Article
pubs.acs.org/JACS

Modulation of Thermoelectric Power Factor via Radial Dopant
Inhomogeneity in B‑Doped Si Nanowires
Fuwei Zhuge,† Takeshi Yanagida,*,† Naoki Fukata,‡ Ken Uchida,§ Masaki Kanai,† Kazuki Nagashima,†
Gang Meng,† Yong He,† Sakon Rahong,† Xiaomin Li,∥ and Tomoji Kawai††

Institute of Scientiﬁc and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan
National Institute for Material Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan§
Department of Electrical Engineering, Keio University, 3-14-1 Hiyoshi Kouhokuku Yokohama 223-8522, Japan∥
Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China‡

S Supporting Information*

ABSTRACT: We demonstrate a modulation of thermoelectric power factor via aradial dopant inhomogeneity in B-doped Si nanowires. These nanowires grown via
vapor−liquid−solid (VLS) method were naturally composed of a heavily doped
outer shell layer and a lightly doped inner core. The thermopower measurements
for a single nanowire demonstrated that the power factor values were higher thanthose of homogeneously B-doped Si nanowires. The ﬁeld eﬀect measurements
revealed the enhancement of hole mobility for these VLS grown B-doped Si
nanowires due to the modulation doping eﬀect. This mobility enhancement
increases overall electrical conductivity of nanowires without decreasing the
Seebeck coeﬃcient value, resulting in the increase of thermoelectric power factor.
In addition, we found that tailoring the surface dopant distribution by introducing
surface δ-doping can further increase the power factor value. Thus, intentionally
tailoring radial dopant inhomogeneity promises a way to modulate the thermoelectric power factor of semiconductor nanowires.
increasing the power factor (S2/ρ) of nanowires at room
temperature has been diﬃcult due to the surface states, which
reduces the mobility and conductivity via the surface trappingand scattering.10,11 One simple solution to overcome this issue
is to create the mobile carriers far from the nanowire surface.
Utilizing a core/shell structure might be the solution to achievethis.12−15 Moon et al. have demonstrated that the power factorof Ge/Si core/shell nanowires exceeded that of bulk value.15
The hole trasnport of Ge nanowire conﬁned by energy bandoﬀset allowed an enhancement of hole mobility.15 Althoughintentionally controlling the radial dopant inhomogeneity
might be a promising way to create such high mobility carriers
even without the use of heterointerfaces,16 the role of radial
dopant inhomogeneity on thermoelectric power factor of
nanowires has not been clariﬁed yet. The spatial dopant
distributions at the nanoscale in semiconductor nanowires havebeen an important issue to control the transport properties.17−21 It has been shown that a dopant inhomogeneity exists
along the radial direction for vapor−liquid−solid (VLS) grown
Si and Ge nanowires.21 For example, B doping in VLS grown Si
nanowires has resulted in a heavily doped outer shell layer anda lightly doped core due to the naturally occurring sidewall
vapor−solid (VS) growth.17 Since the inhomogeneous dopant
spatial distribution is highly detrimental for the applications to

1. INTRODUCTION
Thermoelectric power generation holds great promise for waste
heat recovery.1 Intensive eﬀorts have been devoted to improvethe energy conversion eﬃciency of thermoelectric devices.2−4
The ﬁgure of merit ZT is well-known to determine theconversion eﬃciency, which is deﬁned as S2T/ρκ, where S, ρ, κ,and T are the Seebeck coeﬃcient, electrical resistivity, thermal
conductivity, and temperature, respectively. However, due tothe strong intercorrelation between these parameters, 4enhancing the ZT value has been limited in bulk materials.
Decreasing the thermal conductivity via increasing the phonon
scattering in nanostructures has been a promising approach to
improve the ZT.2−4 Among various nanostructures, selfassembled semiconductor nanowires hold great promise for
improving the ZT. For example, Hochbaum et al.5 and Boukai
et al.6 have reported the signiﬁcant enhancement of ZT inchemically etched Si nanowires, which have been interpreted interms of the decreased thermal conductivity. Another possible
advantage of nanowires is the potential to increase thethermoelectric power factor by decoupling S and ρ via low
dimensional eﬀect.7 Recently, Tian et al.8 and Wu et al.9 haveobserved the enhancement of Seebeck coeﬃcient values due tothe low dimensional quantum eﬀect using InAs nanowires.
However, such quantum eﬀects have been observed only at low
temperature range below 100 K due to perturbations fromsurroundings.8 Although the thermal conductivity has beensuccessfully reduced for various nanowires, maintaining and/or© 2014 American Chemical Society

Received: June 3, 2014
Published: September 17, 2014
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Articlemeasured ΔV and ΔT was observed for the current temperature
gradient range <2 K. The Seebeck coeﬃcient S= −ΔV/ΔT was thenestimated from above linear relationship between ΔV and ΔT. Since
an average temperature coeﬃcient of resistivity (TCR) (∼0.35%) of Pt
thermometer was adopted during the determination of ΔT, thevariation of TCR among diﬀerent devices may lead to a statistical errorof ∼8% for the Seebeck coeﬃcient. However, with the low noise level
for ΔV measurement, the overall error for S determination was
estimated to be <10%. The electrical resistivity of Si nanowires wasdetermined from 4-probe measurements by using the formula: ρ =R4‑probeπd2/4L, where R4‑probe, d, and L were the 4-probe resistance,
nanowire diameter, and nanowire length, respectively. The nanowire
diameter was estimated from the SEM and TEM images. See thedetails in Supporting Information sections 1−3. Note that the present
Seebeck voltage measurements were reliably performed even for thosehighly resistive nanowires (the maximum resistance ∼109 Ω) by
utilizing a high input impedance (∼1018 Ω) preampliﬁer equipped in
the Keithley system. The raw thermovoltage measurement data for a
relatively resistive nanowire (ρ = 100 Ωcm) is shown in Figure S1e.
2.3. Field Eﬀect Measurements to Determine Hole Mobility
and Carrier Concentration. The hole mobility was extracted fromthe ﬁeld eﬀect measurements by using the bottom Si substrate as thegate electrode. The gate voltage Vg was swept from −10 to 10 V, while
the source-drain voltage Vds was ﬁxed to be 0.02 V. The hole mobility
μ was determined from the measured transconductance curves (Ids ∼Vg) using the formula, μ = (dIds/dVg)L2/(CgnVds), where L was the
nanowire length and Cgn was the gate-nanowire coupling capacitance.23 Cgn was approximated based on the “metal cylinder on plane”
model,24 in which it was expressed as Cgn = 2πε0εrL/cosh−1(1/2 + dox/d), where ε0, εr, and dox were the vacuum permittivity, dielectric
constant, and thickness of the gate oxide, respectively. An eﬀective
value of εr = 2.2 was used for SiO2 to address the dielectric
discontinuity at the oxide−vacuum interface.24 It is noted that, due tothe metallic assumption, the approximation of Cgn was valid for heavily
doped nanowires.23 For lightly doped nanowires, the nanowire
capacitance become small. As a result, the overall capacitance wasstrongly gate dependent, and nonlinear transconductance curve wasobserved. Thus, the hole mobility in this work was only extracted for
those nanowires with ρ < 0.05 Ωcm, where the linear transconductance curve was observed. See details in the Supporting
Information section 6.
2.4. Surface Etching on Si Nanowire Device. Surface etching of
Si nanowire devices was performed by a wet etching process using theSC1 solution (NH3H2O:H2O2:H2O = 1:1:5). In this solution, Si
nanowires were fast oxidized by H2O2 and protected from overetchingby the presence of NH3H2O. The overall etching rate was determinedby the dissolution of SiO2 in NH3H2O, which was ∼1 nm/h for ourconditions. After etching, the devices were thoroughly rinsed withwater (80 °C) and isopropanol solvent to remove ions and organic
residuals. The resulted surface density of states has been characterized
to be as low as ∼1012 cm−2,25 which was almost similar to that ofnaturally oxidized H-terminated Si.

electrical devices of nanowires, intensive eﬀorts have been
carried out to achieve uniform dopant distribution.21,22 In thisstudy, we aim to utilize the previously detrimental dopant
spatial inhomogeneity to modulate the thermoelectric power
factor of Si nanowires.

2. EXPERIMENT AND METHODS
2.1. Growth of Si Nanowires. B-doped Si nanowires were grown
by Au catalyzed VLS process using a chemical vapor deposition(CVD) system. Si(111) wafer was used as the substrate. The growthtime was ∼30 min. The growth temperature was set to be 600 °C, andthen the vapor sources of SiH4 (19 sccm) and B2H6 (0.2 sccm) wereintroduced into the reaction chamber. The dopant distribution ofthese VLS grown nanowires was naturally inhomogeneous. This wasshown by the surface etching experiments in the later section. To
further increase such radial dopant inhomogeneity within nanowires,δ-doped nanowires were also prepared to study the eﬀect of dopant
spatial inhomogeneity on the thermoelectric properties. Si nanowires
were grown under the temperature of 550 °C by introducing only SiH4
(19 sccm) for 30 min. Subsequently, the temperature was elevated to
750 °C, and B2H6 (5 sccm) was introduced into the chamber for 1 min
to perform δ-doping. The representative scanning electron microscopy(SEM) and transmission electron microscopy (TEM) images of asgrown B-doped Si nanowires are shown in Figure 1a and b,
respectively. The diameters of these nanowires ranged from 20 to
200 nm.

Figure 1. (a) SEM image of VLS grown B-doped Si nanowires, (b)TEM image of VLS grown B-doped Si nanowires, (c) SEM image of
device conﬁguration used in this work to characterize the resistivity
and Seebeck coeﬃcient, and (d) correlation data between thermovoltage ΔV and temperature diﬀerence ΔT to determine Seebeck
coeﬃcient S.

3. RESULTS AND DISCUSSIONFirst, we examine the thermoelectric properties of VLS grown
B-doped Si nanowires. Figure 1a,b shows the SEM and TEM
images of employed B-doped Si nanowires. The present Si
nanowires were grown along the ⟨111⟩ growth direction.26 The
core−shell-like structures of present Si nanowires can be seenin the TEM images. This spatial inhomogenity has been
considered as a consequence of VS ﬁlm growth on the
nanowire surface with the decomposition of dopant sources(B2H6).20 As discussed by Amit et al., such a shell layer was
dopant-rich when compared to the inner core, where thedopant atoms were merely incorporated into nanowires
through metal catalyst.20 Although we do not have the dopant
distribution data, the existence of such heavily doped shell layer
in the present B-doped Si nanowires is probed by a series of

2.2. Seebeck Coeﬃcient and Electrical Resistivity Measurement. The electrical measurements of Si nanowires were performed
using 4-microprobe systems with the electrical characterization system(Keithley 4200SCS). Figure 1c shows the SEM image of device
conﬁguration fabricated by electron-beam lithography processes. All
nanowire devices were fabricated on Si substrates with SiO2 layer of
300 nm thickness. An external power source (WF1946, NF Co. Ltd.)was connected to the microheater in Figure 1c to generate the local
temperature gradient. The thermovoltage ΔV and temperature
diﬀerence ΔT along the Si nanowire were measured. Figure 1dshows typical results of the measured thermovoltage when varying thetemperature diﬀerence ΔT. The linear relationship between the14101

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Article∼1.6 times higher than the reference data (∼1000 μV/K). In
such lightly doping region, the theory based on so-called Mott
relation well describes the electric contribution of Seebeck
coeﬃcients,32 as shown in Figure 2a (dashed line). The
calculation was performed based on the nondegenerated
assumption of Si by using the resistivity values estimatedfrom the empirical hole mobility in B-doped Si.33,34 Details of
the calculation can be seen in the Supporting Information
section 5. As can be seen, the theoretical prediction based on
the Mott relation well predicted the Seebeck coeﬃcient forhomogeneously B-doped Si samples, but not for the present Bdoped Si nanowires. Figure 2b shows the comparison between
the present data and reference data on the power factor values.
The power factor of present nanowires showed the maximum
value (1.46 mW/K2 m) at the resistivity of ∼10−2 Ω cm, whichis still lower than the optimized power factor data (4.7 mW/K2m)30 for homogeneously B-doped Si polycrystalline samples atthe lower resistivity range of 3 × 10−3 Ω cm. The data of ref 5
for B-doped Si nanowires, which were treated by postgrowth
gas-phase B doping (i.e., the possible spatial dopant
inhomogeneity), showed the only higher power factor value(3.3 mW/K2 m); however, other previous power factor valuesof homogeneously B-doped Si nanowires were lower than the
maximum value of the present nanowires.
There are several possible scenarios to explain the observed
modulation of power factor in the present B-doped Si
nanowires. First, the Seebeck coeﬃcient value can be increased
by a low dimensional quantum eﬀect on the density of statesaccording to the theoretical predictions.7 However, considering
the present nanowire size range down to 20 nm, thetemperature range employed (room temperature) and the
Bohr radius required for quantization (∼4.3 nm), such aquantum eﬀect is unlikely to emerge within the limit of thepresent experiments.35 As indirect evidence, the electricaltransport properties of the present Si nanowires did not show
any apparent diameter dependences, as shown by Figure S3 in
the Supporting Information. This result also excludes the roleof surface states on the observed modulation of power factor.
The other scenario is based on the presence of inhomogeneous
dopant distribution within our B-doped Si nanowires grown by
VLS process (i.e., heavily doped outer shell and lightly doped
inner core). If there is a diﬀerence between the heavily doped
outer shell and the lightly doped inner core on the electricalconductivity due to the diﬀerent dopant concentration, thevariation of physical properties should also exist along the radial
direction of present nanowires.36 Thus, the combination ofboth core and shell properties, including the Seebeck coeﬃcientand conductivity, determines the physical properties ofnanowires.37 In addition, the mobile carriers might diﬀusefrom the heavily doped outer shell to the lightly doped innercore to align the Fermi level, as can be seen in our calculation
data in Supporting Information section 7. If such diﬀused
carriers exist in the lightly doped core, the apparent mobility ofnanowires should be increased when compared with homogeneously doped systems due to the suppression of ionized
impurity scattering.
To examine the above scenario, the ﬁeld eﬀect measurements
were performed to extract the mobility and the carrier
concentration in our B-doped Si nanowires. Figure 3 showsthe extracted hole mobility data plotted as a function of thehole carrier concentration. Reference data of homogeneously Bdoped Si are shown for comparison.33,38 As seen in the ﬁgure,the mobility data of the present B-doped Si nanowires were

surface etching experiments, as will be discussed in the later
section.
Figure 2a shows the measured Seebeck coeﬃcient data for Bdoped Si nanowires, whose electrical resistivity values were

Figure 2. (a) Seebeck coeﬃcient and (b) power factor data of present
VLS grown B-doped Si nanowires as a function of resistivity. For
comparison, reference data of homogeneously B-doped Si and thetheoretical calculated line based on the Mott relation are shown.

ranged from 10−3 to 102 Ωcm. Although the nanowires werecollected from the same sample, the resistivity values were
widely distributed. We found that the resistivity distribution of
nanowire is mainly caused by the variation of apparent dopant
concentrations within nanowires rather than surface damages
during device fabrication process, as shown in the Supporting
Information section 4. Note that we intentionally utilized theresistivity distribution to examine the correlation between the
Seebeck coeﬃcient and electrical resistivity. The reference dataof Seebeck coeﬃcients for B-doped Si nanowires,5,6,27−29
polycrystalline30 and single crystalline31 samples are shown in
Figure 2. Since the phonon-drag eﬀects were negligible innanowires, the present data of nanowires should be comparedto the reference data for nanostructures and polycrystalline
samples, where the electronic contribution on the Seebeck
coeﬃcient is dominant. As seen in Figure 2a, for a relatively low
resistivity range below 10−2 Ω cm, both the nanowire and thereference values were ranged below 400 μV/K. Above 10−2 Ω
cm, the Seebeck coeﬃcient value of nanowires tends to besigniﬁcantly higher than the reference data. For the resistivity∼102 Ω cm, the Seebeck coeﬃcient value (∼1640 μV/K) was
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Articleinner core might occur, as supported by our electrostatic
simulations in Supporting Information section 7. This mightenhance the apparent mobility of nanowires when comparedwith homogeneously doped nanowires due to the decreased
impurity scattering in the inner core.
Next, we experimentally probe the existence of the heavily Bdoped shell within Si nanowires by performing a wet etching of
the Si nanowire surface. This is because the conventional
composition analysis methods are not capable of detecting the
low concentration of B dopants within the present Si
nanowires.17,22 The etching experiments were performed byusing the widely used SC1 solution (H2O2:NH3/H2O:H2O =1:1:5) for Si processing.25 Figure 4a shows the schematic of the
Figure 3. Hole mobility data of present VLS grown B-doped Si
nanowires as a function of hole concentration, which were determinedby ﬁeld eﬀect measurements. For comparison, the reference data for Bdoped Si systems are shown in the ﬁgure. The inset shows theextracted relationship between Seebeck coeﬃcient data and holeconcentration.

higher than the data of homogeneously B-doped Si when the
carrier concentration was ranged below around 1019 cm−3. This
carrier concentration range is in fact well consistent with theresistivity range ρ > 10−2 Ω cm in Figure 2, where the Seebeck
coeﬃcient and the power factor tend to deviate from thereference data of homogeneously B-doped Si. When the carrier
concentration was higher than 1019 cm−3, the hole mobility was
lower than those of the homogeneously B-doped system. Notethat the lower mobility values were comparable with those ofearlier VLS grown B-doped Si nanowires.29 In such heavily B
doping range for nanowires, the degraded crystallinity39,40 due
to the presence of nonactivated B dopants possibly lowers thehole mobility. From the hole mobility and electrical resistivity
data, we examine the relation between the Seebeck coeﬃcientand the carrier concentration, as shown in the inset of Figure 3.
There was no signiﬁcant diﬀerence between the present
nanowires and homogeneously B-doped Si on the Seebeck
coeﬃcient data as a function of the carrier concentration. Thus,
the mobility enhancement increases overall electrical conductivity of nanowires without reducing the Seebeck coeﬃcientvalue, which increases the power factor of nanowires. Hence,these mobility data are consistent with the scenario based on
the presence of inhomogeneous dopant radial distribution to
explain the observed modulation of the power factor. Since thehole mobility of the nanowire tended to be lower than that ofbulk Si due to the degraded crystallinity in the doping range
above 1019 cm−3, the applicability of the present method basedon dopant modulation eﬀects seems to be limited. One of thepossible approaches to overcome this limitation might be theuse of rapid thermal annealing41 to enhance the crystallinity ofnanowires.42
Here we question the inherent nature of mobility enhancement when the radial dopant proﬁle exists. In general, the holemobility depends on the eﬀective hole mass and scattering
mechanism. Since the eﬀective hole mass in the ⟨111⟩ directionin Si is relatively heavy,43 the modulation of mobility by thegrowth direction of nanowire is unlikely to occur. The otherscenario is based on the diﬀerence between the inner core andthe outer shell on the carrier scattering. If the sharp gradient of
B dopant concentration exists in the radial direction of thepresent nanowires (heavily doped outer shell/lightly doped
inner core), the carrier diﬀusion from the outer shell to the

Figure 4. (a) Schematic illustration of the in situ surface etchingprocess of Si nanowire device, and the representative SEM images ofnanowire devices after surface etching treatments. (b) Eﬀect of surface
etching treatments on Seebeck coeﬃcient data as a function ofresistivity. The inset shows the variation of Seebeck coeﬃcient data asa function of nanowire diameters during etching. Each color markstands for the same nanowire device.

etching experiments. The nanowires were etched on the device.
In the SC1 solution, the surface oxide on Si nanowire wasslowly etched (∼1 nm/h) by NH3/H2O, while H2O2 was used
to protect the nanowire from overetching by fast reoxidizing
the exposed Si surface. Figure 4a also shows the representative
SEM images of the etched nanowires. The nanowire diameter
was continuously reduced from 58 to 20 nm after three steps ofetching. The typical measured properties of the etched
nanowires, including the resistivity, Seebeck coeﬃcient, andmobility, are shown in Table 1. The device morphology and themeasured transconductance curves before and after etching aresupplied in Supporting Information section 8. We found that
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ArticleTable 1. Comparison between the Original VLS Grown B-Doped Si Nanowires and Nanowires after Surface Etching on the
Physical Properties Including Diameter, Resistivity, Seebeck Coeﬃcient, Hole Mobility, and Carrier Concentration
sampleoriginal
after etchingadiameter (nm)63
57

resistivity (Ω cm)−3

9.94 × 10
1.35 × 10−1

S (μV/K)

μ (cm2/(V s))p (cm−3)

356
511a

82.41
273.67

7.63 × 1018
1.69 × 1017

Theoretical prediction: p = 1.69 × 1017 cm−3, S ∼ 527 μV/K.

removing slightly the surface layer (∼3 nm) signiﬁcantly
increased the resistivity, Seebeck coeﬃcient, and hole mobility.
These variations are consistent with the presence of the heavily
doped shell in the present B-doped Si nanowires. Especially, theobserved enhancement of hole mobility cannot be explained by
the surface etching damage eﬀect, which in general decreases
the carrier mobility. Thus, the enhanced mobility data in theetched nanowires supports the present scenario based on theinhomogeneous dopant proﬁle (heavily doped shell and lightly
doped inner core). In Figure 4b, we show the Seebeck
coeﬃcient data as a function of electrical resistivity fornanowire devices after surface etching treatments in comparison with the data of as-grown VLS grown nanowires and also
the theoretical calculation data based on the Mott relation.32,34
After surface etching, the Seebeck coeﬃcient data of nanowires
tend to be consistent with the theoretical prediction of theMott relation, that is, the homogeneously B-doped Si. The inset
shows the collected Seebeck coeﬃcient variation on diﬀerent
nanowire devices, in which each mark stands for the samedevice. The Seebeck coeﬃcient data increased with decreasing
the nanowire diameter by etching. Since the Seebeck coeﬃcient
data should be constant if the homogeneous dopant
distribution exists, the increased trend of Seebeck coeﬃcient
after etching also supports the presence of the heavily doped
shell and lightly doped inner core in the present Si nanowires.
Thus, these experimental results consistently support thecritical role of the heavily doped outer shell on the observed
modulation of power factor values.
Finally, we try to further enhance the role of heavily doped
shell layer on the power factor. In principle, the thinner doped
shell layer with sharper dopant gradient should enhance thecontribution of diﬀused carriers from outer shell to inner coreon the overall properties of nanowires. Thus, we create suchthinner doped shell layer by utilizing surface δ-doping. The δdoped nanowires were formed by preparing a heavily B-doped
shell layer on the intrinsic Si nanowires, as illustrated by theinset of Figure 5a. Figure 5 shows the measured Seebeck
coeﬃcient and power factor data of δ-doped Si nanowires. For
comparison, the data of B-doped Si nanowires grown by VLS
process are shown in the ﬁgure. Interestingly, the Seebeck
coeﬃcient and power factor values of δ-doped nanowires were
further increased and higher than those of VLS grown B-doped
Si nanowires. This further enhancement of power factor values
via δ-doping highlights the critical role of heavily doped shelllayer thickness on the overall thermoelectric property ofnanowires. Next, we examine the transport properties (mobility
and carrier concentration) of δ-doped Si nanowires byperforming ﬁeld eﬀect measurements to reveal the role of δdoping on the power factor. The inset of Figure 5b shows theextracted hole mobility data of δ-doped nanowires as a functionof the carrier concentration. In contrast to the transport data of
Ge/Si core/shell nanowires with heterointerfaces,15 the present
δ-doped nanowires without heterointerfaces more steadily
exhibited the mobility enhancement, possibly due to theabsence of heterointerfaces. As shown in the ﬁgure, the mobility

Figure 5. Comparison of (a) Seebeck coeﬃcient and (b) power factor
between the δ-doped Si nanowires and the VLS grown B-doped Si
nanowires. The inset of (a) shows the schematic illustration of a δdoped nanowire, composed by a intrinsic core and a heavily B-doped
shell. The inset of (b) shows the comparison between measured holemobility for δ-doped and VLS grown Si nanowires. The mobility
enhancement was clearly consistent with the higher power factor for δdoped nanowires.

values of δ-doped Si nanowires were statistically higher thanthose of VLS grown B-doped Si nanowires. Thus, this further
mobility enhancement, which increases overall electricalconductivity without reducing Seebeck coeﬃcient values,
increases the power factor values of δ-doped nanowires.
When compared to the data of bulk Si, the hole mobility ofnanowires with dopant modulation tended to be lower in thedoping range above 1019 cm−3. As a result, the maximum power
factor value in the present δ-doped Si nanowires is limited to
2.0 mW/K2 m, which is lower than the optimized power factor
value (4.7 mW/K2 m) of polycrystalline samples30 and the dataof nanowires (3.3 mW/K2 m) in a more heavily doped range.5
When compared to the natural VLS grown Si nanowire, thesuperior properties of δ-doped Si nanowires clearly demonstrated the successful application of radial dopant modulation
to engineer the thermoelectric performance of nanowires. As
mentioned earlier, improving the dopant activation process(e.g., by rapid thermal annealing treatment42) in the present
nanowires would be essential to further overcome the current
limitation in enhancing the power factor over that of bulk
materials. In the meantime, our present experimental results
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also infer that the thermoelectric power factor of Si nanowires
can be further enhanced via more sophisticated dopant
engineering in nanowires, that is, by creating thinner heavily
doped shell layer on smaller diameter nanowires based onpresent δ-doped nanowires. Although we have shown thequalitative information as to the dopant spatial distribution, it
would be an interesting issue to quantitatively correlate the real
dopant spatial distribution of nanowires to thermoelectric
properties by performing highly sensitive dopant proﬁling
measurements (e.g., atom-probe tomography) or C−V
measurements.

4. CONCLUSION
In conclusion, we demonstrate the modulation of thermoelectric power factor via radially inhomogeneous dopant
distributions in B-doped Si nanowires. The spatial distributionof B dopants within Si nanowires was inhomogeneous due tothe sidewall vapor−solid growth during the vapor−liquid−solid
nanowire growth, resulting in the heavily doped outer layer.
The ﬁeld eﬀect measurements clariﬁed that the hole mobility
values of these nanowires were higher than those ofhomogeneously B-doped Si systems due to the dopant
modulation eﬀect. This mobility enhancement increases overall
electrical conductivity of nanowires while without reducing the
Seebeck coeﬃcient value, resulting in the enhancement ofthermoelectric power factor. In addition, we found that
tailoring the surface dopant distribution by introducing δdoping can further increase the power factor value. Thus,
intentionally tailoring radial dopant inhomogeneity promises a
way to improve the thermoelectric power factor of semiconductor nanowires with low thermal conductivity.

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ASSOCIATED CONTENT

S Supporting Information*

Details of the Seebeck coeﬃcient measurement, diameter
calibration, error analysis, mobility extraction, a simulation ofcarrier diﬀusion under dopant gradient, additional detailed
results from surface etching. This material is available free ofcharge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

yanagi32@sanken.osaka-u.ac.jp
Notes

The authors declare no competing ﬁnancial interest.

■

ACKNOWLEDGMENTS
This work was supported by NEXT Project. T.K. was
supported by FIRST program. T.Y and K.U. are thankful forthe ﬁnancial support of CREST.

■

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