Role of phonon dimensionality on electron-phonon scattering rates

We analyze the heat power P between electrons and phonons in thin metallic films deposited on free-standing dielectric membranes in a temperature range in which the phonon gas has a quasi two-dimensional distribution. The quantization of the electrons wavenumbers in the direction perpendicular to the film surfaces lead to the formation of quasi two-dimensional electronic sub-bands. The electron-phonon coupling is treated in the deformation potential model and, if we denote by Te the electrons temperature and by T ph the phonons temperature, we find that P ≡ P (0) (Te) − P (1) (Te, T ph ); P (0) is the power "emitted" by the electron system to the phonons and P(1) is the power "absorbed" by the electrons from the phonons. Due to the quantization of the electronic states, P vs (d, Te) and P vs (d, T ph ) show very strong oscillations with d, forming sharp crests almost parallel to the temperature axes. In the valleys between the crests, P ∝ T 3.5 e − T 3.5 ph . From valley to crest, P increases by more than one order of magnitude and on the crests P does not have a simple power law dependence on temperature.The strong modulation of P with the thickness of the film may provide a way to control the electron-phonon heat power and the power dissipation in thin metallic films. Eventually the same mechanism may be used to detect small variations of d or surface contamination. On the other hand, the surface imperfections of the metallic films may make it difficult to observe the oscillations of P with d and eventually due to averaging the effects the heat flow would have a more smooth dependence on the thickness in real experiments.

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“…Using (19) and (21) and changing from summations over k and q to integrals, for the symmetric part we have…”

Section: Contribution Of the S Modesmentioning

confidence: 99%

“…has a temperature dependence proportional to T x e − T x ph , where x < 5 [17][18][19] . On the other hand, a theoretical investigation of the surface effects for a thin metallic film deposited on a half-space (semi-infinite) dielectric showed that the value of x is actually larger than 5 20 .…”

Section: Introductionmentioning

confidence: 99%

Electron–phonon heat exchange in layered nano-systems

Anghel

Cojocaru

2016

Solid State Communications

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“…In a dirty limit with ql < 1, theories predict that n ranges from 4 to 6 depending on type and level of disorder 17,18 . Deviations from n = 5 are experimentally observed in normal metals and alloys [19][20][21][22] . But this hypothesis is still not fully verified as some experiments show that even for samples in the dirty limit, the energy flow rate from electrons to phonons follows the T 5 dependence 23,24 .…”

mentioning

confidence: 99%

“…But this hypothesis is still not fully verified as some experiments show that even for samples in the dirty limit, the energy flow rate from electrons to phonons follows the T 5 dependence 23,24 . The effect of phonon dimensionality and substrate properties on e-p coupling have also been discussed 19,[25][26][27] . Experiments show that n falls below 4.5 for phonons in two dimensions 25 .…”

mentioning

confidence: 99%

Fast thermometry with a proximity Josephson junction

Wang

Saira

Pekola

2018

Applied Physics Letters

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We couple a proximity Josephson junction to a Joule-heated normal metal film and measure its electron temperature under steady state and nonequilibrium conditions. With a timed sequence of heating and temperature probing pulses, we are able to monitor its electron temperature in nonequilibrium with effectively zero backaction from the temperature measurement in the form of additional dissipation or thermal conductance. The experiments demonstrate the possibility of using a fast proximity Josephson junction thermometer for studying thermal transport in mesoscopic systems and for calorimetry.Thermometry is a cornerstone in studies of thermodynamics. When the investigated system is in equilibrium, the working speed of a thermometer may not be an important factor, as the system status does not change with time. In the past decades, much progress has been made in understanding thermal transport in nanoscale systems in the steady state [1][2][3] . If the time scale of interest is shorter than thermal relaxation time τ of the relevant system, one needs to measure the system temperature with a fast thermometer in nonequilibrium. The relaxation time increases with lowering temperature, which makes the thermal relaxation time of electrons experimentally accessible at millikelvin temperatures. A thermometer with large bandwidth is still needed to expand the temperature range and the variety of processes that can be observed in non-equilibrium.Fast thermometry with sub-µs time resolution has been realized with Normal MetalInsulator-Superconductor (NIS) tunnel junctions and superconducting weak links embedded in resonant circuits 4-8 . In these methods, the measurement bandwidth is set by the linewidth of the resonant circuit, which can not be increased indefinitely without sacrificing the readout sensitivity. Recently, Ref.[9] has shown nanosecond thermometry using a superconducting nanobridge, introducing the hysteretic JJ as a fast thermometer for calorimetry with easy integration.In this letter, we perform fast, minimally invasive thermometry of an evaporated thin-film using proximity JJs. Instead of using superconducting nanobridge, we utilize proximity JJs consisting of a normal metal weak link contacting two superconducting leads. The normal section of the weak link is galvanically connected to the thin film under study, whose electron temperature can be elevated by Joule heating pulses. We devise a probing scheme that allows us to study the nonequilibrium electron temperature in the thin film with µs time resolution, vanishing dissipation, and virtually zero added heat conductance to the system under study prior to the measurement pulse. Experimental results show the great potential of using proximity JJ thermometer for precision and fast measurements of electron temperature in metallic films.The JJ thermometer consists of a normal metal wire (cyan) sandwiched between Al superconducting electrodes (blue), shown in Scanning Electron Microscope (SEM) image in Fig. 1(b). The inner four electrodes are used in the experim...

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“…The electron-phonon interaction is accordingly enhanced. This behavior was also observed in experiments [131][132][133].…”

Section: Hot-electron Effect In Bulk Resistorssupporting

confidence: 67%

Strongly coupled, low noise dc-SQUID amplifiers

Pleikies¹

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Role of phonon dimensionality on electron-phonon scattering rates

Cited by 88 publications

References 16 publications

Electron–phonon heat exchange in layered nano-systems

Electron–phonon heat exchange in layered nano-systems

Fast thermometry with a proximity Josephson junction

Strongly coupled, low noise dc-SQUID amplifiers

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