LatinAmerican Journai of Metallurgy and Maierials, Vol. 6, Nos. 1 & 2 (1986)

Hall Effect on Amorphous Thin Films All_xC~

L. F. Castro, P. Ordó ñez, M. Gómez y Pedro Prieto

Physics Department, Universidad del Valle, Apartado Aéreo 25360, Apartado Aéreo 25360, Cali. Colombia

Measurernents ofHall constant were mude on arnorphous thin Iilms of A It-x C'ux. These were nroduced hv "flash evnpornt ion" on subs-trates maintained at Iiquid nitrogen temperature. 'I'he copper concentrution vnried hetwecn :.l0·70 at n•.• mnge in which the films pl'esentan amorphous phase at room ternperature. The f'ilrns gl'O",th \\'as controlled hy meusuring thc resistivity. Thc film i's the input rosistcnce.of an oporntionnl urnplifier. The results can he explaineclusing the rigidhand morlel. that allows to deterrnine (he ¡[\'C'rage concentrationof conduction electrons in each film.

INTRODUCTION

For most of the liquid metal s with high resistivitynot greater than 300}lO cm, the measurements of Hall'seffect can be interpreted using the simple relation [1]

RH = l/nee (1)

This relations is valíd in a nearly free electron model(NFE), where n is the average number of electrons perunit ofvolume and e its charge. Theformer relation eonti-nues to work even in case that the mean free path is com-parable to the interatomic distance (a). This is the case ofamorphous material s, which have the g factor rlefinerl asg = D(d)lD(d)free, where Dtsf) is the density of statesof the Fermi level, is always greater than one.

Using electron diffraction, Lambrecht et al [4],detected the arnorphous phase in Al-Cu films producedby the condensation of its component's vapor over subs-trates at Liquid Helium temperature (4k). In theirresearch they obtained curves of the functions of interfe-rence I(k) and correlation G(r), typical of amorphousmaterials. Mayer et al [5]. made research on the struc-ture and composition of the Al-Cu films. These films areproduced by the condensation of this components at- 160 DC in the range 19 < x < 50. using the electronicmicroscope method, electron diffraction and microanaly-sis with x-rays, The result of this analysis was that thefilms produced under the above conditions are amorp-hous at the deposition temperature. Also, filrns withrange 30 < x < 50 copper remain amorphous during atemperature increase even above room ternperature.

The following report contains measurernents ofresistivity TeR. and Hall effect at room temperature.which allows to determine Hall's constant and the ave-rage density of the charge concentration nnd theirmohility.

EXPERIMENTAL METHODS

Al and Cu of hihg purity was used to elahorate thefilrns using the "flash evaporation" method on a subs-trate mnintnined nt Linuid Nitronen tornnerature at alO-O Ton pressure, Thegrowth ofthe filrns was monito-red by measurinz "in situ" resistance using an operatio-nal amplifier [61. Its thickness was deterrnined hy usingthe Tolansky Method 171.For Hall effect measurement,Cr/ Au contacts were preparen by using masks. f'ollowingthe method described in [8].

RESULTS AND DISCUSSION

Figures 1 and 2 show Hall voltaze hehaviar as afunction of the magnetic field for films with differentCu cornpositions.

Table 1 summarizes the results of the electric pro-perties of the AI1-x CUx films, obtained bythe conducti-vity "in situ" and the Hall constant at room temperature.

Figure S shows the resistivity behaviour as a func-tion of ternperature. showing that at room temperature .:the amorphous phase of the alloy subsists still tempera-tures of 39:) ± 5 K.

x at o,; Cu dínm)

~O405060

~~~~±7.676± ::J':~4± 2:~9± f)

0.0-o.n-0.20

0.122

59 ± 7.6110:::: 8.79f) ± 9.487 ± 14

~.1 -1- 0.911.0 ..•. I.~1~~.2-1-1.C)

:1.7± 1.112.6 ± 'l.11:~.9±:U

t.s·l.71).7

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Revista Latinoamericana de Metalurgia y Materiales. Vol. 6. Nos. 1 & 2 (1986)

30-> AISOCu50 d= 34nm.,.~'-LLI ~ e mAC!> 010 mAct 20

Figure J ~O>...J...J

ct 10::x:

IO .

O 0.1 0.2 03 0.4 0.5 0.6 Q7 0.8

MAGNETlC FIELD (T)

20

- AI4OCU60 d= 39nm.> I~..3 [!) 2 mA

LLI.(!) 6 5 mA«~ 10 0 7 mAO Figure 2.>...J...J«:I: 5

..O

O 0.1 0.2 0.3 0.4 Q5 0.6 0.7 0.8

MAGNETIC FIELD (T)

Figure 3

wUZLLI 1.0.... ~(/):.::-o(/)0~g 0.9e o::LLI'~ ¡::- 08...J-«o::~o::O O.z

010 100 200 300 400

TEMPERA TUR E ( K )

LatinAmeriran Journal af 'Metullu rtn¡ and Moteriols, Vol. 6, Nos. 1 & 2 (1986)

The simplest model that describes the alloy effeetover the band structure is the rizid-hand model. T'hismodel shows that the band form does not change in thealloy, what happens is that the Fermi level changes untilit adjust the number of electrons of the films,

Forthe case ofthe AI-Cn system, whose cornponentshave relatively simple electroriic structures, the almostfree electrón model is applicable. We suppose that in theamorphous phase the Fermi surface is spherical and itssize is deterrnined by the concentration, as the relation2 K, = 2(B 7T2 n 7,e¡)1/3 shows. where n is the average ato-mic concentration:

1.-:: n> = -1000 - x) nAl+ x nCU]100 o o

The n~l and n~uare the atornic concentrations, Zef is thecffeetive valencc of the svstern hy an effect of the al/oy ofa monovalent metal with another of hihger valence

Zer = Z¡Al(100 - x) + Z~u x

in which x is the Cu concentration and 71Aland Z~u are res-

pective valcnces.Considering the applicability of the relation (1) in

our problern and supposing a carrier nZef concentration.the theoretical RH values can he calculated.

It is assumed that, apart frorn the experimentalerrors, the discrepancies arise from the simplificationsmade in our model. In a series of critieism of Zirnan'stheory that is applicable also in the presense of a magne-tic field Faber [91 refers to the relative validity of appro-ximation such as:

a. Therepresentation of the states of the conduc-tion electrons as ordinary plane waves in thenearly free electron model, considering somenormalization conditions.

b. The linear screening theory to calculate thetotal pseudo-potential as the sum ofthe pseudo-potentials due to the individual ions, pseudopo-tentials on the judgrnent that there does notexist a serious overlaping between the ionieshells.

e, The excesive rigidity supposed by Ferrnisphere, and

d. Thevalidity of Born's approximation in the eva-luation of the dispersión probabilities .

REFERF:NCES

J. Matt N. F. nnn Dnvis E. A.: Eledronic Processes in Non t,l'ystn-lline Mnterials. Clarenrlon Press. Oxford (1979).

2. Mader S. and Nowiek A. S.: Appl, Phvs, Letter: 7 (l~fi!)). fi7.

;~. Hunsen M.: Constitution of Binarv Alloys: Mcrlraw-Hill.New York (l9fiS).

~. Lambrecht A .. Leitz. Husse J.: Z. Physik R (1) (10fiO).

!). Muver N. M.: Hoffman H.: Schaf'er A.: Thin Solid-Films. 8(1082) 225.

h. Prieto M. E. de: Tesis Magister. Univ. Nacional. Bogotá(1~ml).

7. Tolnnskv ~.: Multiplc Ream Interf'erometry of Surface andfilms. Clarendorn Press, Oxf'ord (1948).

R. TabaresJ. A.: Castro L. F.: Prieto P. A.: Efecto Hall en PelículasDC'igadas de 0\'0. Anales X Congreso Nacional de Ftsicn,Pasto (1~fi:l).

~. FaherT. K: The Physics of Metals: Electrons. Ed.J. M. Ziman(1979).

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