arXiv:0901.2433v1 [cond-mat.mes-hall] 16 Jan 2009
A Schottky top-gated two-dimensional electron system in a
nuclear spin free Si/SiGe heterostructure
J. Sailer,1V. Lang,1G. Abstreiter,1G. Tsuchiya,2K. M. Itoh,2J. W. Ager III,3
E. E. Haller,3,4D. Kupidura,5D. Harbusch,5S. Ludwig,5and D. Bougeard1, ∗
1Walter Schottky Institut, Technische Universit¨ at M¨ unchen, 85748 Garching, Germany
2Department of Applied Physics and Physico-Informatics,
Keio University 3-14-1, Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
3Lawrence Berkeley National Laboratory,
Materials Sciences Division, Berkeley, CA 94720-8197, USA
4Department of Materials Science and Engineering,
University of California at Berkeley, Berkeley, CA 94720-1760, USA
5Fakult¨ at f¨ ur Physik and Center for NanoScience,
Ludwig-Maximilians-Universit¨ at M¨ unchen,
Geschwister-Scholl-Platz 1, 80539 M¨ unchen, Germany
(Dated: January 16, 2009)
We report on the realization and top-gating of a two-dimensional electron system in a nuclear
spin free environment using28Si and70Ge source material in molecular beam epitaxy. Electron spin
decoherence is expected to be minimized in nuclear spin-free materials, making them promising
hosts for solid-state based quantum information processing devices. The two-dimensional electron
system exhibits a mobility of 18000 cm2/Vs at a sheet carrier density of 4.6 · 1011cm−2at low tem-
peratures. Feasibility of reliable gating is demonstrated by transport through split-gate structures
realized with palladium Schottky top-gates which effectively control the two-dimensional electron
system underneath. Our work forms the basis for the realization of an electrostatically defined
quantum dot in a nuclear spin free environment.
Quantum dots offer a promising two-level system for applications in solid state based
quantum information processing . Within these three dimensionally confining struc-
tures, electrostatically defined quantum dots are a well studied system , mostly in III-V-
materials. A major source of decoherence in such devices is the interaction of the confined
electron spin with the surrounding semiconductor host matrix, in particular with the nuclear
spin bath . Recently, single electron devices have been reported in materials systems like
Si-Ge [4, 5] or C  which contain a reduced amount of nuclear spins in their natural isotopic
composition. As a next step, isotopical purification of the group-IV source materials Si, Ge
and C can give access to virtually nuclear spin free materials. In this letter, we report on the
realization of two-dimensional electron systems (2DES) in a nuclear spin free environment.
A 2DES forms in a strained28Si layer embedded into28Si70Ge. The ability to control the
2DES via top-gates is demonstrated by the implementation of split-gate structures which
are able to locally deplete the 2DES. Suitable voltages allow the complete pinch-off of the
narrow conducting channel.
Samples are fabricated in solid source molecular beam epitaxy (MBE). The base pressure
of the Riber Siva 45 MBE chamber is 1 · 10−11mbar.
28Si and70Ge are evaporated from a
custom made MBE-Komponenten electron beam source and effusion cell respectively.
Fig. 1 a) shows the typical layout of our isotopically engineered Si/SiGe heterostructures.
A SiGe virtual substrate of natural isotopic composition is first deposited onto a (100)
oriented Si substrate. The virtual substrate is realized by increasing the Ge content linearly
by 8%/µm until the desired Ge content is reached. The graded layers are deposited at
a substrate temperature of Ts = 575◦C.The virtual substrate is fully relaxed within the
experimental error of 10%. It typically displays a density of threading dislocations of about
1 · 106cm−2. The active part is then realized in the same fabrication process but from
isotopically purified material. It is composed of a 15 nm thick, fully strained and dislocation
free28Si layer embedded into a28Si70Ge cladding. The lower part of the cladding separates
the nuclear spins of the virtual SiGe substrate from the 2DES. The upper part of the
cladding contains a modulation doping realized with a 15 nm28Si70Ge spacer layer and a
15 nm volume doped28Si70Ge : P layer. The P concentration amounts to 1 · 1018cm−3. The
growth temperature Tswas lowered before depositing the28Si70Ge : P and all subsequent
layers to prevent P segregation to the surface, which could result in a possible lowering of
the Schottky barrier to the gate metal. Finally, the active part of the heterostructure is
SiGe virtual substrate
0,100,15 0,200,25 0,30
FIG. 1: a) Layer structure of an isotopically engineered Si/SiGe heterostructure. The 2DES forms
in the strained28Si layer in a nuclear spin free environment. b) Isotopic abundances of all five
naturally occuring Ge isotopes in a MBE grown layer structure in which a thick layer of70Ge is
embedded into natural Ge. In the70Ge layer, the only nuclear spin carrying isotope73Ge decreases
from approx. 8% to approx. 2.5 · 1018cm−3.
capped with 45 nm natural SiGe and protected against oxidation by a 10 nm thick Si layer
The residual contamination with the nuclear spin carrying isotopes29Si and
both enriched single crystalline source materials,28Si and70Ge, respectively, is below 0.1%.
The abundance of all five naturally occurring Ge isotopes in a MBE grown layer structure
has been determined by high resolution secondary ion mass spectrometry (SIMS) and is
exemplarily shown in Fig. 1 b). To meet the requirements for high concentration resolution
SIMS, a specially designed, MBE grown trilayer consisting of a thick70Ge layer sandwiched
between two layers of Ge of natural isotopic composition was analyzed. In this trilayer,
the abundance of the nuclear spin carrying isotope73Ge decreases by almost 3 orders of
magnitude from approx. 8% in the natural Ge to below 0.025%, i.e. 2.5 · 1018cm−3, in the
70Ge layer. An equivalent suppression of the number of nuclear spins has also been verified
for MBE grown layers involving the28Si source.
Electrical characterization of the 2DES has been done in a
3He cryostat at temper-
atures down to 320 mK and magnetic fields up to 10 T in Hall bar geometry.20 µm
wide Hall bars are defined photo-lithographically and wet-etched in a solution of diluted
hydroflouric acid and concentrated nitric acid. The Ohmic contacts are formed by an
Au/Sb/Au 20/300/1100˚ A trilayer which is annealed at T = 450◦C in an inert N2 at-
mosphere for 180 s and covered with a TiAu bilayer. Longitudinal (Uxx) and transversal
(Uxy) voltage drops were acquired at the same time using two lock-in amplifiers.
Fig. 2 shows a typical result obtained during a magnetic-field sweep from B = 0 T to
B = 10 T at T = 340 mK after illumination of the sample until saturation of the charge
carrier density. Relevant parameters deduced from the measurement prove the high quality
of the 2DES. The 2D sheet carrier density obtained from the low field slope of the Hall
resistance ρxy(B) corresponds very well to the density obtained by a Fourier transform of
the Shubnikov-de Haas oscillations in ρxx and amounts to 4.6 · 1011cm−2. Shubnikov-de
Haas oscillations in ρxx start to develop at B-fields as low as 0.6 T and show the 4-fold
FIG. 2: Longitudinal (black) and transversal (red) Hall resistance for the isotopically engineered
2DES measured at T = 340 mK. Inset: TEM micrograph of the active part of the heterostructure.
The strained28Si layer appears bright. In the SiGe layers, stronger contrasts correspond to a higher
periodicity characteristic for 2DES in Si/SiGe, originating from both, the valley- and spin-
degeneracy. The highest filling factors observed are 32 in ρxxand 12 in ρxy. Spin split levels
can be resolved for filling factors lower than 10. The shoulders in ρxxbetween filling factors
6 and 4 as well as 4 and 2 indicate valley splitting. In the high B-field regime, two very
well defined quantum Hall effect plateaus with corresponding minima of the Shubnikov-de
Haas oscillations for filling factors four and two are visible. Our structures show no sign
for any parallel conduction which might for example arise in the dopant supply layer. This
absence of parallel conduction has additionally been confirmed by Hall mobility spectrum
analysis measurements . The remarkable Hall resistance overshoot visible before filling
factors 3, 4, 6 and 8 is generally observed in our Si/SiGe heterostructure 2DES with narrow
Hall bars and is not induced by the use of isotopically enriched source material. It has also
been observed by other groups [8, 9] and not only for the Si/SiGe material system [10, 11],
but no general picture of its origin has emerged yet. A systematic variation of the Hall bar
geometry and experimental parameters we have carried out on Si/SiGe 2DES both with
natural and isotopically engineered compositions points towards a phenomenon taking place
at the Hall bar edge. The overshoot should thus not impede the realisation of few to one
electron devices in this material. The systematic study will be published elsewhere.
The zero-field Hall mobility of the sample shown in Fig. 2 is 18000 cm2/Vs. A scatter-
ing time analysis [12, 13, 14] performed to determine the main scattering source, suggests
that long range remote impurity scattering is the main mobility limiting scattering mech-
anism. Nevertheless some short range scattering contributions are also observed which are
absent in our Si/SiGe heterostructures of natural isotopic composition. The probable origins
are found through a structural analysis. Cross-sectional transmission electron microscopy
(TEM) analysis as shown in the inset of Fig. 2 for example reveals a material contrast in
the active part. Due to the imaging conditions set, strong contrasts correspond to a higher
Ge content. This indicates a slight mismatch in the Ge content between the28Si70Ge layers
in the active area and the virtual SiGe substrate as well as the SiGe capping respectively.
The resulting lattice mismatch induces potential fluctuations leading to the observed con-
tributions of short range scattering. A suppression of this mismatch via the implementation
of a more sophisticated flux control of the four different sources involved in the fabrication,
Si, Ge,28Si and70Ge, should eliminate the short range scattering contribution and in turn
lead to higher mobilities in future structures.
FIG. 3: Transport through two different split-gates defined on the same isotopically engineered
Si/SiGe heterostructure. Measurements have been done after different cool-downs of the sample
and in two different measurement setups. Inset: AFM micrograph of a nano-constriction. The
scale-bar corresponds to 130 nm.
Electron beam written symmetric split gates with tip-to-tip distances ranging from
130 nm to 200 nm, as for example shown in the AFM micrograph in the inset of Fig. 3,
have been realized on nuclear spin free 2DES with palladium (Pd). The Pd gates proved to
be very stable and reliable over time even after several thermal cycles of the sample between
room temperature and cryogenic temperatures. For all samples, the leakage current of the
Pd gates was below the detection limit of 2 pA of our measurement setups for the whole
range of operation of the gates. Remarkably, the Pd gates deplete the 2DEG underneath al-
ready at zero applied bias (not shown). Fig. 3 shows results obtained for electrical transport
along a narrow conducting channel defined by the narrowest and the widest, 130 nm and
200 nm wide, nano-constrictions fabricated on one Hall-bar. The measurements have been
taken on different days. Complete pinch-off of the narrow conducting channels is achieved
for gate voltages as low as −0.6 V and −0.5 V respectively, opening the possibility to de-
sign a Schottky top-gated quantum dot. We attribute the conductance steps and peaks to
potential fluctuations and thereby induced Coulomb blockade in the vicinity of the narrow
conducting channel .
In summary, employing28Si and70Ge source material in MBE, we have realized a 2DES
in a nuclear spin free environment in strained28Si. Low-temperature magneto-transport
measurements prove the high quality of the 2DES with well defined quantum Hall effect
plateaus. Reliable control of the 2DES and pinch-off a narrow conducting channels has
been demonstrated using split-gates. Our devices represent a promising basis to study the
impact of the absence of nuclear spins on the decoherence of single electron spins by means
of electrostatically top-gate defined quantum dots.
The authors gratefully acknowledge H. Cerva at Siemens AG Corporate Technology for
access to electron microscopy facilities and financial support by the Deutsche Forschungsge-
meinschaft via SFB631 and the Excellence Cluster Nanosystems Initiative Munich (NIM).
The work at Keio was supported in part by MEXT program No. 18001002, by Special
Coordination Funds for Promoting Science and Technology, and by Grant-in-Aid for the
Global Center of Excellence. Work at the LBNL was supported in part by US NSF Grant
Nos. DMR-0405472 and the U.S. DOE under Contract No. DE-AC02-05CH11231.
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