measurements. F r o m the slope o f log cr vs. reciprocal temperature for CuO (Fig. 9), a thermal-gap energy for intrinsic

Table lIl. Electron Occupancy (3d or 4s) for Different Cu Valences

Electron occupancy Cu [0] Cu [ + 1 ] Cu [ + 2] Cu [ + 3]

K ls 2 . . . . L 2s 2, 2p 6 . . . . M 3s 2, 3p 6, 3d l~ 10 10 [or 9] 9 8 N 4s ~ l 0 [or 1] - - - -

Copper Oxides 421

1 . 1

0.9 >, "~.~ 0.7

~ 0 . 1 , - I

-0.1

-0.3 -7

. . , �9 . . . . , . . . . . . . . . 9 6 8 o c

,,Cu20,, "-915 /~=.~,., 881

~ ' ~ Z~___ _

m N

~m ,.-.. ,.-r wv O i l

, ~ /%"cu2o/c , ,o" " ' Phase boundary

I I I I I T I | �9 I I , I

-6 -5 -4 -3 -2 -1 0

Log p02 (atm) 0 . 8 1 ' I v , T , i T , I ,

t T=881oc i " . , 0 7 t - . . . . . . , i t " . . . . . " ~ " L L;U2U , , /~

=';" 0.6~ Slope = 1/8 ~e~, "CuO"" "~ E~ 05[- ~ ~ , i Si~

0.4 i! r 0.3 0~" I ~ " " "Cu20/CuO" _1 O.2eF ~ Phase Boundary

/ 0.1t . . . . .

-6 -5 -4 -3 -2 -1 0

Log p02 (atm) Fig. 7. Log conductivity vs. log p02 at several temperatures, and expanded plot near the

C u 2 0 / C u O phase transition.

422 Park and Natcsan

0.55"

:,~,"T, u.'~o �9 OE �9 I~ tO 0.35

~ ] 0.25.

0 . 1 5

0.05

,,Cu20,, _ ~ 10 -4 (atm)

E a = 0.628 eV

- , . , , 8 8.0 8.5 9.0 9.5

1 04/T (K)

Fig. 8. Log conductivity vs. 1/Tfor nonstoichiometric C u 2 0 at pO2 = 10-4 atm.

electronic semiconduction can be calculated as 2.02 eV. This value agrees with literature values, namely, 1.95-~2.0 eV. 3' Based on electrical-conduc- tivity measurements from the present work and thermodynamic-stability data for copper oxides from the literature, 32 the phase-transition boundary is shown in Fig. 10 for Cu20/CuO in terms ofpO2 and reciprocal temperature.

Defect Spec i e s in Electronic Transport

The present analysis makes use of data from Maluenda e t a [ . ]4 and of data provided by C. L. Wiley of Argonne National Laboratory. Semicon- ducting oxides, e.g., copper oxides, can be characterized by a band structure 33

1 .2 T , ~ T

~-~ 02 -

o , (..) ..~ 0.4

~ O 0.2 E a = 1.01 eV = .

.-I 0.0

- , =

8 . 0 9 . 0 1 0

I 041T (K )

Fig. 9. Log conductivity vs. I / T for CuO.

~>" 1.0 ~ >,-. "--'T.w 0.8

"o 0.6

Copper Oxides 423

}" ' ~ ...., IlSealed Cell "',E~ " 2 I ~ . . ~ ~ ~ ) [~) Open Cell

c,, o/cuo o

t'~ -6 o m ~ \ \ \ ..,I

-8 Cu/Cu20 x,.

. . . . . . . . . i , , ~ f I , 1 r ~

7 9 11 104/T (K)

Fig. 10. Log p02 vs. 1/T for Cu/Cu20 and Cu20/CuO phase boundaries.

in which the conduction and valence bands are, respectively, primarily metal- and oxygen-like. In these materials, bulk transport occurs primarily by elec- tronic carriers, and ionic conduction is generally negligible over most condi- tions of interest. In pure metal oxides, electronic carriers arise from intrinsic electronic disorder, and ionic defects are a consequence of nonstoichiometry associated with the solid-gas equilibrium, i.e., the oxidation/reduction pro- cess. For intrinsic disorder, as shown in Eq. (7) of Table I, 0--~ et+ h . , thermal-hole generation across the band gap can be written as

np= NcNo exp( - Eg/kT) (8)

where E~ is the band gap and Arc and No are the electron and hole effective density of states, respectively. Because each electron is compensated by a hole,

nint =pint = (N~No) 1/2 exp( - EJ2kT) (9)

in which the subscript int denotes intrinsic carrier concentrations, which depends only on temperature. Therefore, the total carrier concentration, p, can be represented by the sum of the carrier concentration from intrinsic defects and from charge-compensating defects by the reaction:

P =Pint +Pno. (10)

where Pno. represents the hole carriers deduced from nonstoichiometric defect reaction and is dependent on temperature and oxygen partial pressure.

424 P a r k and Natesan

Therefore, the total electrical conductivity is composed of the sum of the partial conductivities, %-, associated with each type of charge carrier, i.e.,

a = ~ j (11)

where aj is defined by

a:=pszsqp: (12)

in which p: is the hole-carrier concentration (cm-3), zsq is the effective charge (in coulombs), and pj is the mobility (cm2/V-s) of the jth species. The total conductivity is

O" = ( P i n t +Pnon)Ph" qz (13)

Therefore, we may rewrite as

O" = O'int "[- O'no n (14)

To separate nonstoichiometric-defect behavior in electrical conductivity, it is useful to represent total conductivity as the sum of all contributions:

a= C+ KpO~/n (15)

where C = o-int and O-~on = KpO~/n. Figure 11 shows the dependence of con- ductivity on several integer values of n (n = 1-8), along with experimental data (large filled circles) at 700 and 1100~ The data ~,e well represented in a linear plot with n = 6.0. Figure 12 shows conductivity at temperatures between 700 and 1100~ where pO21/6 provides the best linear fit. From Eq. (15), the intercept yields the intrinsic conductivities (ai,t), which have a fixed value at each temperature.

Because conductivity follows a pO2 u6 dependence at each temperature and the mobility of holes is temperature-dependent, this suggests that con- duction occurs by hole-hopping. If a thermally-activated process is assumed for the hole migration,

# h " = IZo, h " e - E m / k T (16)

where #o,h" is constant and Em is the activation energy for migration of holes. By substitution of Eq. 16 in the expression for conductivity,

a =pqlt o,h" e- e,,/kr (17)

From the measurements of conductivity at fixed compositions, the migration energy can be calculated which in turn can be used to compute defect- formation energy from a plot of log slope (slopes derived from data in Fig. 12) vs. reciprocal temperature.

To calculate the mobility of holes, literature values at different

Copper Oxides 425

0.5 ! T = 7 0 0 ~ n = 1.0 to 8.0

1 12 3 4 5 6 7 8

I.

: : oo.o

o.o o12 0.4 o.~ o.s

[ p 0 2 ( a t m ) ] 1/"

Fig. 11. Conductivity vs. pO2 ~/" for n = 1-8.

stoichiometries z'3'6'8 were combined with the electrical-conductivity data from the present work. When we assume that the ionic defects are totally ionized and the holes are the charge-compensating defects, hole mobility can be calculated by assuming that mobility is not a function of composition in the Cu20 phase. With the conductivity equation modified as followsY"

p = A c r / A p q = A e r / ( z A x / V c e , , ) q (18)

where z and Vce, were defined in Table II, the values of calculated hole mobilities at 900 and 1000~ are listed in Table IV. The values are slightly higher at 1000~ If we assume complete ionization of ionic defects and that the holes (formed as a charge-compensating defect) are localized in the normal copper sites, i.e., Cu +~ then becomes Cu +2, the hole-migration energy can be calculated (using Eq. 3) as 0.29 eV.

426 Park and Natesan

1: I 0 6 -

"OE r ' r " 4- O 0 ~,- .~ .

2 -

0 0.I

1100~

1000

900

- ~ - 7 0 0

= L j j i *

0.1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0.7

[P02 (atm)] 1/6

Fig. 12. Electrical conductivity v s . pO~/6 at temperatures between 700 and 1100~

Thermodynamic Considerations

F o r d i l u t e - s o l u t i o n b e h a v i o r , AHo2 m a y be r e l a t ed to the s t a n d a r d

e n t h a l p y o f f o r m a t i o n o f n o n s t o i c h i o m e t r i c defects . P h e n o m e n o l o g i c a l l y ,

AHo2 is de f ined as the e n t h a l p y c h a n g e tha t a c c o m p a n i e s the r eac t i on

desc r ibed by

L i m i t [O2(g, 1 a t m ) + Cu2Ol + x(s) = Cu201 + x + a(s)] (19) ~---,0

Table IV. Calculated Hole Mobilities for Cu20

Temperature Calculated hole (K) mobility (cm2/V s) Ref. a

1173 0.827 2 0.891 3 0.594 6 1.069 8

1273 1.047 2 1.002 3 0.737 6 1.483 8

aReference number for the x values (Cu2Ol_x) used. V(T) = Vo(1 + aT), where V o = unit cell volume of 77.833 x 10 -24 cm 3 at 298 K and thermal expansion coefficient a = 1.9 x 10-6/~

Copper Oxides 427

where x indicates the deviation from stoichiometry due to the excess oxygen in the lattice. One may consider the microscopic incorporation of oxygen into Cu201 +x by a defect mechanism involving doubly-ionized oxygen interstitials and holes localized on copper ions. The microscopic equivalent to Eq. 19 can be written as

Offg, 1 atm) + 4 C u c . . ~ 2 0 i " + 4Cuc." (20)

The corresponding defect reaction for the formation of doubly ionized oxy- gen interstitials as the nonstoichiometric defect with each component in its standard state is

Oi" + 2 Cuc." --* 2 Cuc.x + 1/2 02 (g); AH ~ (21)

where AH ~ is the standard enthalpy for the reaction. Note that the reaction in Eq. (21) is similar to one-half the reverse of the reaction in Eq. (20). Thus, a consequence of dilute-solution behavior is that

AHo2 = - 2AH ~ (22)

In the cubic structure of cuprite (CUR0), an oxygen interstitial is expected in a body-centered-cubic structure of Cu20, where the oxygen sub- lattice is open. The ionization state for interstitial oxygen is expected to be - 2 because the normal charge of oxygen in both of the stable oxides (CuO and Cu20) is - 2. Figure 13 depicts the log trnon VS. log pO2 for nonstoichi- ometric Cu20.

From the proposed nonstoichiometric-defect reaction in Eq. (3), we can

O ~ 0 �84

.A

-1

1100oC

i i t

6 - 5 - 4 - '3 - 2

Log p02 (atm)

Fig. 13. Log Cr.o. vs. log p02.

1000

428 Park and Natesan

apply the quasichemical approach. The mass-action constant and electroneu- trality condition are given by

gma = (Oi") �9 (h')2/pO~/2 (23)

2(Oi") = (h.) (24)

Therefore, we can denote the concentration of holes as

[h'] =/c"../a3 " pO~/6 (25)

or, by combining the normal conductivity relation, we obtain

O'no n c( Kml~ .pO~/6 (26)

Because

KmaoCKth = exp( - AG~

= exp( - AH~ " exp(AS~ (27)

where Kth is the thermodynamic equilibrium constant, we obtain

a ,o , Ocexp(- AH~ kT) . pO2 U6 (28)

Since O'no, oc [h']q'oh', where the hole mobility is given by Eq. (11), we obtain

O-,o, oc exp{ - (5 / /~ + E,,,)/kT}. p~01/62 (29)

For a defect mechanism of doubly-ionized oxygen interstitials, Oi", where the holes are localized at Cu sites as Cu § or Cuc, ' , the formation energy of 0.65 eV was calculated on the basis of an oxygen-pressure depen- dence of n = 6.0, as shown in Fig. 14. At a constant temperature, a,on is proportional to pO~/6.

a) 0.9 Q. 0 0.7"

0') 0.5" 0

...J 0 . 3

, , , , f , , , , I i , , , I i i , ,

1.:3"

1.1

/

0.1 . . . . . . . . . . . . . . . . . . 7 8 9 1 0

1 0 4 / T (K)

Fig. 14. Log slope (do/dpO~/6) vs. I/T for Cu20.

Copper Oxides 429

The data in Fig. 8 (a plot of log Crnon vs. reciprocal temperature at constant oxygen pressure), yields a slope (AH~ + E,,)/k = 0.628. The activ- ation energy for hole motion is E,,,=0.29 eV and AH ~ is 1.01 eV; conse- quently, the standard enthalpy of formation AHo2, is 2.02 eV, from Eq. (22). These thermodynamic quantities were calculated from model-based defect equilibria and can be compared with thermodynamic values measured directly.

Tretyakov et al . 6 reported oxygen concentrations, as a function of tem- perature and pOE, obtained by high-temperature, solid-state coulometric titration. They analyzed the data by assuming that the deviation from

~ n ~/4 stoichiometry, x (in Cu201 +~), varies with r,,-,2 dependence. We analyzed their data for the case where xocpO~/6. The fit based on our model (Fig. 15a), is good. Log x vs. log pOE w a s replotted in Fig. 15b.

§

0 " Eo o ~ " ; o ._ e-

.-# §

5 o .=_ X v

X

r o ._1

1 6

1 4

1 2

1 0

8

6 0 . 3 0

slope = 2.89 x 10 -3

o.;5 0.;0 0"45 0.;0 o.;5 o.60 [ p 0 2 ( a t m ) ] 1/6

-2.7

-2.8

-2.9

-3.0-

-3.1

-3.2 . . . . l . . . . = . . . . i

- 3 . 0 - 2 . 5 - 2 . 0 - 1 . 5

T = 1000 ~

/ T = 950 ~ /

Log p02 (atm)

~O ~/" Fig. 15. v 2 vs. change of stoichiometry for two examples; logx vs. pO21/6 fit for data in Ref. 6; and (b) log x vs. log pO2.

430 Park and Natesan

Hole Mobility

To determine the mobility of holes, electrical conductivity and weight change were measured simultaneously on thermally-oxidized, large-grain samples of nonstoichiometric Cu20. Sample temperature was varied, and an inert atmosphere was maintained by flowing argon gas through the measur- ing system. 27 The results are shown in Fig. 16. The calculated (from the conductivity-temperature data) activation energy was 0.87 eV and the weight change was essentially zero. The activation energy obtained by this method is higher than that determined under equilibrium conditions (0.628 eV). This suggests a somewhat different behavior in electronic-transport properties in nonstoichiometric Cu20 relative to other nonstoichiometric metal oxides such as Cr20327 or CeO2. 29

In most metal oxides, the activation energy determined under equilib- rium conditions is higher than that obtained from a specimen with a fixed composition, because the activation energy for conduction under equilibrium is the sum of the migration energy and the energy of formation of the defect. However, the electronic-transport properties in nonstoichiometric Cu20 can be explained by two different mechanisms: when the material is in equilib- rium with oxygen, the electronic properties are predominantly controlled by the narrower gap, but when the composition is fixed and the temperature is varied, the electronic defect is controlled intrinsically and this manifests itself as a higher gap energy in nonstoichiometric Cu20.

Another method was also employed to confirm the thermodynamic quantities obtained from electrical conductivity as a function of temperature and pO2. Direct thermodynamic measurements were performed on copper

~ 2.oi :::k " • > '

1.5: C >'T r E 1.0 r ~ o tO--z ~1~.~'7, 0.5

E �9 ~U'~ 0.0 q

~ -0.5

-1.0

? r T

/

Weight

Conduct iv i ty

.10 1 . 1 5 1 . 2 0 1 . 2 5 1 .30

103/ '1 - (K)

Fig. 16. Simultaneous measurements of electrical conductivity and weight change in an argon environment.

Copper Oxides 431

oxide systems by setting up fixed compositions. Figure 17 is a typical plot obtained simultaneously for the log cr and logPpO2 vs. reciprocal temperature at several constant compositions. The oxygen formation enthalpy (AHo2) and hole-conduction energy (E14) were calculated from the slopes in Fig. 17. and are represented in Fig. 18. In this figure, log pO2 corresponds to the equilibrium composition at 994~ for each run. AHo2 is 2.0 4- 0.2 eV and En is 0.824-0.02eV. These results agree with the values obtained at a fixed composition when the temperature was varied by flowing an inert gas. How- ever, at the lowest p Q , AHo2 decreased (Fig. 18); this may be attributed to the decomposition reaction Cu20~Cu + CuO and the subsequent oxidation of copper (i.e., Cu + 1/2 O2~CuO) denoted by the dashed line in Fig. 10. The transition-pO2 values were obtained from Fig. 10. For the large-grain polycrystals of Cu20, however, the type of profile in Fig. 19 was barely detectable during pumping of oxygen while monitoring conductivity and pO2.

The CuO/Cu20 phase transition is clearly evident in the temperature dependencies of EMF, the oxygen concentration in the gas phase (calculated from the ideal gas law, pV=nRT), and electrical conductivity in Fig. 20. The profiles for the temperature-dependent uptake and removal of oxygen are not identical in both phases. In Cu20 at low temperatures, the sample consumes more oxygen, but in the CuO phase, which is stable at higher temperatures and high pO2 values, oxygen absorption is lower. Electrical conductivity of the CuO phase increases at higher temperatures. We could not obtain a fixed-composition measurement in the high-p02 case, because

L / ------

�9 -t 0 -2J ~ Conductivity

7 . 0 e - 4 8 . 0 e - 4 9 . 0 e - 4 1 . 0 e - 3 1.1 e -3

104/T (K)

Fig. 17. Typical results on variation of electrical conductivity and pO2 from constant-composition measurements made as a function of temperature.

3.0 . . . . , . . . . , . . . .

2 .5

>

v 2 .0

IJJ 1.5

r 0 1.o -I-

<~ 0 .5

0.0 - 5

-0.4

AH02

EH T T , I I i i i 1 I i i , T

-4 -3

Log p02 (atm)

Fig. 18. Calculated oxygen-formation enthalpy, AHO2, and hole-con- duction energy, EH.

the sample stoichiometry changes during the experiment. The shape of the conductivity-vs.-temperature curve near the transition region (Fig. 20b), indicates the possibility of a metastable phase between Cu20 and CuO in the Cu-O system.

> , -0.6

~ -0.8

~ - 1 . 0 -1

-1.2 6 2 - 5 - 4 - 3

Log p02 (atm)

432 Park and Natesan

Fig. 19. Electrical-conductivity change with pO2 associ- ated with decomposition of Cu20~Cu + CuO.

Copper Oxides 433

t f I i I

l O O

75 (a)

. . - " _ _ h ,,,," cu2o/cuo

75 T- Phase Transition

- 1 0 0 1 �9 , . , �9 , 8 0 0 9 0 0 1 0 0 0 1 1 O 0

1 2 v , , ,

(b)

r 4

2 Phase T r a n s i t i o n

8 0 900 10'00 11'00 T e m p e r a t u r e (~

Fig. 20. Cu20/CuO phase transition in terms of variation in EMF and electrical conductivity as a function of temperature.

SUMMARY

Oxidation of copper and electronic transport in thermally-grown, large- grain polycrystals of nonstoichiometric copper oxides (Cu:O and CuO) were studied at elevated temperatures. Oxidation rates were determined thermo- gravimetrically at temperatures from 350 to 1000~ The temperature depen- dence of the oxidation rates, coupled with visual examination of the oxide films, suggested three different oxidation mechanisms: bulk diffusion at high temperatures, whisker formation with grain-boundary diffusion at intermedi- ate temperatures, and surface reaction with whisker formation on the outer surface of the oxide at low temperatures. Intensities of EDX spectra for various atomic valences of Cu were represented by the intensity ratio of the Cu( l ) to Cu(Ka) transition. There is no significant difference in the ratio

434 Park and Natesan

for Cu and Cu20, but the values decreased for copper in higher-valence states.

Electrical conductivity of nonstoichiometric Cu20 exhibited p-type behavior, but in CuO only intrinsic behavior was observed. However, elec- tronic transport in nonstoichiometric Cu20 was reconsidered in terms of both intrinsic and nonstoichiometric defects owing to reduction/oxidation processes. Electrical conductivity of Cu20 exhibited a 1/6-power dependence on the oxygen partial pressure, i.e., O'non = K pO~/6. Calculated values for the enthalpy of formation of oxygen (AHo2) and the hole-conduction energy (EH) at constant composition for nonstoichiometric Cu20 are 2.04- 0.2 eV and 0.824- 0.02 eV, respectively.

ACKNOWLEDGMENTS

The authors thank C. L. Wiley of Argonne National Laboratory for supplying the large-grain, cuprous-oxide polycrystals, and for electrical-con- ductivity data that were used in an earlier paper.

REFERENCES

1. P. Kofstad, Non-Stoiehiometry, Diffusion, and Electrical Conductivity in Binary Metal Oxides (Wiley Interseience, New York, 1972).

2. C. Wagner and H. Hammen, Z. Physik. Chem. B 40, 197 (1938). 3. M. O'Keefe and W. J. Moore, J. Chem. Phys. 36, 3009 (1962); H. L. McKinzie and M.

O'Keefe, Phys. Lett. A 24, 137 (1967). 4. S. Mrowee, A. Stoklosa, and K. Godlewski, Cryt. Lat. Def. 5, 239 (1974). 5. M. Yoshimura, A. Revcolevschi, and J. Castaing, J. Mater. Sci. 11,384 (1976). 6. Y. D. Tretyakov, V. F. Komarov, N. A. Prosvirhina, and I. B. Kusenok, J. Solid St. Chem.

5, 157 (1972). 7. J. Maluenda, R. Farhi, and G. Petot-Ervas, J. Phys. Chem. Solids 42, 911 (1981). 8. F. Perinet, S. Barbezat, and C. Nonty, J. Phys. Colloq. C 6, 315 (1980). 9. J. Gunderman, K. Hauffe, and C. Wagner, Z. Physik. Chem. B 37, 148 (1937).

10. M. O'Keefe and W. J. Moore, J. Chem. Phys. 35, 1324 (1961). 11. R. S. Toth, R. Kilkson, and D. Trivich, Phys. Rev. 122, 482 (1961). 12. K. Stecker, Ann. Phys. 7, 55 (1959). 13. N. L. Peterson and C. L. Wiley, J. Phys. Chem. Solids 45(3), 281-294 (1984). 14. J. Maluenda, R. Farhi, and G. Petot-Ervas, J. Phys. Chem. Solids 42, 697 (1981). 15. M. O'Keefe, Y. Ebisuzaki, and W. J. Moore, J. Phys. Soc. Jpn. 18, 131 (1963). 16. Handbook o f Chemistry and Physics, 61st Ed. (CRC press, 1981). 17. W. J. Tomlinson and J. Yates, J. Phys. Chem. Solids 38, 1205 (1977). 18. E. lguchi, K. Yajima, and Y. Saito, Trans. Jpn. Inst. Met. 14, 423 (1973). 19. C. Wagner and K. Grunewald, Z. Phys. Chem. B 40, 197 (1938). 20. J. P. Baur, D. W. Bridges, and W. M. Fassell, Jr., J. Eleetrochem. Soc. 103, 273 (1956). 21. W. Feitknecht, Z. Elektrochem. 35, 142 (1929). 22. S. Mrowec and A. Stoklosa, Oxid. Met. 3, 142 (1971). 23., B. Onay, J. Eleetroehem. Soe. 136, 1578 (1989). 24. R. G. Kaufrnan and R. T. Hawkins, J. Electrochem. Soc. 131(2), 385; 133(12), 2652 (1986);

135(8), 2096 (1988); J. Luminesc. 31 & 32, 509 (1984).

Copper Oxides 435

25. P. Kofstad, High Temperature Corrosion (Elsevier Applied Science, London and New York, 1988).

26. R. A. Rapp, MetalL Trans. A 15, 765 (1984); G. M. Raynaud and R. A. Rapp, Oxid. Met. 21, 89 (1984).

27. J.-H. Park and K. Natesan, Oxid. Met. 33, 31 (1990). 28. J.-H. Park and R. N. Blumenthal, J. Electrochem. Soe. 136, 2867 (1989). 29. J.-H. Park, Physica B 150, 80 (1988). 30. G. Herzberg, Atomic Spectra and Atomic Structure (Dover Pub., New York, 1944). 3l. K. Stecker, Ann. Physik. 7, 55 (1959); 7, 70 (1959). 32. L. B. Pankratz, Thermodynamic Properties of Elements and Oxides, U.S. NBS pub. B 272,

National Bureau of Standards, Gaitherburg, MD, 1982. 33. M. H. Sukkar and H. L. Tuller, in Surface and Near-Sulface Chemistt T of Oxide Materials,

Chap. 15, J. Nowotny and L.-C. Dufour, eds. (Elsevier Science Publishers B. V., Amsterdam, 1988), p. 611.