Understanding the nature of electronic effective mass in double-doped SrTiO$_{3}$

Abstract

We present an approach to tune the effective mass in an oxide semiconductor by a double doping mechanism. We demonstrate this in a model oxide system Sr$_{1-x}$La$_x$TiO$_{3-\delta}$, where we can tune the effective mass ranging from 6--20$\mathrm{m_e}$ as a function of filling or carrier concentration and the scattering mechanism, which are dependent on the chosen lanthanum and oxygen vacancy concentrations. The effective mass values were calculated from the Boltzmann transport equation using the measured transport properties of thin films of Sr$_{1-x}$La$_x$TiO$_{3-\delta}$. Our method, which shows that the effective mass decreases with carrier concentration, provides a means for understanding the nature of transport processes in oxides, which typically have large effective mass and low electron mobility, contrary to the tradional high mobility semiconductors. Comment: 5 pages with 4 figures

Full text

Page 1

arXiv:0809.4706v2 [cond-mat.mtrl-sci] 2 Oct 2009
Understanding the nature of electronic effective mass in double-doped SrTiO3
J. Ravichandran,1W. Siemons,2M. L. Scullin,3, 4S. Mukerjee,2,5M.
Huijben,2, 6J. E. Moore,2,4R. Ramesh,2,3,4and A. Majumdar3,4,7,8
1Applied Science and Technology Graduate Group,
University of California, Berkeley, Berkeley, CA 94720
2Department of Physics, University of California, Berkeley, CA 94720
3Department of Materials Science and Engineering,
University of California, Berkeley, Berkeley, CA 94720
4Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720
5Department of Physics, Indian Institute of Science, Bangalore 560012, India
6Faculty of Science and Technology and MESA+ Institute for Nanotechnology,
University of Twente, P.O. BOX 217, 7500 AE, Enschede, The Netherlands
7Department of Mechanical Engineering, University of California, Berkeley, Berkeley, CA 94720
8Applied Science and Technology Program, University of California, Berkeley, Berkeley, CA 94720
(Dated: October 2, 2009)
We present an approach to tune the effective mass in an oxide semiconductor by a double doping
mechanism. We demonstrate this in a model oxide system Sr1−xLaxTiO3−δ, where we can tune the
effective mass ranging from 6–20me as a function of filling or carrier concentration and the scatter-
ing mechanism, which are dependent on the chosen lanthanum and oxygen vacancy concentrations.
The effective mass values were calculated from the Boltzmann transport equation using the mea-
sured transport properties of thin films of Sr1−xLaxTiO3−δ. Our method, which shows that the
effective mass decreases with carrier concentration, provides a means for understanding the nature
of transport processes in oxides, which typically have large effective mass and low electron mobility,
contrary to the tradional high mobility semiconductors.
PACS numbers: 71.55.-i, 71.18.+y, 73.50.-h
Effective mass is one of the fundamental quantities de-
termining the transport properties of a material. Varia-
tion of effective mass as a function of carrier concentra-
tion and temperature has been widely characterized in
small band-gap (0.1–1 eV) and low effective mass (0.1–
0.01me) semiconductors such as InAs [1], HgTe [2] and
InSb [3] and has been reviewed by Zawadzki [4]. Such sys-
tems show an increasing effective mass with carrier con-
centration which is sufficiently explained by Kane’s band
model [5]. At the other end of the spectrum, complex
oxides or transition metal oxides typically have larger ef-
fective masses (1–10me) and band-gaps (1–10 eV). Com-
plex oxides offer a variety of compounds showing no
electron-electron correlation (band limit) to strong cor-
relation (Mott limit). Strong correlations give rise to a
very large effective mass (100–1000me) in heavy fermionic
systems [6] at cryogenic temperatures.
the effect of strong correlation on effective mass and
other transport properties remains an intriguing ques-
tion, there is little literature on the study of effective
mass as a function of carrier concentration in oxides in
the band limit. Moreover, a thorough understanding and
tuneability of effective mass will have wide implications
on phenomena such as thermoelectricity [7] and photo-
voltaics [8].
Even though
In order to study the effective mass in the band limit,
we have chosen SrTiO3 (STO). STO is a model com-
plex oxide system with very weak or no correlation and
a wide range in n-type electrical conductivity, controlled
by doping at the A-site (for example La doping in Sr
sites), B-site (for example Nb doping in Ti sites) and
by creating oxygen vacancies. The cation doping the A-
site of STO is more suitable than doping on the B-site
to study the nature of filling without changing the band
structure drastically, because the conduction band has Ti
3d characteristics. The effective mass of La doped STO
has been reported as 6–6.6me [9] and the introduction
of oxygen vacancies results in a large effective mass of
∼16me[10] and has been attributed to the flat impurity
band created by these vacancies [11]. In this Letter, we
demonstrate double doping in STO thin films by inde-
pendently controlling oxygen vacancy concentration and
La concentration. We performed optical spectroscopy to
establish the formation of impurity band in STO due
to oxygen vacancies. Transport measurements show the
changes in scattering mechanism at the different limits of
doping. We modeled our system using Boltzmann trans-
port theory and show tuneability of the effective mass in
the range of 6–20me.
Thin films (150 nm) of Sr1−xLaxTiO3−δ were grown
via pulsed laser deposition (PLD) from dense polycrys-
talline, ceramic targets (each nominally containing either
0, 2 or 15% La) onto (LaAlO3)0.3-(Sr2AlTaO6)0.7(LSAT)
(001) single-crystal substrates (a=3.872 ˚ A).
was carried out in oxygen partial pressures ranging from
10−1–10−7Torr and a laser fluence of 1.75 J/cm2at a
repetition rate of 8 Hz. Films were grown at a temper-
ature of 450◦C to create a non-equilibrium amount of
Growth

Page 2

2
?
?
?
?
?
?
?
?
?
?
?
?
??
FIG. 1:
diffraction at 300 K versus oxygen partial pressure during
thin film growth for Sr1−xLaxTiO3−δ (the dashed line is a
logarithmic fit to the 2% data as a guide to the eye).
The c-axis lattice parameter measured by x-ray
oxygen vacancies, by avoiding the equilibrium reached
during the cool down from higher temperatures. X-ray
diffraction (XRD) was carried out on these films with
a Panalytical X’Pert Pro thin film diffractometer using
Cu Kα radiation. Low temperature resistivity and Hall
measurements were performed using a Quantum Design
physical property measurement system (PPMS). Ther-
mopower measurements at room temperature were done
using a setup with T type thermocouples. UV-Visible
(UV-Vis) transmission and reflection measurements were
obtained from a Perkin Elmer Lambda 950 spectrome-
ter and Hitachi U-3010 spectrometer respectively. The
photoluminescence (PL) data was acquired using a setup
with a 325 nm laser excitation source.
XRD patterns of the thin films indicate that they are
single phase, nearly single-crystal perovskites. The full-
width-at-half-maximum (FWHM) of the rocking-curve
(002) thin film peaks indicate the films are crystalline
(ωFWHM
002
< 0.3◦) and (00l) epitaxially oriented. Typi-
cally, La doping has a negligible effect on the c-axis lat-
tice parameter [12], but oxygen vacancies will expand the
lattice significantly as the Ti-Ti bond length is greater
than that of Ti-O-Ti and induces a tetragonal distor-
tion [11, 13]. Reciprocal space mapping of the (013) peak
of the thin films reveal they are indeed tetragonal, with
an in-plane lattice parameter of ∼3.90˚ A across all La
concentrations and oxygen partial growth pressures, and
a 0.023˚ A increase in the c-axis lattice parameter per
order of magnitude decrease in oxygen partial pressure
during growth (Fig. 1). For samples grown at 10−7Torr
—or a maximum concentration of oxygen vacancies in
our study— the c-axis lattice parameter is 4.075˚ A for
Sr0.98La0.02TiO3−δ [14], corresponding to a c/a ratio of
123456
0
1
2
3
α0.5
Energy (eV)
300400500 600700
0.0
0.2
0.4
0.6
0.8
1.0
Energy (eV)
3
Intensity (arb. unit)
Wavelength (nm)
4
(c)
2
Donor
defect band
Conduction band
Valence band
Density of States
Energy
Γ Γ
k
M
Separation
0.4 eV
Indirect band gap
3.3 eV
E
(a)
(b)
FIG. 2: (a) Schematic of the band model for the oxygen va-
cancy doped La-STO. (b) Plot of square root of absorbance as
a function of photon energy for UV-Visible absorption spec-
troscopy. The intercept of the linear part of the curve gives
the indirect band gap energy. (c) Plot of Photoluminescence
intensity as a function of energy. The red arrow indicates the
peak position corresponding to the energy gap between the
impurity level and the valence band. The data shown corre-
sponds to measurements at 300 K on 15% La doped sample
grown at 10−7Torr.
1.045.
This oxygen vacancy induced tetragonal distortion is
expected to lift the three-fold t2g degeneracy of the
conduction band. Theoretical predictions indicate that
this leads to the formation of a heavy oxygen vacancy
impurity band lying below a light conduction band
edge [11, 15, 16]. In order to validate the predicted band
model, schematically shown in Fig. 2, we performed UV-
Vis spectroscopy and PL to map the important energy
levels in the band model. UV-Vis spectroscopy was used
to determine the energy gap between indirect band edge
and the valence band and PL reveals the energy gap be-
tween the valence band edge and the oxygen vacancy im-
purity band. Fig. 2 shows the results obtained for 15%
La doped sample grown at 10−7Torr. The indirect band
gap determined from UV-Visible was ∼3.3 eV, very close
to the value observed in bulk STO 3.27 eV [17]. The PL
spectra show a characteristic peak corresponding to ∼2.9
eV [18] suggesting a spacing of 0.4 eV between the indi-
rect conduction band edge and the oxygen vacancy impu-
rity band as predicted by theoretical calculations [11, 15].
Effective mass values have been conventionally evalu-
ated using cyclotron resonance [19], reflectivity [20], pho-
toemission [21] and Shubnikov-de Haas effect [22] for vari-
ous single crystals of semiconductors. The other common

Page 3

3
?
?
?
?
?
???
???
??
??
?
?
?
??
?
?
?
?
?
?
?
?
?
?
?
FIG. 3: Low temperature (a) resistivity (b) Hall mobility
and (c) Hall carrier concentration data for 2% La doped STO
grown at 10−7Torr and 15% La doped STO grown at 10−4
Torr.
method is using transport data to calculate the density of
states effective mass [9, 10]. Some of these methods are
impractical for thin films and hence, we resorted to calcu-
lating the density of states effective mass using transport
data. All transport data were measured in the plane of
the (001)-oriented films. To evaluate the effective mass
at room temperature, we need the low temperature mo-
bility and resistivity data to learn about the dominant
scattering mechanism and the carrier concentration and
thermopower at room temperature.
perature resistivity, mobility and carrier concentration
data are shown for two representative samples in Fig. 3.
The measured transport parameters for all the samples
at room temperature is recorded in Table I. The samples
containing low doping of La (0% or 2%) but with oxy-
gen vacancies showed a constant mobility as a function of
temperature, indicating the presence of partially ionized
impurity scattering or neutral impurity scattering [23].
In this limit, the transport is dominated by the oxygen
vacancies, which ionize partially if they are clustered to-
gether [24, 25] and clustering of vacancies in SrTiO3has
been observed experimentally [26]. In the case of samples
containing 15% La a small polaron conduction mecha-
Typical low tem-
nism was observed by fitting the low temperature resis-
tivity data to ρ ∼ sinh2(1
T). Recently, Liang et al. [27],
suggested the possibility of small polaron conduction in
films grown under similar conditions. Fig. 3 shows the
fit for both the conduction mechanisms in the respective
samples. The optical phonon mode’s characteristic tem-
perature (Topt) derived by the fit was 100–120 K for the
samples. It is interesting to note that this characteris-
tic temperature is very close the soft mode transition in
SrTiO3 at 110 K [28]. This indicates that the suitable
scattering parameter for these samples at 300 K is r=1
(for T ≪ Topt, r=1
2and T ≫ Topt, r=1 [29]).
With the scattering mechanism known, we can solve
the Boltzmann transport equations. To simplify our cal-
culations, we have modeled our system with an effective
single parabolic band with effective mass m∗. The value
of m∗were determined from the measurements of ther-
mopower and carrier concentration n (from the Hall mo-
bility and resistivity). We have assumed that the pres-
ence of oxygen vacancies lifts the six fold degeneracy and
hence the conduction band is only four fold degenerate.
The equations used for the model [23] are
S =−kB
e
?(r + 2)Fr+1(η)
(r + 1)Fr(η)
− η
?
(1)
n = 2πz
?2m∗kBT
h2
?3
2
F 1
2(η) (2)
Fr(η) =
?∞
0
xr
1 + ex−ηdx (3)
where kB, h, e, η, z, r, m∗are the Boltzmann constant,
Planck’s constant, electronic charge, reduced chemical
potential (µ/kBT), degeneracy of the conduction band,
scattering parameter and effective mass respectively. The
scattering parameter gives the energy dependence of the
scattering time and is of the form τ(ǫ) = τ0ǫr−1
is the energy of the carrier. Knowing the scattering pa-
rameter from the temperature dependent mobility data,
we can solve equations (1) and (2), to obtain η and m∗.
All the measured and calculated values are listed in Table
I.
2, where ǫ
The measured thermopower and the calculated values
of the effective mass as a function of carrier concentration
are plotted in Fig. 4. The measured thermopower val-
ues for the samples at low carrier concentration (≤ 1021
cm−3) lie on log fit, indicating non-degenerate doping.
For higher carrier concentration, we see some deviation
from the logarithmic behavior as the doping tends to the
degenerate limit. The reduced chemical potential listed
in Table I also concurs with this line of analysis. Fig. 4b

Page 4

4
?
?
?
?
?
?
?
?
?
?
?
??
?
?
??
??
FIG. 4: (a) Measured thermopower and (b) calculated effec-
tive mass in Sr1−xLaxTiO3−δ as a function of carrier concen-
tration n at 300 K. Effective mass values from Ohta et al. [9]
and Frederikse et al. [10] are also shown for reference.
shows we can influence the effective mass as a function
of carrier concentration and scattering mechanism. Re-
markably, the effective mass decreases with increasing
carrier concentration unlike the conventional small band-
gap semiconductors.This behavior is consistent with
our assumption that the material should follow a simple
parabolic model as has been observed in the past [7, 9].
In summary, we have outlined a methodology to
tune the effective mass in n-type oxide semiconductors
through double doping with both an A-site dopant and
oxygen vacancies in STO. The nature of m∗is mainly
filling controlled, specifically it decreases with increasing
carrier concentration and can be tuned in the range of
6–20 me by chosing a given doping combination. The
tuneability is achieved by the presence of a high effective
mass impurity band which is separated from the conduc-
tion band by a small gap, as has been theorized prior to
our observation of this energy level. A good understand-
ing of the critical parameters may be used to better tai-
lor the thermoelectric and photovoltaic response of oxide
materials.
The authors would like to acknowledge discussions
with Choongho Yu, assistance of Dr. Costel Rotundu
in Hall measurements, the UC Berkeley/LBNL thermo-
electrics group and support from the US Dept. of Energy.
[1] M. Cardona, Phys. Rev. 121, 752 (1961).
[2] C. Verie, and E. Decamps, Phys. Stat. Sol. 9, 797 (1965).
[3] P. Byszewski,J. Kolodziejczak, and S. Zukotynski, Phys.
Stat. Sol. 3, 1880 (1963).
[4] W. Zawadzki, Adv. Phys. 23, 435 (1974).
[5] E. O. Kane, J. Phys. Chem. Solids. 1, 249 (1957).
[6] G. R. Stewart, Rev. Mod. Phys. 56, 755 (1984).
[7] T. Okuda et al., Phys. Rev. B 63, 113104 (2001).
[8] M. A. Green, Physica E 14, 65 (2002).
[9] S. Ohta et al., Appl. Phys. Lett. 87, 092108 (2005).
[10] H. P. R. Frederikse, and W. R. Hosler, Phys. Rev. 161,
822 (1967).
[11] W. Luo et al., Phys. Rev. B 70, 214109 (2004).
[12] J. E. Sunstrom IV et al., Chem. Mater. 4, 346 (1992).
[13] T. Zhao et al., J. Appl. Phys. 87, 7442 (2000).
[14] Since the sensitivity of techniques such as EELS, RBS,
and EDS is only ∼ 2% for impurity atoms and much
higher for vacancies, characterization of the number of
oxygen vacancies can only be estimated through measure-
ment of n, and the precise relationship between oxygen
growth pressure and δ is unknown.
[15] W. Wunderlich, H. Ohta, and K. Kuomoto, Physica B
404, 2202 (2009).
[16] T. Tanaka et al., Phys. Rev. B 68, 205213 (2003).
[17] M. Capizzi, and A. Frova, Phys. Rev. Lett. 25, 1298
(1970).
[18] S. Mochizuki, F. Fujishiro, and S. Minami, J. Phys.: Con-
dens. Matter 17, 923 (2005).
[19] G. Dresselhaus, A. F. Kip, and C. Kittel, Phys. Rev. 98,
368 (1955).
[20] J. L. M. van Mechelen et al., Phys. Rev. Lett. 100,
226403 (2008).
[21] M. Takizawa et al., Phys. Rev. B 79, 113103 (2009).
[22] H. P. R. Frederikse et al., Phys. Rev. 158, 775 (1967).
[23] C. B. Vining, J. Appl. Phys. 69, 331 (1991).
[24] H. Shanthi, and D. D. Sarma, Phys. Rev. B 57, 2153
(1998).
[25] D.D. Cuong et al., Phys. Rev. Lett. 98, 115503 (2007).
[26] D. A. Muller et al., Nature 430, 657 (2004).
[27] S. Liang et al., Solid State Comm. 148, 386 (2008).
[28] P. A. Fleury, J. F. Scott, and J. M. Worlock, Phys. Rev.
Lett. 21, 16 (1968).
[29] B. M. Askerov, Electronic Transport Phenomena in
Semiconductors (World Scientific, Singapore, 1994).

Page 5

5
TABLE I: Various measured and derived physical quantities as a function of La doping and growth pressure in Sr1−xLaxTiO3−δ
at 300 K; ρ is resistivity, S is thermopower, n is Hall carrier density, µ is mobility, r is scattering parameter, m∗is effective
mass, me is electron mass and η is reduced chemical potential(µ/kBT).
S. No.La%Growth pressureρnµSr
m∗
me
η
(Torr)
10−7
10−3
10−7
10−3
10−4
10−7
(mΩ cm)
16.3
1.5x104
15.9
4.6
1.7
2.7
(x1021cm−3)
0.6
3.1x10−3
1.1
2.1
2.7
3.1
cm2V−1s−1
0.64
0.13
0.36
0.65
1.36
0.75
(µV/K)
-274
-832
-190
-154
-101
-81
1
2
3
4
5
6
0
2
2
15
15
15
0.5
0.5
0.5
1
1
1
8.3
18.6
7.1
7.1
6.1
6.0
-0.6
-7.2
0.6
1.7
2.7
3.1