R. Nowak et al. / Journal of Advanced Research in Physics 3(2), 021202 (2012)
1
Electron filling in phosphorus donors
embedded in silicon nanostructures observed
by KFM technique
Roland Nowak1,2, Miftahul Anwar1, Daniel Moraru1, Takeshi Mizuno1,
Ryszard Jablonski2, and Michiharu Tabe1,*
1
Research Institute of Electronics, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu, 4328011, Japan
2
Institute of Metrology and Biomedical Engineering, Warsaw University of Technology, Sw. A. Boboli
8, Warsaw, 02-525, Poland
Abstract — Low Temperature Kelvin Probe Force
Microscope (LT-KFM) is used to investigate the surface
potential of phosphorus-doped thin silicon-on-insulator field
effect transistor. Ionized phosphorus donors induce local
potential modulations due to their Coulomb potential. Here, we
show results of electron injection into neighboring donors by
gradually increasing the backgate voltage. Such single donor
neutralization can be observed if neighboring donors are
isolated from each other by a potential barrier. The potential
barrier can be directly related to the inter-donor distance, as
shown by a statistical analysis of donor pairs.
Keywords — single dopant potential, Kelvin probe force
microscope, SOI-FET, single-electron filling
I. INTRODUCTION
As a consequence of continuous downscaling,
electronic devices reached dimensions smaller than 100 nm.
In this situation, the random number and location of
discretely distributed dopants is a serious problem in terms
of reproducibility of device characteristics [1]. On the other
hand, it has been demonstrated that individual dopants,
donors [2-4] and acceptors [5], may work as quantum dots,
thus allowing the development of dopant-based singleelectron transistors. Several applications have been
proposed utilizing the properties of individual dopants, such
as quantum computing [6], quantum cellular automata [7],
single-electron turnstile [8], single-photon detection [9],
[10] and single-electron memory [11]. Simultaneously, new
techniques for deterministic ion implantation or atomic
manipulation of dopants [12], [13], as well as for dopant
mapping [14]-[16] have been proposed.
In most studies, single-electron transport through dopant
atoms is mainly investigated from the electrical
characteristics of the devices. However, in order to fully
understand and characterize the mechanism of charging or
discharging in single dopants, as a first step, it is crucial to
directly observe the potential of ionized dopants. One of the
most straightforward tools for this purpose is Kelvin probe
force microscope (KFM) [17]. We have already shown that,
at low temperature (13 K), it is possible to observe
Manuscript received September 07, 2011
*
Corresponding author: ([email protected])
individual dopants in silicon-on-insulator field-effect
transistors (SOI-FETs) during normal operation [15], [18].
Low temperature is important for this experiment because it
allows us to minimize the effect of screening by free
carriers, present in the channel region [18]. At low
temperature, the density of free carriers changes abruptly
around Fermi level. In this way, we can fully deplete free
carriers even when applying small gate voltages, thus
allowing the observation of bare dopant potentials.
As a next step, it is essential to observe electron charging
in individual dopants. In this work, we present KFM
observation of successive electron filling in neighboring
isolated phosphorus (P) donors by gradually increasing the
backgate voltage. For clarifying the necessary conditions for
controlling electron capture by individual donors, a
statistical analysis of the relationship between inter-donor
distance and barrier height is also shown.
II. DEVICE STRUCTURE AND KFM MEASUREMENT SETUP
In Fig. 1(a), the schematic structure of the studied SOIFETs and the KFM measurement setup are presented.
The channel, with length and width of around 500 nm, is
defined by means of electron-beam lithography as a
constriction between larger Si pads working as source and
drain. Top Si thickness is about 15 nm. In order to passivate
the surface and protect it from contamination, 2-nm-thick
SiO2 layer was thermally grown by dry oxidation. Top Si
layer was doped with phosphorus donors, diffused from a
spin-coated silica film containing P2O3. Doping
concentration, estimated based on four-point probe
measurements, is ND ≅ 1 × 1018 cm-3. This value corresponds
to the average inter-dopant distance of about 10 nm.
For the KFM measurement, the sample was inserted in
the low-temperature (13 K) and ultrahigh vacuum chamber
(base pressure <5 × 10-9 Torr), with the electrodes connected
to external voltage sources. Source and drain electrodes,
with contacts made by Au wire bonding, were grounded in
this experiment, while the p-type substrate (NA ≅ 1 × 1015
cm-3) was used as a backgate.
We measured the KFM surface potential images in a
scan area located in the device central region (as shown in
Fig. 1).
R. Nowak et al. / Journal of Advanced Research in Physics 3(2), 021202 (2012)
2
Fig. 1. Schematic structure of the SOI-FETs studied and simplified circuit
for the LT-KFM measurements.
Since both source and drain electrodes are grounded, no
current flows in the device. This way, we are able to study
the static charge distribution in the channel. Without any
applied bias, it is expected that most donors are neutral due
to the strong freeze-out effect [19] that occurs at the low
temperature (13 K) used in this study. However, we apply
negative backgate voltage (VBG) to deplete the channel of
free carriers (electrons). The internal electric field existing
inside the channel is most likely sufficient to ionize the
donor electrons [19] which will be collected at the grounded
source and drain electrodes. By this procedure, during the
KFM scan, the channel potential is practically given by the
immobile charges of the ionized donors. In fact, in our
previous studies we have shown that the observed potential
fluctuations can be ascribed to ionized donors based on
analysis of dimensions and potential depths of the
fluctuations and comparison with simulations [15], [18].
III. OBSERVATION OF ELECTRON FILLING IN DONORS
An example of a potential landscape (color map
surface) measured by LT-KFM is shown in Fig. 2(a), for
VBG = -3 V. In the area shown here, three potential wells can
be observed. Each well has a spatial extension <10 nm and
an electronic potential depth of 10-30 mV. These features
suggest that each potential well is created by one ionized P
donor. This can be confirmed by comparison with
simulations of three neighboring P donors, with Coulomb
potentials, as shown on the right-hand side, in Fig. 2(f).
In order to gradually allow injection of free carriers, i.e.,
electrons, from source and drain pads into the initially
depleted channel, we increased VBG from -3 to 0 V in steps
of 1 V. For the example shown here, significant changes in
the potential landscape can be noticed. First, at VBG = -2 V,
as shown in Fig. 2(b), one of the potential wells (A) vanishes.
At VBG = -1 V, a second potential well (B) disappears, as
observed in Fig. 2(c). The last remaining potential well (C)
vanishes at VBG = 0 V [Fig. 2(d)]. These changes can be
more clearly observed as line profiles along A-B direction,
shown in Fig. 2(e), which illustrate successive flattening of
neighboring potential wells. These changes can be ascribed
to electron filling in donor-induced potential wells, since
donors can be neutralized by the capture of one electron.
The results presented above represent a direct
observation of electron filling in individual donors. More
importantly, in the case shown here, the KFM consecutive
Fig. 2. (a)-(d) Potential landscapes measured by LT-KFM in a 40 × 40 nm2
area in the center of a nanoscale SOI-FET. Backgate voltage, VBG, is used
as a parameter, from -3 to 0 V in steps of 1 V. Potential wells (A, B, C)
vanish successively at more positive VBG’s due to electron filling in
individual donors. (e) Line profiles taken in the A-B direction, illustrating
the injection of a first and second electron in the system. Lines are offset to
compensate for potential changes induced by charging outside the shown
area. (f) Simulation of the potential landscape for a system of 3 P donors.
measurements illustrate successive electron filling in a
triple-donor system, a key unit for the development of more
complex donor-based functionalities.
It can be understood that, for the observation of singleelectron injection in neighboring donors, it is essential that
the donors are sufficiently isolated from each other. If this
condition is met, the electron wavefunction can be localized
within the Coulomb potential well of individual donors.
For that, the critical parameter is the barrier height
between donors. In order to clarify this point, we performed
a statistical analysis of the relationship between inter-donor
distance and barrier height, from our experimental data
measured in a wider scan area (500 × 500 nm2). A large
number of donor pairs were selected and analyzed. For each
pair of donors, the barrier height was estimated as the
potential difference between the bottom of the potential well
and the potential maximum along the segment coupling the
two donors. The results are shown in Fig. 3, with the basic
procedure described in the inset.
Inter-donor distances, dxy, are estimated in the x-y
measurement plane, so it should be noted that the actual
distance between two donors may be larger than the
indicated value due to different depths. It can be seen that, in
most cases, neighboring donors are located at distance dxy of
5-15 nm from each other, which is consistent with the
expected average inter-donor distance of around 10 nm,
estimated from doping concentration. For these cases, the
barrier heights, as measured by LT-KFM, are distributed
R. Nowak et al. / Journal of Advanced Research in Physics 3(2), 021202 (2012)
3
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Fig. 3. Relationship between inter-donor distance in the x-y plane (dxy) and
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selected from a 500 × 500 nm2 KFM scan area in an SOI-FET. The dashed
curve is drawn as a guide for the eyes. Estimation procedure is
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We showed low-temperature KFM results on successive
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ACKNOWLEDGEMENT
We thank M. Ligowski and Y. Kawai for contributions
during experiments. This work was partially supported by
Grants-in-Aid for Scientific Research (20246060, 22656082
and 23226009) from the Ministry of Education, Culture,
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