Supplementary Information
The two-dimensional electron gas in delta-doped SrTiO3
Bharat Jalan and Susanne Stemmer
Materials Department, University of California, Santa Barbara, CA 93106-5050, U.S.A.
Shawn Mack and S. James Allen
Department of Physics, University of California, Santa Barbara, CA 93106-9530, U.S.A.
1.
Dopant profile in delta-doped SrTiO3 films
Lanthanum concentration depth profiles in delta-doped SrTiO3 layers were obtained
using secondary ion mass spectrometry (SIMS). A 6650 Dynamic Quadrupole SIMS
(Physical Electronics, Chanhassen, MN, USA) was operated at or below a chamber
pressure of 5×10-10 Torr. A 2 keV O2+ primary ion beam was scanned over an area of
200 × 230 µm2, with positive secondary ions (139La+, 46Ti+ and 84Sr+) accepted from the
center 15% of the crater area. Figure S1 shows a sharp doping profile at the undoped
buffer/delta-layer interface. La atoms are confined to the doped layer, within the
resolution of the measurement. The bottom delta-layer/undoped buffer interface appears
more spread out, because of the transfer of the sputter energy to the La atoms and other
SIMS-specific broadening processes [1, 2].
Figure S1: SIMS depth profile of a SrTiO3 films delta-doped with La as a function of sputter
time (depth).
2.
Longitudinal and transverse magnetoresistance data
Figures S2 and S3 show the raw data obtained from measurements of the longitudinal and
transverse magnetoresistance, Rxx and Rxy, of the delta-doped SrTiO3 film, respectively.
1
Figure S2: (a) Measured (red) longitudinal magnetoresistance as a function of applied magnetic
field at T = 0.41 K. The cubic polynomial fit that was used to subtract the background is also
shown (blue line). (b) Unsmoothed, longitudinal magnetoresistance after background subtraction.
(c) Same data as in (b), but plotted as a function of 1/B to allow for direct comparison with Fig.
1(b).
Figure S3: (a) Measured (red) transverse magnetoresistance as a function of applied magnetic
field at T = 0.41 K. The linear fit (blue line) is a guide to the eye to show the weakly non-linear
behavior.
2
3.
Hall mobility
Figure S4 shows the measured Hall mobility and the carrier density of the delta-doped
SrTiO3 film as a function of temperature. At 1.8 K, the sheet carrier concentration and
the mobility were 3×1013 cm-2 and 1500 cm2/Vs, respectively.
Figure S4: Hall mobility (filled symbols) and sheet carrier concentration (open symbols) of the
delta-doped SrTiO3 film as a function of temperature.
4.
Sub-band electron effective mass
Temperature-dependent Shubnikov de-Haas oscillations were used to estimate the
electron effective mass in the sub-band that gives rise to the oscillations. The two most
prominent oscillations in the high magnetic field range (occurring at 1 B values between
0.82 T-1 and 0.92 T-1) were used in the analysis. The normalized (to the value at 0.41 K)
Shubnikov-de Haas amplitudes were plotted as a function temperature and fit to the
following expression [3]:

A(T )
T
sinh( 2 2 k bT0 / h c )

A(T0  0.41K ) sinh( 2 2k bT / h c )
T0
(S1)
Note that this expression assumes that s = 1 is dominating the oscillation amplitude.
Figure S5 shows the fit to the data using Eq. (1). For  c a value of 1.32×1012 s-1 is

obtained, which corresponds to an effective mass, m  eB  c 1.56  0.08me . The
error given here reflects the range of B-values for the two oscillations.


3
Figure S5: Temperature dependence of the normalized Shubnikov-de Haas oscillation amplitude
of the two strongest oscillations seen in Fig. 2. The solid line is a fit to Eq. (S1).
5.
Two sub-band model for the Shubnikov-de Haas oscillations
To determine if the observed Shubnikov-de Haas oscillations originate from two
occupied sub-bands with no spin-splitting, the standard expression [3] for a twodimensional electron gas was used to fit the experimental data at T = 0.41 K:
2s1 B


Rxx  4R0  exp 2s kB TD / h c
cos
 s
B
s1
sinh 2s 2 k B T / h c







2

2s 2 kB T h c


(S2)
Figure S6 shows the experimental oscillations and the results from the fit to Eq. (S2),
using the experimentally determined effective mass. The parameters obtained from the
fit were TD1 = 2.11 K and TD2 = 2 K for the Dingle temperatures of the two sub-bands
and frequencies of 21 T and 54 T, respectively. These frequencies do not match the
experimentally determined frequencies. Figure S6 shows that the model does not
describe the periodicity of the oscillations.
Figure S6: Experimental and modeled (two sub-band model) Shubnikov-de Haas oscillations as a
function of the inverse magnetic field.
4
References
[1]
T. L. Alford, L. C. Feldman, and J. W. Mayer, Fundamentals of Nanoscale Film
Analysis (Springer, New York, 2007).
[2]
H. S. Luftman, in Delta-doping of semiconductors, edited by E. F. Schubert
(Cambridge University Press, Cambridge, 2005), p. 201.
[3]
A. Isihara, and L. Smrcka, J. Phys. C 19, 6777 (1986).
5