Low Temperature Electron-Phonon Interaction in DisorderedMetal Thin Films and Applications to Fast, SensitiveSub-Millimeter Photon Sources and DetectorsA DissertationPresented to the Faculty of the Graduate SchoolofYale Universityin Candidacy for the Degree ofDoctor of PhilosophybyMinghao ShenDissertation Director: Robert SchoelkopfDecember 2005c°2005 by Minghao Shen.All rights reserved.AbstractLow Temperature Electron-Phonon Interaction in Disordered MetalThin Films and Applications to Fast, Sensitive Sub-Millimeter PhotonSources and DetectorsMinghao ShenMay, 2005The electron–phonon interaction in metals becomes very weak at very low temper-atures (sub–Kelvin temperatures). It is very challenging to measure such weak inter-action with traditional techniques. In this thesis work, we develop a new dynamic mi-crowave noise thermometry technique for study the low temperature electron-phononinteraction in disordered metal thin films. The high sensitivity and fast time responseof the thermometry allow us to study the electron–phonon interaction in nano–scaledisordered metal thin films. Both long diffusive metal wires and short wires in SNSstructures are observed. We measure the electron–phonon heat conductance Ge−phin steady states, and the electron–phonon time τe−phand electronic heat capacityCefrom the electron thermal dynamic in the time domain. The results of the threequantities are consistent within themselves for each device, and can be explainedqualitatively by the theory (Sergeev & Mitin 2000). However, the measured valuesfor Ge−phand Ceare 10–50 times larger than the expected book values.We also develop a new on-chip calibration scheme for ultra–sensitive submillimeterdetectors, with phonon-cooled hot electron sources. The sources are essentially metalthin films, whose hot electron induced Johnson noise is equivalent to one-dimensionalblackbody radiation. The weak electron–phonon interaction in the film makes thesource very accurate and fast at low temperatures for low photon power generation.2Acknowledgements1Contents1 Introduction 151.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.2 Calibration of sub-mm detectors with hot electron blackbody photonsource . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.2.1 Hot electron blackbody photon source . . . . . . . . . . . . . 181.2.2 Electron-phonon interaction at low temperatures . . . . . . . . 201.2.3 On-chip Calibration Scheme . . . . . . . . . . . . . . . . . . . 231.3 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 Metal Film Resistor Blackbody Photon Source 272.1 Overview of Blackbody Radiation . . . . . . . . . . . . . . . . . . . . 272.1.1 Blackbody Radiation in General . . . . . . . . . . . . . . . . . 272.1.2 One Dimensional Blackbody Radiation . . . . . . . . . . . . . 282.2 Overview of Johnson Noise . . . . . . . . . . . . . . . . . . . . . . . . 302.3 Planar phonon cooled hot electron Blackbody Photon Source . . . . . 332.3.1 Johnson Noise is Blackbody Radiation . . . . . . . . . . . . . 333 Theoretical background on electron-phonon decoupling in disorderedmetal films 363.1 Thermal model of metal thin film resistors on insulating substrates . 372Contents3.2 Interactions of electrons with the surroundings in disordered metal films 403.2.1 Electron-electron scattering in disordered metal films . . . . . 403.2.2 Electron-phonon scattering rate . . . . . . . . . . . . . . . . . 413.2.3 Electron-impurity scattering . . . . . . . . . . . . . . . . . . . 413.2.4 Comparison of rates . . . . . . . . . . . . . . . . . . . . . . . 423.3 Electron Joule heating . . . . . . . . . . . . . . . . . . . . . . . . . . 443.4 Electron cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.4.1 Electron cooling by inelastic scattering . . . . . . . . . . . . . 453.4.2 Electron-Phonon Cooling in Long Diffusive Wires . . . . . . . 473.4.3 Electron-Phonon Interaction in SNS Structures . . . . . . . . 493.5 Electron-phonon Interaction in low temperature thin metal films . . . 513.5.1 Electron-Phonon interaction in pure metal . . . . . . . . . . . 523.5.2 Impurity modifications to electron-phonon scattering . . . . . 553.5.3 Electron-phonon interaction in disordered metals . . . . . . . 563.5.4 The electron energy loss rate . . . . . . . . . . . . . . . . . . . 633.5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.6 Electron radiation cooling . . . . . . . . . . . . . . . . . . . . . . . . 653.7 Metal Film - Insulator Kaptiza Conductance . . . . . . . . . . . . . . 683.7.1 Acoustic mismatch theory . . . . . . . . . . . . . . . . . . . . 693.7.2 Diffuse mismatch theory . . . . . . . . . . . . . . . . . . . . . 703.7.3 Kapitza heat conductance in our system . . . . . . . . . . . . 703.8 Electronic Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . 713.9 Hot electron blackbody photon sources and hot electron bolometers . 734 Dynamic Microwave noise thermometry 754.1 Review of techniques for measuring electron-phonon interaction . . . 753Contents4.2 Microwave noise thermometry setup . . . . . . . . . . . . . . . . . . . 794.2.1 Microwave setup . . . . . . . . . . . . . . . . . . . . . . . . . 794.2.2 DC bias line . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854.3 Electron temperature Tecalibration . . . . . . . . . . . . . . . . . . . 864.4 Electron-phonon interaction measurement setups . . . . . . . . . . . . 894.4.1 Steady state measurement setup . . . …