Top-gated germanium nanowire quantum dots in a few-electron regimeSung-Kwon Shin, Shaoyun Huang, Naoki Fukata, and Koji Ishibashi Citation: Applied Physics Letters 100, 073103 (2012); doi: 10.1063/1.3684941 View online: http://dx.doi.org/10.1063/1.3684941 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/100/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Growth and optical properties of CdTe quantum dots in ZnTe nanowires Appl. Phys. Lett. 99, 113109 (2011); 10.1063/1.3630004 Advanced core/multishell germanium/silicon nanowire heterostructures: Morphology and transport Appl. Phys. Lett. 98, 163112 (2011); 10.1063/1.3574537 The growth and radial analysis of Si/Ge core-shell nanowires Appl. Phys. Lett. 97, 251912 (2010); 10.1063/1.3531631 Band engineered epitaxial Ge – Si x Ge 1 − x core-shell nanowire heterostructures Appl. Phys. Lett. 95, 033101 (2009); 10.1063/1.3173811 Top-gate defined double quantum dots in InAs nanowires Appl. Phys. Lett. 89, 252106 (2006); 10.1063/1.2409625

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Top-gated germanium nanowire quantum dots in a few-electron regime

Sung-Kwon Shin,1,2 Shaoyun Huang,1,a) Naoki Fukata,3 and Koji Ishibashi1,2

1Advanced Device Laboratory, RIKEN, Wako, Saitama 351-0198, Japan2Department of Electronics and Applied Physics, Tokyo Institute of Technology, Yokohama 226-8503, Japan3International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba,Ibaraki 305-0044, Japan

(Received 5 January 2012; accepted 26 January 2012; published online 13 February 2012)

Top gated quantum dots (QDs) have been fabricated from n-type chemically synthesized

germanium nanowires (GeNWs) by constricting its length with metal electrode contacts. With an

intermediate HfO2 thin film, the constricted GeNW was fully covered by an Omega-shaped

top-gate. The QD was probed and characterized by single-electron transport measurements at liquid

helium temperature and has been found to reach a few-electron regime, in which the number of

confined electrons was tunable from zero. The absolute zero-electron was confirmed with a charge

stability diagram, and it was revealed that the extremely small QD arose from potential fluctuations

due to phosphorus donors. VC 2012 American Institute of Physics. [doi:10.1063/1.3684941]

Germanium nanowires (GeNWs) could be one of the

attracting building-blocks for spin based quantum devices

owing to their several inherent properties that make the spin

coherence large.1,2 Germanium (Ge) of group IV semicon-

ductors possesses small electron spin-orbit interactions

because of inversion symmetric crystal structure and even

small hyperfine interactions due to natural abundance of

spin-zero nucleuses. Besides, Ge nanostructures show much

more significant quantum effects than Si counterparts, aris-

ing from smaller effective electron-mass of Ge.3 Our previ-

ous results showed that a n-type GeNW dot was not

completely depleted, also called “pinch-off,” at the back-

gate voltage (Vbg) of �10 V. In the many-electron region, the

dot showed the electron number even-odd effect, an alternate

change of the total electron spin of the quantum dot (QD)

between 0 and 1/2 as the number of electrons is increased

one by one.4 This fact allows the initialization of the single

spin qubit in the QD when the number of electrons are odd.

However, the simpler scheme to realize the single spin is to

prepare the absolute single electron in the QD. This requires

efficient capabilities of gating on the dot to approach to the

pinch off state.

A highly doped silicon (Si) substrate covered with a

thermally grown thick Si dioxide (SiO2) layer was employed

for a capacitive back-gate in many works.2–5 The SiO2 layer

was usually in thickness of 100–600 nm for the robust device

fabrication processes. As a consequence, the global gating

effects with regards to nanowire dots and metal electrodes

were quite inhomogeneous. Depleting the nanowire dot into

few-electron regimes required a high jVbgj more than 10 V.2

The attempt to constrict the lateral size of quantum dots by

means of shrinking the distance between source and drain

electrodes for much more prominent quantum effects could

further degrade the gating efficiency, because there were

increasing screening-effects from the surrounding electrodes.

In this work, we report on reducing the number of confined

electrons down to zero in an n-type GeNW, i.e., realized a

few-electron QD, by using a top-gate to improve the device

gating performances.

Phosphorus-doped monocrystalline GeNWs were syn-

thesized via a gold-catalyst assisted vapor-liquid-solid

method in a chemical vapor deposition system at 400 �C for

30 min.6 The donor concentration is at a range from 1018 to

1020 cm�3, deduced from cold temperature conductance

measurements, and the nanowires turn out to be degener-

ately doped. The nanowires were grown fast in an axis

direction and slowly at a radial direction, therefore

exhibited a tapered morphology with diameters gradually

changing from 10 to 100 nm at catalyst and root ends,

respectively. Figures 1(a) and 1(b), respectively, show sche-

matics and scanning electron microscopy (SEM) images of

a top-gated device. Nickel with thickness of 80 nm was de-

posited onto the GeNW for source and drain electrodes,

which were separated by 300 nm. In order to protect the

nickel electrodes from oxidation and improve their conduc-

tivity, 20 nm gold thin films were subsequently deposited on

the nickel electrodes. Employing nickel to contact with Ge

nanowire is because nickel can stick with Ge and SiO2 very

well with less interfacial states. The work function differ-

ence between nickel and Ge is reasonable small to give rise

to small contact resistance.7 The diameter at the center of

the constricted GeNW was 30 nm. Prior to the fabrication of

Omega-shaped top-gate (50 nm titanium and 30 nm gold in

thickness), a hafnium oxide (HfO2) thin film with a thick-

ness of 10 nm was deposited onto the GeNW as a gate insu-

lating layer by using atomic layer deposition (ALD)

methods. The highly doped Si substrate covered with

200 nm SiO2 film served as a back gate. The source drain

current (Ids) through the dot explored at the liquid helium

temperature as functions of the local top-gate (Vtg) and

source-drain bias (Vds). The nanometer-scaled magnetic

electrodes without polarization could not give meaningful

contributions to electron transport characteristics because an

external magnetic field is not applied in the following

experiments. Two devices on a chip were studied, which

showed similar transport characteristics. In the followings,

we focus on one of two devices.

a)Electronic mail: syhuang@riken.jp. Tel.: þ81-48-467-9369. Fax: þ81-48-

462-4659.

0003-6951/2012/100(7)/073103/4/$30.00 VC 2012 American Institute of Physics100, 073103-1

APPLIED PHYSICS LETTERS 100, 073103 (2012)

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In the linear response region with Vds¼ 0.3 mV, the be-

ginning of successive Coulomb oscillations of Ids were found

when Vtg was swept from �600 to �125 mV, as shown in

Fig. 2. For the clarity, the position of first peak is indicated

by an arrow at Vtg¼�485 mV. The peak is not clearly seen

at the present scale because Ids is quite weak when the Vtg

approaches to the pinch-off. Alternatively, the position can

be deduced from the following peak periods and related

charge-stability diagrams, plots of differential conductance

as a function of Vds and Vtg, around pinch-off region, as

shown in the inset of Fig. 2. The last closing point of the

Coulomb diamond on the leftmost side indicates the position

of first peak. There are two strong evidences to support that

the closing point at Vtg¼�485 mV is the last available

energy level of the dot. First, there are no more visible peaks

behind Vtg¼�485 mV, and the charge stability diagram on

the left side of the first Coulomb diamond does not close

even throughout Vtg¼�600 mV and Vds¼640 mV. The

right edges of the zero-electron diamond, indicated by

dashed lines, is linear rather than an exponential change

which may arise from increased tunnel barrier resistances

with deeply depleting the QD. Second, two high conductance

lines, as indicated by the solid arrows (a and b), run parallel

to the right edges of the zero electron diamond and can be

found symmetrically in Vds. The lines represent the first

exciting state. It is worthwhile to point out that another high

conductance line, indicated by open arrow-c, ending at the

right upper edge of the zero-electron diamond is not coming

from exciting states but from mesoscopic density-of-states

fluctuations in source/drain contacts.8 As a consequence, the

transition of the number of electrons between 1 and 0 can be

certainly recognized at Vtg¼�485 mV. The spin configura-

tions with respect to each electron filling could be identified

by investigating ground state magnetospectroscopy, which is

not included in this letter.

The charge-stability diagram of the top-gated GeNW

dot near the pinch-off state is shown in Fig. 3. Diamond

shaped white regions represent zero-conductance, i.e., elec-

tron tunneling events are blockaded. These regularly shaped

Coulomb diamonds as well as the close points at a zero Vds

bias between neighboring Coulomb diamonds indicate that

the electron tunneling occurs via a single QD. The number

of confined electrons residing in the QD is constant in these

Coulomb diamond regions and can be populated from zero

up to 10 at one by one sequence by tuning Vtg from �485 to

�145 mV at zero Vds. It is worthwhile to mention that the

FIG. 1. (Color online) (a) Cross sectional view of a top-gated GeNW field-

effect device; (b) a representative image of Scanning-Electron-Microscopy

(SEM) of the device.

FIG. 2. Coulomb oscillation characteristics of the top-gated GeNW dot with

Vds¼ 0.3 mV at liquid helium temperature; the magnitudes of first succes-

sive five oscillations are increased by five factors for clarity and the arrow at

�485 mV indicates the position of first Ids peak. The inset shows a charge

stability diagram around pinch-off Vtg. The gray gradient from dark to white

represents change of conductance from high to low value, respectively. The

position of first peak is deduced from the closing point of the two broken

lines. Solid arrows a and b indicate the first exciting energy level and open

arrow c points out the high conductance line arising from mesoscopic den-

sity-of-states fluctuations in source/drain contacts.

FIG. 3. Charge stability diagram of the top-gated GeNW dot at liquid he-

lium temperature; as numbered in the diamond shaped regions, the GeNW-

QD could be tuned with successive single-electron from zero to ten by

applying Vtg from �485 to �145 mV. The inset shows the addition energy

(Ea) as the function of number of electrons (N).

073103-2 Shin et al. Appl. Phys. Lett. 100, 073103 (2012)

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Coulomb diamond of No. 10 is a little bit irregular and is not

aligned exactly with the others because an accident gate volt-

age jump happens at Vtg¼�160 mV. The accident jump is

not reproducible and does not frequently present in the meas-

urements. The effect of jump is simply shift the diamond

along the Vtg, giving little impact on the overall performance

of the quantum dot. This random effect could arise from sur-

face random charging events around the quantum dot and

could be eliminated easily by improving device fabrication

processes. When Vtg was applied in a positive direction

greater than �145 mV, clear Coulomb diamonds were not

found any more, i.e., the QD had a finite capability to confine

electrons at the temperature. We will get back to this point

later. It can be seen that the peak spacing (DVtg) and the

dimensions of the Coulomb diamonds vary as the number of

electrons are changed, revealing significant variation of the

electron addition energy (Ea),9 which is shown in the inset of

Fig. 3 as a function of the number of electrons. Based on the

constant interaction (CI) model,9 the Ea is simply the sum of

two components, a constant charging energy, determined by

mutual capacitances, and a varied energy level separation,

determined by complex single-particle wavefunction nature.

The inset does not confirm clear shell filling effects,10 indi-

cating that the QD does not possess good dimensional sym-

metries in part because the confinement barriers are

asymmetrical due to the inhomogeneity of the donors.

According to the first excitation line of the first Coulomb dia-

mond (indicated by “a” in Fig. 2), the energy level separation

turns out to be as large as 14 meV, which is much greater

than the thermal kinetic energy at 4.2 K and comparable with

the charging energy, 18 meV, obtained from the size of the

first Coulomb diamond.

According to the “orthodox” theory,11 the QD nature can

be studied with mutual capacitances. The self-capacitances

between QD and surroundings can be estimated, for example,

from the dimensions of the first Coulomb diamond corre-

sponding to the occupation of one confined electron, N¼ 1.

The capacitance between top-gate and dot, Ctg, is 3.2 aF cal-

culated from DVtg¼ 50 mV between first two Ids peaks. The

total capacitance (CR) thus turns out to be 8.9 aF, which con-

sists of Ctg, Cs, and Cd. Here, Cs¼ 3.2 aF (Cd¼ 2.5 aF) is the

capacitance between dot and source (drain). Therefore, the

gate conversion factor atg : Ctg/CR is calculated to be 0.36,

which is more than an order larger than the value of the back-

gate in our similar devices.

The addition energy of the first Coulomb diamond

(18 meV) is more than two orders larger than that of our typical

devices with many electrons (�0.1 meV), where the entire

nanowires between two contacts forms a single QD.4 In this

case, the Coulomb blockade effects are not observable at liquid

He temperatures. To get insight on the origin of the extremely

small QD and to be more quantitative on the size of the QD,

we consider a model of metallic cylinder on infinite metal plate.

Ctg can be formulated by geometry parameters as follows:12

CLtg ¼

pe0erL

ln dL

2RLþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffid2

L

4R2L

� 1

r� � ; (1)

dL ¼ 2ðRL þ trÞ; (2)

where e0 is a vacuum permittivity, er a dielectric constant of

the gate insulator (�25 for HfO2), L the GeNW length under

the gate, RL a radius at the center of the GeNW, tr a thickness

of the gate oxide, and dL the separation between the cylinder

and its mirror image behind the plate, i.e., radial center to

center distance. With an experimental value of Ctg¼ 3.2 aF,

we get L¼ 2.5 nm, which is much smaller than the NW

length under the top gate. Another model of a metallic spher-

ical dot on infinite metal plate is adopted as followings:12

Cdtg ¼ pe0erRd

2tr þ Rd

tr; (3)

where Rd is the radius of equivalent spherical dot. With the

experimental Ctg, we get a QD with radius of 2.1 nm, a simi-

lar value obtained from the other model. Apparently, the

formed QD is significantly smaller than either the length or

the diameter of the constricted GeNW.

The extremely small QD formation has been reported in

Si QDs, which could arise from (1) nanowire surface rough-

ness,13 (2) strain effects,14 (3) unexpected axial nickel diffu-

sion from source and drain electrodes,2 (4) single donors,15

and (5) donor inhomogeneity.16 The surface roughness on

the nanometer scaled channel may induce band bending in

the band diagrams. Potential barriers are thus generated and

give rise to narrow potential wells in the channel. Mechani-

cal strain effects during fabrications may also modulate the

channel potential locally, resulting in the same effect. These

unintentional structural potential wells mainly happen in

QDs fabricated with top-down etching approaches, but not in

the GeNWs synthesized by the self-assembling bottom-up

approach that usually produces atomically smooth surfaces

and strain relaxation.17 Therefore, (1) and (2) can be reason-

ably ruled out. An extremely small QD could be realized in a

Ge nanowire by taking advantage of size constriction with

Ni diffusion from the source and drain contacts along the

axis at a temperature greater than 380 �C.18 However, it may

not the case in the present processes with temperatures

below 180 �C. Many recent studies theoretically depicted

and experimentally demonstrated single-electron transport

through two energy-levels of a single donor even in an envi-

ronment of many donors in a Si nanowire.19 However, the

successive occupation of ten electrons excludes this possibil-

ity. The potential fluctuations due to random donors are the

most plausible origin for the extremely small QD formation.

By taking into account the source/drain symmetry (Cs�Cd)

and the local top-gate effect, the center of 300 nm long con-

stricted GeNW could be the top position of ECB, where two

significant bending-up potentials become higher than Fermi

energy level (EF) and happen to confine electrons in the in-

termediate segment, the QD.20 The local gate effect limits

the area of highest ECB and could allow the presence of just

one QD rather than a serial arrangement of QDs. The QD

dominates the transport characteristics of the GeNW chan-

nel. The size of the QD is at the order of the distance

between two neighboring donors. Considering the nature of

the potential fluctuation with a length scale of the order of

�10 nm, estimated from the possible donor concentration,

and the Bohr radius of a neutral D0 donor in the bulk Ge,

3.9 nm (Ref. 21), we could roughly speculate that the size of

073103-3 Shin et al. Appl. Phys. Lett. 100, 073103 (2012)

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the QD is at the length scale of �5 nm. Meanwhile, an energy

scale of the order of the ionization energy of the donor,

12.6 meV (Ref. 22) can be a rough measure of the charging

energy. The order estimates agree well with extracted results

from the charge stability diagrams of Fig. 3. The ten Coulomb

diamonds shown in Fig. 3 indicates that ten separated energy

levels are responsible to the single-electron tunneling events.

The experimental observation suggests that filling about ten

electrons in the QD could pull EF beyond the confining bar-

riers. As the number of electrons increases, the dot size may

become larger due to Coulomb repulsion and the confinement

effect becomes weaker. This speculation may be consistent

with the Coulomb diamonds in Fig. 3, where the effects of the

zero-dimensional levels are clearer for the small number of

electrons and becomes smeared as the number of electrons

increases. Our future efforts will decrease the temperature

down to milli-Kelvin and concentrate on spin configurations

of consecutive electrons based on the evolution of Coulomb

oscillation peaks in magnetic fields.

In summary, a top-gated few-electron GeNW QD, in

which the number of confined electrons was tunable from

zero, was fabricated and characterized at liquid helium temper-

ature. The top gate demonstrated better capacitive coupling

effects than a back-gate, which made the realization of “pinch-

off” state available with a reasonable gate voltage range. The

QD turns out to be created due to the potential fluctuations at

the center of the constricted GeNW. The realized few-electron

QD could help us to further study spin configurations as well

as fluctuation effects of donors in semiconducting nanowires.

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