Electron-phonon and electron-electron interaction times for ultrtathin Nb film in quasiequilibrium

1
MSPU
Hot-electron bolometer as direct and heterodyne
detector
Gregory Goltsman
Moscow State Pedagogical University Moscow, Russia
2
Lecture 2. Hot-electron bolometer as direct and
heterodyne detector Hot-electron phenomena in
thin superconducting films
Inelastic electron-electron scattering time in
clean and disordered metals Electron-phonon and
electron-electron interaction times in
quasiequilibrium, electron temperature Two-tempera
ture model for hot electrons and phonons in thin
superconducting films
Hot-electron bolometer (HEB) as a direct detector
for electro-magnetic radiation
Non-equilibrium energy cascade in a HEB Electron
temperature relaxation times phonon cooling
against diffusion cooling Responsivity and noise
equivalent power
Hot-electron bolometer (HEB) as a heterodyne
detector for electro-magnetic radiation HEB
mixer
Operation principles Non-linearity of the HEB
resistance vs electric field Basics of signal
mixing HEB mixer characteristics conversion gain
and conversion gain bandwidth, noise temperature,
noise bandwidth, local oscillator power
Applications of HEB mixers
Terahertz radioastronomy Remote sensing of the
Earth atmosphere Terahertz imaging
3
Electron-electron interaction in clean metal
Scheme of collision between two electrons with
momenta k1 and k2. The Pauli principle permits
only collisions with unoccupied final states k3
and k4.
s0 scattering cross section for Coulomb
interaction, 10-15 cm2 for typical metals
For 10K le-e10-1 cm
4
Electron-electron interaction in clean metal
e2lte1 ? e3, e4 gt 0 ? 3 and 4 unoccupied
e2gte1 ? e3, e4 lt 0 ? 3 and 4 occupied

1. Electrons in states 1 and 2 after collision can
   occupy states 3 and 4 if they were unoccupied
   before the collision and the laws of momentum
   conservation and energy conservation are not
   violated.
2. In this case the collision is not possible
   because there are no unoccupied final states
   which satisfy laws of momentum conservation and
   energy conservation. States 3 and 4 are occupied
   and the Pauli principle forbids this collision.
3. Centre of mass of particles 1 and 2 is marked as
   cross. States 3 and 4 satisfy the laws of
   momentum conservation and energy conservation if
   only they coincide with the ends of diametre of
   sphere of final states.

5
Electron-electron interaction in disordered metal
In thin films with short electron mean free path
the electron-electron interaction is
substantially enhanced.
?
?
?
6
Basics of signal mixing
Electric field, a.u.
Electron temperature, a.u.
HEB
Time
Time
Esig Esigsin(wW)t
ELO ELOsin(wt)
Esum Esigsin(wW)t ELOsin(wt)
Esum2 Esig2sin2(wW)t 2EsigELOsin(wt)sin(w
W)t ELO2sin2(wt) 0.5(Esig2
ELO2) EsigELOcos(Wt) - EsigELOcos(2wW)t
0.5Esig2cos(2wt)
0.5ELO2cos2(wW)t
7
Electron-phonon relaxation time in Nb and YBaCuO
films
K

• Modulation frequency dependence of the voltage
  shift caused by irradiation (l 2.2 mm) at
  different temperatures for Nb (dotted lines) and
  YBaCuO (solid lines) samples

K
te-ph
K
K
K
8
Electron-phonon and electron-electron interaction
times for ultrtathin Nb film in quasiequilibrium

• The dependences of t (o, D, ?, ?) and tj (?, ?)
  for devices based on 12 nm (o, ?) and 15 nm (D,
  ?, ?, ?) thick Nb films on sapphire substrates.
  Data were extracted from DU(f) dependencies in
  the resistive state (o, D), in the normal state
  under magnetic field HgtHc2(T) (?), from
  temperature dependencies of DU and dU/dT in the
  normal state (?). Solid lines represent tT-2,
  dashed lines tT-1. The inset shows t(T) near the
  Tc for a device based on 12 nm thick Nb on
  sapphire (solid line represents t(1-T/Tc)-1/2.

te-ph
tD
tD
te-ph
te-e
9
Response time of HEB vs Nb film thickness

• The dependence t(d) for Nb films with D1.0 cm2/s
  at two temperatures o 1.6K D 4.2K. Dashed
  lines represent fitting tte-phtb curves solid
  lines represent derived dependences ttbd and
  tte-ph

tb tes
te-ph
10
Energy flow in hot electron bolometer
Thermalization scheme showing subsequent channels
of the energy transfer in a hot-electron device
that relaxes towards global equilibrium.
d film thickness, a acoustic transparency
between film and the substrate, u speed of sound
cp, ce phonons and electrons specific heats
respectively
11
Lecture 2. Hot-electron bolometer as direct and
heterodyne detector Hot-electron phenomena in
thin superconducting films
Inelastic electron-electron scattering time in
clean and disordered metals Electron-phonon and
electron-electron interaction times in
quasiequilibrium, electron temperature Two-tempera
ture model for hot electrons and phonons in thin
superconducting films
Hot-electron bolometer (HEB) as a direct detector
for electro-magnetic radiation
Non-equilibrium energy cascade in a HEB Electron
temperature relaxation times phonon cooling
against diffusion cooling Responsivity and noise
equivalent power
Hot-electron bolometer (HEB) as a heterodyne
detector for electro-magnetic radiation HEB
mixer
Operation principles Non-linearity of the HEB
resistance vs electric field Basics of signal
mixing HEB mixer characteristics conversion gain
and conversion gain bandwidth, noise temperature,
noise bandwidth, local oscillator power
Applications of HEB mixers
Terahertz radioastronomy Remote sensing of the
Earth atmosphere Terahertz imaging
12
Two-temperature model for hot electrons and
phonons in thin superconducting films
Linearized time dependent heat balance equations
c the specific heat T the temperature ?
time Valid in the limit of Te Tph Tb
Perrin and Vanneste Phys. Rev B, 1983
13
Superconducting phonon-cooled HEB
Phonon-cooled HEB mixer E.M.Gershenzon,
G.N.Goltsman et al. Sov. Phys. Superconductivity
3,1582,1990 Diffusion-cooled HEB mixer
D.Prober, Appl.Phys.Lett. 62(17), 2119, 1993
Au
Au
te-e
e
e
tdiff
ph
e
Substrate
14
Electron temperature relaxation times phonon
cooling against diffusion cooling

• The dependence of energy relaxation time on
  bridge length in NbC at T 4.2 K. Dots represent
  experimental data, solid line represents the
  contribution of hot electrons out-diffusion,
  dashed line represents the contribution of
  electron-phonon interaction, dotted line
  represents the sum of two contributions

te-ph
td
B.S. Karasik, K.S. Ilin, E.V. Pechen, S.I.
Krasnosvobodtsev, Diffusion cooling mechanism in
a hot-electron NbC microbolometer mixer, Appl.
Phys. Lett. 68, 16, 2285-2287, 1996
15
Response of a YBCO HEP to a femtosecond
infraredpulse experimental data (solid line)
and simulations (dashed line) based on the 2-T
model
Alexei D Semenov, Gregory N Goltsman, and Roman
Sobolewski, Hot-electron effect in
superconductors and its applications for
radiation sensors, Supercond. Sci. Technol. 15
(2002)
16
Hot-electron relaxation diagrams and
characteristic time constants
ultrathin NbN film
thin-film YBCO
Alexei D Semenov, Gregory N Goltsman, and Roman
Sobolewski, Hot-electron effect in
superconductors and its applications for
radiation sensors, Supercond. Sci. Technol. 15
(2002)
17
Responsivity and noise equivalent power for hot
electron bolometer
Responsivity, dU/dT0 is for temperature steepness
of voltage U G thermal conductance to
substrate W,L film dimensions
Absorption coefficient, Rsq r/d resistance of
unit square of the film, R0 377 Ohm
characteristic impedance of free space
Noise equivalent power, first term corresponds to
thermal fluctuations due to heat exchange with
the substrate, second term is for Johnson noise,
third is for fluctuations of background radiation
with brightness temperature Tj (S area, W
angular aperture), forth is for excess noise of
various origins
18
Lecture 2. Hot-electron bolometer as direct and
heterodyne detector Hot-electron phenomena in
thin superconducting films
Inelastic electron-electron scattering time in
clean and disordered metals Electron-phonon and
electron-electron interaction times in
quasiequilibrium, electron temperature Two-tempera
ture model for hot electrons and phonons in thin
superconducting films
Hot-electron bolometer (HEB) as a direct detector
for electro-magnetic radiation
Non-equilibrium energy cascade in a HEB Electron
temperature relaxation times phonon cooling
against diffusion cooling Responsivity and noise
equivalent power
Hot-electron bolometer (HEB) as a heterodyne
detector for electro-magnetic radiation HEB
mixer
Operation principles Non-linearity of the HEB
resistance vs electric field Basics of signal
mixing HEB mixer characteristics conversion gain
and conversion gain bandwidth, noise temperature,
noise bandwidth, local oscillator power
Applications of HEB mixers
Terahertz radioastronomy Remote sensing of the
Earth atmosphere Terahertz imaging
19
Basics of signal mixing
20
Spiral antenna coupled NbN HEB mixer
SEM micrograph of the central area of HEB mixer
chip
21
The substrate with the HEBs on silicon lenses
22
Waveguide mixer chip designed for 1.5 THz
The 1.5THz chip's sizes are 72 um wide, 1100 un
long and 18 um thick
23
Experimental setup for noise and gain bandwidth
measurements
24
Noise temperature versus bias at 2.5 THz
Current, mA
Bias voltage, mV
Device 18014, 3 mm X 0.2 mm
25
Normalized output power vs intermediate frequency
26
Receiver noise temperature at 1.6 THzversus
intermediate frequency
27
Optimal LO power versus mixer volume
28
Heterodyne radiation pattern
Radiation pattern of the integrated antenna (feed
antenna on an extended 12-mm hemispherical lens)
at 2.5 THz. Solid black line represents simulated
Gaussian profile. Beam diameter for the
simulation was concluded from the best fit of
experimental data obtained by blending a
large-area black body source.
29
Noise temperature versus LO frequency for
heterodyne terahertz receivers
HEB
Schottky
SIS
LO power required lt 1 mW for HEB 1 mW for
Schottky
Low required LO power and high sensitivity make
HEB mixers most attractive to be used at
frequencies above 1 THz
30
Lecture 2. Hot-electron bolometer as direct and
heterodyne detector Hot-electron phenomena in
thin superconducting films
Inelastic electron-electron scattering time in
clean and disordered metals Electron-phonon and
electron-electron interaction times in
quasiequilibrium, electron temperature Two-tempera
ture model for hot electrons and phonons in thin
superconducting films
Hot-electron bolometer (HEB) as a direct detector
for electro-magnetic radiation
Non-equilibrium energy cascade in a HEB Electron
temperature relaxation times phonon cooling
against diffusion cooling Responsivity and noise
equivalent power
Hot-electron bolometer (HEB) as a heterodyne
detector for electro-magnetic radiation HEB
mixer
Operation principles Non-linearity of the HEB
resistance vs electric field Basics of signal
mixing HEB mixer characteristics conversion gain
and conversion gain bandwidth, noise temperature,
noise bandwidth, local oscillator power
Applications of HEB mixers
Terahertz radioastronomy Remote sensing of the
Earth atmosphere Terahertz imaging
31
The spectral content in the submillimeter band
for an interstellar cloud
A schematic presentation of some of the
spectral content in the submillimeter band for an
interstellar cloud. The spectrum includes dust
continuum, molecular rotation line and atomic
fine-structure line emissions.
32
Atmospheric transmission
Atmospheric transmission at Mauna Kea at an
altitude of 4200 m, with 1 mm of precipitable
water.
Atmospheric transmission from the Kuiper Airborn
Observatory at an altitude of 12000 m
33
Orion Molecular Cloud (OMC 1)
MoscowStatePedagogicalUniversity
Harvard Smithsonian Center for Astrophysics
CO J 9 ? 8 (1.037 THz) SAO-RLT Cerro
Sairecabur, 2004
An example of the results of FTS calibration
technique. Shown are two spectra of Orion KL
in CO J 9 ? 8 (1.037 THz), each required 1
minute of on-source integration time and the two
observations were made one hour apart. The system
temperature increased by 56 between the
observations, but the difference between the two
calibrated spectra is almost consistent with the
rms noise seen in the baseline channels.
34
0.83 THz, 1.037 THz, 1.27 THz and 1.46 THz HEB
receiver
35
0.83 THz, 1.037 THz, 1.27 THz and 1.46 THz HEB
receiver in Chile
36
Herschel Space Observatory
The Herschel Space Observatory - the mission
formerly known as FIRST - will perform photometry
and spectroscopy in the 60-670 µm range. It will
have a radiatively cooled telescope and carry a
science payload complement of three instruments
housed inside a superfluid helium cryostat. It
will be operated as an observatory for a minimum
of three years following launch and transit into
an orbit around the Lagrangian point L2 in the
year 2007. Herschel is cornerstone number 4 (CS4)
in the European Space Agency Horizon 2000'
science plan. It will be implemented together
with the Planck mission as a single project.
37
Mixer for the Heterodyne Instrument (HIFI)of the
Herschel Space Observatory
Band 6L (NbN HEB)
38
Stratospheric ObservatoryFor Infrared Astronomy
Remote on-board sensing of upper atmosphere in
submillimeter waveband for monitoring of
heterogeneous chemical reactions catalyzed by
atmospheric trace gases which are presumably
responsible for ozone destruction and global
warming.
39
TELIS TeraHertz Limb Sounder
Heterodyne spectrometer on a balloon platform
measures important atmospheric constituents in
the lower stratosphere (OH, HO2, NO, HCl, ClO,
BrO, ...)
40
Conclusions

• Energy relaxation of HEB consists of several
  subsequent processes, characterized by
  electron-electron and electron-phonon interaction
  times and by non-equilibrium phonons escape time
• HEB has two parallel cooling mechanisms
  electron-phonon interaction and hot electrons
  out-diffusion. In small signal case it is
  quantitatively described by two-temperature model
• HEB can be successfully used as a heterodyne
  detector due to non-linearity of the HEB
  resistance vs electric field.
• HEB mixers are chosen as heterodyne instruments
  at highest local oscillator frequencies for
  multiple international projects aimed to
  radioastronomical observations, remote sensing
  and terahertz imaging. Waveguide HEB mixer is
  successfully applied for astronomical
  observations on practical radiotelescope.