J. Appl. Phys. 111, 043715 (2012); https://doi.org/10.1063/1.3687938 111, 043715

© 2012 American Institute of Physics.

Polarization engineered 1-dimensionalelectron gas arraysCite as: J. Appl. Phys. 111, 043715 (2012); https://doi.org/10.1063/1.3687938Submitted: 23 October 2011 . Accepted: 30 January 2012 . Published Online: 27 February 2012

Digbijoy N. Nath, Pil Sung Park, Michele Esposto, David Brown, Stacia Keller, Umesh K. Mishra, andSiddharth Rajan

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Polarization engineered 1-dimensional electron gas arrays

Digbijoy N. Nath,1,a) Pil Sung Park,1 Michele Esposto,1 David Brown,2 Stacia Keller,2

Umesh K. Mishra,2 and Siddharth Rajan1

1The Ohio State University, Department of Electrical and Computer Engineering, Columbus, Ohio 43210, USA2University of California, Santa Barbara, Department of Electrical Engineering, Santa Barbara, California93106, USA

(Received 23 October 2011; accepted 30 January 2012; published online 27 February 2012)

One-dimensional electron gas based devices are of great interest due to their promise in

high-performance electronics and future device applications. However, synthesis and patterning of

arrays of nanowires is a challenge in all material systems. Here we demonstrate a novel system based

on vicinal AlGaN/GaN heterostructures that enables direct electrostatic tuning of the dimensionalityof electrons from 1 D to 2 D. Our approach, based on polarization engineering, enables top-down

fabrication of dense arrays of pure 1-dimensional electron channels with carrier confinement

equivalent to 90 meV, that are capable of carrying technologically relevant current densities up to

130 mA/mm. A direction-dependent small-signal capacitance-voltage profiling to probe the Fermi

occupation function of electron gas was used to demonstrate distinct signatures of 1-dimensional

density of states and transport in these structures at room temperature. The system discussed here is

based on polarization-induced anisotropic charge in vicinal AlGaN/GaN heterostructures. We

developed a 2-sub-band model consisting of 1-D and 2-D sub-bands to describe the behavior of these

wires. We find excellent agreement between our model and experimental data, confirming the

channels are indeed 1-dimensional. Our demonstration of 1-dimensional electron channel arrays in

this system could enable optical, electronic and magnetic devices with added functionalities and

performance. VC 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3687938]

I. INTRODUCTION

Semiconductor nanowires, owing to their quantum-

confined one-dimensionality, present an excellent system to

explore phenomena at the nanoscale and harness them for use-

ful device applications like nanowire based field effect

transistors,1–8 future device applications,9–11 as well as for

nanowire photonic devices12–16 including microcavity lasers,

LEDs, solar cells, and photodetectors. However, achieving

controlled assembly of high-density nanowire arrays for

large-scale integration, which is crucial for practical applica-

tions, is still a major challenge for both top-down2,17,18 and

bottom-up14,17–20 approaches. While achieving high quality

nanowires with sub-20 nm dimensions becomes a challenge

for top-down approach, the bottom-up approach suffers from

issues such as poor surface control, poor longitudinal control

of doping profiles, and possible metal contamination due to

requirement of metal as catalysts for growth initiation.21

In our previous work,22 we showed that the anisotropy

in the 2-dimensional electron gas (2DEG) charge introduced

by polarization in vicinal AlGaN/GaN heterostructures can

lead to lateral confinement along the steps of the vicinal sub-

strate (Fig. 1). Such a vicinal AlGaN/GaN system with ani-

sotropic transport properties is being increasingly

investigated in more details recently.23,24 In this work, we

show that when combined with the vertical confinement

(due to a heterostructure conduction band offset), such a

system shows signatures of a 1-dimensional electron gas

(1DEG) at room temperature. A direction-dependent small-

signal capacitance-voltage (C-V) profiling method to probe

the Fermi occupation function of the electron gas was used

to demonstrate clear signatures of 1-dimensionality. The

experimentally obtained data matched excellently with

those predicted by a 2-sub-band theoretical model consisting

of a 1-D and a 2-D sub-band which we propose here. In

addition, we demonstrate electrostatic tuning of the dimen-sionality of 1-dimensional and 2-dimensional electron

gases, and show that these may co-exist in this system

depending on the position of the Fermi level. Such an

approach can provide both high density self-defined arrays

of nanowires, which are not lithographically, but electro-

statically obtained, and combines the advantages of both the

top-down and bottom-up approaches without having their

limitations.

II. EXPERIMENTAL DETAILS

The epitaxial structure used for this study (Fig. 2(a)) was

grown by metal organic chemical vapor deposition

(MOCVD) on a vicinal sapphire substrate with a miscut of

4� toward the a-direction. The details of the growth of the

epitaxial stack grown by MOCVD used here have been

reported elsewhere.25 Due to kinetics of step-flow growth,

the atomic terraces and steps characteristic of the vicinal sub-

strate replicate26,27 in the AlGaN/GaN epitaxial layers grown

by MOCVD as shown by atomic force microscopy (AFM) of

the surface of the sample after AlGaN deposition (Fig. 2(b)).

For a 4� miscut in GaN, the atomic terraces are expected to

be 8-16 nm wide (the variation is due to step-bunching). The

a)Author to whom correspondence should be addressed. Digbijoy N. Nath,

205 DL, 2015 Neil Ave., Electrical Engineering Department, The Ohio

State University, Columbus, OH 43210, USA. Electronic mail:

nathd@ece.osu.edu.

0021-8979/2012/111(4)/043715/7/$30.00 VC 2012 American Institute of Physics111, 043715-1

JOURNAL OF APPLIED PHYSICS 111, 043715 (2012)

energy band diagram of the N-polar28,29 AlGaN/GaN hetero-

structure described here was obtained using self-consistent

1-dimensional Schrodinger-Poisson (BandEng)30 simulations

(Fig. 2(c)). A 2DEG is induced at the top interface between

GaN and AlN due to fixed spontaneous and piezo-electric

polarization.31 Ohmic contact pads were fabricated using

standard optical lithography by evaporating a metal stack of

Ti(20 nm)/Al(120 nm)/Ni(30 nm)/Au(50 nm) and then sub-

jecting to a rapid thermal annealing at 850 �C for 30 s to ena-

ble the metals to spike through the top layers to the electron

gas. Mesas were defined by using a BCl3/Cl2 based induc-

tively-coupled-plasma/reactive ion (ICP/RIE) etch chemistry

with 30 W of RIE power to etch 100 nm of the epitaxial layer

so as to isolate the 2DEGs of individual devices. The Ohmic

contacts were fabricated on the sample such that when a bias

voltage is applied between two adjacent contacts, the direc-

tion of current flow between them would be either parallel or

perpendicular (Fig. 2(d)) to the atomic terraces characteristic

of the vicinal surface. A contact resistance of 0.6 X-mm was

extracted from four point transfer length method measure-

ments while sheet resistances in the directions parallel and

perpendicular to the atomic terraces were extracted to be 357

and 467 Xs/square, respectively. This anisotropy in sheet re-

sistance can be attributed to the anisotropy in the 2DEG

charge density.22 Schottky contacts were defined by evapo-

rating Ni (30 nm)/Au (300 nm)/Ni (50 nm) metal stack to

form gates for Schottky diodes to measure C-V.

III. RESULTS AND DISCUSSIONS

A. Capacitance-voltage (C-V) profiling

We are interested in investigating the dimensionality

of the channels. Conventionally, the signature of

1-dimensionality for a nanowire is obtained through magneto-

transport measurements at cryogenic temperatures or gated

conductance measurements (where the conductance is quan-

tized as a multiple of e2/h for each 1-D channel). However, in

FIG. 2. (Color online) Sample and measurement descriptions. (a) The epitaxial structure used in this study; (b) AFM image of the sample surface after AlGaN

deposition: 1 lm� 1 lm scan size, gray scale: 10 nm; (c) The energy band diagram for the epitaxial structure as simulated by 1-D Schrodinger-Poisson solver; (d)

Schematic defining measurement of orientation-dependent currents between two adjacent Ohmic contact pads: parallel and perpendicular to atomic terraces.

FIG. 1. (Color online) Energy profile modeled. Conduction energy band

profile at the interface containing electron gas, corresponding to one atomic

terrace. Inset: It assumes a saw-tooth profile for an array of such terraces.

043715-2 Nath et al. J. Appl. Phys. 111, 043715 (2012)

our system of atomic-terrace defined nanowires, we have a

large ensemble (� 0.5� 106/cm) of self-aligned 1 D channels,

and statistical fluctuations make it difficult to observe the tra-

ditional 1-D characteristics. However, the electron density

populating the ensemble of 1 D channels in our system would

still have a 1/p

E dependence on energy E due to 1 D density

of states. This can be investigated by probing the electron den-

sity as the Fermi level of the electron gas is tuned. For this, we

performed C-V measurements in directions parallel and per-

pendicular to atomic terraces as shown schematically in

Fig. 3(a). The C-V measurement was done as follows: on a

Schottky or gate metal pad (200lm� 200 lm), a sinusoidal

signal of very small magnitude (30 mV) and a frequency

between 100-500 KHz was applied, which rides on a large-

signal DC bias also applied on the gate. An Ohmic pad

(200 lm� 100 lm), situated 4 lm from the gate pad, is con-

nected to the ground. The charge on the gate metal is reflected

in the electron gas populating the channel beneath the gate.

For an incremental voltage DV on the gate, the increase in the

channel charge DQ is measured. Thus, the small-signal charge

flowing between the gate and the Ohmic metals through the

electron gas channel provides the value of the capacitance at a

particular gate bias as C¼DQ/DV. However, only those elec-

trons (or charge) whose wave-vectors are not quantized in the

direction of gate-to-Ohmic can actually flow between the two

contact pads through the channel and hence will contribute to-

ward the capacitance value measured in that direction (i.e.,

parallel to or perpendicular to atomic terraces). For either

direction (parallel or perpendicular), the density of electrons,

ns, (cm�2) corresponding to a given gate bias Vg1 can be

found by integrating the area under the C-V curve to Vg1 from

pinch-off (i.e., the Schottky bias at which the capacitance

starts to rise from zero indicating electrons are starting to pop-

ulate the electron gas),

nsðVg1Þ ¼1

q

ðVg1

Vpinch�off

CðVgÞdVg; (1)

where q¼ 1.6� 10�19 C is the charge of an electron.

Therefore, irrespective of the actual charge that exists

beneath the gate, the measured charge might be different

depending on the dimensionality (or quantized state) of the

electrons and the measurement direction.

The capacitance (normalized to the area) measured par-

allel and perpendicular to atomic terraces is shown in Fig.

3(b). It is interesting to observe that the turn-on (or rise) of

the capacitances in the two directions is different which man-

ifests as two different zero-bias charge densities in the two

directions as extracted using Eq. (1): 7.6� 1012 cm�2 paral-

lel to and 5.7� 1012 cm�2 perpendicular to atomic terraces.

This anisotropy arises from the dependence of the charge on

the dimensionality of the electrons and the measurement

direction as mentioned before.

B. Two sub-band model: Tuning of dimensionality andcomparison with experimental data

To explain the direction-dependence of the C-V profile

and the charge, as well as to establish the 1-dimensional na-

ture of the system, we propose a 2-sub-band theory with a

sub-band E0<Ebar and a sub-band E1 just above Ebar,

where Ebar is the lateral confinement energy corresponding

to the saw-tooth profile (simplified representation in Fig.

3(c)). Electrons populating E0 are quantized in two dimen-

sions (x and z) and can carry current in only one dimension

(momentum wave-vector ky) leading to 1-dimensional

channel transport. The electrons populating E1 have

only wave-vector kz quantized due to heterostructure

FIG. 3. (Color online) Capacitance measurement and 2-sub-band model. (a) Schematic showing orientation of Schottky and Ohmic contacts for C-V measure-

ments parallel and perpendicular to atomic terraces. (b) Normalized capacitance as a function of applied gate bias when probed for transport parallel and per-

pendicular to atomic terraces. (c) Saw-tooth energy band profile (simplified as triangular wells) in the lateral direction along atomic terraces (as shown in

Fig. 2(b)). Electrons in sub-band E0 have wave-vectors non-quantized in y-direction only and hence are purely 1-dimensional. Sub-band E1 consists of pure

2-dimensional electrons with only kz wave-vector quantized in z-axis (growth direction).

043715-3 Nath et al. J. Appl. Phys. 111, 043715 (2012)

confinement in vertical direction but can carry current in

the other two directions (momentum wave-vectors kx and

ky) (as shown in Fig. 3(c)), thus contributing to pure 2-

dimensional transport.

When the gate voltage is lower than pinch-off voltage

of the channel (�7 V in this case), the capacitance is zero

indicating the entire charge is depleted. At pinch-off volt-

age which is ��6 V and ��5 V for transport parallel and

perpendicular to atomic terraces, respectively, the capaci-

tance starts to rise indicating that electrons start populating

the first sub-band. As gate-bias is increased, the Fermi level

EF rises from below sub-band E0 to above E1 to account for

the gradually increasing electron density populating the two

sub-bands. At any given position of EF, electrons populat-

ing only E1 (or electrons with non-quantized wave-vector

kx) are sensitive to (or measured by) C-V profiling in the

direction perpendicular to atomic terraces while C-V profil-

ing in the parallel direction will measure electrons populat-

ing both E0 and E1 (or electrons with wave-vector ky).

Thus, the capacitance shown in Fig. 3(b) corresponding to

perpendicular direction is a direct measurement of a pure

2DEG density while that corresponding to parallel direction

gives the total of 1DEG and 2DEG densities. The differenceof the capacitances measured in the two directions is the ca-

pacitance for the 1-dimensional charge populating the E0

sub-band only.

Thus we have

n1D Vg

� �¼ nparallel Vg

� ��nperpendicular Vg

� �: (2)

Evaluating the area under this C-V curve gives the pure

1-dimensional charge density in dimensions of cm�2 which

can be converted to effective 1-dimensional charge density

in unit of cm�1 or m�1 by multiplying it with the nanowire

pitch or in this case, the average atomic terrace width.

Theoretically, at any position of Femi level EF, the total

number of electrons populating the E0 sub-band, which are

purely 1-dimensional, is given by the integration of the prod-

uct of the 1-D density of states and the Fermi occupation

function,

n1D EFð Þ ¼ð1

E0

ffiffiffiffiffiffiffiffiffi2m�p

p�hffiffiffiEp

� 1

1þ expE� EF

kT

� �� � 1

tterrace

dE; (3)

where m* is the effective electron mass in GaN (¼ 0.2 times

free electron mass), k is Boltzmann constant (¼ 1.38� 10�23

SI units), T is room temperature (¼ 300 K) where measure-

ments are performed and �h(¼ 1.054� 10�34 SI units) is the

reduced Dirac constant. The expression is divided by the aver-

age atomic terrace width tterrace in order to normalize the

1-dimensional density of electrons (cm�1) in units of cm�2.

Similarly, at any Fermi level, electrons occupying the E1 sub-

band, which are purely 2-dimensional, is given by the inte-

grating the product of 2-D density of states and the Fermi

occupation function

n2DðEFÞ ¼ð1

E1

m�

p�h2

1

1þ expE� EF

kT

� �� � dE: (4)

The choice of E0 and E1 is explained as follows: As a

simplified approximation, let us consider E0, the 1st sub-band,

as reference, i.e., E0¼ 0. There is no absolute or universal

relation between E0 and E1, because that depends on the total

charge in the system. Depending on how much 1-dimensional

and 2-dimensional charge exists in the system, the position of

E1 will be different. The further E1 is from E0, the more is the

1-dimensional and less is the 2-dimensional charge for a

given total charge. In our system investigated, we have a total

1-dimensional charge of �2� 1012 cm�2 and total charge

(1-Dþ 2-D) of �7.5� 1012 cm�2 as obtained from C-V mea-

surement. These charges will determine the position of sub-

band E1 relative to E0. Of course, the total charge in the sys-

tem will determine the position of Fermi Level (EF) relativeto E0 (or to E1, once E1-E0 is determined) at zero gate bias.

The dependence of EF on gate bias also needs to be calculated

at this point to estimate the relative position of E1. To

do this, we calculate the total electron density of the system

as a function of Fermi level, which is simply given by

nTotal(EF)¼ n1D(EF)þ n2D(EF), where n1D and n2D are

obtained from Eqs. (3) and (4), respectively. Dividing the

total charge Qtotal(EF)¼ q(n1Dþ n2D) by the zero-bias capaci-

tance of the system gives the voltage shift needed to apply on

the gate to achieve the given amount of charge. This voltage

shift is required to be added to the pinch-off voltage to obtain

the true gate bias corresponding to any given charge and

hence the Fermi level. The normalized zero-bias capacitance

is given by the ratio of the di-electric constant of GaN (e �8.9) and the separation between gate and the electron gas

(which is �30 nm in this case). For a total charge of

�7.5� 1012 cm�2 in our system, we found that a position of

EF approximately �0.18 eV above E0, is consistent with the

total charge at zero gate bias. Subsequently, a position of E1

� 0.09 eV above E0 gives a reasonably accurate value of pure

1-dimensional charge close to �2� 1012 cm�2 which we

observe experimentally. Thus, the positions of E1 and EF rela-tive to E0 are purely dependent on the system under investiga-

tion and hence behave like fitting parameters.

It is noteworthy that while the 1-D density of states has

an inverse dependence onp

E, the 2-D density of states is a

step function and hence has no dependence on energy. This

implies that at higher energies, 1-dimensional electrons have a

decreasing number of states of energy available for occupa-

tion while for 2-D electrons, energy level is immaterial since

its density of states is a step function of a particular sub-band.

This fundamental difference in the dependence of 1-D and 2-

D density of states on energy is clearly observable in Fig. 4

which shows the theoretically calculated variation of both 1-D

and 2-D electron densities as the gate bias is increased. While

1-D electron density tends to increase very slowly at higher

energies, 2-D electron density continues to increase sharply at

higher energy. The experimentally obtained values for the

same as extracted from Eq. (2) and preceding discussions are

also plotted in the Fig. 4.

043715-4 Nath et al. J. Appl. Phys. 111, 043715 (2012)

It is interesting to note that till the Fermi level reaches the

sub-band E1, the total electron density in the system is mostly

contributed by purely 1-D electrons (occupying sub-band E0).

As the Fermi level rises past E1, the contribution from 2-D

electrons starts to dominate as (1-D) electrons occupying E0

have a decreasing availability of energy states on account of

the 1/p

E dependence of the 1-D density of states.

Two important observations are, firstly the theoretical

and experimental values for both 1D and 2D electrons match

up excellently, both in their bias-dependent behavior and in

FIG. 5. (Color online) Engineering dimensionality of electrons. (a) As-

grown simplified N-polar GaN/AlGaN heterostructure with its correspond-

ing energy band diagram along the dotted line. (b) Etching the active layer

to reduce its thickness lowers the total charge and ‘pushes’ the Fermi level

below.

FIG. 4. (Color online) Charge density. Pure 1-D and pure 2-D electron den-

sities as a function of gate-bias (solid lines: theoretically calculated; dash:

experimental data at room temperature). The sharp difference in the behav-

ior of 1 D and 2 D electrons as predicted by theory is excellently matched in

experimentally obtained data.

FIG. 6. (Color online) Etch-and-measure study

to achieve pure 1-D transport: The current

between two adjacent Ohmic contacts after

etching the active region for (a) 0 mins, (b) 3

mins, (c) 4 mins 30 s, (d) 6 mins, (e) 6 mins

15 s.

043715-5 Nath et al. J. Appl. Phys. 111, 043715 (2012)

magnitudes. This proves the 1-dimensionality of the elec-

trons existing in the system at room temperature besides pro-

viding a concrete proof to our 2-sub-band model. Secondly,

depending on the position of the Fermi level, 1-D and 2-D

electrons co-exist in the system. While for EF>E1, transport

is purely due to 2-D electrons in direction perpendicular to

atomic terraces, for EF<E1, transport is purely due to 1-D

electrons in direction parallel to atomic step. This system

therefore enables direct electrostatic tuning of the dimen-

sionality of electron gases and can provide an excellent plat-

form to explore physics of low-dimensional systems even atroom temperature.

C. Pure 1-D transport: Fermi Level engineering

To demonstrate pure 1-D transport in our system, we are

required to reduce the total charge and thus ‘push’ the Fermi

Level below E1 sub-band so that only E0 sub-band can con-

tribute to transport. This can be achieved by etching the

active layer (GaN) to some critical depth. Since it is not fea-

sible to experimentally obtain the absolute position of EF

with respect to E0, we performed an etch-and-measure study.

The region between two adjacent Ohmic pads was etched in

steps of 15-30 s and the current between adjacent Ohmic

contacts was measured after every etch step. For this, an

additional level of lithography was performed where photo-

resist was exposed and developed to open a part of the spac-

ing between two such adjacent pads. Thus, on exposing the

sample to ICP-RIE chamber with standard plasma-etch rec-

ipe, only the region opened by photo-resist between two ad-

jacent Ohmic pads would be etched.

The epitaxial structure for the as-grown N-polar GaN/

AlN/AlGaN/GaN heterostructure was shown in Fig. 2(a).

Since AlN in our structure is less than 1 nm and its primary

purpose being to enhance the mobility, it can be ignored for

simplicity in explanation. Hence, it is not shown in Fig. 5(a),

where we only consider a simple N-polar GaN/AlGaN/GaN

heterostructure. The schematic of its energy band diagram

along the red-dotted line (indicated in the structure) is shown

to its right. Current is measured on such structures between

adjacent Ohmic contacts source (S) and drain (D). However,

if we etch the active region between them (as shown in Fig.

5(b)) to reduce the thickness of the GaN channel layer, the

vertical electric field in it increases as shown in the energy

band diagram to its right (due to constant Fermi pinning of

the surface). This lowers the charge existing at the top inter-

face of GaN and AlGaN.

To investigate dependence of current levels in the two

directions on etch depth, a controlled etch recipe which gives

an etch rate of �6 nm/min for N-face GaN was used to etch

the sample in steps of 15-30 s. As the top GaN thickness starts

to decrease with increasing etch time leading to a decreasing

charge (in both directions), we would expect to measure a

decreasing current level between two pads for the same

applied bias. Since the exact epitaxial structure used in this

study had a 5 nm SiNx passivation layer and a 2 nm

Al0.6Ga0.4 N on top of the active GaN channel layer, the etch-

ing would initially result in a ‘dead’ time in which the SiNx

and Al0.6Ga0.4 N would be etched without any appreciable

effect on the current levels (Figs. 6(a)–6(c)). After 6 mins of

total etch time as shown in Fig. 6(d), current in the direction

perpendicular to atomic terraces starts to drop significantly

although that in the parallel direction stays nearly the same.

With further etching, the current in both directions starts to

decrease (Fig. 6(e)), indicating a gradual lowering of the

charge as expected. At a critical etch depth corresponding to a

total etch time of 6 mins and 45 s when the Fermi level has

been ‘pushed’ below E1 but above E0 as shown in Fig. 7(a),

we observe current up to 130 mA/mm in the parallel direction

but negligible current in the direction perpendicular to atomic

terraces (Fig. 7(b)) implying achieving a 1-dimensional condi-

tion. This observation of 1 D transport is consistent and

repeatable for Ohmic contacts separated by various spacing

levels (6 lm to 22 lm) and across various regions of the sam-

ple. To our knowledge, this is the first demonstration of 1-D

transport without lithographically synthesized, designed or

fabricated nanowire structures.

IV. SUMMARY AND CONCLUSION

We demonstrated the co-existence of 1-D and 2-D elec-

tron gases in a polarization-engineered vicinal AlGaN/GaN

hetero-structure system. We also showed that C-V profiling

can be used as a tool to probe as well as to tune the dimen-

sionality of electron gas between 1-D and 2-D. We proposed

a two sub-band model to explain the dimensionality-

dependence of electron gases on Fermi level position which

we verified with experimentally measured data. Finally,

using our model, we engineered the Fermi Level to show

clear and sharp signatures of pure 1-D transport (parallel to

atomic terraces) at room temperature. Each atomic terrace,

characteristic of the vicinal substrate, defines one 1-D chan-

nel at the GaN/AlGaN interface when transport is considered

parallel to the terraces. The terrace width and hence channel

dimension (�10-20 nm) is defined by the miscut angle of the

FIG. 7. (Color online) Demonstration of pure 1-D transport. (a) Saw-tooth

energy profile with Fermi Level below E1 sub-band when the total charge is

reduced. (b) Pure 1-D transport: current flows parallel to atomic terraces

while negligible current is observed perpendicular to it. Inset: GaN channel

etched to a critical depth corresponding to 6 mins 45 s of total etch time to

reduce charge to achieve condition shown in (a).

043715-6 Nath et al. J. Appl. Phys. 111, 043715 (2012)

vicinal substrate and these 1-D channels are not lithographi-

cally, but electrostatically defined. Since our approach using

this novel system enables us to achieve self-defined, regu-

larly-spaced dense arrays of 1-D channels of electrons, it

holds lot of promise for practical electronic and optical de-

vice applications and to provide a unique platform to probe

low-dimensional systems.

1J. Xiang, W. Lu, Y. Hu, Y. Wu, H. Yan, and C. M. Lieber, Nature 441,

489 (2006).2Q. Li, X. Zhu, Y. Yang, D. E. Ioannou, H. D. Xiong, J. S. Suehle, and C.

A. Richter, IEEE Conf. Nanotech. (NANO), 526 (2008).3C.-M. Lee and B.-Y. Tsui, IEEE Elect. Dev. Lett. 32, 327 (2011).4H. Ko, K. Takei, R. Kapadia, S. Chuang, H. Fang, P. W. Leu, K. Ganapa-

thi, E. Plis, H. S. Kim, S.-Y. Chen, M. Madsen, A. C. Ford, Y.-L. Chueh,

S. Krishna, S. Salahuddin, and A. Javey, Nature 468, 286 (2010).5J. Nah, E.-S. Liu, K. M. Varahramyan, and E. Tutuc, IEEE Trans. Elect.

Dev. 57, 1883 (2010).6J. Guo, J. Wang, E. Polizzi, S. Datta, and M. Lundstrom, IEEE Trans.

Nanotech. 2, 329 (2003).7A. B. Greytak, L. J. Lauhon, M. S. Gudiksen, and C. M. Lieber, Appl.

Phys. Lett. 84, 4176 (2004).8P.-C. Chang, Z. Fan, C.-J. Chien, D. Stichtenoth, C. Ronning, and J. G.

Lu, Appl. Phys. Lett. 89, 133113 (2006).9H. Yan, H. S. Choe, S. Nam, Y. Hu, S. Das, J. F. Klemic, J. C. Ellenbogen,

and C. M Lieber, Nature 470, 240 (2011).10Y. Cui, Q. Wei, H. Park, and C. M. Lieber, Science 293, 1289 (2001).11F. Qian, Y. Li, S. Gradecak, D. Wang, C. J. Barrelet, and C. M. Lieber,

Nano Lett. 4, 1975 (2004).12R. Yan, D. Gargas, and P. Yang, Nat. Photonics 3, 569 (2009).13M. H. Huang, S. Mao, H. Feick, H. Yan, Y. Wu, H. Kind, E. Weber, R.

Russo, and P. Yang, Science 292, 1897 (2001).14H.-J. Choi, J. C. Johnson, R. He, S.-K. Lee, F. Kim, P. Pauzauskie, J.

Goldberger, R. J. Saykally, and P. Yang, J. Phys. Chem. B 107, 8721

(2003).

15C. P. Svensson, T. Martensson, J. Tragardh, C. Larsson, M. Rask, D.

Hessman, L. Samuelson, and J. Ohlsson, Nanotechnology 19, 305201

(2008).16M. Law, L. E. Greene, J. C. Johnson, R. Saykally, and P. Yang, Nat.

Mater. 4, 455 (2005).17W. Lu, P. Xie, and C. M. Lieber, IEEE Trans. Elect. Dev. 55, 2859 (2008).18P. Yang, R. Yan, and M. Fardy, Nano Lett. 10, 1529 (2010).19M. S. Gudiksen, L. J. Lauhon, J. Wang, D. C. Smith, and C. M. Lieber,

Nature 415, 617 (2002).20S. D. Carnevale, J. Yang, P. J. Phillips, M. J. Mills, and R. M. Myers,

Nano Lett. 11, 866 (2011).21H. Wang, M. Sun, K. Ding, M. T. Hill, and C.-Z. Ning, Nano Lett. 11,

1646 (2011).22D. N. Nath, S. Keller, E. Hsieh, S. P. DenBaars, U. K Mishra, and S.

Rajan, Appl. Phys. Lett. 97, 162106 (2010).23G. A. Umana-Membreno, T. B. Fehlberg, S. Kolluri, D. F. Brown, G. Par-

ish, B. D. Nener, S. Keller, U. K. Mishra, and L. Faraone, Microelect.

Engg. 88, 7 (2011).24G. A. Umana-Membreno, T. B. Fehlberg, S. Kolluri, D. F. Brown, S. Kel-

ler, U. K. Mishra, B. D. Nener, L. Faraone, and G. Parish, Appl. Phys.

Lett. 98, 22 (2011).25S. Kolluri, S. Keller, D. Brown, G. Gupta, S. Rajan, S. P. DenBaars, and

U. K. Mishra, J. Appl. Phys. 108, 074502 (2010).26S. Keller, N. A. Fichtenbaum, F. Wu, D. Brown, A. Rosales, S. P.

DenBaars, J. S. Speck, and U. K. Mishra, J. Appl. Phys. 102, 083546

(2007).27S. Keller, C. S. Suh, Z. Chen, R. Chu, S. Rajan, N. A. Fichtenbaum, M.

Furukawa, S. P. DenBaars, J. S. Speck, and U. K. Mishra, J. Appl. Phys.

103, 033708 (2008).28M. Sumiya, K. Yoshimura, T. Ito, K. Ohtsuka, S. Fuke, K. Mizuno, M.

Yoshimoto, H. Koinuma, A. Ohtomo, and M. Kawasaki, J. Appl. Phys. 88,

1158 (2000).29S. Rajan, A. Chini, M. H. Wong, J. S. Speck, and U. K. Mishra, J. Appl.

Phys. 102, 044501 (2007).30M. Grundmann, BANDENG, 2005, http://michaelgrundmann.com.31F. Bernardini, V. Fiorentini, and D. Vanderbilt, Phys. Rev. B 56, 024

(1997).

043715-7 Nath et al. J. Appl. Phys. 111, 043715 (2012)