Digital Object Identifier 10.1109/MMM.2013.2288710
Measurement Techniques for
RF Nanoelectronic Devices
Scaling of electronic device dimensions into the nanoscale regime has been at the basis of the semiconductor industry for several decades. Traditional materials have been pushed to their limits, which means that entirely new
materials and new device structures are now required.
The development of emerging technologies that include quantum confinement, spin transport, and molecular or correlated materials places increasingly stringent requirements on metrology of these novel devices. Advances in fundamental nanoscience, design of new nanostructures, and progresses in manufacturing of
Henri Happy, Kamel Haddadi, Didier Théron, Tuami Lasri, and Gilles Dambrine
Henri Happy ([email protected]), Kamel Haddadi, Didier Théron, Tuami Lasri, and Gilles Dambrine are with the Institut d’Electronique, de Microélectronique et de Nanotechnologie, UMR-CNRS
8520, BP 60069, Avenue Poincaré, 59652 Villeneuve d’Ascq Cedex, France.
Image lIcensed by Ingram PublIshIng
FOCUSED
ISSUE FEATU
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Date of publication: 21 January 2014
January/February 2014 31
next-generation nanodevices will all depend on our abil-ity to measure accurately and reproducibly the proper-ties and performance characteristics at the nanometer scale over a wide frequency range.
Researchers have dedicated large efforts to the investigation of the dynamic properties of nanode-vices in the microwave and millimeter-wave ranges. These miniaturized devices are presenting imped-ances much larger than 50 X, where the sensitivity
of microwave network analyzers becomes low (see “Problem of Impedance Mismatch for Micro-
wave Measurements”). The contact pads of these nanodevices are also necessarily small
in size, and they cannot be easily contacted. Traditional electrical characterization methods
for microwave and millimeter-wave devices are based on a vector network analyzer (VNA) associ-
ated with an on-wafer probing system. For nanode-vices, this approach requires dedicated contacting structures that allow the scaling of the electrical con-tacts from the milli- or microscale to the nanoscale.
In this article, we review the progress toward radio-frequency (RF) characterization of nanodevices. We will consider RF characterization of a single-wall carbon nanotube (SWCNT) for illustration, and some solutions related to new equipment will be proposed to overcome the problems of impedance and scale mis-match. It should be mentioned that similar problems occur when considering nanoribbons materials (gra-phene or other two-dimensional materials).
Problems of RF Characterization of High-Impedance NanostructuresIn recent years, progress has been made in improv-ing fabrication of nanomaterials such as carbon nano-tubes (CNTs), nanowires, and associated nanodevices. Because of their small size, high mobility, and ballistic or near-ballistic transport, nanodevices such as CNTs are predicted to be inherently fast [1]. Nevertheless, it remains a critical challenge to prove experimentally the ultimate frequency limits of such nanodevices. Overcoming these limitations is of prime importance for 1) the understanding of the fundamental trans-port mechanisms, 2) setting the basis for an efficient optimization of device architecture and fabrication process, and 3) improving accuracy in modeling and design of future integrated circuits.
Indeed, on one hand, nanodevices such as individual SWCNT field-effect transistors (FETs), for example, are characterized by high-input impedance (in the order of the quantum resistance h/e2 ` 26 kX [2], [3]); on the other hand, the output impedance of conventional mea-surement equipment is typically 50 X. This mismatch is a source of measurement problems. In fact, minimizing the mismatch between conventional RF equipment and devices under test (DUTs) is necessary to enhance the
sensitivity and accuracy of the RF measurement. Dur-ing the last decade, a number of approaches have been investigated to handle the impedance mismatch and measure the RF broadband properties of passive and active (one-port and two-port) nanodevices.
RF Characterization of Active Nanodevices High-frequency (HF) properties of CNT FETs have been investigated using several approaches, including the following:
• Extrapolation of HF properties from circuit anal-ysis. Here, the nanotube transistors act as reso-nators [4] or microwave detectors [5]–[6]. These latter experiments demonstrate an operation in HF, but the HF figures of merit such as cut-off frequencies, gains, etc. cannot be assessed using this method. The same limitation arises when common gate topology is used [7] or when circuit analysis is applied to frequency domain measure-ment techniques [8].
• Direct measurement methods of CNT FETs dynamic properties either with a spectrum ana-lyzer [8] or temporal pulse response [9] and VNAs [7]. The devices used in these references were characterized by a lower driving current corre-lated to a small number of CNTs in their channel and therefore high-input impedance. For improv-ing sensitivity using a VNA, which means reduc-ing input impedance of the device, CNT FETs with high density of parallel or random arrays of nano-tubes have been developed [10]–[14]. These devices are able to provide high-driving current, and significant progress has been made in multigiga-hertz range characterization. The high-frequency S-parameters data were measured using a VNA calibrated with a standard full two-port calibration using short, open, load, and through calibration structures. Considering the fact that the nano-structures are embedded into the macroscopic access structures, the measurement of adequate de-embedding structures is required to extract the properties of the intrinsic part of the device. This approach is particularly well suited for determination of RF and HF figures-of-merit from S-parameters measurements of the intrinsic device (cut-off frequencies, gains, and electrical circuit modeling). This is the first step toward construction of CNT circuits in the GHz range [15]. Despite such progress, the results obtained do not give access to the full HF properties of individual CNT. Reviews on the CNT synthesis and CNT FET fabrication can be found in [16] and [17].
32 January/February 2014
Problem of Impedance Mismatch for Microwave Measurements
The problem of microwave measurement of high impedances is highlighted in the following. The reflection coefficient measured by the VNA is expressed as
Z ZZ Z
0
0C =+- , (S1)
where Z0 is the 50-X reference impedance of the measurement system. The reflection coefficient C represented as a function of a real impedance is given in Figure S1(a).
Figure S1(b) represents the resistance uncertainty deduced from the reflection coefficient uncertainty as a function of the magnitude of S11 or S22 for different frequency ranges up to 6 GHz. This corresponds to a generation of VNAs with very low resolution bandwidth of 10 Hz, and with one of the best coaxial standards (7 mm). It should be noted that the uncertainties in the case of probe measurement may be higher. For a resistance of 10 kX (which is close to the quantum resistance), the corresponding reflection coefficient is close to 0.99, and the uncertainty for such a resistance may be higher than 100%. One can note that the measurement sensitivity is at maximum for impedances around 50 X (linear reflection coefficient near 0). But when very high impedances are considered, the VNA becomes insensitive to the variations of the reflection coefficient and the uncertainty increases.
For transmission measurements, the situation is slightly different. As seen in Figure S1(c), the uncertainties on the determination of the magnitude and the phase-shift of the transmission coefficient do not exceed a few dB and a few degrees, respectively, even for very low transmission coefficients.
Figure S1. (a) The reflection coefficient C as a function of a real impedance. (b) Uncertainty on associated resistance deduced from VNA measurements using a precise calibration (coaxial 7 mm environment), considering different frequency ranges. (c) Uncertainty on transmission coefficient magnitude. (From Agilent Technologies user manual guide.)
(a)
0.1 1 10 100 1,000 10,000 100,000-1.0
-0.5
0.0
0.5
1.0
Z = R + j0 (X)C
RF Electronics
50
RFNanoelectronics
(b)
Resistance Uncertainty
0.001
0.01
0.1
1
10
100
0 0.2 0.4 0.6 0.8 1
Reflection Coefficient (Linear)
Res
ista
nce
Unc
erta
inty
(%
)
300 KHz–1.3 GHz
1.3–3 GHz
3–6 GHz
8753ES H16 (Typical) with 85033D Calibration Kit
S21 = S12 = 0; Cal Power = -10 dBm;Measured Power = -10 dBm
8753ES H16 (Typical) Full Two-Port Cal Using 85033D
IF Bandwidth = 10 Hz; Average Factor = 1
Isolation Cal Omitted
(c)
S11 = S22 = 0; Cal Power = -10 dBm;Measured Power = -10 dBm
January/February 2014 33
An illustration of the difficulties encountered when a VNA is used for RF characterization of a CNT FET with an individual CNT is given in [18]. Due to the large impedance mismatch, additional circuits (Figure 1) were mounted directly at the input and output ports of the probe station to minimize standing waves. To compen-sate for output attenuation and small voltage gain, low-noise amplifiers are used at the output. As a consequence, measurements were restricted to the transmission coef-ficient ,S21 and the other parameters are extracted from calculation using several devices and different condi-tions of polarization.
This work shows the necessity of developing new tools and dedicated equipment that are well suited for measuring gigahertz trans-port properties of nanodevices or nano-objects that exhibit high-input impedance.
RF Characterization of Passive NanodevicesAnother possible way of mea-suring the RF characteristics of SWCNTs is to validate experi-mentally the theoretical values of the resistance, inductance, and capacitance of SWCNTs at high frequency, which are predicted for ballistic con-ductors with few quantized conduction channels. In fact, theoretical models have pre-dicted that an SWCNT should have a kinetic inductance ,Lk of 4 nH/nm, and a quantum capacitance Cq on the order of 100 aF/nm [5], [19]–[21]. Quite similar to active devices, one possibility is using a VNA to make a direct measurement of a massive parallel array of CNTs. In this case, from a broadband measurement [21]–[23], it appears that the kinetic
inductance of an individual CNT is correlated to the total inductance of the array of CNTs. Considering the value of the intrinsic quantum capacitance with respect to the geometrical one, this approach is not suited to extract such a small contribution. Nevertheless, this work shows an easy way to measure real and imaginary impedance of a dense array of CNTs.
To provide a much more efficient circuit model, other approaches need to be considered. The importance of the calibration and the de-embedding procedure when an individual CNT is used as passive device is illus-trated in [24]. In this case, where a unique SWCNT is integrated into a coplanar waveguide (CPW) structure, the conventional high-frequency S-parameter data
Figure 1. (a) The CNT FET with one SWCNT as the channel under characterization. (b) A schematic of the measurement circuit.
(b)
Vexc Z0
+19 dB +30 dB-10 dB -10 dB -3 dBPort 1 Port 2
RabIds
-6 dB D
S
G
Vg VdsV
A A
(a)
Figure 2. The Wheatstone bridge structure: (a) the top view of the Wheatstone bridge and synoptic of the measurement setup, (b) the cross section of the SWCNT structure under test, and (c) a scanning electron microscope (SEM) picture of one SWCNT onto aminopropyl-triethoxy-silane (APTS) zone and connected by palladium/gold (Pd/Au) at its extremities [25].
SiO2
NiCr
Pd/Au
SWNT
(b)
Ti/Au
SiGate
AI
R
(a)
P1
P2
CalibratedPlans
R
SWNT
R
R
Low-NoiseAmplifier
VectorialNetworkAnalyzer
Port 2
Port 1
0–7 GHz
(c)
SWNTUnder Test
APTSArea
34 January/February 2014
were measured using a VNA calibrated using a stan-dard full two-port calibration (short, open, load, and through) structures.
The S-parameters are measured for both the com-bined CNT and the CPW. Therefore, a set of custom calibration structures, free of any CNTs, were used for de-embedding the true CNT S-parameters from the CPW circuit. These de-embedding structures need to be developed by assuming parasitic impedance topol-ogy. The de-embedding procedure is associated with an optimization model to deduce HF characteristics of the individual SWCNT.
To avoid calculations requiring optimization, it is possible to improve the sensitivity of an RF measure-ment by inserting a high-impedance nanodevice in a specific structure, which contributes to reducing the
impedance mismatch between the VNA and CNT and thus minimizes the measurement error. This technique is applied in [25] by means of a Wheatstone bridge structure. The resistance of the Wheatstone bridge, in the range of 700 X–3 kX, helps to reduce the impedance mismatch between the VNA and the high-impedance nanodevice, as illustrated in “High-Impedance System for Microwave Characterization of Nanodevices.” The bandwidth of the system decreases as resistance of the Wheatstone bridge increases.
Applying this approach to an individual SWCNT (Figure 2), it is possible, by measuring the DUT and the associated de-embedding structure, to extract the parameters of the SWCNT from the measure-ments without any optimization. These measure-ments have been made using a high-impedance
High-Impedance System for Microwave Characterization of Nanodevices
A high-impedance integrated setup system has been developed in [25] to measure, in a one-port configuration, high-frequency properties of nanodevices. This system is based on a Wheatstone bridge structure [Figure S2(a)] where the device under test (DUT) is a nanodevice integrated in one of the four branches of the bridge. This structure acts as a directive coupler that separates the incident and reflective waves. Considering the imperfections brought by the microfabrication of the bridge [Figure S2(b)] and the systematic errors inherent to the VNA, we can relate the reflection coefficient measured by the VNA to the reflection coefficient of the nanodevice using a one-port error model defined by the three complex calibration terms: 1) the directivity Di , 2) the insertion loss Rf , and 3) the mismatch Des as shown in Figure S2(c).
The signal measured by the VNA can be expressed as a function of the reflection coefficient of the DUT ( )DUTC by
D DR
1 es DUT
DUTM i
fCC
C= +
-, (S2)
where DUTC is the reflection coefficient of the DUT.To determine the three unknown parameters ,Di
Rf , and Des , it is necessary to use a set calibration structures, with specific DUTC . To this end, three specific structures (shown in Figure S3) are fabricated on the same wafer of the nanodevice to be characterized. The resulting structures are three Wheatstone bridges that include a short circuit (CC), an open circuit (CO), and a calibrated resistance (Zc), respectively.
The experimental technique is based on a differential measurement to determine the reflection
coefficient ( ) .MC Therefore, S-parameters are measured in two positions (p1 and p2), by means of a high-impedance passive probe (HI) (Cascade Microtech FPM # 100) connected to port 2 of the VNA via a wideband low-noise amplifier (20 dB gain). This amplifier compensates for the signal attenuation
(a)
N1
N2N4
N3
R1
R3
R4
N1
N4
N3
R1
R3
R4
(b)
a1
M
CDUT
M
a
Rf
Error Adapter
RF in
CDUT
CM
RfRF in
CM
Di Des
1
(c)
Detector
DUT
Figure S2. (a) A schematic of the Wheatstone bridge structure. (b) A schematic of the directional coupler. (c) A flow graph of the Wheatstone bridge for the determination of mC .
January/February 2014 35
across HI probe. The use of an HI probe is required to minimize the perturbation of the measured circuit.
After calibration, the reflection coefficient ( )DUTC of any unknown DUT can be determined by the inversion of (S2)
Z Z 11
DUTDUT
DUTc CC
=-+ ,
where Zc is the reference impedance of the bridge.
The fabricated Wheatstone bridge structure is illustrated in Figure S4, as well as the measurement procedure. The resistances of the bridge (in the range of 700 X–3.5 kX) contribute to reducing
the impedance mismatch between the VNA and the CNT (The DUT in reference [24]) and hence minimize the measurement error.
The accuracy of this system is validated on a test impedance of 11 kX, with the resistance of the Wheatstone bridge of 3.5 kX. Figure S5 shows measurement with accuracy better than 5%, compared to the dc value of this resistance. Such accuracy can not be obtained with a conventional measurement system operating in a reflection configuration.
Figure S3. Calibration kits used: Equilibrated bridge (Zc), open (CO), short (CC) [25].
ZC Open
p2
p1HF Probe
Short
Figure S4. The fabricated Wheatstone bridge structure for nanodevices characterization [25].
Vectorial NetworkAnalyzer
Port 1 Port 2
0–18 GHzCable
Amplifier0.1–18 GHz
Sonde5 kX —FPM # 100Sonde Coplanaire
0–18 GHzCascade Microtech,Picoprobe
Figure S5. The validation of calibration kit by measuring a 11.2-kX resistance: (a) comparison of measurement between conventional system and the method proposed; (b) comparison of measurement error in the whole frequency bandwidth [25].
(b)
(a)
Frequency (GHz)0 1 2 3 4 5
Measure with 50-X Conventional System
15
Rea
l (Z
) kX
12
9
6
3
0
dc Value ofResistance
Measure with 3.5-kXWheatstone Bridge
Frequency (GHz) 0.5–2
<15
<1
2–3.5
<20
<5
3.5–5
<30
<15
0–0.5
<30
<1
VNA 50 X (%)
WheatstoneBridge (%)
probe from Cascade Microtech. Recently, we have shown that by integrating a resistance into the sys-tem [Figure 3(b)], it is possible to avoid the use of a high impedance probe.
It should be mentioned that to determine the contact resistance of the unique nanotube, dc measurements are usually performed considering an equivalent small sig-nal circuit illustrated in Figure 3(a). For an SWCNT, the value of the contact resistance of 22 kX was obtained. This value can be obtained also by exploring the real part of the impedance at low frequency.
Interferometric TechniqueAnother method for reducing the impedance mismatch is to develop novel ad-hoc instrumentation that is able to operate in any measurement configuration: that
means in the range of low and high impedances (from a few tens to hundreds of kilo-ohms). Therefore, in con-trast with conventional resonator methods, the imped-ance of the probes should be adjusted precisely with a low-noise and fully programmable impedance tuner.
Consequently, a modified VNA architecture has been developed to yield high-measurement sensitivity in any measurement configuration [26]. The illustration is given in Figure 4, considering the general block dia-gram of VNA in a one-port measurement configuration. The technique, often called reflectometry, is based on the use of power dividers and/or directional couplers connected to the microwave source and to the DUT with impedance .Z (See “Interferometric Technique: Theory and Calibration.”) In Figure 4(a), one part of the reference wave (denoted )R is collected by the power
36 January/February 2014
divider, and the coupler separates the reference wave from the reflected one (denoted A). The resulting reflec-tion coefficient measured by the VNA is expressed as
withZ ZZ Z
RA Z 50
0
00 XC =
+-
= = . (1)
When very high impedances (or very low) are considered, most of the incident wave on the DUT is reflected back so that the VNA becomes insensitive to the variations of the reflection coefficient C . So, to extend the VNA measurement capabilities for imped-ances greater than the kX, an interferometric tech-nique has been proposed. It consists of canceling the reflected wave A at the frequency of interest. To that
end, a tunable high-impedance reference device (with impedance ZREF ) is connected to the coupled port of the hybrid, as illustrated in Figure 4(b). The imped-ance ZREF is adjusted to cancel the total reflected wave
.A Consequently, the waves reflected respectively by the DUT (with impedance Z) and the reference device have the same magnitude but are phase-shifted by 180°. So, the total reflected signal and the resulting reflection coefficient are theoretically zero. In fact, this technique brings the high impedance to 50 X.
Ideally, the cancellation technique could be done under any configuration in terms of operating fre-quency, impedance, and level of the magnitude of the reflection coefficient. The implementation of the technique is straightforward and can be implemented using traditional microwave functions. Different inter-ferometric setups have been studied [27]–[30], and an example of an experimental modified VNA archi-tecture based on the interferometric architecture is depicted in Figure 5.
The measurement system is a broadband network analyzer. A coaxial 3 dB, 90° hybrid coupler is con-nected to port 1 of the VNA. The direct and coupled ports are connected to the high-impedance DUT (with impedance Z) and to the impedance tuner, respec-tively. The impedance tuner is built up with a high-resolution programmable delay line connected to a motor-driven variable attenuator. A mechanically
Figure 4. Configurations for the measurement of microwave impedances. (a) A generalized network analyzer setup in a one-port configuration and (b) a modified network analyzer setup based on the interferometric principle for the measurement of high impedances.
(a)
(b)
AR
Z
ZREF
AR
Z
CREF
C
C
S21
A A
Z U
Figure 5. Experimental set-up based on the proposed interferometric method for the microwave measurement of high impedances.
Figure 3. (a) An illustration of an equivalent circuit of a unique CNTs and (b) a new Wheatstone bridge structure with integration of high impedance.
(a)
Rc RcLk
Cel
RCNT
Cel
(b)
January/February 2014 37
Ideally, the cancellation technique could be done under any configuration in terms of operating frequency, impedance, and level of the magnitude of the reflection coefficient.
variable attenuator is inserted between the direct port of the hybrid coupler and the high-impedance DUT to compensate the losses in the impedance tuner. A broadband low-noise amplifier can be added to improve the signal level. In the following, an applica-tion of the technique is proposed through a demon-stration of a scanning microwave microscopy for the measurement of attofarad capacitances.
The interferometric system is connected between a conventional VNA and a microwave atomic force microscope (AFM) platform developed by Agilent Technology [31], [32]. The nanodevices considered in this study consist of metal-oxide semiconductor (MOS) microcapacitors whose values range from 0.1 to 10 fF. The MOS microcapacitors are composed of circular gold electrodes evaporated on silicon dioxide deposited on a P-type silicon substrate of resistivity: 1–3 X.cm. The measurement kit is depicted in Figure 6. To vary the capacitances of the microcapacitors, the diameter of the upper gold pad varies from 1 to 4 nm, and the SiO2 thickness ranges from 50 to 300 nm.
The experiment has been performed at the test fre-quency 3.50 GHz using an intermediate frequency (IF)
Figure 6. Measurement kit based on scaled MOS microcapacitors. The SiO2 layer is etched to obtain steps with different thickness. The gold electrodes are deposited on the different SiO2 steps. The top-right inset shows the top view of the measurement kit. The top-left inset represents the AFM probe configuration.
Alumina
CaCb
Cc
Metal
Insulator Probe1–4 nm
50–300 nm COX
CBulk
SiO2
Si
Figure 7. The measured magnitude of the reflection coefficient as a function of the modeled capacitance phase-shift U at . .F GHz3 50= The inset shows the measured capacitance as a function of the modeled capacitance.
5 # 10-4 10-3 1.5 # 10-3 2 # 10-3
-35
-30
-25
-20
-15
-10
-5
Capacitance Phase-Shift (°)
KCO
(dB
)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.1
0.2
0.3
0.4
0.5
0.60.70.80.9
1
Modeled Capacitance (fF)
Mea
sure
d C
apac
itanc
e (f
F)
38 January/February 2014
of 100 Hz. We focused the study on the sub-fF capaci-tance measurement. The microcapacitors have been pre-liminarily modeled by finite element modeling using COMSOL Multiphysics software. From the calculated capacitances, the phase-shift of the reflection coefficient of the capacitance is calculated by the relation
a ( C )tan2 50 ~U =- . (2)
For capacitance values between 150 and 900 aF, the capacitance phase-shift U varies from about 0.35 to 2 millidegrees at the test frequency; therefore it can-not be measured accurately by a conventional VNA. The interferometric technique is then applied. Figure 7 presents the measured magnitude of the reflection coefficient C by the VNA as a function of the phase-shift capacitance. There is a variation of C better than 20 dB in the capacitances range of interest. Con-
sequently, it is demonstrated that impedance contrasts can be enhanced by the interferometric technique to a large extent. Using a modified one-port calibration procedure depicted in [33], the capacitances can be determined from the measured microwave reflection coefficient. The inset of Figure 7 presents the capaci-tances measured by the microwave microscope com-pared to the modeled capacitances. Excellent agree-ment is found over the whole investigated range.
The results plotted in Figure 7 demonstrate that sub-fF capacitances can be measured accurately in the microwave frequency regime with the interero-metric-based method just described. The technique proposed avoids the use of conventional resonators that limit the frequency band of operation. The exper-imental results show that the technique is very prom-ising for measurements of small impedance contrasts, which is essential for characterizing high-impedance nanoscale devices.
SummaryThe emergence of new materials (nanowires, nano-tubes, graphene tapes, and thin films) and devices with nanoscale dimensions give rise to the necessity for developing dedicated techniques that will allow their electrical characterization at high-frequency range.
Interferometric Technique: Theory and Calibration
The programmable delay line and the motor-driven variable attenuator are tuned to cancel the reflection coefficient REFC of a reference load ZREF at the test frequency of interest. Thus, the impedance tuner provides a cancellation wave with the same magnitude and an opposite phase-shift to the wave reflected by the reference load. The microwave characterization is performed by means of the VNA to measure the transmission coefficient .S21
At the test frequency, the transmission coefficient measured is zero, resulting in high-measurement sensitivity for impedances around .ZREF
Before doing any measurement, the system must be calibrated to take into account the imperfections of the interferometer and the VNA. As the accurate measurement is possible only for impedances around
,ZREF traditional one-port vector calibration techniques that make use of calibration loads well distributed on the Smith chart are not suited.
The proposed calibration and measurement methods are detailed as follows:Step 1) A reference load ZREF,1 with reflection
coefficient REF,1C is connected as a DUT. The cancellation wave process is then performed. The measured transmission coefficient is called .S1
Step 2) For the wave cancellation conditions, a traditional one-port vector calibration method model is used to make the link between the reflection coefficient S21 measured by the VNA and the reflection coefficient .DUTC The resulting model is given by
.S E EE E1 DUT
DUT21 11
22
21 12
CC
= +-
(S3)
The complex terms ,E11 E E21 12 , and E22 correspond respectively to the directivity, source match, and reflection tracking errors. These calibration parameters depend on the S-parameters of the interferometer, the reflection coefficient REF,1C , and the imperfections of the VNA. The system (S3) is resolved by a derived short-open-load (SOL) calibration method that makes use of the measurements of the transmission coefficient ,S1 S2 , and S3 of three known standards, namely the load ZREF,1 (used in the cancellation wave process) and two other calibration loads called ZREF,2 and ZREF,3 with reflection coefficients REF,2C and
REF,3C close to .REF,1CStep 3) The DUT is connected. The measured
reflection coefficient S21 is associated to the inversion of the (S3) to determine .DUTC
Another method for reducing the impedance mismatch is to develop novel ad-hoc instrumentation that is able to operate in any measurement configuration.
January/February 2014 39
In this article, two possible views have been high-lighted to tackle the issue of the measurement of high-impedance nanoscale devices. The first solution is based on the integration of a high-impedance reflectometer and a nanoscale device on the same chip. The micro-wave impedance of a single CNT has been successfully measured up to 6 GHz using this technique. The second solution consists of inserting an adjustable microwave interferometer between a traditional VNA and the high-impedance device. The interferometer allows adjust-ment of the impedance to be measured to the highest measurement sensitivity of the measurement system. In particular, capacitances down to 0.35 fF have been mea-sured with an error estimated to be less than 10% using the interferometric technique combined with a scanning microwave microscope.
These proofs of concept on one-port nanodevices open the route towards the case of two-port active devices with high impedance. Advances in the manu-facturing of next-generation nanodevices will depend on our ability to measure electrical properties and per-formance characteristics accurately and reproducibly at the nanoscale regime over a broad frequency range.
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