Investigation of Wang's Model for Room-Temperature Conduction ...

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Abstract—This paper investigates Wang's application of Har- rison's screening potential theory, which is used for the modeling of room-temperature conduction ...
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 4, APRIL 2005

Investigation of Wang’s Model for Room-Temperature Conduction Losses in Normal Metals at Terahertz Frequencies Stepan Lucyszyn, Senior Member, IEEE

Abstract—This paper investigates Wang’s application of Harrison’s screening potential theory, which is used for the modeling of room-temperature conduction losses in normal metals at terahertz frequencies. The methodology formulated for this theoretical model is examined in detail. Fundamental equations are derived from first principles and used as reference in this investigation. A summary of the derivations and the results from this work are reported for the first time. From this detailed investigation, it has been found that there are serious discrepancies with Wang’s general methodology. As a result, it appears that it may be inappropriate to use Wang’s model to describe the intrinsic frequency-dispersive nature of normal metals at room temperature. The findings from this work add weight to the view that there is neither theoretical nor experimental evidence to support the existence of anomalous behavior in normal metals at room temperature. Index Terms—Conduction loss, metals, surface resistance, terahertz.

I. INTRODUCTION

W

ITH THE ever increasing commercial interest in exploiting the millimeter-wave (mm-wave) and sub-millimeter-wave parts of the frequency spectrum, it is important for designers to be able to accurately characterize the frequency behavior of the materials used to realize the components that operate at such high frequencies. For example, with normal metals at room temperature, Drude’s classical relaxation-effect model can be approximated by the simpler classical skin-effect model below 40 GHz. At millimeter-wave and sub-millimeter-wave frequencies, over the past few decades, a number of research groups worldwide have reported discrepancies between loss measurements and classical theoretical predictions with even simple structures [1]. This phenomenon has been attributed to some form of anomalous intrinsic frequency dispersion that is thought to exist within normal metals at room temperature. For the first time, a comprehensive survey of reported experimental data for the room-temperature surface resistance of normal metals, from dc up to the edge of the mid-infrared frequency range, has recently been published by the author. It was concluded that there was no clear experimental evidence to support the view of any anomalous room temperature intrinsic frequency dispersive Manuscript received June 20, 2004; revised August 14, 2004 and September 16, 2004. The author is with the Optical and Semiconductor Devices Group, Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, U.K. (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2005.845758

behavior in normal metals at terahertz frequencies, since any deviation from nonclassical theory could be attributed to any number of factors associated with the overall measurement setups [1]. In addition to experimental measurements, a theoretical model has also been reported that tries to further promote the case for anomalous frequency-dispersive behavior in normal metals at room temperature [2]. Developed at Howard University, Washington, DC, and supported by the NASA Goddard Space Flight Center, Greenbelt, MD, this model continues to be widely cited within the scientific and engineering communities [3]–[8]. The methodology used to formulate this theoretical model will be examined in detail, using equations derived from first principles. A summary of the derivations and the resulting findings from this rigorous analysis will be reported for the first time. II. WANG’S APPLICATION OF SCREENING POTENTIAL THEORY It is well known that, at sufficiently high frequencies, the conductivity of normal metals exhibits both temporal (i.e., frequency) and spatial (i.e., one-dimensional) dispersion. Harrison introduced the frequency- and wavenumber-dependent dielectric function for a semiclassical free-electron gas [9]. This model describes the screened Coulomb potential effect that a spatial charge-density fluctuation has on a free electron as it travels through a periodic lattice of fixed positive ions. It can be helpful to think of induced conduction current within a normal metal as flowing in lamina-type sheets: almost parallel to the surface ( – -plane) of the conductor and having an amplitude that decays exponentially from its surface into the bulk material. The resulting electric and magnetic fields and conducand spation current distributions inside the metal have time tial ( -direction) variations of the form (1) where angular frequency is given by , is the fre, is the quency, propagation constant is given by attenuation constant, and is the phase constant. Also, , is the modified wavenumber. where is used throughout and Note that the complex operator used in other cited references. Failure to that this replaces adopt a consistent notation can result in errors. Wang assumed that the periodic nature of the conduction current density gives rise to a screening potential effect on free electrons as they travel in a direction perpendicular to the surface of

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LUCYSZYN: INVESTIGATION OF WANG’S MODEL FOR ROOM-TEMPERATURE CONDUCTION LOSSES IN NORMAL METALS

the air–metal boundary. With spatial charge-density fluctuations being attributed to lamina-type sheets of conduction currents, as an analogy to a periodic lattice of fixed positive ions, Wang adopted Harrison’s screening potential theory. To this end, Harrison’s semiclassical expression for intrinsic bulk conductivity was used to calculate Wang’s surface impedance [2] as follows:

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where

(3b) (3c)

(2a) (3d)

where (2b)

where

and

and (2c)

where permeability of free space; relative complex permeability (purely real and for the metals considered here); intrinsic bulk conductivity at dc; lattice wavenumber (Harrison) or modified wavenumber (Wang, ; mean distance traveled by the electron between collisions (i.e., mean-free path length); velocity between collisions of the free electron, having kinetic energy at the Fermi level; scattering relaxation time of the free electron (i.e., mean time between collisions). In deriving (2), it was assumed that electrons at all angles, with respect to the metal surface in the half-space, will contribute to the conductivity within this semiclassical free-electron gas analysis [2]. Moreover, the modified wavenumber considered here is at least two orders of magnitude lower than the Fermi wavenumber and, therefore, a quantum mechanical analysis is not necessary. It was assumed that, with such long wavelengths of potential, there is no difference between conductivities for transverse and longitudinal fields in cubic materials [2]. In the 1970s, Tischer reported excess room-temperature conduction losses in copper, giving measurement excess conduction loss data at 35 [10], [11] and 70 GHz [12], [13], which are not within anomalous frequency regions. Wang used (2) to account for the excess conduction losses at these two frequency points and to predict the losses across the entire microwave, millimeter-wave, and sub-millimeter-wave frequency spectra—up , where to the collision damping frequency, [2]. Even though 35 GHz and 70 GHz were extracted from Tischer’s measurements, there are still at 35 GHz , least four other unknowns to be solved [i.e., 70 GHz , 35 GHz , and 70 GHz ], which makes finding a direct solution difficult. For this reason, a new methodology was presented by Wang [2]. Wang quoted new , skin depth , and expressions for surface impedance excess conduction loss factor (3a)

(3e)

where is the classical skin-effect surface resistance. Wang suggests that, if the excess conduction loss factor is known, then the corresponding modified wavenumber can be determined. To this end, it can be clearly seen that (2) can be rewritten in the following form:

(4a) where (4b) (4c) where is the classical relaxation-effect intrinsic bulk conductivity. By replacing the logarithmic term in (4a) with its equivalent , we have series expansion, for (5a)

(5b)

Equation (5b) is obtained for long wavelengths, when only the first two terms of the logarithm’s series expansion are considered to be significant. At low frequencies and long wavelengths, it can be shown that Harrison’s expression for intrinsic bulk conductivity reduces to Wang’s simplified expression for intrinsic to yield bulk conductivity (6a) where (6b) It can be shown that, by inserting the real part of in (3), Wang’s modified wavenumber into

from (6) becomes (7)

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Wang calculates , using (7), by fitting data to below in (2) with from 70 GHz. Therefore, by replacing (7), Harrison’s complex conductivity and Wang’s surface impedance and theoretical excess conduction loss factor can all be calculated at low frequencies and long wavelengths. Since experimental values of excess conduction loss were only taken at 35 and 70 GHz, Wang extrapolates values of between dc (where ) and 35 GHz (where 35 GHz ) and interpolates values between 70 GHz ). When Wang 35–70 GHz (where carried out his work, more than a quarter of a century ago, modern-day computing facilities were not readily available and so it is reasonable to assume that be-spoke curve-fitting (e.g., using universal curves) was applied directly to the dc , 35-, and 70-GHz data points. The assumption for this ad hoc approach is reinforced by the absence of any empirical or analytical models given by Wang. Above 70 GHz, Wang assumes a monotonically increasing against frequency. Wang interpolates values of function of between 70 GHz [where 70 GHz is obtained using (7) 70 GHz ] and GHz [where a value of with can be entered into (2) so that ]. The calculation of this value of excess conduction loss factor was based on the ineffectiveness concept [14]–[16] associated with the extreme anomalous skin-effect region). Since Wang does not quote any mathematical models, it is reasonable to assume that be-spoke curve-fitting was applied directly to these two data points. Fig. 1 shows an accurate graphical reproduction of Wang’s frequency response for copper’s excess conduction loss factor at room temperature. Wang observed that the theoretical excess conduction loss factor increases with frequency, from its unity value (at dc) to a peak value of almost 1.35 (at 2000 GHz), and then decreases (beyond 2000 GHz) to the anomalous value of 1.212 (at 6715.4 GHz).

III. ANALYSIS OF METHODOLOGY Wang noted that good agreement between experimental and theoretical results was obtained. Here, any agreement occurs at the four frequency points of dc, 35, 70, and 6715.4 GHz, were made to fit. There is no where the assumed values of independent agreement or verification at any other frequency points. Indeed, Wang’s application of the screening potential theory runs into a number of fundamental problems associated with the data values used and the general methodology adopted. A. Anomalous Data Values It has been assumed that the four discrete data values are without error and that ideal curve-fitting was performed. With the former, only the theoretical value of is certain. With all other data points, the following anomalies exist. 1) For the 35-GHz data point, Tischer went to great lengths to manufacture a copper rectangular waveguide cavity under near perfect conditions [10], [11]. However, the value of 35 GHz was then extracted from

Fig. 1. Comparison of excess conduction loss models (the circles represent Wang’s data points).

the following approximation for the unloaded

where

-factor

(8)

where , , , and represent the unloaded -factor contributions from the sidewalls, top, bottom, and end walls, rerepresents the spectively, is a geometric factor, and surface resistance of the sidewalls. With a modern measurement setup, having traceable calibration and verification waveguide standards, and perhaps even a less approximate equation for extracting the surface resistance, the extracted value for 35 GHz may be very different from the one quoted by Tischer. Indeed, it has been found that a higher level of 15% in the excess conduction loss is calculated [1] when the more accurate value for is used [17]. Unfortunately, since Tischer undertook his 35-GHz measurements more than three decades ago, it is not possible to establish a reasonable estimate for the corresponding measurement errors. is defined as follows: 2) Excess conduction loss factor (9) where is the measured or modeled surface resistance and is the normalizing classical skin-effect or relaxation-effect surface resistances By measuring the insertion loss of a metal-pipe rectangular waveguide transmission line, the value for surface resistance can be extracted from the associated attenuation constant , using the following approximation: (10) where is the intrinsic impedance for a plane wave in free space and is a geometric factor Alternatively, if the simple power-loss method is used, as represented by (10), one can apply the following definition directly to the measurements of the transmission lines (11)

LUCYSZYN: INVESTIGATION OF WANG’S MODEL FOR ROOM-TEMPERATURE CONDUCTION LOSSES IN NORMAL METALS

where is the measured attenuation constant and is the normalizing attenuation constant, using the classical or relaxation-effect model skin-effect For the 70-GHz data point, Tischer employed this alternative method on two different lengths (813 and 914 mm) of metal-pipe rectangular waveguide transmission lines, mode of designed for operation in the fundamental propagation. It is worth pointing out that (9) and (11) give different results when the classical relaxation-effect model is used as a reference and/or more accurate methods are employed to calculate the theoretical attenuation constant . Having said this, from the current investigation, it was found that at 70 GHz there is only a small error introduced by Wang’s use of the classical skin-effect within the simple power-loss surface resistance method for calculating the attenuation constant —as opposed to the preferred use of the relaxation-effect , within the more general variation surface impedance method [18], [19]. This is because the standard WR-12 waveguide is designed for low loss operation and, at mode’s 70 GHz, it is well away from either of the 48-GHz and 97-GHz cutoff frequencies. Once again, with a modern measurement setup, having traceable calibration and verification waveguide stan70 GHz may be very dards, the extracted value of different from the one quoted by Tischer. Indeed, it has been found that a higher level of 23% in the excess conduction loss is calculated [1] when the more accurate is used [17]. Since Tischer undertook his value for 70-GHz measurements almost three decades ago, it is not possible to establish a reasonable estimate for the corresponding measurement errors. It is interesting to point out that, if the 15% and 23% levels of excess conduction losses at 35 and 70 GHz, respectively, did indeed reflected natural behavior, then the scientific and engineering communities would have widely reported similar occurrences at these relatively low frequencies. In practice, this has not happened because the relaxation-effect model is sufficiently accurate to describe the natural behavior of normal metals at room temperature. Indeed, this has been shown to be the case between 900 GHz and 12.5 THz [1]. 3) For the 6715.4-GHz data point, Wang’s values for inand corresponding excess trinsic conductivity conduction loss factor were calculated according to (12a)

(12b)

(12c)

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Equation (12a) does not constitute the self-consistent solution for the ineffectiveness concept. The correct equations are given as follows [14]–[16]: (13a) since (13b)

(13c) where is the effective skin depth and is the corresponding conductivity calculated using the ineffectiveness concept It can be clearly seen that Wang’s excess conduction loss has been inflated by 7.5% from the more appropriately calculated value of 13.7%. 4) Pippard’s ineffectiveness concept, as described by (13a), is only aimed to give a qualitative understanding and not a quantitative measure. Moreover, this oversimplified model only applies within the extreme anomalous skin-effect region, where the effective skin depth is much ). smaller than the mean-free path length (i.e., However, from calculations in (13), it is found that and, therefore, it is not appropriate to use the ineffectiveness concept here. As pointed out by Matick, in the more accurate theory, the extreme anomalous effect should not appear until the period of the applied frequency is comparable with the time required by an electron to transverse the skin depth, which is much smaller than the scattering relaxation time [15]. 5) The discrepancies associated with 2)–4) raise questions with frequency about how the monotonic increase in was implemented and later interpreted. For example, the following empirical equation can be used to fit Wang’s data points, at 70 and 6715.4 GHz, for a monotonically against frequency: increasing function of THz (14) By inserting (14) into (2), the frequency response of excess conduction loss factor does indeed peak between the values of 70–6715.4 GHz. However, this peaks just below 29% at 1600 GHz, as opposed to almost 35% at 2000 GHz found by Wang. This example clearly shows that can be found when curve-fitting the variation in for using different approaches. Wang does not give a physical explanation as to why excess conduction loss factor exhibits a peak in its frequency response. Indeed, following his line of reasoning, excess conduction loss factor should continue to increase as frequency increases further into the anomalous and then extreme anomalous skin-effect regions. 6) Wang’s values for the scattering relaxation time, fs, and bulk dc conductivity, S/m, are low by more accurate modern-day values of fs[1] and S/m [17], respectively, for polycrystalline copper at a room temperature

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of 20 C (by approximately 5.3% and 2.7%, respectively). Moreover, to minimize errors, a surface resistance renormalization process is required to calculate the excess conduction loss factor when the reference temperature is different from the temperature at which the measurements were carried out [1]. Revised values for excess conduction loss factor have been given in 1) and 2), for the classical skin-effect model.

11)

B. Discrepancies in Methodology 7)

8)

Instead of an analytical solution, an empirical technique was applied to just four data points. There is significant uncertainty with the three non-dc data values but still interpolation was performed across more than two decades of bandwidth, using ad hoc be-spoke curve fitting. Wang quoted (7) and suggested that it was derived by to satisfy the following equation: approximating (15) From first principles, the following was found to be the case: (16)

9)

10)

Equation (7) is actually derived from the solution of the quadratic function in (16), although (15) would be valid if is replaced by . with Without justification, a monotonic increase in frequency was assumed within the far-infrared region. Although the lowest spectral absorption line may exist within the near-infrared region (e.g., 142 THz for aluminum [17]), even with normal metals there may be a significant effect within the far-infrared region, due to the presence of the lower frequency absorption tail created by interband transitions [20]. For this reason, the assumption of a monotonic frequency behavior may not be invalid. Harrison suggested that a possible solution for the electromagnetic wave within a metal is to introduce wavenumber dependence in the conductivity, as with his screening potential theory [9]. Here, the modified wavenumber must be a complex quantity to account for the exponential decay into the bulk metal, since one is dealing with evanescent electromagnetic wave propagation at room temperatures. Otherwise, if both the frequency and wavenumber are real quantities, then there cannot be a solution unless the intrinsic conductivity is purely imaginary [9]. It is evident from Wang’s methodology that there is a contradiction, since both frequency and modified wavenumber are purely real quantities and yet the resulting intrinsic conductivity is not a purely imaginary term. In other words, with reference to (1) and (2), Wang has replaced Harrison’s real lattice wavenumber with a real modified , instead of the complex variwavenumber term . The large imaginary term in the modiable fied wavenumber represents the considerable attenuation of the evanescent wave and cannot be ignored. For Wang’s must be met, correassumption to be valid, , which is not the case sponding to a wavelength with normal metals at room temperature.

12)

13) 14)

Wang’s interpretation of Harrison’s semiclassical work on free electron gas (i.e., Coulomb’s screening of conducting valence electrons by donor atom potentials) and its subsequent application to calculate the surface impedance was also undertaken by Slepyan [5]. Wang states that only long-wavelength variations of potential exits and, at such long wavelengths, there is no difference between conductivities for transverse and longitudinal fields in cubic metals. However, as later pointed out by Ilyinsky et al. [7], the presence of spatial dispersion in an otherwise isotropic medium effectively transforms it into an anisotropic medium defined by the spatial orientation of the modified wave vector . As a result, with the presence of the type of spatial dispersion considered here, there must be an inherent difference between longitudinal and transverse conductivities within the metal. Coulomb’s screening only affects the longitudinal conductivity, however, surface impedance is a function of the transverse conductivity. In other words, Wang effectively tries to calculate surface impedance using the wrong spatial conductivity. , With reference to (13c), there will be a frequency in this case, at which . This below represents the widely accepted boundary between the classical skin-effect and anomalous skin-effect regions. and are calculated The approximate values for as 3.15 THz (using Wang’s values) or 2.75 THz (using modern day values) and 6.72 THz (using Wang’s values) and 6.36 THz (using modern day values), respectively. At and, therefore, this boundary frequency, . This contradicts the findings of Wang, where at all frequencies up to and exceeding . Moreover, with respect to 5), the onset of the anomalous skin-effect region is at 3.15 THz, but Wang shows that, as frequency increases through this boundary, then the excess conduction loss factor drops sharply. Finally, with being above , Wang ignored any residual effects from spatial dispersion. Wang’s equation for skin depth, given in (3c), is an overcannot be ignored. simplification, since When comparing the classical Drude model of intraband transitions (representing the spectral region associated with the relaxation effect) with the classical skin-effect model (representing the spectral region associated with ohmic losses), the corresponding excess conduction loss can be represented by the following: factor (17a)

where

(17b) is the classical relaxation-effect surface resiswhere tance. The frequency responses for excess conduction loss factor for Wang’s model and the classical skin-effect and relaxation-effect models are shown in Fig. 1, which were

LUCYSZYN: INVESTIGATION OF WANG’S MODEL FOR ROOM-TEMPERATURE CONDUCTION LOSSES IN NORMAL METALS

calculated using the original values of scattering relaxation time and bulk dc conductivity. The classical skin-effect is taken as reference. , for all frequencies, It can be seen that as demonstrated by Schwab and Heidinger [21]. Equation (17a) contradicts the findings of Wang, where at all frequencies up to and exceeding . This is because Wang calculates the excess conduction loss factor according to the following: (18)

15)

Again, this is an oversimplification, since cannot be . From (18), it is clear ignored from calculations of how Wang demonstrates an excess conduction loss factor of greater than unity with the classical relaxation-effect model, relative to the classical skin-effect model, even though the converse is true. Wang calculates excess conduction loss factor with reference to the classical skin-effect surface resistance given in (3e). However, from the recent study by the author, when more accurate room-temperature experimental data were examined, above 1 THz, it was found that the excess conduction loss factor is close to unity when the , given in classical relaxation-effect surface resistance (17b), is taken as reference [1]. Indeed, below 40 GHz, is simply an approximation to the more natural bemust be havior expressed by , given in (4b). In turn, and, therefore, is not approan approximation of priate as the reference surface resistance used to calculate the excess conduction loss factor at millimeter-wave and sub-millimeter-wave frequencies.

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[5] G. Y. Slepyan, “On the boundary conditions for nonideally conducting bodies,” Zh. Tekh. Fiz., vol. 54, no. 2, pp. 403–405, 1984. [6] K. Kikuchi, “Measurements of the surface resistance of a metallic thin-film at a wavelength of 10.6 m,” IEEE Trans. Instrum. Meas., vol. 39, no. 2, pp. 395–398, Apr. 1990. [7] A. S. Ilyinsky, G. A. Slepyan, and A. Y. Slepyan, Propagation, Scattering and Dissipation of Electromagnetic Waves. London, U.K.: IEE Press, 1993, pp. 18–24. [8] K. J. Song and T. G. Castner, “Calibration of a helical resonator for microwave dielectric and conductivity measurements of metals,” AIP Rev. Sci. Instrum., vol. 72, no. 3, pp. 1760–1769, Mar. 2001. [9] W. A. Harrison, Solid State Theory. New York: McGraw-Hill, 1970, pp. 280–290. [10] F. J. Tischer, “Anomalous skin effect of single-crystal copper in the millimeter-wave region at room temperature,” Phys. Lett. A, vol. 47, no. 3, pp. 231–232, Mar. 1974. , “Excess conduction losses at millimeter wavelengths,” IEEE [11] Trans. Microw. Theory Tech., vol. MTT-24, no. 11, pp. 853–858, Nov. 1976. [12] , “Experimental attenuation of rectangular waveguides at millimeter-wavelengths,” in IEEE MTT-S Int. Microwave Symp. Dig., 1977, pp. 492–494. , “Experimental attenuation of rectangular waveguides at mil[13] limeter-wavelengths,” IEEE Trans. Microw. Theory Tech., vol. MTT-27, no. 1, pp. 31–37, Jan. 1979. [14] F. Wooten, Optical Properties of Solids. New York: Academic, 1972. [15] R. E. Matick, Transmission Lines for Digital and Communication Networks. New York: McGraw-Hill, 1969, pp. 141–148. [16] R. Kubo and T. Nagamiya, Eds., Solid State Physics. New York: McGraw-Hill, 1969. [17] D. R. Lide, Ed., CRC Handbook of Chemistry and Physics, 83rd ed. Boca Raton, FL: CRC. [18] S. Lucyszyn, D. Budimir, Q. H. Wang, and I. D. Robertson, “Design of compact monolithic dielectric-filled metal-pipe rectangular waveguides for millimeter-wave applications,” Proc. Inst. Elect. Eng., pt. H, vol. 143, no. 5, pp. 451–453, Oct. 1996. [19] R. E. Collin, Field Theory of Guided Waves. New York: McGraw-Hill, 1960, pp. 182–195. [20] Handbook of Optical Constants of Solids, vol. 4, E. D. Palik, Ed., Academic, Boston, MA, 1998. [21] R. Schwab and R. Heidinger, “Experimental and theoretical studies of the surface resistance in open resonator mirror materials,” in Proc. 21st Int. Infrared Millimeter Waves Conf., Berlin, Gemany, Jul. 1996.

IV. CONCLUSION This paper has investigated Wang’s application of Harrison’s screening potential theory, used for the modeling of room-temperature conduction losses in normal metals at terahertz frequencies. From this detailed investigation, it has been clearly demonstrated that there are serious discrepancies within the general methodology. It appears that it may be inappropriate to use Wang’s model to describe the intrinsic frequency dispersive nature of normal metals at room temperature. The findings from this study add weight to the view that there is neither theoretical nor experimental evidence to support the existence of anomalous behavior in normal metals at room temperature. REFERENCES [1] S. Lucyszyn, “Investigation of anomalous room temperature conduction losses in normal metals at terahertz frequencies,” Proc. Inst. Elect. Eng., pt. H, vol. 151, no. 4, pp. 321–329, Aug. 2004. [2] Y.-C. Wang, “The screening potential theory of excess conduction loss at millimeter and submillimeter wavelengths,” IEEE Trans. Microw. Theory Tech., vol. MTT-26, no. 11, pp. 858–861, Nov. 1978. [3] C. Vittoria, “Ferrite uses at millimeter wavelengths,” J. Magn. Magn. Mater., vol. 21, no. 2, pp. 109–118, Aug.–Sep. 1980. [4] P. Bhartia and I. J. Bhal, Millimeter Wave Engineering and Applications. New York: Wiley, 1984, pp. 197–197.

Stepan Lucyszyn (M’91–SM’04) joined Imperial College London, London, U.K., in June 2001, as a Senior Lecturer within the Optical and Semiconductor Devices Group. Prior to this, he was a Senior Lecturer with the University of Surrey, Surrey, U.K. He was the Principal Investigator on, and Coordinator for, two large multiuniversity millimeter-wave research projects and a Co-Investigator on other projects. During the summer of 2002, he was a Guest Researcher within the Microelectromechanical Systems (MEMS) Laboratory, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan. For the past seven years, he has taught “MMIC Measurement Techniques” at the IEE Vacation Schools on Microwave Measurements, National Physical Laboratory (NPL), Teddington and Malvern, U.K. He has authored or coauthored 78 research papers in both national and international conferences and journals in the broad area of microwave and millimeter-wave engineering. In addition, he co-edited and wrote three chapters in MMIC Design (London, U.K.: IEE Press, 1995) and four chapters in RFIC and MMIC Design and Technology (London, U.K.: IEE Press, 2001). Dr. Lucyszyn was the recipient of two recent Engineering and Physical Sciences Research Council (EPSRC) research grants. The first is to investigate millimeter-wave RF MEMS filters, utilizing conventional surface micromachining techniques on silicon. The second is to develop ultraquiet millimeter-wave detectors using C AT’s nanowhiskers. He was also the sole applicant to represent Imperial College London within the European Union’s Framework VI Network of Excellence on Advanced MEMS for RF and Millimeter Wave Communications (AMICOM).