PHYSICAL REVIEW B VOLUME 26, NUMBER 7 1 OCTOBER 1982

Temperature dependence of some structures in electrontransmission spectra of Xe solid films

G. PerluzzoDepartement de Medecine Nucleaire et de Radiobiologie, Faculte de Medecine,

Uni versite de Sherbrooke, Quebec, Canada J1H 5N4

G. Bader and L. G. CaronDepartement de Physique et Groupe de Recherche sur les Semi-Conducteurs et les Dielectriques,

Facuite des Sciences, Universite de Sherbrooke, Sherbrooke, Quebec, Canada J1K 2R1

L. SancheDepartment de Medecirie Nucleaire et de Radiabiologie, Faculte de Medecine,

UniversIte de Sherbrooke, Quebec, Canada J1H 5N4

(Received 8 June 1982)

We report on the temperature dependence of the 3—7-eV structures in the electron transmis-

sion spectra of solid Xe films (600 A). These spectral features are related to the structure fac-

tor. We observed an irreversible process consisting of a disorder-order transformation and a re-

versible process characterized by a Debye-Wailer factor e

In recent papers, ' we studied electron trans-mission (0—15 eV) through Xe and Kr solid films(0—3000 A) deposited on platinum polycrystal-line foil. Attempts have been made to correlatestructures in current-versus-energy plots of thetransmitted current with specific electron-target in-teractions. One of the mechanism that received muchinterest is interference effects related to the energydependence of the structure factor. We report herethe first electron transmission results where the spec-tral features of the current-versus-energy plots are

clearly related to the structural and thermal order ofthe thin solid film. The present results were recordedin Xe solid films 600 A thick using a high-resolution

spectrometer. ' The range of temperature we used is18 to 45 K. Actually 18 K is the minimum tempera-ture we can reach under the conditions of the experi-ment and 45 K is the maximum at the base pressure10 ' Torr without desorbing the films. The purity ofXe was better than 99.995%.

Figure 1 shows a typical result of electron transmis-sion spectra at measured (T,) and deposited (Te)

io- 30X10 AO (a)

3- 600 A Xej/Pt

T = Td —45K

I s s e i I ~ i a & l

10

ELECTRON ENERGY (sV)

FIG. 1. A typical current-vs-energy plot of thetransmitted current through a 6004-thick Xe solid filmdeposited on a clean platinum polycrystalline foil. Td and T,are the temperatures of the positions and measurements,respectively. The primary current was 30 x 10 o A.

I ~ I I I I I I I I I I ~ I I I I i I I I I

20 30

TEMPE RATURE

t I I l I I ~ I I ~ I I I I

40 50

(K)FIG. 2. Temperature dependence of the structure EI&

(see Fig. 1): (a) Td= T, =18—45 K; (b) Td=25 K,Te = 18—45 K; and (c) Td = 18 K, Te =

26 3976

26 RAPID COMMUNICATIONS 3977

-T/e

O 4—

3— e=61K

Io

CD

00

e=74Ke=70g, -

220e=5&K

~ I ~ I I I

0.1I

2

l I l l

20 30 40 50

TEMPERATURE ( K)FIG. 3. Temperature dependence of structures AI& and

EI~ (see Fig. 1) when the film is deposited at 45 K and thecurrent measured from 45 to 18 K (and inversely).

temperatures of 45 K. In the region 0—8 eV whereonly elastic processes take place (if we neglect theelectron-phonon interaction'~), two large structuresaround 4 and 6 eV appear. The intensity of thosestructures b, I~ and AI~ vary as a function of T, andTgo

Three different types of experiments can be done:(I) Deposit films at low temperature and measurefrom low to high temperature (see curves b and c inFig. 2). (2) Deposit films at high temperature andmeasure from high to low temperature and inversely(see Fig. 3). (3) Deposit films and measure at thesame temperature for different temperatures between18 to 45 K (see curve a in Fig. 2).

Irreversible processes arose when T, is increasedabove Td (Fig. 2, curves b and c). AIq (and EIs) in-creased abruptly around 30 K by increasing T,. Thisis a typical structural irreversible reordering effect. Aresistance to thermal reordering of the first fewmonolayers at the film metal interface can explainthe fact that the curves a, b, and c in Fig. 2 do notend up at the same point at 45 K. This is a memoryeffect dependent on the conditions of deposition.Indeed, the order at the film metal interface dependson the nature of the interaction between Xe and themetal substrate, the surface of the substrate and Tz.Reversible processes were observed when T, wasmaintained below Td (Fig. 3). EI„and his increased(decreased) very smoothly by lowering (increasing)T, below Tq. The functional variations were charac-teristic of a Debye-Wailer factor e 9. The deducedvalues 0& = 68 K and 0& = 61 K are consistent withthe previous low-energy-electron-diffraction (LEED)experiment of Ignatiev and Rhodin. 5 Similar values

( io" m-')

FIG. 4. From the experimental results of Ignatiev andRhodin (Fig. 12 of Ref. 5) we have calculated and plottedthe value 1/0 of the Debye-Wailer factor e l' as a func-tion of the square of a reciprocal-lattice vector G for a fcclattice (a =6.17 A). The dashed line is an extrapolation oftheir results.

of 0 can be extrapolated from their results for theDebye-Wailer factor of the first Bragg peaks (seeFig. 4).

From a theoretical point of view, the transmittedintensity is inversely poroportional to the cross sec-tion at large thickness (600 A and higher). '6 In theindependent t-matrix limit, this cross section is relat-ed to the structure factor through the relation":

S (t;k')dQ dQ

where d o,/d 0, d o.,rr/d 0, and S (t;k') are the dif-ferential cross section for the solid, the effective dif-ferential cross section for the atoms, and the struc-ture factor of the solid, respectively. It can be shownthat if a,ff is isotropic, we can write

(ko) = o.„,(k)It (k)

where E (k) has maxima at k = G/2 for a well-ordered crystal (G is a reciprocal-lattice vector).These maxima in E correspond to the minima in thetransmitted intensity. The variation in temperature(T, and Tq) of AIq and 61s is directly related to thevariation in temperature of the structure factor.

ACKNOWLEDGMENTS

We are grateful to the Medical Research Council ofCanada (MRCC) and the Conseil de Recherche enSante du Quebec (CRSQ) for their sponsorship ofthis work. Two of us (G.B. and L.G.C.) were spon-sored by the NSERC.

3978 RAPID COMMUNICATIONS 26

~G. Bader, G. Perluzzo, L. Caron, and L. Sanche (unpub-lished).

L. Sanche, G. Perluzzo, G. Bader, and L. Caron, J. Chem.Phys. (in press),

~L. Sanche, J. Chem. Phys. 71, 4860 (1979).4N. Schwentner, Phys. Rev. B 14, 5490 (1976).

5A. Ignatiev and T. N. Rhodin, Phys. Rev. B 8, 893 (1973).P. J. Chantry, A. V. Phelps, and G. J. Schulz, Phys. Rev.

152, 81 (1966).~J. M. Ziman, Principles of the Theory ofSolids, 2nd ed.

(Cambridge University Press, Cambridge, England, 1972).