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Submitted on 1 Jan 1981
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THE PHONON SPECTRUM EMITTED BY
SUPERCONDUCTING Sn TUNNEL JUNCTIONS
P. Berberich, H. Kinder
To cite this version:
JOURNAL DE P H Y S I Q U E
CoZZoque C6, suppZ6ment au n o 12, Tome 42, dgcembre 1981
THE PHONON SPECTRUM EMITTED BY SUPERCONDUCTING Sn TUNNEL JUNCTIONS
P. Berberich and H. KinderPhysik-Department, Technische Uniuersitic't Hhchen, 0-8046 Garching, F. R. G,
Abstract.
-
The phonon spectra emitted by superconducting tunnel junctions were directly analyzed with high resolution using tunable acceptor states of B in Si as a spectrometer. A consistent and detailed experimental picture of the different parts of the spectra under various injection conditions was obtained for the first time.Tunnel injection of electrons into superconductors leads to energetic quasipar- ticles which relax by phonon emission. This is not only a subject of the growing field of "nonequilibrium superconductivity"/l/ but particularly also the bas for phonon spectroscopy/l/. There was a lot of indirect evidence for various
&
of the emitted phonon spectrum/3/4/, and there were two attempts of direct spectral an- alysis/5/6/. But the information obtained to date was only qualitative.In this paper we present the first quantitative measurements of the phonon spec- tra of superconducting junctions, revealing the shape of the recombination peak, the contribution of direct recombination, the "bremsstrahlung" or "relaxation" phonons and their reabsorption at .tiw>2A,and a "background" which was not yet directly observed.
For the spectral analysis, we used the technique of "burning a hole" by reason- ance scattering into the spectrum of the emitted phonons on their way to the detec- tor/7/5/. Stress tuned boron acceptors in silicon were used as resonant scatterers for the first time. These have several advantages over previous systems, e.g. Ge:Sb 151: (i) Silicon as the host material is known to be "transparent" for ball- istic phonons up to very high frequencies; (ii) the acceptor state has no "chemical shift", forming a true 2-level-system that splits strictly proportional to the applied uniaxial stress; (iii) we observe simple first order scattering which allows a quantitative interpretation of the results; (iv) the frequency resolution was im- proved by a factor of 10.
A Si crystal/8/ of dimensions 2 . 5 ~ 4 ~ 1 5 ma3, containing 5~10'~cm'-~ B was used as the spectrometer. A Sn-oxide-Sn generator junction was evaporated on one 4x15 side, an Al-oxide-A1 detector junction on the opposite side. The phonon path was in
[li~j
direction. Uniaxial stress was applied perpendicularly, in [I1 I] direction, and was monitored by a Kistler ce11/9/. The apparatus for pressure generation was described by Bridges and Zoller/lO/. The sample was immersed in liquid helium at 1.0 K.In all experiments shown here we studied the "differential spectrum" of the Sn- junction which was generated in the usual way/2/ by small pulses superimposed to the dc bias voltage. The spectrum was kept constant while the resonance frequency of the acceptors was swept by stress. Only the fast transverse phonon pulse was detected because of phonon focusing. In Fig.1, the height of this pulse is shown as a function of stress at various bias voltages as indicated. Generally, the signal is constant at low pressures, and then dips down because the phonons of the corresponding fre- quencies are being scattered away from their path into the detector. Eventually the signal recovers when the splitting becomes larger than any phonon frequency.
Interestingly, the signal has exactly the same height at large splitting and at zero splitting (see dashed lines) in all our experiments. At zero splitting, hence,
there is also no scattering. This is in marked contrast to donors/5/. We conclude that higher order processes are insignificant hereill/, so that the scattering can be simply described by first order resonant scattering according to the golden rule/l2/:
7(
l-l(~,o) = N
-
%pv3 M ~ E g (E-DO) ( 1 )
for kT<<E, where 1 is the phonon mean free path, N the acceptor concentration, E the
phonon energy, p the density, v the sound velocity, MZ the coupling constant, and
g(E-Do) the normalized line shape function whose center frequency is given by stress
u times deformation potential D. For 1 greater than the crystal length, the signal
change is proportional to n(~)1-1 (E=Do) where n(E) is the emitted phonon power spec- trum, provided the detector signal is proportional to the incident power/9/. There- fore, the deviation of the signal from 100% is essentially a direct measure of the
spectrum, weighed by the factor E from (1).
Trace (a) shows the differential emission spectrum of a Sn junction
(Imm x Imm x.4um; L=20m SZ) biased at the gap voltage 1.13 mV. There is a pronounced
peak in the spectrum corresponding to 2A-phonons/3/. This peak is not symmetric but has a tail to higher frequencies. The tail can be fitted by the "extended T* model"
of Chang, Lai and Scalapino/l3/ by using T*=1.1 K (dashed curve) while the bath was
at Ta=l.O K. The rounding oftfEpeak at the low frequency side is merely due to the
spectrometer resolution. There is also a broad background of phonons with lower fre- quencies which will be discussed below.
PHONON ENERGY E IrneV)
UNIAXIAL S T R E S S a ( b a r
Fig. 1:
C6-376 JOURNAL DE PHYSIQUE
In trace (b), the bias was increased to 1.4 mV. The differential spectrum now clearly reveals an additional peak (arrow) corresponding to ZEw=eV. These phonons arise from direct recombination of the injected quasiparticles at E=eV-A with thermal ones (E=A)/14/. The peak is even predominant in trace (c) which was obtained from a similar junction with a lower resistance &=3.6m 9. The increased injection leads in this case to an increased steady state number of quasiparticles, making the recombin- ation more probable/l5/ than the down scattering to the gap edge ("relaxation"). The background of low frequency phonons is enhanced in traces (b) and (c) and therefore reflects very clearly the cutoff of the detector sensitivity below the gap 2%.
The traces (d), (e), and (f) were obtained from the first junction (&=20m 9) at 1.6 mV, 1.8 mV, and 2 mV, respectively. The recombination phonon peak is obviously shifted back to 2A. This shows that the relaxation of quasiparticles at higher ener- gies is faster than the direct recombination. Only T*=1.5 K is now somewhat in- creased. As the result of the fast relaxation, the "bremsstrahlung" peaks/2/ at eV-2A have appeared. Their apparently increasing strength is due to the spectrometer weight factor E in (1). The width of the peaks is mainly determined by the spectrometer width which is increasing with stress due to stress inhomogeneity/9/. From the pos- ition of the bremsstrahlung peaks we get an accurate calibration of the stress scale which is indicated on top of Fig.1. Traces (g) and (h) were taken at 2.4 mV and 2.9 mV. Clearly the bremsstrahlung peak is now adding to the 2A-peak, revealing the reabsorption of the bremsstrahlung phonons attTW>ZA. However, T* has increased to 1.6 K and 1.7 K, respectively.
Whenever there are quasiparticles in states well above the gap, the background of low frequency phonons is markedly enhanced. This can be seen from traces (b), (c) and particularly (h) in comparison with ( g ) . This corresponds to black body radiation of these "hot" quasiparticles/l3/. However, there is also some background in trace
(a) where the quasiparticles are "cold". By changing the evaporation conditions (less clean/9/) we were able to enhance this background of the "cold" junction appreciably, as shown in trace (i) for a junction with otherwise similar specifications as that of trace (a). This background may be related to the loss mechanism postulated by Trumpp and Eisenmenger/l6/ from a discrepancy of the calculated and observed 2A-phonon yield REFERENCES
/I/ Nonequilibrium Superconductivity, Phonons, and Kapitza Boundaries, ed.by K.E.Gray, NATO Adv.Study Inst.Ser.B., (Plenum Press 1981), Vo1.65.
/2/ H.Kinder, Phys.Rev.Lett.z,1564(1972); H.Kinder in: Low Temperature Physics, LT14, ed.by M.Krusius and M.Vuorio (North Holland 1975), Vol.V, p.287. /3/ W.Eisenmenger and A.H.Dayem, Phys.Rev.Lett.~,125(1967).
/4/ W.Eisenmenger in: Physical Acoustics, ed.by W.P.Mason and R.N.Thurston (Acad. Press 1976), Vol.XII, p.79; M.Welte and W.Eisenmenger, Z.Phys.~,301(1981). /5/ R.C.Dynes, V.Narayanamurti, and M.Chin, Phys.Rev.Lett.~,181(1971).
/6/ W.Dietsche in: Phonon Scattering in Condensed Matter, ed.by H.J.Maris (Plenum Press 1980), p.309.
/7/ J.P.Morton and H.M.Rosenberg, Phys.Rev.Lett.8,200(1966).
/8/ Wacker Chemitronics, Burghausen, W.-Germany. /9/ Details are given in a forthcoming paper.
/lo/ F.Bridges and W.Zoller, Solid State Comm.~,717(1979). /ll/ K.Suzuki and N.Mikoshiba, Phys.Rev.E,2550(1971).
/12/ See, e.g. L.I.Schiff "Quantum Mechanics" (McGraw-Hill 1955). / 1 3 / .J.J.Chang, W.Y.Lai, and D.J.Scalapino, Phys.Rev.e,2739(1979).
/14/ A.H.Dayem and J.J.Wiegand, Phys.Rev.E,4390(1972); J.J.Chang and D.J.Scalapino, J.Low Temp.Phys.x,1(1978)
/15/ A.Rothwarf and B.N.Taylor, Phys.Rev.Lett.E,27(1967).
