Hot-electron bolometer as direct and heterodyne detector Gregory Goltsman Moscow State Pedagogical...

Hot-electron bolometer as direct and heterodyne detector

Gregory Goltsman

Moscow State Pedagogical UniversityMoscow, Russia

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 metalsElectron-phonon and electron-electron interaction times in quasiequilibrium, electron temperatureTwo-temperature 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 HEBElectron temperature relaxation times: phonon cooling against diffusion coolingResponsivity 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 fieldBasics of signal mixingHEB mixer characteristics: conversion gain and conversion gain bandwidth, noise temperature, noise bandwidth, local oscillator power

Applications of HEB mixers

Terahertz radioastronomyRemote sensing of the Earth atmosphereTerahertz imaging

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.

02)(

F

Bee

Tk

0 – scattering cross

section for Coulomb interaction, 10-15 cm2 for typical metals

nl ee

1

For 10K le-e≈10-1 cm sv

lK

F

eeee

910)10(

k2k1

k3

k4

Electron-electron interaction in clean metal

= 0

ky

kx

2

1

1

3

4

1

ky

kx

2 3

41

23

14

CM

Fermisurface

Sphere offinal states

a) b)

c)

a) 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.

b) 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.

c) 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.

|2|<1 3, 4 > 0 3 and 4 unoccupied

|2|>1 3, 4 < 0 3 and 4 occupied

Electron-electron interaction in disordered metal

122

)(ln2

ReRekTee

In thin films with short electron mean free path the electron-electron interaction is substantially enhanced.

sKee1210)/100,10(

Esig = Esigsin[(+)t]

ELO = ELOsin(t)

Esum = Esigsin[(+)t] + ELOsin(t)

Esum2 = Esig

2sin2[(+)t] + 2EsigELOsin(t)sin[(+)t] + ELO2sin2(t) =

= 0.5(Esig2 + ELO

2) + EsigELOcos(t) - EsigELOcos[(2+)t] +

+ 0.5Esig2cos(2t) + 0.5ELO

2cos[2(+)t]

HEB

Basics of signal mixing

Ele

ctro

n t

emp

erat

ure

, a.

u.

TimeTime

Ele

ctri

c fi

eld

, a.

u.

Electron-phonon relaxation time in Nb and YBaCuO films

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

K

K

K

K

K

e-ph

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

The dependences of (o, , , ) and

(●, ▲) for devices based on 12 nm (o,

●) and 15 nm (▲, , ) thick Nb films

on sapphire substrates. Data were

extracted from U(f) dependencies in the

resistive state (o, ), in the normal state

under magnetic field H>Hc2(T) (), from

temperature dependencies of U and

dU/dT in the normal state (). Solid lines

represent ~T-2, dashed lines ~T-1. The

inset shows (T) near the Tc for a device

based on 12 nm thick Nb on sapphire

(solid line represents ~(1-T/Tc)-1/2.

e-ph

e-ph

e-e

Response time of HEB vs Nb film thickness

The dependence (d) for Nb

films with D=1.0 cm2/s at two

temperatures: o – 1.6K; –

4.2K. Dashed lines represent

fitting =e-ph+b curves; solid

lines represent derived

dependences =b~d and =e-

ph

e-ph

b = es

Energy flow in hot electron bolometer

Thermalization scheme showing subsequent channels ofthe energy transfer in a hot-electron device that relaxes towards global equilibrium.

u

des

4 d – film thickness, a – acoustic

transparency between film and the substrate, u – speed of sound

phee

peph c

c cp, ce – phonons and

electrons specific

heats respectively

Linearized time dependent heat balance equations

Perrin and VannestePhys. Rev B, 1983

)()()( bed

ephe

eph

eee TT

cTT

ctp

dt

dTc

)()( bphes

pphe

eph

ephph TT

cTT

c

dt

dTc

c : the specific heatT : the temperature : time

Valid in the limit of Te ~Tph ~Tb

Two-temperature model for hot electrons and phonons in thin superconducting films

Superconducting phonon-cooled HEB

Phonon-cooled HEB mixer – E.M.Gershenzon, G.N.Gol‘tsman et al. Sov. Phys. Superconductivity 3,1582,1990

Diffusion-cooled HEB mixer – D.Prober, Appl.Phys.Lett. 62(17), 2119, 1993

eephph

esc

eph

phe

SubstrateSubstrate

AuAu AuAu

eeee

e-e

diff

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

d

e-ph

B.S. Karasik, K.S. Il’in, E.V. Pechen, S.I. Krasnosvobodtsev, “Diffusion cooling mechanism in a hot-electron NbC microbolometer mixer”, Appl. Phys. Lett. 68, 16, 2285-2287, 1996

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 Gol’tsman, and Roman Sobolewski, “Hot-electron effect in superconductors and its applications for radiation sensors”, Supercond. Sci. Technol. 15 (2002)

Hot-electron relaxation diagrams and characteristic time constants

thin-film YBCO ultrathin NbN film

Alexei D Semenov, Gregory N Gol’tsman, and Roman Sobolewski, “Hot-electron effect in superconductors and its applications for radiation sensors”, Supercond. Sci. Technol. 15 (2002)

Responsivity and noise equivalent power for hot electron bolometer

GWLdT

dUSu

1

0

Responsivity, dU/dT0 is for temperature

steepness of voltage U; G – thermal

conductance to substrate; W,L – film dimensions

2

00

)21(4 R

R

R

R sqsq Absorption coefficient, Rsq = /d – resistance of

unit square of the film, R0 = 377 Ohm –

characteristic impedance of free space

2

25

22

22 )(844

u

exc

UN S

uSkT

S

kTRGWLkTP

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 T (S

– area, – angular aperture), forth is for excess noise of various origins

Basics of signal mixing

Frequency (GHz)

Po

we

r

1010

Frequency (GHz)

Po

we

r

IF Spectrum

1000 4 8

Signal

LO

Spiral antenna coupled NbN HEB mixer

SEM micrograph of the central area of HEB mixer chipSEM micrograph of the central area of HEB mixer chip

The substrate with the HEBs on silicon lenses

From spiral antenna coupled mixer to the one directly coupled with radiation

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

Experimental setup for noise and gain bandwidth measurements

HEMT

IF amplifiers chain

detector

outputsignalprocessingdevice

bias – tee

mixerblock

mix

erbi

as b

ox

coldblack bodyloadhot black body load

chopper

grid polarizer

H O vapour CW laser

beamsplitter

input windowof cryostat

coldinput filter

helium cryostat

termination

2

tunablefilter

orBWO

or

directionalcoupler

spectrumanalizer

- 20 dB

BWO2

attenuator

or

1

Noise temperature versus bias at 2.5 THz

Cu

rren

t,

A

Bias voltage, mV

Device 180#14, 3 m X 0.2 m

Normalized output power vs intermediate frequency

Receiver noise temperature at 1.6 THzversus intermediate frequency

Optimal LO power versus mixer volume

Heterodyne radiation pattern

-14

-12

-10

-8

-6

-4

-2

0

-3 -2 -1 0 1 2 3

Angle, degree

An

ten

na

gai

n,

dB

Log-spiral antenna2.5 THz12 mm Lens

-14

-12

-10

-8

-6

-4

-2

0

-3 -2 -1 0 1 2 3

Angle, degreeA

nte

nn

a g

ain

, d

B

Double-slot antenna2.5 THz12 mm Lens

E-planeH-plane

Radiation pattern of the integrated antenna (feed antenna on an extended 12-mm hemispherical lens) at 2.5 THz. 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 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.best fit of experimental data obtained by blending a large-area black body source.

Noise temperature versus LO frequencyfor heterodyne terahertz receivers

Low required LO power and high sensitivity make HEB mixers most attractive to be used at frequencies above 1 THz

LO power required: LO power required: < 1 < 1 W for HEB; ~ 1 mW for SchottkyW for HEB; ~ 1 mW for Schottky

SchottkySchottky

HEBHEB

SISSIS

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.

Atmospheric transmission

Atmospheric transmission at Atmospheric transmission at Mauna Kea at an altitude of Mauna Kea at an altitude of 4200 m, with 1 mm of 4200 m, with 1 mm of precipitable water.precipitable water.

Atmospheric transmission from Atmospheric transmission from the Kuiper Airborn Observatory the Kuiper Airborn Observatory at an altitude of 12000 mat an altitude of 12000 m

An example of the results of FTS calibration technique. Shown are two spectra of Orion KL inCO J = 9 → 8 (1.037 THz), each required 1 minute of on-source integration time and the two observationswere made one hour apart. The system temperature increased by 56% between the observations, but thedifference between the two calibrated spectra is almost consistent with the rms noise seen in the baselinechannels.

CO J = 9 CO J = 9 → 8 (1.037 THz)8 (1.037 THz)SAO-RLT Cerro Sairecabur,SAO-RLT Cerro Sairecabur,20042004

Orion Molecular Cloud (OMC 1)MoscowMoscowStateStatePedagogicalPedagogicalUniversityUniversity

Harvard – Harvard – Smithsonian Smithsonian Center for Center for AstrophysicsAstrophysics

0.83 THz, 1.037 THz, 1.27 THz and 1.46 THz HEB receiver

0.83 THz, 1.037 THz, 1.27 THz and 1.46 THz HEB receiver in Chile

Herschel Space ObservatoryHerschel Space Observatory

The Herschel Space Observatory - the mission formerly known as FIRST - will perform 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 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 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 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 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' 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 projectscience plan. It will be implemented together with the Planck mission as a single project ..

Mixer for the Heterodyne Instrument (HIFI)of the Herschel Space Observatory

Band 6L (NbN HEB)Band 6L (NbN HEB)

Stratospheric ObservatoryFor Infrared Astronomy

RemoteRemote on-board sensing of upper atmosphere in submillimeter waveband for on-board sensing of upper atmosphere in submillimeter waveband for monitoring of heterogeneous chemical reactions catalyzed by atmospheric trace monitoring of heterogeneous chemical reactions catalyzed by atmospheric trace gases which are presumably responsible for ozone destruction and global gases which are presumably responsible for ozone destruction and global warming.warming.

TELIS – TeraHertz Limb Sounder

Heterodyne spectrometer on a Heterodyne spectrometer on a balloonballoon platformplatform m measures easures importantimportant atmospheric atmospheric constituents in the lower constituents in the lower stratosphere (OH, HO2, NO, stratosphere (OH, HO2, NO, HCl, ClO, BrO, ...)HCl, ClO, BrO, ...)

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.

Hot-electron bolometer as direct and heterodyne detector Gregory Goltsman Moscow State Pedagogical...

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