Thin Solid Films, 125 (1985) 25-31
ELECTRONICS AND OPTICS
25
SURFACE AND INTERFACE SCATTERING OF CONDUCTION
E L E C T R O N S IN Au/In D O U B L E LAYERS*
J. P. CHAUVINEAUAND C. MARLIERE
Bgttiment 503, Institut d'Optique, Laboratoire associ~ au CNRS 14, Centre Universitaire d'Orsay, B.P. 43,
F-91406 Orsay C~dex (France)
(ReceivedAugust 13, 1984;acceptedOctober 29, 1984)
The electrical resistance of metallic double layers of gold and indium was
measured during the growth and heat treatment of an indium overlayer deposited
onto a recrystallized gold film at 77 K. The initial increase in the electrical resistance
observed during the condensation of the first (111) monolayers of indium onto the
Au(111) crystal surface is partly ascribed to the scattering of the gold conduction
electrons by the potential barrier localized at the A u - I n interface. Analysis of
the experimental results by means of a simplified model for the electrical
conductance of double layers shows that some of the gold conduction electrons
impinging on the interface are specularly reflected either without transmission
through the interface or with transmission and specular reflection at the external free
surface of the indium layer. Consequently, the electrical resistance of the double
layer is sensitive to atomic scale variations in the roughness of the overlayer free
surface as well as to the structural changes in the A u - I n interface observed when the
indium overlayer is heated for the first time above 120 K.
1. INTRODUCTION
It has been established that in most cases the superposition of a thin continuous
metallic overlayer on a smooth gold film leads to an initial increase in the electrical
resistivityl-S; this fact is generally explained as due to a change from specular
reflection of the conduction electrons at the free surface of gold to diffuse scattering
by the overlayer. The scattering processes are assumed to occur at the new free
surface or in the bulk of the overlayer, and also at the interface if the bulk periodic
potentials of the two superposed metals are different. By comparison with the grain
boundary resistivity in metals 6, the interface resistivity can be ascribed to three
causes: (1) a short-range effect due to the local lack of periodicity in the potential at
the junction of two different crystal lattices (the interface may also show some
roughness because of steps and kinks in the crystal boundaries); (2) a medium-range
* Paper presented at the Sixth International Conferenceon Thin Films, Stockholm, Sweden, August
13-17, 1984.
0040-6090/85/$3.30
© ElsevierSequoia/Printedin The Netherlands
26
J . P . CHAUVINEAU, C. MARLIERE
effect due to elastic strains or interfacial dislocations in the neighbourhood of the
boundary; (3) a bulk effect related to the difference in the electron states of the two
metals (depending on the shape and relative orientation of the Fermi surfaces on
each side of the boundary, the electron wavefunctions can be refracted or reflected
by the potential step at the interface).
Given the complexity of the actual process, calculations of the electrical
conductance of metallic double layers have made Use of simplifying assumpti0ns 2' 7-9.
The metals are assumed to have spherical Fermi surfaces; the behaviour of the
conduction electrons at the interface is described by coefficients characterizing the
probabilities of transmission through or reflection by the boundary.
The purpose of this work is to provide some experimental information on the
contribution of the interface scattering to the electrical resistance of Au/In double
layers. With this aim we deposited ultrathin indium overlayers onto recrystaUized
gold films, the free surface of which was nearly (111) oriented. We evaluated
independently the amount of scattering by surface and bulk defects in the overlayer
by analysing the electrical resistance of single indium layers grown under similar
conditions.
2.
EXPERIMENTAL RESULTS
It has been shown that indium overlayers can be deposited onto gold films
without alloying if the substrate temperature is lower than 250 K 1o. Over a wide
range of temperatures the growth mechanism is of the layer-by-layer type, as shown
by surface roughness oscillations s'l o at low temperatures. Electron microscopy and
X-ray. diffraction examination of the double layers confirm that the atomic layers are
(111) planes of the tetragonal structure of indium. Just as for the epitaxial growth of
indium condensed onto indium layers, no further recrystallization of the indium
overlayer deposited at 77 K onto a gold film (which was previously annealed at
430 K) occurs while the temperature of the double layer is raised to 250 K (Fig. 1,
curves B and C). The irreversible increase in electrical resistance which occurs above
250 K is due to the formation of an A u - I n alloy.
From these investigations we conclude that ultrathin continuous indium
overlayers deposited onto recrystallized gold base films possess bulk and surface
structures very similar to those of thicker single indium layers condensed onto floatglass substrates at 77 K and subsequently annealed (Fig. 1, curve A).
The electrical resistance of an Au/In double layer is shown as a function of the
indium layer thickness in Fig. 2. The general shape of the curve does not depend
markedly on the substrate temperature between 16 and 250 K. There is a marked
initial increase in the electrical resistance during the condensation of about three
indium monolayers; then the resistance remains almost constant (with damped
oscillations at low temperature) as the indium overlayer thickness increases from 1
to 5 nm before it begins to decrease slowly as expected for a metallic film increasing in
thickness. We shall attempt to explain the occurrence of the plateau in the electrical
resistance ofmetaUic double layers with ultrathin overlayers. We shall use the model
of Dimmich and Warkusz (DW) derived from Fuchs' theory to describe the electrical
conductance of double layers 9'11. The interaction between the conduction electrons
SCATTERING OF CONDUCTION ELECTRONS IN A u / I n DOUBLE LAYERS
27
0
÷
+
÷
÷
÷ ÷
7
~
÷.-
B.....--'/
5
••
• tb
l
i
l
a
,
I 50
,
,
,
,
Inn
,
,
,
,
150
,
,
J
I
i
i
2OO
I
n
i
i
n
n
l
25O
TENPERATURE(~olv~,~
Fig. 1. Annealing of three indium layers 25 nm thick deposited at 77 K: curve A, on a float-glass
substrate; curve B, on an annealed indium base layer; curve C, on an annealed gold base layer.
4
3.5
I--
a
o¢
r~
5
10
15
20
25
30
IHOI~ THICKNESS
Fig. 2. Electrical resistance of an Au/In double layer as a function of the indium overlayer thickness at
120 K (rate of indium deposition, 0.015 nm s- ~;gold l~v~rthickness, 21.5 nm).
a n d the interface will be described by only t w o parameters, n a m e l y the specular
reflection R a n d the t r a n s m i s s i o n T w i t h o u t scattering probabilities, in place of the
three coefficients W, P a n d Q used by D W to which they are related by
R=
1--W--P
T = W-Q
(la)
(lb)
A p a r t from this change we use the same n o t a t i o n s as D W , s u m m a r i z e d in Fig.
28
J" P" CHAUVINEAU, C. MARLIERE
3(a). We analyse the case of ultrathin overlayers for which the reduced thickness
12 = h/22 tends towards zero. The general expression calculated by DW (ref. 9, eqns.
(22) and (23)) for the conductivity of the base layer can then be reduced to
°"1 ~ 1--
0.10 ~'~
f,o
dt
-~-
1-exp(-llt)} x
x {(2--p~-Q)+(pl + Q - 2 p l Q ) e x p ( - l ~ t ) } { 1 - p ~ Q e x p ( 2 l l t ) }
-1
(2)
where
Q = R-~
(3)
P2 T2
1 --pzR
To the same order of approximation, the conductivity of the overlayer is given by
(72 ~ 0. Equation (2) is identical with the expression obtained by Lucas 12 for the
electrical conductivity of films with two unlike surfaces, the specularity parameters
of which are P l and Q respectively.
/
kl
/
R
~
pj~
"2
p_~Rr"
"2
I
Id
I
.....j
,
!
I
(a)
(b)
Fig. 3. (a) Boundary scattering parameters used for the calculation of the electrical conductance of
metallic double layers; (b) electron trajectories for specular reflection in a metallic double layer with an
ultrathin overlayer.
Hence the main effect of the ultrathin overlayer is to change the scattering
probability of the conduction electrons from the initial value P0 for the base layer to
the final value Q defined by eqn. (3). The electrical conductance of the double layer is
nearly independent of the overlayer thickness h as long as h is small compared with
the base layer thickness d and the bulk mean free path 22 in the overlayer. This is
effectively observed in the Au/In double layer after a first transition stage in which
the indium overlayer thickness is in the atomic scale range (h < 1 nm).
Equation (3) for the equivalent specularity parameter Q can be obtained from
simple considerations by summing the contributions of single and multiple specular
reflections, as shown in Fig. 3(b):
Q = R + P2 T2 { 1 4- p2 R 4- (p2R) 2 4-...}
=Rq
p2 T2
1 --p2 R
S C A T T E R I N G OF C O N D U C T I O N E L E C T R O N S I N
Au/In D O U B L E
LAYERS
29
The quantum size effect giving rise to oscillations on the electrical resistance at low
temperature is a consequence of interference effects between the partially reflected
wavefunctions in the indium overlayer 1o.
Equation (3) can be used to calculate the parameters R and T from two
electrical resistance measurements of a double layer with first a smooth and then a
rough free surface. The specularity parameters Pl and P2 of the external surfaces are
calculated from the variation in electrical resistance of gold and indium single layers
grown by epitaxy on a recrystallized layer of the same material. In this process the
bulk and surface structures are fixed while the thickness is increased; the electrical
resistance is then approximately proportional to the inverse thickness lit in
accordance with the formula
3 l 1-p
Pt ~ P ~ + ~ P o o t
(4)
where Po and lo are respectively the resistivity and the electron mean free path
determined by phonon scattering in the pure metal; p® is the resistivity of infinitely
thick films and takes account of scattering by impurities and defects in the hulk of
the layer 13. The specularity parameter p is assumed to be the same for the two
surfaces. We obtained Pl --- 0.85 for the gold layers and P2 = 0.4 for the indium
layers. The deposition of half a monolayer of indium onto the indium-free surface
decreases the specularity parameter from P2 ----- 0.4 to P2' = 0.15. Similarly, Q and Q'
are calculated by applying eqn. (4) to the measured electrical resistance of the double
layer respectively before and after the surface roughening. In this case Po~ and polo
have the values corresponding to a gold single layer, while the specularity parameter
is taken as the arithmetic mean value p ,~ (p~ + Q)/2 of the two surface parameters 14
The values of R and T obtained for three similar Au/In bilayers are reported in
Table I as functions of the annealing temperature Ta of the double layer. The
thicknesses are 21.5 nm for the gold film and 1.5 nm for the indium overlayer
deposited at 77 K. In spite of the simplifications used in the model describing the
electrical conductance of the double layer, these results clearly show that the
scattering probability of conduction electrons by the interface, given by 1 - ( R + T),
increases as the annealing temperature increases from 120 to 180 K. The enhancement of interface scattering is responsible for the irreversible increase in electrical
resistance which occurs during the initial rise in temperature after the deposition of
the indium overlayer at 77 K (Fig. 4, curve A). This process does not correspond to
the volume or surface rearrangements observed for gold or indium single layers and
it does not take place when the indium coverage is lower than or equal to one atomic
layer (Fig. 4, curve B). Consequently it can be assumed that an irreversible change in
the interface structure occurs in Au/In bilayers between 130 and 200 K. This may
TABLE I
INTERFACE PARAMETERS FOR VARIOUS ANNEALING TEMPERATURES OF A u / I n DOUBLE LAYERS
Ta (K)
R
T
1 - ( R + T)
120
0.32
0.50
0.18
150
0.12
0.39
0.49
180
0.05
0.22
0.73
30
J . P . CHAUVINEAU, C. MARLIERE
.E
• 75
^
*
0
.85
0
0
0
¢e
.S5
0
~o
0
Q
O
o
o
0
0
0
0
0
0
0
•
B
÷÷
.41~
I
I
I
÷÷ ÷+*÷
I
I
100
÷*~
I
÷~+**~÷÷,~**~÷÷**+****~**
i
I
I
I
ISO
I
I
I
I
TENF~RATiJRE ~ . 1 vl,~
Fig. 4. Annealing of an ultrathin indium overlayer deposited onto a recrystallized gold base layer. The
mean thicknesses of the indium overlayer correspond to 2.3 (111) atomic layers (curve A) and 1.0 (111)
atomic layers (curve B).
concern mainly the first atomic indium layer which is constrained by the underlying
gold lattice. The observed increase in interface scattering of conduction electrons
suggests that the interface reconstruction results in a decrease in coherency at the
interface.
3. CONCLUSION
A decrease in electrical conductance is observed while a gold layer with smooth
surfaces is covered with an ultrathin continuous indium overlayer. A simple freeelectron model is used for the analysis of the electrical conductance of the double
layers; the interface is characterized by the reflection and transmission parameters R
and T. In the particular case of ultrathin continuous overlayers it is shown that the
values of R and T can be deduced from the measurements of the electrical resistance
of a double layer before and after a given change in the surface roughness of the
overlayer free surface• For A u / l n double layers, the values of R and T are found to
depend on the annealing temperature; this behaviour is attributed to an irreversible
change in the interface structure that occurs above 120 K when the indium overlayer
thickness exceeds one atomic layer. It is expected that careful electrical resistance
measurements could provide information on changes in the interface structure in
situations where classical surface analysis techniques cannot be employed.
REFERENCES
1 K . L . Chopra and M. R. Randlett, J. Appl. Phys., 38 (1967) 3144.
2 M . S . P . Lucas, Thin Solid Films, 2 (1968) 337.
3 C. Pariset and J. P. Chauvineau, Surf. Sci., 78 (1978) 478.
SCATTERING OF CONDUCTION ELECTRONS IN
4
5
6
7
8
9
10
11
12
13
14
Au/In
DOUBLE LAYERS
B. Fischer and G. V. Minnigerode, Z. Phys. B, 42 (1981) 349.
D. Schumacher and D. Stark, Surf. Sci., 123 (1982) 384.
E. VanderVoortandP. Guyot, Phys. StatusSolidiB, 47(1971)465.
G. Bergmann, Phys. Rev. B, 19 (1979) 3933.
V. Bezak, M. Kedro and A. Pevala, Thin Solid Films, 23 (1974) 305.
R. Dimmich and F. Warkusz, Thin Solid Films, 109 (1983) 103.
J.P. Chauvineau and C. Pariset, J. Phys. (Paris), 37 (1976) 1325.
K. Fuchs, Proc. Cambridge Philos. Soc., 34 (1938) 100.
M.S.P. Lucas, J. Appl. Phys., 36 (1965) 1632.
C.R. Tellier and A. J. Tosser, Size Effects in Thin Films, Elsevier, Amsterdam, 1982, p. 48.
A.A. Cottey, Thin Solid Films, 1 (1967-1968)297.
31