Contains reports on two research projects.Joint Services Electronics Programs (U.S. Army, U. S. Navy, and U. S. Air Force) under Contract DAAB07-71-C-030

Smith, J. M.

Strandberg, Malcom W. P.

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II. MICROWAVE SPECTROSCOPYAcademic and Research StaffProf. M. W. P. StrandbergProf. R. L. KyhlJ. D. KiersteadGraduate StudentsJ. B. Barton J. U. Free, Jr. J. M. SmithL. R. Fox R. M. Langdon, Jr. A. TachagumpuchJ. K. RainesA. WORK COMPLETED1. SURFACE EFFECTS IN THE MAGNETO-SURFACE IMPEDANCEOF METALSThis research has been completed by J. B. Barton, and submitted to the Departmentof Physics, M.I.T., August 1971, in partial fulfillment of the requirements for the degreeof Doctor of Philosophy. A summary of the thesis follows.The classical theory of the surface impedance of a metal at low temperatures isreviewed for the case in which there is no externally applied magnetic field. Thenthe effects of applying a magnetic field are discussed. We used a simple trajectorymodel for electronic conduction. In our model surface scattering effects were approx-imated by an angle-dependent probability of specular reflection. We found evidence fora simple relation between the rf surface impedance and the nonlocal conductivity of ametal, and used this relation in conjunction with the trajectory model to predict thequalitative dependence of the low magnetic field surface impedance line shape on thetype of surface scattering present.We discussed procedures for measuring the absolute value of the real part R s of therf surface impedance. As a prerequisite for this discussion, the subject of impedancerelationships along a transmission line was dealt with in some detail. A method wasdescribed for eliminating most of the effects of a line on measurements of R s , and foraccurately computing the remaining influences of the line.We described techniques for increasing the speed of a marginal oscillator's responseto changes in the impedance of its tank circuit, and analyzed, to a limited extent, therelationship between the response time and the sensitivity of the oscillator. For alarge enough sample signal, increasing the response speed of the oscillator permittedus to make a real-time display of the low-field line shape.We tabulated results of static and dynamic measurements of R s for single-crystalThis work was supported by the Joint Services Electronics Programs (U. S. Army,U. S. Navy, and U. S. Air Force) under Contract DAAB07 -7 1-C-0300.QPR No. 103(II. MICROWAVE SPECTROSCOPY)disks of gallium. The absolute values measured for R are compared with values for1 sX s cited by Cochran and Shiffman, and the line shapes observed in the dynamic measure-ments are also compared with data obtained by those researchers. We found that theline shape exhibits a strong peak at B = 0 in all the crystal orientations which we studied.Its width, however, exhibited no measurable dependence on parameters such as tem-perature and surface roughness, so positive comparison with the theoretical model wasnot possible.In an appendix, we explored a quasi-classical theory for scattering of a wave packetfrom a statistically defined rough surface. An enhancement of specular reflection wasfound to occur when the diameter of the wave packet becomes smaller than the corre-lation length for surface irregularities.M. W. P. Strandberg 'References1. J. F. Cochran and C. A. Shiffman, Phys. Rev. 140, A-1678 (1965).B. CRITICAL-POINT FLUCTUATIONS IN SUPERCONDUCTINGTHIN FILMSFurther study has been made on the noise properties of superconducting thin filmsnear the transition temperature. Excess noise (noise not caused by ordinary tempera-ture fluctuations) has been observed in both tin and indium films when those films wereplaced in a perpendicular magnetic field and biased by a current source. These films,deposited on sapphire disks one inch in diameter, were photo-etched using masterdrawings so that the final film geometry could be accurately controlled. In this way wecould study the dependence of the excess noise on such parameters as film width, length,thickness, current density, magnetic field, and temperature.The usual procedure for studying the excess noise is the following. The supercon-ducting film, held at some temperature and biased by a fixed current density, is sweptthrough the transition region by the application of a perpendicular magnetic field. Theexcess noise is observed only in this transition region, and this noise peaks typicallywhen the film reaches 1/10 of the full normal resistance. When the film has reached1/2 normal resistance or greater, the excess noise is negligible.The peak-integrated noise power for a film swept through the transition region isroughly proportional to (J-J )2, where J is the bias current density, and Jo is a param-eter that increases almost linearly with decreasing temperature. For J < J no excessnoise is observed. The value of Jo depends greatly on film thickness, and, in general,the thinner the film the smaller will be Jo for a fixed temperature.QPR No. 103(II. MICROWAVE SPECTROSCOPY)The noise power spectrum from 10 kHz to 200 kHz follows roughly a 1 /fa dependencewhere a is close to unity. A high-frequency tail with a more gradual falloff is alsoobserved at the higher frequencies (from 200 kHz to 50 MHz). Below 10 kHz bubble noisewith its 1/f 2 dependence dominates. This noise, caused by the boiling of liquid heliumproducing temperature fluctuations in the film, prevents the accurate study of the excessnoise below 10 kHz.There are several reasons why we believe the observed excess noise is caused bya flux-flow mechanism. The peaking of the noise in the lower part of the transitionregion is characteristic of flux flow in type I superconductors. The existence of theparameter Jo is consistent with general flux-flow arguments describing the stability ofthe intermediate superconducting state. The observed noise spectrum with its 1/f depen-dence agrees with the flux-flow model which assumes that the flux bundles are stoppedmany times on their passage from one side of the film to the next. The magnitude ofthe observed noise is reasonably close to the predicted level. The lack of any othersimple mechanism that could produce the observed noise characteristics supports ourconclusion that flux -flow noise is being observed.J. M. SmithQPR No. 103

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