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TEMPERATURE DEPENDENCE OF THE ELECTRIC RESISTIVITY OF AMORPHOUS
BISMUTH FILMS
Yu. Komnik, B. Belevtsev
To cite this version:
Yu. Komnik, B. Belevtsev. TEMPERATURE DEPENDENCE OF THE ELECTRIC RESISTIVITY OF AMORPHOUS BISMUTH FILMS. Journal de Physique Colloques, 1980, 41 (C8), pp.C8-493-C8- 496. �10.1051/jphyscol:19808123�. �jpa-00220220�
JOURNAL DE PHYSIQUE CoZloque C8, supple'ment au n08, Tome 41, aoCt 1980, page (28-493
TEMPERATURE DEPENDENCE O F T H E E L E C T R I C R E S I S T I V I T Y O F AMORPHOUS B I S M U T H F I L M S Yu.F. Komnik and B.I. Belevtsev
Physico-Technical I n s t i t u t e o f Low Temperatures, UkrSSR Academy o f S c i e n c e s , 47, Lenin Prospekt, Kharkov, 310164, USSR.
Abstract.- The reversible temperature-induced variation of the electric resistivity is studied on amorphous bismuth films condensed onto helium temperaKure substrates in the region of existence of the amorphous phase. The films studied ( 1 0 to 130 A thick) had negative temperature resistance coefficient. In the range 10-30 K the resistance difference (in reference to the initial value) is proportional to T~ ; howeyer, superconducting fluctuations allowed for, it becomes proportional to T2. For thin films (< 30 A) it varies as T 2 in both the cases ; at temperature above 3 0 K it is proportional to T. The results obtained are discussed in terms of up-to-date theoretical models.
Amorphous metals are characterized by tion
/
61, or of incoherence of electron weak electric resistivity response to scattering by phonons in amorphous,metals changing temperature, The study of proper-171
were thought of. These factors cause ties of transition metals amorphous alloys resistance to rise with temperature, All (metal glasses) suggested that in the low the mentioned mechanisms, both for nega- temperature region the temperature resis- tive and for positive TRC, make resistance tance coefficient (TRC) may be both nega- vary as T~ at lox temperature (TLfin)
tive and positive; the resistance versus and as T at higher temperatures (T
),QB
1.temperature curve may even display a mini- It is only for very low temperatures, that mum or a maximum. These results aroused the anharmonic model
/
4 / as well as the considerable theoretical interest, and a tight binding model/
8 / predict decrease number of papers proposed various models to of (3 proportional to T 4 , The tight bind- account for the negative TRC. Some authors ing model 181 admits of a low temperature associated it with the peculiarities of the resistance maximum and also predicta (as transition metal band structure and the did ref. 6) saturation at high temperatu- magnetic nature of the alloy component at- re. Thus, a number of models have been oms; in particular the resistance decrease proposed to account for temperature depen- with temperature may be related to electron dence of resistance of amorphous metals, scattering from localized spins. Other with no agreement between them.authors referred to nonuniform distribution Amorphous metal films condensed onto of atoms of different elements in metallic helium temperature substrates are conveni- glasses, resulting in formation of metal ent to study properties of amorphous me- clusters surrounded by metalloid atoms tala, since their amorphous state, unlike which behave as potential barriers for con- that of metal glasses, does not depend on duction electrons. It was also proposed impurity atoms, The amorphous bismuth is that the negative TRC may result from a superconductor with strong electron-pho- amorphous metal structure disorder and non interaction. On heating, amorphous should be the caee in systems of similar bismuth film resistance decreases irrever- atoms. Thus, the TRC may become negative in sibly because of irreversible changes of amorphous and high resistance disordered the coordination structure 191. As a cer- metals influenced by the Debye-Waller fac- tain temperature TAK is attained, resis-
tor / I - 3
/.
Refs.4
and 5 considered some tance jumps up several times as a resultdifferent mechanisms to explain the nega- of crystallization of the film. Tempera- tive TRC: the effect of anharmonicity of ture TAEC becomes higher, as the film atom vibrations and the specific features thickness decreases / 9 / . If heating is of hopping conductivity in highly resistive stopped at a temperature within the amor- metals. On the other hand, the contribution phous bismuth region and the sample cooled to resistance of the inelastic electron down to helium temperature, then resist- scattering
/
3 / , the effect of inefficiency ance changes under repeated heating and of the electron-long wave phonon interac- cooling are reversible. This reversibleArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19808123
C8-494 JOURNAL DE PHYSIQUE
change of the amorphous bismuth film re- sistance is the subject of this paper.
~emperature-induced variation of the resistance of an amorphous bismuth film 25 A 0 thick condensed onto helium temperature substrate and subsequently heated to various annealing tempera- tures, The single ( - ) and double ( = ) arrows indicate the irreversible and reversible, respectively, resis- tance evolution,
This investigation was carried out on a series of samples 10 to 135
%
in thickness condensed onto a helium tempe- rature substrate, As the film thickness decreased, the crystallization temperature Tu rose from 24 to 135 K, while the su- perconducting transition temperature Tc dropped from 5.5 to about 2 K,Upon completion of the n-s transi- tion, the amorphous bismuth resistance rises monotonically up to temperature T
, ,
= 10
-
14 K and then decreases (see the figure), Temperature Tma, is practic- ally unchanged as the annealing tempera- ture increases, The increasing resistance in the vicinity of Tc may be ascribed to the effect of fluctuation pairing of el-ectrons in the normal phase, in accordance with the Aslamazov-Larkin theory /lo/,' Note that another possible fluctuation mechanism proposed by W i and Thompson /I11 associated with relaxation processes in electron scattering may be ignored since amorphous metals have electron mean free path as small as the interatomic se- paration, near Tc (to about 1.3 the te- mperature dependence of resistance is well described by the Aslamazov-Larkin relation for the two-dimensional case:
where Rn is the normal state resistance (derived from an analysis of R(T) for T > Tmx), Z = In (T/T,"), TCR is the extrapolated temperature of the nonzero conductivity onset. Above 1.3 Tc there was a deviation from eq, (1) to lower va- lues of Rn- R(f) /R(T), probably because of the maximum existing-in the resistance- temperature dependence in the normal
state,
Above Tmax the resistance obeys the relation:
Since the Ro value is unknown, for precise determination of power exponent n the derivatives method was used; that is, n was picked so that the plot of n R T against A (T~) should have been praatical- ly a straight line, From the known value of n, R was found by extrapolation to T = 0 K, It differed from R0 ,, quite negligibly (by less than 0.1 76). If as- sume that the superconducting fluctuations play a significant role in the range not above T-, i.e, roughly up to (2.5-3,5)Te then the resistance decrease in films exceeding 25
1
in thickness in the 14-25 K range is characterized by the power exponent of 4, As the thickness decreases from 70 to 30x ,
coefficient A changes from 8 x 10'~ to3
x 10'~ K-$,For 25
-
302
films, the resistance reduc- tion in the temperature range 20-
35 Kis characterized by the power exponent of 2 (A =(1.5
-
2) x 10'~ Km2), and at high- er temperatures, resistance is a linear function of temperature. Por films of thickness smaller than 25%
having alarge temperature range of the amorphous phase, in the low temperature range
(12
-
20 K) the exponent is 3 or 2, whereupon follows a linear dependence, and at temperatures above 50 K it tends to saturation (that is the power exponent n becomes smaller than 1). The power type of the reversible alteration of resistance with temperature is persistent after film annealing, although it causes irreversible residual resistance reduction.If we take into account the possible effect of superconducting fluctuations at any large temperature T* Tc, the result is somewhat different. In this case one has to analyse the change with temperatm of the calculated resistance R* found from R by allowing for the Aslamazov- Larkin summand:
(g and
2
are the measured film width and length). This correction, though small, affects appreciably the temperature de- pendence of the resistance of amorphous Bi films in the temperature range 14 to 24 K in the vicinity of the maximum. NOW n ia 2 for all thicknesses, however still tending to higher values (to about 3 ) at temperatures near T,,, When the measured R varies as 'T (20-
35 K), allowance for the fluctuation effect leaves the power exponent unaltered, though causes slight changes in coefficient A. It proved to depend on the film thickness. For n = 2, decreasing thickness leads to an increase in coefficient A within (1.0-
4.5) x10'~ Ko2; for n = 1 this range is (0.6
-
1.1) 10-3 K-I.It should be noted that the conduc- tivity of these materials approaches the
minimum metallic conductivity (the resis- tivity, according to Mott, is around 200
P
52 cm): as the film thickness decre- 0 ases in the range 130 to 20 A,yo
risesfrom 160 to 300 $2 cm, Therefore the experimental data should be compared to theories suitable for very short mean free path, approaching the interatomic separation. The resistance decrease pro- portional to T 4 has not been definitely evidenced by the available data. Although we measured the resistance of amorphous bismuth films to vary as Ro(l
- AT^),
itseems that for materials with so high a resistance, superconducting fluctuations play an appreciable role and should be included even at 15 to 30 K, the result- ing power exponent of T being thus lower than 4,
Unfortunately it is not possible to quantitatively compare the measured and theoretical values of A for all cases examined in theoretical papers, since most papers contain rather rough A esti- mates. Direct comparison can only be made for papers of Markowitz
/
1/
and 0hkawa/5/with n = 2 and 1, The following parame- t e r ~ for amorphous bismuth were substi- tuted into the correspondent equations of refs. 7 and 5: KF = 1.61
i-'
(as cal- culated in terms of the free electron model), ionic mass as about 3.85 x 10 5 times tha free electron mass, Q1) = 77 K(obtained in ref. 12 for amorphous
Bi
+
20 % Sb film 1200 thick). The IYIar- kowitzts relation, with these values, gives A = 1,.46 x 10'~ K-* for n = 2 and A r 6.83 x 10'~ K-' for n = 1. The Ohka- wals theory/
51 yields: A = 2.6 x 10-~1L"for n = 1.
Thus, the A coefficients calculated by mark ow its*^ relation, which makes al- lowance for the effect of the Debye-Wal- ler factor, fall within the range of our experimental data, namely are close to those for the thickest of our films, The magnitudes calculated by the Ohkawa equa- tion are higher than any measured ones,
The revealed variation of the ex- perimental A values with film thickness
c8-496 JOURNAL DE PHYSIQUE
indicates that there is a certain size effect. The changes of the A coefficient was found to-correlate with the "resist- ance per squarew magnitude R tll = ~ o / L : the ratio A h C I is practically independent of the thickness and for n = 2 assumes the average value of 3.5 x
loe8
K-~Q-' and for n = I it averages to6.5 x
lom7 K-' R-'.
Ratio A/RO is con- stant also for n = 4. If assume that the resistance changes are due to the Debye- Waller factor, the conclusion suggests itself that the only quantity entering into the Debye-Waller factor exponent which could change with the film thick- ness is the Debye temperature, The obser- ved dependence of A on the film thickness suggests that $D decreases with the thickness as L",
where d;. J, 1 provided that the P o - L relation is neglected, or slightly larger that that value, if thep,(L) dependence is allowed for. Decre- asing in thin films may be due to in- creasing contribution of surface atoms, whose square of thermal vibration ampli- tude is appreciably larger (roughly 2 times) than that of internal atoms /13/.
References
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