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Measuring the specific contact resistance of contactsto semiconductor nanowires

S.E. Mohney a,*, Y. Wang b, M.A. Cabassi b, K.K. Lew a, S. Dey a,J.M. Redwing a, T.S. Mayer b

a Department of Materials Science and Engineering and Materials Research Institute, The Pennsylvania State University,

109 Steidle Building, University Park, PA 16802, USAb Department of Electrical Engineering, The Pennsylvania State University, University Park, PA 16802, USA

Received 19 March 2004; received in revised form 17 July 2004; accepted 13 August 2004

Available online 29 September 2004

The review of this paper was arranged by Prof. A. Zaslavsky

Abstract

Ohmic contacts to semiconductor nanowires are essential components of many new nanoscale electronic devices. Equations for

extracting specific contact resistance (or contact resistivity) from several different test structures have been developed by modeling

the metal/semiconductor contact as a transmission line, leading to the development of equations analogous to those used for planar

contacts. The advantages and disadvantages of various test structures are discussed. To fabricate test structures using a convenient

four-point approach, silicon nanowires have been aligned using field-assisted assembly and contacts fabricated. Finally, specific con-

tact resistances near 5 104Xcm2 have been measured for Ti/Au contacts to p-type Si nanowires with diameters of 78 and 104nm.

2004 Elsevier Ltd. All rights reserved.

PACS: 73.40.Cg; 73.40.C; 85.40.Ux; 73.40.NKeywords: Nanowire; Ohmic contact; Nanocontact; Specific contact resistance; Contact resistivity

1. Introduction

Semiconductor nanowires are drawing increasing

attention as building blocks in bottom-up assembly of

nanoscale devices and circuits [1]. In fact, chemical

and biological sensors [2], field effect transistors [3],

and logic circuits [4] have already been demonstrated.Ohmic contacts to semiconductor nanowires are essen-

tial for devices such as these, and research on ohmic

contacts to semiconductor nanowires is of current

interest.

Important parameters in the study of metal/semicon-

ductor contacts are the contact resistance Rc and specific

contact resistance qc, also frequently referred to as the

contact resistivity. The specific contact resistance is a

particularly useful area-independent parameter for com-

paring contacts of different geometries, and it is typically

expressed in units ofXcm2

. The contact resistance Rc isthen given by qc/A, where A is the active area of the con-

tact. What complicates the determination of qc is that

current transport does not always occur uniformly in a

contact; rather, it may take place primarily near the

edges in certain geometries. Therefore, modeling is often

required to determine the active area of the contact and

extract qc.

Using a variety of test structures, methods have

long since been established for extracting the contact

0038-1101/$ - see front matter 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.sse.2004.08.006

* Corresponding author. +1 814 863 0744; fax: +1 814 865 2917.

E-mail address: mohney@ems.psu.edu (S.E. Mohney).

www.elsevier.com/locate/sse

Solid-State Electronics 49 (2005) 227232

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resistance and specific contact resistance of planar con-

tacts. One common situation is to have lateral contacts

to a semiconductor layer that is on a non-conducting

substrate or is electrically isolated from the substrate

by a pn junction. A transmission line model (TLM) is

often used to describe current transport in lateral con-

tacts made to such semiconductor layers [5,6].In this manuscript, we develop equations and pro-

pose multiterminal test structures for analogous meth-

ods of extracting the specific contact resistance of

contacts to semiconductor nanowires. We then describe

the advantages and disadvantages of these test struc-

tures. Finally, we demonstrate the use of the most exper-

imentally convenient of these test structures to measure

the specific contact resistance of contacts to a p-type Si

nanowire.

2. Nanowire transmission line model

Fig. 1 shows a nanowire placed on a metal pad and

then covered with another layer of the same metalliza-

tion. This geometry is the one we are examining for

our metal/semiconductor contacts. We assume that the

entire circumference of the nanowire of radius r is in di-

rect contact with the metallization along a length L of

the nanowire. We also assume that the voltage is uni-

form throughout the entire metal contact and that it var-

ies in the semiconductor only along the length of the

nanowire. Finally, we assume that the resistivity and ra-

dius of the semiconductor nanowire beneath the contact

is not altered by the fabrication of the contact.We may use a transmission line model to describe

current transport at the metal/semiconductor interface,

as shown in Fig. 2, where qs is the resistivity of the sem-

iconductor, qc is the specific contact resistance, r is the

radius of the wire, L is the length of the contact, I(x)

is the current in the semiconductor nanowire, v0 is the

voltage drop between the metal contact and the semi-

conductor at x = L (beneath the end of the contact),

and V(x) is the voltage drop in the semiconductor

between x and x = L. The differential resistance at the

metal/semiconductor interface along a length of the

nanowire dx is given by qc/(2pr dx), while the resistance

of the semiconductor along a length dx is given by qsdx/

(pr2). In our model, the current is therefore distributed

homogeneously throughout the cross-section of the semi-

conductor nanowire. To ensure that the current will flowvertically through the contact region into the cross-

section of the nanowire, the resistance at the metal/

semiconductor interface must be high compared to that

of nanowire segment beneath it, a condition that is met

for the measurements we report later in the manuscript.

An analogous requirement for applying the transmission

line model to planar contacts was described previously

by Berger [6].

For this situation, we can describe the current and

voltage in the semiconductor using

dV

dx

qs

pr2I

1

and

dI

dx

2pr

qc

v0 V: 2

Together these equations give

d2I

dx2

2qsrqc

I 0: 3

For a contact of length L, I(x) grows from 0 at x = 0 to

the total current i0 at the end of the contact (x = L).

Therefore,

Ix i0sinhx=LT

sinhL=LT; 4

where the transfer length LT is given by

LT

ffiffiffiffiffiffiffirqc

2qs

r: 5

Differentiating Eq. (4) and inserting it into Eq. (2), we

find that

Vx v0 qci0

2prLT

coshx=LT

sinhL=LT: 6Fig. 1. Image from a scanning electron microscope of a nanowire with

top and bottom contacts at one end.

Fig. 2. Model of the metal/semiconductor nanowire contact.

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With V(L) = 0 and using Eq. (5), we find that

v0 qsi0LT

pr2cothL=LT: 7

Since the contact resistance Rc is simply v0/i0, we obtain

Rc qsLT

pr2

cothL=LT: 8

In the limit of a long contact (L > 3LT), the expression

simplifies to

Rc qsLT

pr2; 9

or using Eq. (5),

Rc qc

2prLT: 10

3. Test structures

We can envision several different test structures that

would allow us to measure contact resistance, specific

contact resistance, and nanowire resistivity using the

equations above. All of these test structures require that

each contact in the structure have the same specific con-

tact resistance as the others, which is a common require-

ment for test structures for both planar contacts and

other geometries. Furthermore, we neglect the effects

of any depletion or accumulation at the surfaces of the

nanowires between the contacts, and we assume when

we extract the resistivity of the nanowires that the cur-

rent is carried by the full cross-sectional area. In themeasurements reported later in this paper, the nano-

wires are very heavily doped, which is the situation that

most closely allows us to meet this requirement. How-

ever, this issue becomes increasingly important for very

small nanowires and nanowires that are not heavily

doped.

The first structure is shown in Fig. 3. Pairs of contacts

are separated by different distances (l1, l2, etc.), and a dif-

ferent nanowire is located between each pair of contacts.

There is no way to separate the resistance of the contacts

from the resistance of the semiconductor when only one

of the nanowires is measured; however, with nanowires

of varying length, there is an easy approach analogousto that commonly used for planar contacts [7].

As long as we have long contacts (L > 3LT), the exact

length L of each contact is not important, and the total

resistance RT between a pair of contacts separated by a

segment of nanowire of length l is given by

RT 2Rc qs

pr2l; 11

or

RT qs

pr22LT l: 12

In this case, all that is necessary is to fit the data for RTversus l to the equation for a straight line, yielding a

slope of qs/(pr2), an intercept at RT = 0 of 2LT, and

an intercept at l= 0 of 2Rc. Thus, qs is readily obtained

from the slope and radius of the wire, and qc can be ob-

tained from LT using Eq. (5), qs, and r.

An advantage of this method is the simplicity of fab-

rication. However, a serious disadvantage is that we

must assume that all the nanowires have identical radii

and resistivity. This assumption is often not fully met

with the nanowires under study today, since current fab-

rication methods typically yield nanowires of slightly

varying radii [8], more than one different crystallo-

graphic orientation within the same batch of nanowires

[8], and a fraction of nanowires that are bicrystals [9].

A second test structure makes use of multiple con-

tacts along the length of a nanowire, as shown in Fig.

4. If contacts 15 are all long compared to LT, we

may measure RT between pairs of contacts 1 and 2,

Fig. 3. Multiwire test structure.

Fig. 4. Test structure with multiple contacts.

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2 and 3, etc. Then we may again fit data for RT as a func-

tion of l to Eq. (11) to extract qs and Rc and use LT to

find qc, as described previously for the multiwire ap-

proach. However, it is not unusual for LT of a metal/

semiconductor contact to be on the order of a micron;

thus, the total length of the test structure could be on

the order of 30lm or greater. This approach thereforerequires rather long nanowires.

If the middle contacts 2, 3, and 4 are not long com-

pared to LT, it is in principle possible to obtain data

from only the identical middle contacts 2, 3, and 4 of

length L and then fit pairs of data points (RT, l) to

RT qs

pr22LT coth

L

LT l

: 13

However, this approach is more cumbersome than sim-

ply fitting data to a straight line, which is all that is re-

quired for the case of long contacts.

A third test structure, which is particularly conven-

ient for shorter nanowires, is shown in Fig. 5. This ap-

proach differs from those described previously in that

the resistivity of the nanowires is measured using a four

point probe technique, where the current I14 is sourced

between the two end contacts, and the voltage drop be-

tween the two middle contacts V23 is measured. To

avoid large measurement error, the input impedance of

the voltmeter must be much greater than the resistance

of the nanowire, which can be achieved using commer-

cially available test equipment. The resistivity of the

nanowire is then given by

qs V23

I14

pr2

l2 : 14

Then we can measure RT between the two end contacts

and determine the contact resistance Rc using

RT 2Rc qs

pr2l1: 15

Finally, using Eqs. (9) and (10), we can extract qc. We

assume in this analysis that the potential drop along

the length of the nanowire is not altered by the presence

of the two middle contacts, a condition that is well met

for ohmic contacts with low barrier heights.To avoid large errors when using this measurement

technique, it is also necessary for the two middle con-

tacts to be short compared to LT, or else a significant

portion of the current may be transported through the

middle contacts rather than the semiconductor nanowire

when we measure RT between contacts 1 and 4, making

inaccurate our use of l1 as the length of the semiconduc-

tor nanowire in Eq. (15). This error is further minimized

if the middle contacts are very short compared to l1.

4. Example from experiments

The four point test structure in Fig. 5 was used to

measure qc for contacts to p-type Si nanowires, the con-

ductivity type of which was verified by field effect meas-

urements reported elsewhere [11]. The nanowires were

grown using the vaporliquidsolid technique with tri-

methylboron as the dopant. An estimate of the B con-

centration in excess of 1019cm3 was obtained using

secondary ion mass spectrometry (SIMS) for nanowires

grown under the same conditions as those in our exper-

iment [11], although the SIMS measurements contain

added uncertainty due to the difficulty of performingsuch measurements on nanowires. The nanowires were

aligned on Ti (20nm)/Au (80nm) end contacts using a

field-assisted assembly technique [10]. Electron beam

lithography was then performed to pattern all four top

contacts shown in Fig. 5, and after the native oxide on

the nanowire was stripped, 80nm of Ti followed by

200nm of Au was evaporated on the nanowire. A com-

pleted test structure is shown in the field emission scan-

ning electron microscope (FESEM) image in Fig. 6 for

sample 2 from Tables 1 and 2.

Table 1 provides the dimensions of two test struc-

tures, as measured using FESEM, along with resistance

measurements. These data were used along with the

equations developed for the four point approach to ex-

tract the resistivity of the nanowire, contact resistance,

transfer length, and specific contact resistance, as listed

for each test structure in Table 2. The length L of the

contacts is much greater than 3LT for sample 1 and

nearly 3LT for sample 2, so the long contact approxima-

tion is fairly well justified. Furthermore, the middle con-

tacts are much shorter than LT, so the use of the four

point approach is also reasonable.

The values of qc extracted above are calculated

assuming that the entire circumference of the nanowireFig. 5. Four point test structure.

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is in contact with the metallization at the ends of the

nanowires. This approximation is not perfectly met in

our measurements. The nanowires were aligned on Ti/

Au contacts, with the Au in direct contact with the

nanowires. Past work in our laboratory has revealed

that negligible current is transported through the nano-

wires before the native oxide is stripped and the top Ti/Au contact is deposited (this time with the Ti in direct

contact with the nanowire). By performing cross-sec-

tional transmission electron microscopy of segments of

nanowires beneath other contacts, we have found that

the metallization deposited on top of similarly sized

nanowires is in direct contact with approximately 75%

of the circumference of the nanowire. In this case, Eq.

(1) still applies, while we have

dI

dx

3pr

2qcv0 V 16

instead of Eq. (2). The transfer length LT then becomes

LT

ffiffiffiffiffiffiffiffiffi2rqc3qs

s; 17

and we obtain values of qc of 4.5 104Xcm2 and

5.0 104Xcm2 for samples 1 and 2, respectively.

5. Conclusions

Methods for extracting the specific contact resistance

of contacts to semiconductor nanowires have been de-

scribed, and advantages and disadvantages of different

approaches have been discussed. An example is de-

scribed in which a four point technique is used to meas-

ure specific contact resistances near 5 104Xcm2 for

Ti/Au contacts to p-type Si nanowires with diameters

of 78 and 104nm. Other contact metallizations and con-

tacts to Si nanowires of other radii and doping densities

are currently under investigation.

Acknowledgment

This work was supported by the National Science

Foundation under grant DMR-0103068 and the Penn

State Materials Research Science and Engineering Cen-

ter (MRSEC) on Nanoscale Science.

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Fig. 6. FESEM image of an actual four point test structure.

Table 1

Measurements from two test structures

Sample r (nm) 2 (lm) 1 (lm) V23/I14 (X) RT (X)

1 52 2.24 5.86 1.93 106 5.85 106

2 39 1.10 3.81 2.60 105 1.41 106

Table 2

Parameters extracted from the measurement of the four point test

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Sample Rc (X) qs (Xcm) LT (lm) qc (Xcm2)

1 4.0 105 0.73 0.46 5.9 104

2 2.6 105 0.11 1.1 6.7 104

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