Optical Phonons in Some Very Thin II-VI Compound Films

Abstract

We have used electron tunneling to determine the longitudinal optical (LO) phonons in thin films of CdS, CdO, Zns, and ZnO. The II-VI compounds were used as a tunneling barrier separating two metal films, and in some instances they were no more than 10-30 Å thick. The LO-phonon energies obtained in the various compounds agree very well with the values that have been obtained from Raman scattering and infrared spectroscopy on bulk materials.

Full text

VOLUME
21,
NUMBER
19 PHYSICAL REVIEW LETTERS 4
NOVEMBER
1968
OPTICAL PHONONS
IN
SOME VERY THIN II-VI COMPOUND FILMS
I. Giaever
and H. R.
Zeller
General Electric Research
and
Development Center, Schenectady,
New
York
(Received
2
October
1968)
We have used electron tunneling
to
determine
the
longitudinal optical
(LO)
phonons
in
thin films
of
CdS,
CdO, Zns, and
ZnO.
The
II-VI compounds were used
as a
tunneling
barrier separating
two
metal films,
and in
some instances they were
no
more than
10-30
A thick.
The
LO-phonon energies obtained
in the
various compounds agree very well
with
the
values that have been obtained from Raman scattering
and
infrared spectroscopy
on bulk materials.
Jaklevic
and
Lambe1 have shown
in a
nice
and
convincing experiment that
it is
possible
to
obtain
the molecular vibrational spectra
of
hydrocar-
bons using electron tunneling.
The
hydrocarbon
molecules
are
adsorbed
on the
insulating layer
in
a tunnel junction
and the
vibrational modes
are
excited directly
by the
tunneling electrons. This
increases
the
conductivity
of the
junctions
at ap-
plied voltages which correspond
to the
resonant
frequencies
of the
hydrocarbons.2 Since
the
con-
ductivity steps
are
small, they
are
most easily
detected
by
plotting
the
first
or
second derivative
of
the
current
/
with respect
to the
voltage
V as a
function
of the
voltage. This discovery
of
Jakle-
vic
and
Lambe
led to the
suggestion that
it
should
be possible
to
excite normal modes
in the
bar-
rier
itself,
such
as
phonons
and
magnons.3
In-
deed, Rowell4
has
tentatively identified various
peaks
in the
second derivative curves
in a Pb-
PbO-Pb junction
as
reflecting
the
phonon spec-
trum
in
PbO.
Of
course
it is
known from tunnel-
ing experiments
in p-n
junctions,5
in
metal-semi-
conductor junctions,6
and
also
in
superconducting
tunneling junctions7 that
a
small structure
in the
current-voltage curves reflects
the
electron-pho-
non interactions
in the
electrodes.
We
empha-
size that
in the
present experiments where
we
have prepared insulating barriers
of
II-VI com-
pounds,
we are
able
to
separate
the
excitations
in
the
barrier from
the
excitations
in the
elec-
trodes. Because
the
optical phonon spectra
for
some
of the
barriers
we
have used
are
known
from Raman scattering
on
single crystals,8'9
we
are able
to
establish clearly that
the
electrons
interact with
the
phonons
in the
barrier
itself.
The
CdS and
ZnS
barriers were prepared
by
first evaporating
a
thin layer
of the
appropriate
substance onto
a
freshly evaporated metal film.
Because thin
CdS and
ZnS
films contain pinholes,
it
is
necessary that
the
substrate metal
is al-
lowed
to
oxidize after
the
deposition
of
CdS
or
ZnS such that
an
insulating oxide
can
form
in the
pinholes
as
previously described
in
some detail
by
one of
us.10
The
junction areas used were
about
1 mm2 and the
tunneling resistance
in the
range 10-1000
fi.
While
it is
possible
to
tunnel
through
an
apparent thickness
of a few
hundred
angstroms
of
CdS,
the ZnS
must
be
kept only
a
few tens
of
angstroms thick.
We
have success-
fully used
Pb, Sn, and Al as
substrate materials,
as well
as
counter electrodes.
The
CdO and
ZnO
junctions were prepared
by
simply oxidizing
an
evaporated film
of Cd or Zn.
All
our
films have been evaporated onto sub-
strates kept
at
room temperature,
and
because
of difficulty
in
getting
Zn or Cd to
stick
to a
glass
slide,
a
very thin
Al
layer, less than
30 A
thick,
was used
to
provide nucleation.
The
quality
of
the oxide layers
on
both
Zn and Cd
appeared
to
be
a
strong function
of the
visual appearance
of
the films. Films with mirrorlike appearance
gave good, usable oxides, while brownish
or
milky appearance often resulted
in
shorts.
Be-
cause
the
appearance
of the
film edges
was
poor,
we found
it
helpful
to
cover them,
as we
suspect-
ed
the
edges
to
contribute
to the
number
of
short
circuits obtained.11
We
also found
it
necessary
to
use Pb as the
second electrode,
as all
other
materials tried
as
counter electrodes resulted
in
very
low
resistances
or
short circuits.
The ox-
ides were always formed
at
room temperature
and atmospheric pressures;
the
junction areas
were approximately
i mm2 and the
resistance
of
the junctions
in the 10- to
1000-ft range.
The first
and
second derivative
of the
voltage
with respect
to the
current
and as a
function
of
voltage
was
obtained directly
by a
modulation
technique using
a
lock-in amplifier
in a
bridge-
like circuit, constructed after
a
design described
by Adler.12
In
order
to get
maximum sensitivity,
peak-to-peak modulation-voltage signals
as
large
as
a few
millivolts were sometimes used
to ob-
tain
the
second derivative while considerably less
amplitude could
be
used
for the
first derivative.
By using smaller voltages
we
could minimize
signal distortion.
1385

VOLUME
21, NUMBER 19 PHYSICAL REVIEW LETTERS 4 NOVEMBER 1968
TEMPERATURE
4.2 °K
l
i 1 i I i 1 i 1
0
20 40 60 80
VOLTAGE
IN
MILLIVOLTS
FIG.
1. d2V/dI2 as a
function
of
voltage
for
four
dif-
ferent
barriers.
The
arrows
indicate
the
position
of
the
long-wavelength
LO
phonons
obtained from Raman
scattering
data
(Ref. 9).
A summary of the experimental data is shown
in Fig. 1, where
d2V/dI2
is plotted as a function
of V. The longitudinal optical phonon energies
available from Raman scattering are shown for
comparison. As can be seen from the data the
longitudinal optical phonons can be easily identi-
fied, mainly as the last rapid change in the sec-
ond derivative. As seen in the curve for CdS,
various peaks are also present at lower energies.
Although the low-energy peaks are reproducible
on any given sample and thus do not represent
electrical noise, we can, in general, reproduce
only the longitudinal optical phonon peaks from
sample to sample. At first sight it is somewhat
surprising to find approximately the same values
for the energies of the optical phonons in these
films and in single crystals; however, we be-
lieve that the optical phonons are in a sense
closely related to molecular vibrations and rela-
tively insensitive to crystal structure. The
peaks at lower energies might be caused by pho-
nons more sensitive to crystal structure and ori-
entation; thus they are difficult to reproduce and
indeed often absent, and little or no information
can be obtained from them.
In the curve for ZnS the large peak at low volt-
age is caused by the phonon spectrum in the elec-
trodes, in this case Sn. It compares well with
Rowell's earlier data.4 If Al electrodes are used,
this peak is absent. The peak further out in ener-
gy is caused by the ZnS layer. The peak is rath-
er broad as can be seen, and it is tempting to as-
sociate the onset with the TO modes which are
known to be at 33 meV. An alternative explana-
tion is to associate the width of the peak with the
LO-phonon bandwidth.13
In the curve for CdO we do not show the data at
lower voltages because at these voltages the sec-
ond derivative is completely dominated by the
phonon spectrum in the superconducting Pb elec-
trode. From the curve we judge the LO-phonon
energy to be at 47 meV.
The ZnO gave us the best data. Again at lower
voltages the structure in the curves is associated
with the phonons in the electrodes, in this case
Pb and possibly Zn. The shoulder at approxi-
mately 55 meV is however always present togeth-
er with the peak at 72 meV. Again from Raman
scattering data it is clear that the peak at 72 meV
is associated with the LO phonon, while we may
attribute the shoulder at 55 meV to the TO modes,
or to the bandwidth of the LO-phonon spectrum.
The effect is rather large in ZnO. In Fig. 2 we
show a first derivative curve, where for compar-
ison the phonon peaks caused by superconducting
Pb are also shown. The biggest resistance
change which we have observed at 72 meV is ap-
proximately 1%. In Fig. 2 is also shown the sec-
ond derivative for both polarities; as can be seen
the shape of the characteristic is polarity depen-
dent. Also there is a small effect as expected
depending on whether the counter electrode Pb is
superconducting (#
=
0) or normal (H
=
30 kG).
The optical-phonon spectra of all these mater-
ials are rather complex as there are nine optical
and three acoustical branches in the wurtzite
structure. Some of the materials are known to
exist in a cubic form as well. Where the phonon
spectrum has been determined by Raman scatter-
ing, well-defined single crystals have been used.
However, at least in Zns the difference between
the optical-phonon spectrum in the two struc-
tures is below our resolution. While the Raman
scattering and infrared spectroscopy select out
phonons of long wavelength, no such selection
rule is known to exist for tunneling, and phonons
of all wavelength should contribute to the obtained
peaks. Since our barriers are indeed ill defined,
i.e., we do not know the crystal structure of the
films and in some instances they may even be
1386

VOLUME
21,
NUMBER
19 PHYSICAL REVIEW LETTERS
4
NOVEMBER
1968
>-
oc
Zn
NEGATIVE
H
= 30K6
Zn
POSITIVE
H=30KG
Zn-ZnO-Pb
4.2°K
20
40 60
VOLTAGE
IN
MILLIVOLTS
80
FIG.
2. The top
curves illustrate
the
polarity depen-
dence
of a
ZnO sample.
A
small change
is
also seen
depending
on
whether
the
counter electrode
Pb is
nor-
mal (ff=0)
or
superconducting (ff=30 kG).
The
lower
curve
is a
plot
of
dV/dl versus voltage, which com-
pares
the
phonon structure
at
low voltages
due to the
superconducting
Pb
with
the
structure
at
72 meV
due to
ZnO.
The
zero
has
been offset.
amorphous,
it is
somewhat surprising
to us
that
we
get
such good agreement with
the
existing data
for
LO
phonons
of
long wavelength.
By and
large
this agreement emphasizes that
the
optical-pho-
non spectrum must depend upon short-range
or-
der rather than long-range order
in the
crystals.
In
Fig. 3 we
have plotted
the
second derivative
obtained from
a
100-A-thick
Ge
film sandwiched
between
two
films
of Sn. The
sample
is
pre-
pared similarly
to the ZnS and CdS
samples.
As
seen,
the
effect
of the
optical phonons
is
clearly
visible
in the
curves; however,
our
structure
is
rather broad.
Ge
films prepared under
our
con-
ditions
are
known
to be
amorphous, thus
the
broad curve
can be due to
bonding
of
various
strengths.
We can
also interpret
the
width
of the
peaks
to
reflect
the
width
of the
phonon band
as
tunneling does
not
favor long-wave length phonons.
At present these preliminary experiments
clearly show that
it is
possible
to
observe some
of
the
phonons
in the
barrier; however,
not
enough
is
known about
the
barrier itself
to
make
detailed calculations.
For
example,
Fig. 3
shows
30
40 50
VOLTAGE
IN
MILLIVOLTS
FIG.
3.
d2V/(U2
as a
function
of
voltage
for
two
dif-
ferent
barriers. The
Ge
barrier
has
been evaporated
and
is
believed
to be
amorphous.
The
known LO-pho-
non
energies
(Ref. 13) are
indicated both
at the
Brill-
ouin-zone
boundary,
b, and at the
center
of the
zone,
c.
The
lower curve
is for
naturally grown MgO.
a plot
of a
Sn-MgO-Mg sandwich,
and
though
most
of
this structure
is
reproducible between
samples,
we
judge
it at
present almost impossi-
ble
to
interpret.
Mg is
known
to
form oxide,
hy-
droxide,
and
carbonate
on
exposure
to air and
for this reason will have
a
rather complicated
spectrum.
To
realize
the
full potential
of
tunnel-
ing
as a
probe
for
barrier excitations,
the
barri-
ers must
be
better characterized than
we are
able
to do at
present.
For
example, epitaxial
growth
of
barriers under high-vacuum conditions
might prove very rewarding.
It
is a
pleasure
to
acknowledge
the
contribu-
tions
of Dr. S.
Roberts
who
generously helped
in
building
and
testing
the
derivative plotter.
*R.
C.
Jaklevic
and J.
Lambe,
Phys.
Rev. Letters J/7,
1139
(1966).
2D.
J.
Scalapino
and S. M.
Marcus,
Phys.
Rev. Let-
ters
18, 459
(1967).
3C.
B.
Duke,
S. D.
Silverstein,
and A. J.
Bennett,
Phys.
Rev. Letters
_19,
312
(1967).
4J.
M.
Rowell,
in
Proceedings
of
the Advanced Study
Institute
on
Tunneling Phenomena
in
Solids,
Riso,
Den-
mark
(to be
published).
5N.
Holonyak,
Jr., I. A.
Lesk,
R. N.
Hall,
J. J. Tie-
mann,
and H.
Ehrenreich,
Phys.
Rev. Letters c$,
167
(1959).
6F.
Steinrisser,
L. C.
Davis,
and C. B.
Duke,
Phys.
Rev.
(to be
published).
7J.
M.
Rowell
and L.
Kopf,
Phys.
Rev. .137,
907
(1965).
8T.
C.
Damen,
S. P. S.
Porto,
and B.
Tell,
Phys.
1387

VOLUME 21, NUMBER 19 PHYSICAL REVIEW LETTERS 4 NOVEMBER 1968
Rev. 142, 570 (1966).
90.
Brafman and S. S. Mitra, Phys Rev. 171, 931
(1968).
10I.
Giaever, Phys. Rev. Letters 20, 1286 (1968).
llrThe "edge effect" was a controversial subject at the
Advanced Study Institute on Tunneling Phenomena in
Solids, Riso, Denmark. This is the first time in our
experience that we have found it helpful to cover the
edges; however, we do not know if it was necessary.
12J. G. Adler and J. E. Jackson, Rev. Sci. Instr. _37,
1049 (1966).
13F.
A. Johnson, Progr. Semicond. 9, 181 (1965).
EXPERIMENTAL DETERMINATION OF THE EFFECTIVE ATOMIC-SCATTERING FACTOR
AND RIGID-LATTICE INTERFERENCE FUNCTION IN LOW-ENERGY ELECTRON DIFFRACTION*
Max G. Lagally and Maurice B. Webb
University of Wisconsin, Madison, Wisconsin 53706
(Received 29 July 1968)
The elastic scattering of low-energy electrons from Ni is examined at temperatures
where the multiphonon scattering is dominant. The effective atomic-scattering factor is
extracted. The specularly reflected intensity is examined and the corrections necessary
to determine the rigid-lattice interference function are discussed.
The understanding of low-energy electron
dif-
fraction is presently not satisfactory. Recently
there have appeared a number of dynamical the-
ories,1"7
some of which extend band-structure
calculations to the incident-electron energies
and match wave functions at the vacuum-crystal
interface, and others which treat the multiple
scattering explicitly. Generally these theories
either neglect inelastic processes or treat them
with an adjustable parameter, use oversimplified
atomic-scattering factors or lattice potentials,
and consider only the rigid lattice. The experi-
mental data are also deficient in many respects.
Besides questions of real surfaces not being
ideal, experimental results have not been direct-
ly comparable with theory because they have not
been corrected for the diffuse scattering, the
Debye-Waller factor, and the Lorentz factor.
Experimental information about the atomic scat-
tering has been available for only a few atoms,
and then generally from gas data.
It is the purpose of this Letter to demonstrate
a generally applicable method of measuring the
square of the effective atomic-scattering factor
for back angles and to present the results for Ni,
to separate the specularly reflected intensity as
a function of incident energy into its Bragg and
diffuse components, and to illustrate several
significant corrections to the Bragg intensity
necessary to extract features of the rigid-lattice
interference function that appears in the kinema-
tic description of the diffraction.
We make use of the multiphonon scattering,
which has been discussed previously using a
kinematic description.8*9 Although the kinematic
theory is inadequate in some respects, it pro-
vides a convenient and at present the only frame-
work in which to describe the phonon scattering.
It should be emphasized that most of the results
presented are meaningful independent of this the-
oretical description. The time-averaged intensi-
ty scattered per unit solid angle per unit incident
intensity is given by
KS)
=\f(9,E)
?% exp[«£- (rrT.))]
=\f(e,E)\*s(s),
(1)
where f(Q,E) is the atomic-scattering factor,
S =k-ko is the diffraction vector, and 0(5) is the
interference function. If the f's are the equili-
brium atomic positions, this becomes the rigid-
lattice interference function 0O(S). For a ther-
mally disordered crystal, the interference func-
tion can be separated into three parts,
HS)=*
(S)+4 (3)+ 4 AS). (2)
Bragg 1-ph m-ph
Its integral over the Brillouin zone is
/ 3(S)d$ =
e~2M[l
+
2M+(e2M-l-2M)]
zone
x/ ^0(S)^S
=
const, (3)
zone
where the three terms correspond to those in the
interference function and 2M is the exponent in
the Debye-Waller factor. Equation (3) was ex-
perimentally verified in Ref. 8. There it was
also suggested that the multiphonon interference
1388