Conference-ISSS-4-Null method for four-point probe measurement using high resistance probes

A null method, using a bridged circuit, is applied to the so-called four-point probe method using highly resistance probes. A commercial resistor (150 kΩ-10 MΩ) is serially connected with a voltage measurement probe (made of tungsten) in order to give high resistance. The resistivity of a patterned Pt-Pd film about 50 nm thick is successfully measured for the probe spacing down to the submicron scale. The obtained values of resistance remain unchanged irrespective of the inserted resistors. [DOI: 10.1380/ejssnt.2006.115]


I. INTRODUCTION
Recently, nanostructured materials attract much attention because they have unique electronic properties originated from their low-dimensional shape.Carbon nanotube or deoxyribonucleic acid (DNA) is expected to be a ultimate wire connecting between nano-devices [1,2].In order to realize sure wires, we need to clarify electric conductance of these materials.Scanning probe microscopy (SPM) is a powerful tool to investigate the physical properties of nanomaterials.Recently, multiprobe microscopy based on SPM techniques is developed to characterize electric resistivity with nano to micron spacing.Takumi, et al. have developed a twin probe scanning tunneling microscope with two probes driven independently [3].The measurement using two probes tends to be influenced by both probe resistance and contact resistance.On the other hand, a four-point probe method is free from such influence because the probes for introducing sample current and these for measuring voltage drop by a resistance of sample are separated [4].Shiraki, et al. report on a four-probe system operated in scanning electron microscope (SEM) where the surface conductance strongly depends on the probe spacing [5,6].
In order to minimize the probe spacing in the fourpoint probe method, a special probe with small apex and high aspect ratio is highly needed.A carbon nanotube is a promising material for such a probe because of their unique physical properties.However, it is known that the carbon nanotube-attached probe shows generally high resistance at the junction between carbon nanotube and conductive matrix.The resistance of CNT probe is ∼100 kΩ and sometimes reaches 10 MΩ when using such high resistance probes.In this case, a voltmeter does not work because no sufficient current flows into the voltmeter.Hence, a new method should be developed to measure small voltage drop using high resistance probes.In this paper, we have applied a null method to four-point probe method with high resistance probes, and have measured voltage drop on the patterned Pt-Pd film even if the probe resistivity is as high as 10 MΩ.

II. EXPERIMENTAL
Figure 1 shows a schematic of a null method proposed in this study.Seriate three resistors (R 1 , R 2 , R 3 ) correspond to a total sample resistance.R 2 is the resistance to be measured.The constant current I 1 is introduced by voltage source V S and current limit resistor R lim .The resistors R C and R C " represent the overall resistance (probe and contact resistance) of voltage measurement probes.The reference voltage source V r and the ammeter are serially connected between the two probes.The current I 2 in the closed circuit has a relation with V r as follows: The spacing between inner probes are 2.9 µm (b) and 600 nm (c), respectively.
V r is adjusted so that the current I 2 equals to zero (zero point), and this value of V r corresponds to R 2 • I 1 , just like a bridged circuit, independent of R c and R c ". Since I 1 is given, the value of R 2 is deduced.It is practically hard to adjust I 2 zero by controlling V r .Consequently, I 2 -V r characteristic is measured as shown in Fig. 1(b) and the zero point is determined by the calculation.Two computational methods are examined for comparison.One method is that zero point is calculated from the two points (shown as boxes in Fig. 1(b)) around the zero point by the interior division.Another is that zero point is calculated from a fitting line using six points (shown as boxes and circles) around the zero point using the least square method.It is found that the former one is preferred within the minimum resolution of voltage step 5 mV in the present study.This is because the current (I 2 ) could induce structural change in contact area although details are not clear at present.
All the measurements in this article are performed using a custom-made four probe microscopy built in scanning electron microscope (S-4500, Hitachi) [6].The sample is a patterned Pt-Pd film (Pt:Pd=80:20, thickness ∼50 nm) on a SiO 2 substrate.Thus the film is treated as a ribbon with width of 7.4 µm.A SEM image during the measurement is shown in Fig. 2. Four electrochemically etched tungsten probes are arranged in line on the film (Fig. 2(a)).Outer pair of probes introduces sample current into the film up to 2 mA.The V r -I 2 characteristic is measured by a D/A converter (PCI-3523A, Interface) and a picoammeter (model 486, KEITHLEY).The contact of the probe with the sample is confirmed by SEM observation.V r is swept from -150 mV to 500 mV by 50 mV.Several commercial resistor (150 kΩ, 2.2 MΩ, 6.2 MΩ, 10 MΩ) are used as R c and R c ".

III. RESULTS AND DISCUSSION
Figure 2(a) again shows the SEM image in operation, and Fig. 2(b) shows a magnified image of the inner two probes.The spacing between two probes along the lon-gitude direction of the pattern is 2.9 µm.?The spacing is reduced to 600 nm in Fig. 2(c).For the two probe spacings, I-V (I 1 -I 1 • R 2 ) curves are plotted with different resistors (150 kΩ and 10 MΩ), as shown in Fig. 3. Figure 3(a) shows one of I 2 -V r curves around zero point to plot Fig. 3(b).V r at zero point is determined by the intersection with the horizontal axis.Open and filled circles (triangles and boxes) represent the I-V data using 150 kΩ and 10 MΩ for the probe spacing of 2.9 µm (600 nm), respectively.The measured voltage drops are independent of the resistance R c and R c " for the same probe spacing.
The slope of the fitted line represents the resistance of the sample between inner probes, R 2 .The slope gives 5.05 Ω for the spacing 2.9 µm and 1.03 Ω for 600 nm.The ratio of two slopes meets the ratio of probe spacings.Thus, the resistivity of the film ρ is calculated from the macroscopic relation R = ρL/wt.The width w and the thickness t correspond to the width of the raised pattern and the thickness of the film, respectively.The length L is the probe spacing.As a result, the resistivity of the film is obtained as (6.5 ± 1.2) × 10 −5 Ωcm.The value is 6.5 times as large as that of bulk platinum (9.8 × 10 −6 Ωcm at 20 • C), which is reasonable because the film is made of clusters and includes many grain boundaries in it.The measured resistivity also matches well with the resistivity macroscopically determined by a commercial mΩ tester (model 3227, Hioki).The present measurement is easily applicable to much smaller spacings because the resistivity generally increases with decreasing the measured size.The measurement with such small spacing is now in progress using carbon nanotube probes, which will be published elsewhere.

IV. CONCLUSION
We have applied a null method to the four-probe point measurement, where high resistance probes are used.Using this method, the resistivity of the patterned Pt-Pd is successfully measured.The method will enable us to adopt a four-probe point method using high resistive probes such as carbon nanotube probes for nanoscale characterization of electric properties of nanostructured materials.

FIG. 1 :
FIG. 1: (a) Schematics of four-point probe measurement using null method, where a bridge circuit is used.(b) Zero crossing point (I2 = 0) is calculated by several data points.