Free-carrier optical absorption in Nb-doped SrTiO3

J. Phys. Chem. Solids, 1972, Vol. 33, pp. 951-954. PergamonPress. Printed in Great Britain

TECHNICAL

Free-carrier optical absorption in Nb-doped SrTiO3* (Received 22 January 1971 )

FREE-CARRIER optical absorption in hydrogen reduced SrTiOa recently studied by Baer[l] revealed an interesting peak at 2.4eV superposed on the intraband background. No correlation was found between the intensity of this peak and the carrier concentration and thus no definite conclusions could have been made about its origin. A possibility has been suggested that the peak may be due to an electron trapped at an oxygen vacancy. In order to shed light on the mechanism leading to the 2.4 eV peak, we decided to look at the free carrier absorption in the Nb-doped SrTiO:3. The latter represents a more defined conducting system leading to mobilities 2-3 higher than for reduced specimens [2]. There is also a more general interest in the optical absorption experiments on this material, since it can supply information on the excited states, complementing the previous ground state studies [2, 3]. The optical absorption of Nb-doped SrTiO3 single crystals was studied at several temperatures for 3 different Nb203 dopings as grown by the National Lead Company. One of these crystals (I) was from the same boule which was used for studying electron tunneling[3]. The carrier concentrations were: Sample 1,4.5 × 1019/cm'~; Sample II, 2.3 x 1019/ cm3; Sample III, 5 x 10Wcm 3. These samples were ground to an appropriate thickness on a grinding machine, and optically polished with 0-05 micron polishing alumina type 3-C. The

THE

NOTE optical absorption was measured in a Cary Model 14R Spectrometer with the samples in an optical tail sis dewar with quartz windows. The absorption and reflection losses of the quartz windows were compensated for experimentally by placing identical windows in the reference path, and it was assumed that the reflection losses in all samples were the same since they had received identical polishing treatments. The results are similar to those obtained for hydrogen reduced samples by Baer[1]. The 2.4eV peak is systematically I~resent in all our specimens, in contrast with Ref. [1] where only one sample showed this peak. Also, the area under the peak is well correlated with the carrier concentration (see Fig. 1). The relation is linear and this suggests that the peak is due to the interband transition of the conduction electrons. In order to test for possible F_L-center type absorption, Samples I and II and the SrTiO.~ (H2 anneal) sample were reannealed in air at 800°C for 15 hr. In the two Nb doped samples, TEMPERATURE

(K)

I00

200

300

I

I

I

500

400 I J r

8 -

I 0

-0

o

T

35

~2 <

I

2

CONCENTRATION

3

4

5 X I019

(CM -3)

Fig. 1. A r e a o f 2 . 4 e V absorption peak in S r T i O 3 : N b (4.5 x 10'gem a) vs. t e m p e r a t u r e (curve T) a n d vs. carrier concentration (curve C) for T = 78"K.

* S u p p o r t e d by the U.S. A i r Force Office of Scientific R e s e a r c h on G r a n t A F O S R 523-67, 951

952

T E C H N I C A L NOTE

no change was seen in the 2.4eV energy peaks. However, the corresponding peak in the H., annealed sample was completely bleached by this process. Subsequent reannealing of this sample in purified H., gas at 800°C and atmospheric pressure for 39 hr reestablished the peak at 2.4eV. This excludes the F.-center model mentioned in Ref. [1]. Another possible candidate to be considered is the 10 Dq transition of localized 3d electrons at TP +. This seems to be a tempting interpretation because the visible absorption band of the TP + complexes happens to peak very closely to 2-4eV[4]. However, there are strong arguments against this model. First the oscillator strength f in TP + complexes, due to vibrational-electronic interactions is only about 10 -4 at room temperature[5]. From out" data, we determine (after subtracting the Drude b a c k g r o u n d ) f ~ 10-'-' per carrier. Secondly, it is hard to imagine that the concentration of TP + traps would increase linearly with the carrier concentration. Finally, most convincing is the fact that Nb-doped TiO., with localized carriers (in nonconducting region) does not show any observable trace of the 2.4eV peak[6]. That the peak is not due to Nb-traps is shown by its observation[l] in H-reduced specimens. Thus we are left with the possibility of the band ~ band transiton of the 3 d-conduction electrons• The direct (k-conserving) transitions between the portion of the occupied 3dband and a higher 3d band are rendered impossible by group theoretical arguments. The indirect (nonvertical) 3d-3d band transition caused by phonons and impurities is improbable because of the following reasons. First the observed intensity is too high to be explained by this process, second the temperature dependence of the area under the peak does not increase as expected from phonon induced transitions. The experimental temperature dependence of the 2.4eV peak is shown in Fig. 2. After subtracting the Drude background as indicated, the area under the peak shows a behavior

] ,.4 1.2

[ ,, ,"

H ,.o "o ~ .s --

~

,,,,\

',,\ \ //,'7 ,,X,~,~" \,\%.J'/// / ~ /

.......

529 481 442 404

K

300 78

,o

',

,,x

.6

.4

-----....... . . . . . . . . ...........

"-..

,2

a\ \

" x 7 % \ \ %','.\ X / "~----~--_"~.~~._x~,.:x\ \ . / I / /

I

O 2,00

2,40

2,80

3.20

ENERGY (eV) Fig. 2. Spectral dependence of the absorbance of SrTiO:~:Nb (4.3× 10Wcm:') in the vicinity of 2.4eV at indicated temperatures.

characteristic for direct interband transitions. Fig. 1 shows a decrease of the area with temperature. This may be interpreted qualitatively in terms of a decrease of thermal mean square potential (Debye-Waller factor). Quantitative conclusions cannot be made from Fig. 1 because of the uncertainty in subtracting the background absorption. Figure 2 also shows a shift of the threshold towards lower energies as the temperature is increased. We note that the temperature dependence of the absorption edge displays a similar behavior. For the latter, the mechanisms suggested previously are the thermal dilation of the lattice and the phonon selfenergy effect[7]. The same mechanisms are probably responsible for the observed shift of the 2.4 eV peak. To interpret the origin of this peak we are left with the possibility of a transition from the occupied 3d band to a higher conduction band of p-character. This band may be viewed as consisting of the tight-binding Bloch waves constructed from the 4p-orbitals of Ti. But in view of the large radius ef the 4p-orbitals, their atomic identities are lost and one can

TECHNICAL

equally speak of an oxygen 4p-like) excited band. In a free Ti 3+ ion the 3d-4p separation is about one Rydberg[5]. In the oxides we expect a screening of the bulky 4p state due to oxygen ions which are strongly hybridized with the 4p states of TP +. This causes a large depression of the 4p state explaining the small energy of our observed interband transition. The intensity of the interband free-carrier absorption can be related to that of the intraband (Drude) absorption via the f-sum rule [9]: 2 ,'/'r

[o'linter(t.O) nt- O-li"tra (tO) ] dto -- NeZ i~/

(1)

where o-~(to) is the real part of the conductivity, N is the density of carriers and m is the free-electron mass. In (I) we assume that the interband part of o-~(oJ) can be separated from the intraband part and that the carrier states do not mix optically with the lower occupied bands. We have not followed the intraband absorption to sufficiently long wavelength to evaluate the intraband part of the integral in (1). However, Baer's measurements[l] (made on his sample No. 2) provide sufficient number of points for a reasonable estimate of the above quantity. It is useful to relate the Drude area to the optical effective mass via the sum rule [9] __2fo o o'lintra((o) do = N e 2 "/T

(2)

Here m* is the optical effective mass and (1/m*) is an average taken over the occupied parts of the 3d-bands. The conductivity o-li"m'(co) can be related to the absorption coefficient ~(w) by the relation O-lilllra(o)) m

~(OJ)ITC 4rr

(3)

where n is the refractive index of SrTiO:3. Using the measured values of "0(co) and n = 2.31 (see Ref. [1]) we obtain from (3) a value

NOTE

953

(0,m)

'

Since only small portions of the Briilouin zone are occupied we can compare (5) with the expression

~n* = 3\mr

-~;

(5)

where mt and mt are the longitudinal and transverse effective masses at the minimum of the occupied part o f 3 d b a n d , respectively. It is interesting that the result (4) is close to the value (0.7 m) -1 obtained from (5) using the recent tunneling results of Sroubek [3], but differs appreciably from Barker's[10] value (2.5 m)-L Equation (l) cannot be used since the optical mixing of the valence with the 3dconduction bands is quite strong. In fact, a 'negative' interband conductivity results from (1) and (2), when (l/m*) > 1/m. Actually, intensity has to be borrowed from the allowed transitions of the valence electrons to compensate for this[l 1]. This effect is another manifestation of the covalent mixing [12] between titanium 3d and oxygen 2pstates which is also responsible for the small value of Int in SrTiOa. Because of the fact that (l/m*) = (0-5 m) -~, this mixing effect is quite strong and we cannot determine the interband oscillator strength of the free-carriers from equation (1). But it is not surprising that our directly observed f is small relative to the free-ion value ( f - 1) for the allowed 3d 4p transition. The optical matrix element between d-band and p-band must differ significantly from the free-ion value in view of the strong delocalization of the d-electrons. Acknowledgement-We would like to thank Prof. Z. Sroubek for helpful discussions and for supplying the specimens which enabled this study. We would also like to thankJana Smith for assistance in the measurements. Universityof California,

Riverside,

Calif92502, u.sA.

E. SIM,~NEK

N . L . H U A N G LIU

R.L. WILD

954

TECHNICAL NOTE

REFERENCES 1. BAER W. S., Phys. Rev. 144, 734 (1966). 2. S C H O O L E Y J. F. and T H U R B E R W. R., J. phys. Soc. Japan 21,639 (1966). 3. S R O U B E K Z., Solid State Commun. 7, 1561 (1969), and Phys. Reo. to be published, October 15, 1971. 4. H O L M E S O. G. and M c C L U R E D. S., J. chem. Phys. 26, 1686 (1957). 5. L I E H R A. D. and B A L L H A U S E N C. J., Phys. Rev. 106, 1161 (1957). 6. W I L D R. L., unpublished result. 7. F A N H. Y., Phys. Rev. 82, 900 (1951). 8. M O T T N. F., Rev. mod. Phys. 40, 677 (1968). In

this paper a related case of screening of the d-d coulomb correlation is discussed. For effects of electronic polarization on band energies, see F O W L E R W. B., Phys. Rev. 151,657 (1966). 9. K U B O R.,J. phys. Soc.Japan 12, 570(1957). 10. B A R K E R A. S., in Proceedings of the International

Colloquium on Optical Properties and Electronic Structure of Metals and Alloys, Paris, 1965, North Holland, Amsterdam (1965). II. P H I L L I P H. R. a n d E H R E N R E I C H H.,Phys. Rev. 129, 1550(1963). 12. Z O O K J. D., Phys. Rev. Lett. 20, 848 (1968).