1. 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-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 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 k 1 and k 2. The Pauli principle permits only collisions with unoccupied final states k 3 and k 4.  0 – scattering cross section for Coulomb interaction, 10 -15 cm 2 for typical metals For 10K l e-e ≈10 -1 cm

4. Electron-electron interaction in clean metal 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 | 0  3 and 4 unoccupied |  2 |>  1   3,  4 < 0  3 and 4 occupied

5. Electron-electron interaction in disordered metal In thin films with short electron mean free path the electron- electron interaction is substantially enhanced.  

6. E sig = E sig sin[(  +  )t] E LO = E LO sin(  t) E sum = E sig sin[(  +  )t] + E LO sin(  t) E sum 2 = E sig 2 sin 2 [(  +  )t] + 2E sig E LO sin(  t)sin[(  +  )t] + E LO 2 sin 2 (  t) = = 0.5(E sig 2 + E LO 2 ) + E sig E LO cos(  t) - E sig E LO cos[(2  +  )t] + + 0.5E sig 2 cos(2  t) + 0.5E LO 2 cos[2(  +  )t] HEB Basics of signal mixing Electron temperature, a.u. Time Electric field, a.u.

7. 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

8. 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>H c2 (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 T c for a device based on 12 nm thick Nb on sapphire (solid line represents  ~(1-T/T c ) -1/2.  e-ph  e-e  

9. Response time of HEB vs Nb film thickness The dependence  (d) for Nb films with D=1.0 cm 2 /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

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 c p, c e – 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-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 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. Linearized time dependent heat balance equations Perrin and Vanneste Phys. Rev B, 1983 c : the specific heat T : the temperature  : time Valid in the limit of T e ~T ph ~T b Two-temperature model for hot electrons and phonons in thin superconducting films

13. 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 e ph Substrate AuAu e e  e-e  diff

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 d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

15. Response of a YBCO HEP to a femtosecond infrared pulse: 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)

16. 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)

17. Responsivity and noise equivalent power for hot electron bolometer Responsivity, dU/dT 0 is for temperature steepness of voltage U; G – thermal conductance to substrate; W,L – film dimensions Absorption coefficient, R sq =  /d – resistance of unit square of the film, R 0 = 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 T  (S – area,  – 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-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 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 Frequency (GHz) P o w e r 1010 Frequency (GHz) P o w e r IF Spectrum 1000 48 Signal LO

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

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,  A Bias voltage, mV Device 180#14, 3  m X 0.2  m

25. Normalized output power vs intermediate frequency

26. Receiver noise temperature at 1.6 THz versus 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 Low required LO power and high sensitivity make HEB mixers most attractive to be used at frequencies above 1 THz LO power required: < 1  W for HEB; ~ 1 mW for Schottky Schottky HEB SIS

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-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 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. 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. CO J = 9 8 (1.037 THz) CO J = 9 → 8 (1.037 THz) SAO-RLT Cerro Sairecabur, 2004 Orion Molecular Cloud (OMC 1) Moscow State Pedagogical University Harvard – Smithsonian Center for Astrophysics

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 Observatory For 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.