Patent Publication Number: US-7724005-B1

Title: High-frequency structures for nanoelectronics and molecular electronics

Description:
FIELD OF THE INVENTION 
     The present subject matter relates to high-frequency characterization of small devices and minute amounts of materials. More specifically, the present subject matter discloses methods and apparatus for carrying out an on-chip subtraction process to reduce parasitic effects in measurement fixtures including coupling capacitance effects. 
     BACKGROUND OF THE INVENTION 
     Parasitic effects from measurement fixtures are difficult to handle in microwave characterization of small devices and materials. It is even more challenging when the expected signal level is low. Such devices include magnetroelectronic/spintronic devices and high-impedance devices, for instance a metallic single-walled-carbon-nanotube (mSWNT), a SWNT transistor, a minimum-size deep-submicron metal-oxide-semiconductor (MOS) field-effect-transistor (FET), a sub-micron MOS FET that is operating in sub-threshold region, and a molecular device. Such materials include on-chip biofluids, chemicals and thin films. The microwave characteristics of these devices and materials are of great interest in their development and applications. Considering a metallic SWNT as an example; its high-frequency characteristics are important for potential interconnect and sensor applications. Metallic SWNTs are also considered an ideal, one-dimensional model for fundament condensed matter physics studies. Their high-frequency properties, which correspond to collective Plasmon oscillations, would be a direct verification of Luttinger liquid theory that was proposed to describe one-dimensional material. 
     A proposed RF transmission line model as illustrated enclosed in the dashed-line box  130  in  FIG. 1(   c ), has often been the focus and foundation for previous mSWNT studies. It has been predicted that mSWNTs have very high characteristic impedance, on the order of 10 kΩ due to high kinetic inductance and includes a large contact resistance component of a few kΩ or higher. Under these conditions, signal attenuation and reflection are very high when currently available microwave measurement systems are used for their characterizations. The difficulty is further complicated by the parasitic effects coming from RF test fixtures, especially the effects from gap coupling capacitor equivalently illustrated at C′ p  ( FIG. 1(   c )) and C p  ( FIG. 1(   d )), in typical measurement arrangements. 
     The calculated scattering parameters, S 21 , of the equivalent circuit  140  ( FIG. 1(   d )) as illustrated in  FIGS. 2(   a ) and  2 ( b ) of several situations exemplify the measurement challenge. At low frequencies, the contact resistance (R) dominates; at high frequencies, the coupling capacitance (C p ) dominates. The inductance effect, which is an indication of transmission line characteristics is indistinguishable from the combined coupling capacitance and contact resistance effects. Moreover, measurement uncertainties, including contact uncertainties from one measurement to another, make it difficult to use various de-embedding or off-chip approaches that have been developed for deep sub-micron CMOS device characterizations. As a result, only limited success has been achieved in the efforts on high-frequency mCNT property and potential application investigations. These efforts include the development of measurement methods for CNT devices. Previously attempted direct scattering parameter measurements, resonant circuit techniques, and heterodyne methods have not been successful in addressing the measurement difficulties for the characterization of the equivalent transmission line model of a mCNT. For instance, the exceptionally large and unique “kinetic” inductance associated with mCNTs has not yet been experimentally verified and characterized. 
     While various measurement methods for characterizing CNT devices have been developed, no design has emerged that generally encompasses all of the desired characteristics as hereafter presented in accordance with the subject technology. 
     SUMMARY OF THE INVENTION 
     In view of the recognized features encountered in the prior art and addressed by the present subject matter, an improved methodology for characterizing, i.e., taking electrical measurements of, small devices and minute amounts of materials has been developed. 
     In an exemplary configuration, parasitic capacitance effects resulting from a coupling gap capacitor effect are reduced. 
     In one form, the present subject matter provides an on-chip subtraction mechanism to reduce parasitic effects of a test fixture. 
     In accordance with aspects of certain embodiments of the present subject matter, microwave structure for on-chip parasitic effect subtraction is provided. 
     In accordance with certain aspects of other embodiments of the present subject matter, methodologies have been developed to direct an incoming signal along two paths or branches of a hybrid to produce at an output of the hybrid a difference signal with significantly reduced parasitic components. 
     In accordance with aspects of still further embodiments of the present subject matter, similar test fixtures or a test fixture and a capacitive component having a capacitive value similar to a test fixture may be positioned in a hybrid device such that signals from each fixture or fixture and capacitive component are effectively subtracted from each other to cancel parasitic effects that may inhibit accurate characterization of a device or material under test secured in a test fixture. 
     Additional objects and advantages of the present subject matter are set forth in, or will be apparent to, those of ordinary skill in the art from the detailed description herein. Also, it should be further appreciated that modifications and variations to the specifically illustrated, referred and discussed features and elements hereof may be practiced in various embodiments and uses of the invention without departing from the spirit and scope of the subject matter. Variations may include, but are not limited to, substitution of equivalent means, features, or steps for those illustrated, referenced, or discussed, and the functional, operational, or positional reversal of various parts, features, steps, or the like. 
     Still further, it is to be understood that different embodiments, as well as different presently preferred embodiments, of the present subject matter may include various combinations or configurations of presently disclosed features, steps, or elements, or their equivalents (including combinations of features, parts, or steps or configurations thereof not expressly shown in the figures or stated in the detailed description of such figures). Additional embodiments of the present subject matter, not necessarily expressed in the summarized section, may include and incorporate various combinations of aspects of features, components, or steps referenced in the summarized objects above, and/or other features, components, or steps as otherwise discussed in this application. Those of ordinary skill in the art will better appreciate the features and aspects of such embodiments, and others, upon review of the remainder of the specification. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A full and enabling disclosure of the present invention, including the best mode thereof, directed to one of ordinary skill in the art, is set forth in the specification, which makes reference to the appended figures, in which: 
         FIG. 1(   a ) is a cross-section of an exemplary mCNT test set-up including metallic electrodes for facilitating characterization measurements; 
         FIG. 1(   b ) is a top-view of the test setup of  FIG. 1(   a ); 
         FIG. 1(   c ) is an equivalent circuit model of the test setup; 
         FIG. 1(   d ) is a simplified equivalent circuit model of the test setup; 
         FIGS. 2(   a ) and  2 ( b ) graphically illustrate the simulated scattering magnitude and phase parameters respectively of the equivalent circuits of  FIGS. 1(   c ) and  1 ( d ); 
         FIG. 3(   a ) is a schematic diagram of a microwave hybrid structure in accordance with the present subject matter; 
         FIG. 3(   b ) is a graphical representation of simulated scattering parameters between the two branches of the hybrid structure of  FIG. 3(   a ); 
         FIGS. 4(   a ) and  4 ( b ) provide graphical magnitude and phase comparisons respectively of measured scattering parameters determined by the present and conventional methodologies; 
         FIGS. 5(   a ) and  5 ( b ) illustrate respectively extracted inductance and resistance values for different resistive and inductive combinations; 
         FIGS. 6(   a ) and  6 ( b ) illustrate layouts of measuring circuits used to evaluate the technology of the present subject matter; 
         FIG. 7(   a ) graphically illustrates on-chip parasitic effects cancellation; 
         FIG. 7(   b ) graphically illustrates variations between measured and simulated capacitance values based on a normalized increasing gap width; 
         FIGS. 8(   a ) and  8 ( b ) graphically illustrate magnitude and phase effects comparisons respectively of non-symmetrical gap capacitance on extracted scattering parameters; and 
         FIGS. 9(   a )- 9 ( d ) graphically illustrate the effects of non-symmetrical attenuation and phase delay on extracted scattering parameters. 
     
    
    
     Repeat use of reference characters throughout the present specification and appended drawings is intended to represent same or analogous features or elements of the invention. 
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     As discussed in the Summary of the Invention section, the present subject matter is particularly concerned with an improved methodology for characterizing, i.e., taking electrical measurements of, small devices and minute amounts of materials. 
     Selected combinations of aspects of the disclosed technology correspond to a plurality of different embodiments of the present invention. It should be noted that each of the exemplary embodiments presented and discussed herein should not insinuate limitations of the present subject matter. Features or steps illustrated or described as part of one embodiment may be used in combination with aspects of another embodiment to yield yet further embodiments. Additionally, certain features may be interchanged with similar devices or features not expressly mentioned which perform the same or similar function. 
     Reference will now be made in detail to the presently preferred embodiments of the subject device characterization apparatus and methodologies. Referring again to  FIGS. 1(   a ) to  1 ( d ), it will be seen that  FIGS. 1(   a ) and  1 ( b ) correspond to cross-sectional and top views respectively of a test set-up  100  including a metallic carbon nanotube mCNT  120  coupled between a pair of metallic electrodes  110 ,  112  to facilitate characterization measurements. In an exemplary configuration mCNT  120  and electrodes  110 ,  112  may be mounted on a SiO 2  layer  114  overlying a Si substrate  116 . Substrate  116  may itself be mounted on a metallic support structure  118  which may be coupled to a reference (ground) potential. 
     As may be seen in  FIG. 1(   c ), the test set-up of  FIGS. 1(   a ) and  1 ( b ) may be represented by equivalent circuit  150 . A transmission line model of mCNT  120  is generally represented by the equivalent circuitry illustrated within dash line box  130 . The pair of resistors R′ represent the dominant contact resistance component. Capacitor C′ p  represents the coupling capacitance of the gap  140 , which is required to host a device under test (DUT). In the present exemplary configuration, capacitor C′ p  represents the capacitance created by ends  142 ,  144  of electrodes  110 ,  112 , respectively, and the gap  140  between such electrode ends  142 ,  144 . 
     Capacitors C ox  represents excess electrode capacitance due to end effects while resistors R sub  and R sub1  represent substrate resistances. Capacitors C s  represent the excessive coupling capacitance between the signal lines and ground due to end effects. 
       FIG. 1(   d ) represents a simplified equivalent circuit  160  where the substrate parasitic components are ignored, mCNT is approximated by setting R equal to 2R′ and the value of L remaining equal to the value of L in  FIG. 1(   c ). In instances where a high resistivity substrate is used in the test set-up, corresponding resistances can be considered infinite. Coupling capacitor C p  in simplified equivalent circuit  160  includes contributions from all the other relevant capacitive components illustrated in  FIG. 1(   c ). 
     With reference now to  FIGS. 2(   a ) and  2 ( b ) there are graphically illustrated simulated scattering magnitude and phase parameters respectively of the equivalent circuits of  FIGS. 1(   c ) and  1 ( d ) with C p =2fF, R=2R′=7 kOhm, L=4 nH and with different circuit component combinations as noted on the graphs. These exemplary parameters were selected based on present knowledge of metallic SWNTs. It should be apparent to those of ordinary skill in the art that a mCNT transmission line model can be simplified as is shown in  FIG. 1(   d ) as previously discussed. It should also be clear that resistance R dominates performance of CNT. When frequency is above about 10 GHz, C p  dominates performance of the circuit. As a result, it is difficult to characterize inductance L by use of conventional characterization methods. 
     In accordance with the present technology, a new methodology has been developed for the characterization of small devices that uses on-chip subtraction to significantly reduce parasitic effects of the test fixture with a focus on reducing the coupling gap capacitor effect. 
     With reference to  FIG. 3(   a ), there is illustrated a schematic representation of a microwave structure  300  constructed in accordance with the present technology for on-chip parasitic effect subtraction. As may be seen in  FIG. 3(   a ), an incoming microwave signal coupled to Port  1  is evenly split via a 3-dB power divider into two branches. Strong reflections will occur at the two gaps  302 ,  304  along the two branches. Resistor  306  in the power divider will absorb the reflected signal and provide isolation between the two branches. Signals that are transmitted across gaps  302 ,  304  then propagate to the “rat-race” hybrid  308 . 
     As may be seen from  FIG. 3(   a ), the signal passing through gap  302  enters rat-race  308  and passes along a λ/4 portion of the rat-race until it reaches Port  2 . In similar fashion, a signal passing through gap  304  enters rat-race  308  and passes along a 3λ/4 portion of the rat-race before reaching Port  2 . Since the signals arriving at Port  2  are separated by λ/2, i.e. 180°, the output signal from Port  2  corresponds to the difference of the two signals that come from gaps  302  and  304 . Resistor  316  coupled between Port  3  and a reference potential (ground) will absorb common mode signals from the two branches. As a result the parasitic effects, including the coupling effects, are greatly reduced as illustrated in  FIG. 3(   b ). 
     It should be readily understood by those of ordinary skill in the art that if gaps  302  and  304  are substantially identical, the transmission paths from the gaps toward rat-race  208  are substantially identical, and the transmission paths around the rat-race are substantially λ/2 different as they each arrive at Port  2 , the signal at Port  2  will be substantially zero. That is, the signals passing through each branch of the circuit will substantially balance each other out thus compensating for any parasitic effects that may be present in the test fixture corresponding to gap  302  or, alternatively, gap  304 . 
     With further reference to  FIG. 3(   a ), a measurement approach to the characterization of small devices may proceed as follows. In the following example, one may assume that the reference impedance of the measurement system is Z 0  which is also the matching impedance of the power divider and the hybrid  308  in  FIG. 3(   a ). Assume low-loss transmission lines with signal propagation factors exp(−α ij 1 i −jβ ij 1 i )=exp(−α1 ij −jθ ij ) in  FIG. 3(   b ). If the attenuation constant α ij  and the phase propagation constant β ij  are the same for the corresponding line sections in each branch, then the scattering parameter S 21  is: 
                     S   21     =       exp   ⁡     (         -   α     ⁢       ∑   i     ⁢           ⁢     l   i         -     j   ⁡     (       ∑   i     ⁢     θ   i       )         )       ⁢     (       S     21   ⁢     (     CNT   +     C   p       )         -           ⁢       exp   ⁡     (       -   αλ     /   2     )       ⁢     S     21   ⁢     (     C   p     )             )     ⁢     (     S     21   ⁢     (     Power   ⁢           ⁢   Divider     )         )     ⁢     (     S     21   ⁢     (   Hybrid   )         )               eq   .           ⁢   1               
where S 21(CNT+Cp)  is the scattering parameter of the gap with an mCNT and S 21(Cp)  is the scattering parameter of the other gap. The attenuation and phase delay associated with the transmission lines in the test fixture can be calculated and/or experimentally obtained by use of a dummy structure, such as the one shown in  FIG. 6(   b ). The structure is identical to the test fixture of  FIG. 6(   a ), but with only a gap in one branch. The coupling capacitance values of the gap can be obtained through measurement, calculation or simulation.
 
     When the used mCNT is a few μm long and the operating frequency is on the order of 10 GHz, a lumped RL model can be used to approximate the distributed transmission line CNT model, as is shown in  FIG. 1(   d ). The calculated s-parameter S 21  of the mCNT using the simplified model are shown in  FIGS. 4(   a ) and  4 ( b ). It is clear that signals passing through the coupling capacitance of the gap dominate if no subtraction is applied, consistent with the information obtained in  FIGS. 2(   a ),  2 ( b ), and  3 ( b ). The method in accordance with the present technology yields results that are good approximations of the mCNT even when the coupling capacitance is relatively large and varies across a relatively large range. 
     From the obtained scattering parameters, resistance R and inductance L can be obtained through the following equations. 
                   R   ≈         2   ⁢       Z   0     ⁡     (     1   -          S   21            )                S     21              ⁢     (   Ω   )                 eq   .           ⁢   2     ⁢     (   a   )                     L   ≈         (       2   ⁢     Z   0       +   R     )     ⁢           ⁢     tan   ⁡     (     -     Angle   (     S   21     )       )         -     4   ⁢     Z   0     ⁢       ω   ⁢   RC     p           ω     ⁢     (   H   )               eq   .           ⁢   2     ⁢     (   b   )                 
The extraction of L still needs the knowledge of C, unless the corresponding term is small in eq. (2b). Nevertheless, as shown in  FIGS. 4(   a ) and  4 ( b ), the accuracy of the extracted CNT parameters on the accuracy of C, is de-sensitized even though the accuracy of the method in accordance with the present technology deteriorates when the gap capacitance becomes large. On the other hand, a gap with a few fF of capacitance is amicable for fabrication and device characterization, where reasonable accuracy can be achieved.
 
     The method in accordance with the present technology may be tested numerically using a known network having the topology as illustrated in  FIG. 1(   d ).  FIGS. 5(   a ) and  5 ( b ) present extracted inductance and resistance for different given R and L combinations using the present technology. As is evident from an inspection of  FIGS. 5(   a ) and  5 ( b ), resistance R extraction does not depend on L values, while L extraction does depend on R slightly. The smaller the gap capacitance is, the more accurate the extracted parameters are. As may further be observed from  FIGS. 5(   a ) and  5 ( b ), the accuracy of the present characterization methodology does vary somewhat from the ideal as represented by the reference line, however, it is believed that the attained accuracy is quite acceptable considering the challenges of the targeted measurement applications. 
     Since it is difficult to find circuit components that can be used to mimic the network in  FIG. 1(   d ) to verify the methodology of the present technology, small capacitors are used instead. These capacitors are realized by changing the microstrip line gap width, shown in  FIG. 6(   a ). The capacitance value is chosen so that the output signal level is similar to that from a single mCNT. In order to demonstrate operation of the present technology, three test structures were fabricated with their gap widths increased by 10%, 30%, and 50%, compared to the original 50Ω microstrip-line width. The gap space was 20 mils. The structures consist of a conventional 3 dB Wilkinson power divider and a 3 dB 180° phase shift ring-hybrid (Rat-race hybrid) at 5 GHz. A “THRU” structure (i.e., a structure without a gap) in  FIG. 6(   b ) is used to characterize the transmission coefficients in eq. (1). All ports are matched to 50Ω. Roger RT/Duroid 5870 substrate with thickness h=31 mils and  E ,.=2.33 was used. ADS simulations are also conducted to verify both theoretical analysis and experimental results. A modified equation gives the capacitance as: 
     
       
         
           
             
               
                 
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                                   S 
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                     F 
                   
                 
               
               
                 
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       FIG. 7(   a ) shows the cancellation effects of the fabricated structures. If the two signal paths are symmetric, the output signal should be approximately zero after the cancellation, such as the lowest signal point of the simulated results (at −5 GHz). In practice, however, various factors affect the effectiveness of the cancellation process. Two prominent ones are the fabrication variations and surface wave excitations. Despite these complications, the measured S 21  in  FIG. 7(   a ) demonstrate a approximate 23 dB reduction of the parasitic (gap coupling) effects when compared with the measured results of a single gap at 5 GHz. When compared with the predicted S 21  in  FIG. 4 , the subtraction process should be reasonable for mCNT characterization. 
       FIG. 7(   b ) shows that the extracted capacitance values from the measured data are close to the simulated results with ADS. Furthermore, the measured capacitance ratios are approximately the gap-width ratios, as expected. These agreements verified the validity of the proposed method. When the gap has about 10% width increase, the discrepancy between the simulated and the measured capacitance are larger. This is due to the relatively lower signal level that is closer to the noise background. 
     There are a few issues that determine the accuracy, sensitivity and applications of the proposed measurement method. The symmetry of the proposed structures is an important such feature. Any non-symmetric geometry between the upper branch and the lower branch will cause non-symmetric electrical behaviors, which will eventually appear at the output port in  FIG. 3 . For instance, a non-symmetric 3-dB power division, non-symmetric transmission line widths (hence different attenuation constant, phase constant and gap capacitance) and non-symmetric hybrid connections will introduce a difference signal at port  2 . A non-symmetric substrate will further complicate the cancellation process. In addition, any non-symmetric fabrication scratches on the substrate surface would probably contribute to a less than ideal on-chip subtraction process. 
     When a gap is needed for characterization purposes (such as mCNT characterizations), its attenuation will dramatically reduce the effects of the non-symmetric power division and the non-symmetric transmission line sections that lead to the gap. As a result, the symmetry of the gap and the sections of the structure after the gap are more important.  FIG. 8  shows the extracted s-parameter S 21  the non-symmetric gap capacitance at 5 GHz provided the rest of the structure is ideally symmetric. Clearly, larger error occurs when gap non-symmetry increases. Fortunately, it is not too difficult to control gap symmetry to a level that satisfies a reasonable accuracy under current fabrication technology. 
       FIG. 9  shows the effects on the extracted scattering parameters from non-symmetric phase constant and attenuation constant. It is expected that the main attenuation limitation comes from the half-wave-length line (attenuation) difference of the hybrid. This attenuation dictates the choice of substrates and structure design for nano-device characterizations. 
     The structures in  FIGS. 6(   a ) and  6 ( b ) are big, comparable with the microwave wavelength. The dimensions of the designed structures are mainly determined by the power divider and the hybrid-ring. For GHz frequency or below, the structures may be too big to meet the sample size limitations of some nanofabrication equipment. As a result, miniaturized designs need to be developed. The results of some current efforts, such as the dramatic size reduction of a rat-race hybrid and power divider can be exploited. 
     The method in accordance with the present technology works ideally at one frequency only. Both the measured and simulated results show a very narrow band. This bandwidth limitation mainly comes from the design of the hybrid, where a 180′ phase shift is needed for the two incoming common-mode signals to cancel each other. 
     Metallic SWNT is used as an example in this work to illustrate the present microwave characterization method, where the gap coupling capacitance dominates. There are other application situations where no gap is needed to host the device-under-test (DUT) or material-under-test (MUT) while the expected signal level is relatively weak. One example is the characterization of individual micro/nano magnetic structures. The present cancellation method is still effective, as is shown in  FIG. 7(   a ) when both THRU are used. Therefore, it is anticipated that the present method can be extended for such applications. 
     The method in accordance with the present technology subtracts parasitic effects on-chip by use of passive microwave devices. Weak signals from small and high-impedance devices then emerge from the dramatically reduced background, particularly the otherwise overwhelming coupling capacitance effects. The data extraction procedure is straightforward and its accuracy depends on the symmetry and loss of the microwave structures. The design guidelines are straightforward. 
     While the present subject matter has been described in detail with respect to specific embodiments thereof, it will be appreciated that those skilled in the art, upon attaining an understanding of the foregoing may readily produce alterations to, variations of, and equivalents to such embodiments. Accordingly, the scope of the present disclosure is by way of example rather than by way of limitation, and the subject disclosure does not preclude inclusion of such modifications, variations and/or additions to the present subject matter as would be readily apparent to one of ordinary skill in the art.