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EFFECTIVE QUASIPARTICLE RECOMBINATION
TIMES AND ELECTRONIC DENSITY OF STATES
AT THE FERMI LEVEL IN SUPERCONDUCTING
FILMS
P. Epperlein, K. Laßmann, W. Eisenmenger
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplkment au no 8, Tome 39, aozit 1978, page C6-515
EFFECTIVE OUASIPARTICLE RECOMBINATION TIMES AND ELECTRONIC DENSITY OF
STATES AT THE FERMI LEVEL IN SUPERCONDUCTING FILMS
P.W. Epperlein, K. LaBmann and W. Eisenmenger
Universitiit Stuttgart, PhysikaZisches Institut, TeiZinstitut 1, 7000 Stuttgart 80, R.F.A.
R6sumb.- Les temps de recombinaison des quasiparticules,mesurQs directement dans des jonctionstunnel supraconductrices d'btain et d'aluminium, correspondent assez bien aux valeurs, calcul6es d'aprss le modsle rayon-acoustique d1Eisenmenger et al. Texp dQcroPt dans les jonctions d'aluminium granulbes. Les temps, mesurbs au plomb, indiquent des pertes des 2A-phonons 1 l'intgrieur du volume du film. La densit6 d'btat Qlectronique sur le niveau de Fermi N dans les films d16tain, de plomb et d'alumi- nium diffsre moins que 5 % de N de la matisre massige.
Abstract.- Quasiparticle recombination times 'rexp, directly measured in evaporated superconducting Sn- and Al-tunnel junctions, show reasonable agreement with the values calculated on the basis of the ray-acoustic trapping lifetime model of Eisenmenger et al. T~~ decreases in 0 -perturbed gra- nular Al-junctions
.
In Pb the measured times indicate 2A-phonon voyume losses. ~he~electronic den- sity of states at the Fermi-Level N in Sn-, Pb- and Al-films differs less than 5 % from No of the corresponding bulk material.STATEMENT OF PROBLEMS.- The indirect steady-state method for measuring T in a sandwich-structure of
exP
two tunnel junctions requires the knowledge of N as resulting from heat-capacity measurements of the clean bulk material /I/ ; alternatively, also the band-structure quantity /2/ has been used. The sam- ples, in contrast, consist of vacuum-deposited films of microcrystalline structure, usually with high di- sorder. Consequently, the question arises for the value of N in disordered metal films. We here re- port on direct measurements of T in superconduc-
exp
ting Sn-, Al- and Pb-tunnel junctions and a new ex-
T from the current-voltage characteristic and X(o), T form the time decay of 6N. Current pulses
exp
,
0were used for the generation of 6N. 6N was determi- ned experimentally from the change of the tunnelling current in the thermal tunnelling regime at voltages o < U < 2A/e, i.e. 6N/Nth = 6i/ith. A mean least- squares fit of the nonexponential decay function X(t), calculated from the rate equations, on the experimental decay curves supplies values for X(t=o) at the switch-off time t=o of the injection pulse and for T
exp
,
o 'perimental technique to determine No in thin films. EXPERIMENTAL RESULTS.- TIN : (figure 1) The measu- Comparisons between the measured T and calcula- red T = T .T-'/~
.
e A(T) /kgTexv exD
.
.o , is T exo.0.
, o withtions based on the ray-acoustic trapping lifetime T = 0.58 ns and A(T)
"
.A = 585 peV. From the cal- model of Eisenmenger et al. / 3 / have been made in- .
equations of Rothwarf-Taylor 1 4 1 , and the excess
Fig. 1 : Experimental quasiparticle recombination quasiparticle density 6N under a stationary injec- time vs 1/T for a superconducting Sn-tunnel junction
tion rate I
.
This expression contains the quanti- immersed in liquid 'He. Quasiparticle excitation byo current (A,o)-, laser (+)
-
pulse. Symbol a corres-ties T, A, Io, T (at 6N/Nth << I), and ponds to a run with trapped magnetic flux (0.2 G).
exp
,
06 ~ ( t . ~ ) / ~ ~ ~ = H(t=O).
mere
values can be obtained berinjection by the "twoparticle current" i2 at the biasing point UB = 0.k' mV > A/e has been gonsi- from a single symmetric tunnel junction, i.e. il and deredthe linear thickness (d) range of T assuming the exp
validity of the relation
%
>> A between the mean 1000;W
-
500:free paths of 2A-phonons due to reabsorption
(AW)
-
o
and bulk loss processes
(%).
6
b
EXPERIMENTAL PROCEDURE.- An expression for the ab- solute determination of No has been derived fromthe
j
Sn-I-Sn; Sapphire ,*e;-9"?; UB=+0.8mV . .A = 585 peV dbbl = 4200
A
w.*' N ~ % / N ~ , , 1 10 yo:
by i2p 9 T-112 T~,,, = 0.58,10-[rnl
e b / U IS] 1-
Tsystemrelations for the BCS density Nth of thermally exci- 2%60 a65 0.70 0.75
-
a00 0.65 0.90 0.95 1.00 1.651/T
ICC'I
ted quasiparticles, the lifetime TexD from the rate
culation results r = 1.1 or 0.6 ns according to the
used average phonon transmission coefficient 0.25 10' ' AI-I -'A[ ; sabphlre ' T, = 1.23 K 1.49K 1.85K :
/5/ or 0.5 161 at the boundary Sn/He. T exp
,
0 depend on quasiparticle excitation by current and laser pulse at the same sample. The "two-particle current" i has to be considered as an injection2P
I current with I. = i2p/eVTu (VTu = junction volume).
At low temperatures
;
is reduced by trapped ma- 1 0 ~ 1 .exp
,
0-I
gnetic flux (vortices). A reduced reemission and 25 30 3.5 4.0
-
4.5 5.0 55 60 6.5 7.0Aex,,(T)/~T
reabsorption of 2A-phonons is the "vortices-doped" films is responsible for this effect. The average
Fig. 2 : Experimental recombination time vs A/kBT value for N (with both spins) in the evaporated Sn for three tunnel junctions with different degrees of films was
dztemined
to (2.71 a 0.06) 102zceV
c m 3 ~ - 1 perturbation and direct contact to liquid '~e compared to the bulk value 2 . 7 7 ~ 1 0 ~ ~ Lev cm3]-' /7/.ALUMINIUM.- With increasing perturbation of the films by oxygen background evaporation r and the
e p , 0
average grain size
5
(2000. . .
I30 A) decrease, the transition temperature Tc and the energy-gap A in- crease (figure 2). The decrease of r at theexp
,
0junction with T = 1.85 K cannot be explained with the dependence T a d / ~ ~ . Possible reasons are
exp
,
oan enhanced 28-phonon escape by diffuse phonon scat- tering at the microcrystalline, irregular junction boundaries and an increase of the electron-phonon
1000r
Pb-I-Pb; Si; vacuum5001 dtOh, = NOOA
-
Ao= 133meVC
- T, : 7.2 K
coupling - -
a2
(w).
The measured recombination time foran t.undisturbedtt smple (Tc = K, = 5000
9
Fig. 3 : Experimental recombination time vs b / k B ~ for a Pb-tunnel junction under vacuum conditions amounts to T /d = (0.024 f 20 %) [s/cm] atex^ - . , o
T = A/4 kg and A = 200 UeV ; the calculated time is T /d = (0.031 f 30 %) [s/cm]. Within
~ X P
,
0 References1.23 K ( T < 1.85 K the mean value for N in the C
-
films varies between 3.3 and (3.4 0.05)xlo~~
/I/ Miller, B.J., Dayem, A.H., Phys. Rev. Lett.
18
[ e ~ cm3]-I (bulk value : 3.45 1 022 ).
The observed (1967) 1000T -enhancement ip the granular films can be comple- / 2 / Long, A.R., J. Phys. F. (Metal Phys.)
2
(1973) Ctely attributed to the quantization of the phonon 2040
states in the small grains 181. /3/ Eisenmenger, W., LaBmann, K., Trumpp, H.J.,
Krauss, R., Appl. Phys.
fi
(1976) 307141 Rothwarf, A., Taylor, B.N., Phys. Rev. Lett.
2
LEAD.- The measured T meets the exponentialexp ,o (1967) 27
temperature dependence above T = 1.8 K with 151 Trumpp, H.J., LaBmann, K., Eisenmenger, W., Phys. T = 0.08 ns (figure 3). The calculation, however, Lett.
3
(1 972) 431suvplies
- -
T = 1.35 ns. This difference indicates 161 Parker, W.H., Sol. St. Commun.15
(1974) 1003 2A-phononzoolure
losses(%
>> invalid). me No /7/ Kittel, C . , Introduction to Solid State Physics,3rd Ed. New York : John Wiley 1 967 value in the films agrees with that in the bulk
