Surface Barriers on Zinc Oxide
R. C. Neville and C. A. Mead
Citation: Journal of Applied Physics 41, 3795 (1970); doi: 10.1063/1.1659509
View online: http://dx.doi.org/10.1063/1.1659509
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JOURNAL
OF
APPLIED
PHYSICS
VOLUME
41,
::-<UMBER
9
AUGUST
1970
Surface
Barriers
on
Zinc
Oxide
R.
C.
NEVILLE
AND
C.
A.
MEAD
Department
of
Electrical Engineering, California Institute
of
Technology, Pasadena, California 91109
(Received 9 February 1970; in final form
16
April
1970)
The surface barrier systems consisting
of
gold and palladium on chemically prepared zinc oxide have
been investigated in detail. Surface barrier energies have been determined
by
photoresponse, forward
current versus voltage, thermal activation energy, and capacitance-voltage methods. Agreement in barrier
energies obtained
by
the four methods
is
excellent.
The
barrier energy for gold is 0.66
eV
and for palladium
is
0.60
eV.
Forward current-voltage characteristics were in quantitative agreement with simple Bethe
diode theory as modified
by
the presence of image force lowering. The reverse current-voltage characteristic
is
in quantitative agreement with
that
expected from the simple image force lowering of the barrier, over
a bias range of from
0.1
to 3
V.
Carrier concentration derived from resistivity and Hall measurements
agreed with
that
obtained from capacitance-voltage measurements. We believe this represents the first
comprehensive study where such quantitative consistency has been demonstrated on a compound semi-
conductor barrier system. Existence of a deep level trap
is
indicated via the effects on capacitance measure-
ments.
INTRODUCTION
Zinc oxide
as
a material has been known since the
Bronze
Age.'
It
was not until relatively recently
that
detailed investigations into the electronic properties of
this hexagonal crystal have been conducted. Rupprecht
2
and Bogner
3
determined the mobility
of
bulk samples
of
zinc oxide.
The
dielectric constant for zinc oxide was
determined
by
Collins and Kleinman
4
and an effective
mass for the charge carrier was measured by Dietz
et
al.
5
Mead
6
determined the surface barrier energies of
several metals
on
vacuum-cleaved zinc oxide.
The
barrier energy for gold was determined to be
0.71
e V
and 0.65
eV
was obtained as barrier energy for palla-
dium.
We report here the results of an extensive investiga-
tion
of
the barrier-semiconductor systems formed
by
gold and palladium
on
zinc oxide. Barrier energies were
determined
by
photoresponse, forward current-voltage,
thermal activation energy, and capacitance-voltage
methods. Forward and reverse current-voltage charac-
teristics were studied and are analyzed in terms
of
the
simple Bethe diode
theory,7 as modified
by
the presence
of
image force lowering.
8
,9
SAMPLE PREPARATION
Undoped hexagonal zinc oxide crystals with free
electron concentrations between 1 X
10
16
and
2X
10
17
per cubic centimeter were used.
'o
The
crystals were
first cleaned by immersion in concentrated phosphoric
acid for a period
of
15
min, followed
by
a la-min soak
in concentrated hydrochloric acid and a rinse in flowing
deionized water. The crystals were dried in a jet of dry
air.
The
samples were then placed in a vacuum chamber
at
a pressure of 10-
6
Torr
or less. Using a heated tung-
sten filament approximately
1000 A
of
gold or palla-
dium was evaporated on the sample through a fine
mesh. The active barrier area was nominally
100
J.L
in
diameter. Contact to the evaporated metal barriers
was made
by
a fine gold wire probe. Ohmic contact to
the bulk crystals was made using 10% silver and
90%
indium solder.
On three
of
the four crystal samples the same crystal
was given both gold and palladium barriers.
RESULTS
AND
INTERPRETATION
Bulk
Measurements
Mobility and resistivity measurements were made
on
the bulk zinc oxide crystals. Mobility
was
determined
by
a Hall measurement using a 4.7 kG permanent magnet.
Resistivity measurements were made using four soldered
contacts
at
both room (296°K) and
at
liquid-nitrogen
(77°K) temperatures. The resistivity was then com-
bined with the mobility
data
to derive an effective donor
concentration
of
N
a
=
l/PJ.Lq,
(
1)
where Nd
is
the donor concentration, P
is
the measured
resistivity,
jJ.
is
the Hall mobility, assumed equal to the
conductivity mobility, and
q
is
the electronic charge.
For a typical crystal the measured mobility was 200
cm
2
/V sec, in good agreement with values quoted in the
literature (Refs.
2,
3).
The
resistivity
of
this sample
at
room temperature was
1.13
Q-cm.
At
liquid-nitrogen
temperatures the measured resistivity was 1.98
Q-cm.
From the resistivity and mobility
at
room temperature
the net donor concentration was calculated to be 2.9X
10
16
/cc.
Surface Barriers
Surface barrier energies were determined using four
independent techniques. The methods used were: photo-
response, zero-voltage forward current intercept, ther-
mal activation energy, and capacitance variation with
applied voltage.
Photoresponse
The barrier energy was determined by a measurement
of
the short circuit photocurrent using light entering
the crystal from the barrier contact side
(a
front wall
configuration). A tungsten-halide lamp was used in
conjunction with a Gaertner Quartz Prism Monochro-
3795
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3796
R.
C.
NEVILLE
AND
C.
A.
MEAD
jf5R3
ARBITRARY
UNITS
2
I
//
°
11°
/ °
/1
/ /
/1
I r
I /
/ I
o /
1/
GOLD
0
/1
PALLADIUM
0
/,
I
.6
.8 .9
1.0
1.1
1.2
hll(ev)
FIG.
1.
Square root of photo current per incident photon as a
function of photon energy for gold and palladium surface barriers
on zinc oxide.
nometer. From simple Fowler theory, the barrier energy
is the intercept for zero response
of
the plot
of
the square
root of the response (photo current per incident photon)
versus the photon energy.
In
Fig. 1 we present the photoresponse
data
from
typidal sample crystals. Four crystals were used with
measurements being taken on between 5
and
15
barriers
per crystal.
The
surface barrier energies, were found to
be
0.645±O.04 eV for gold and 0.59±0.04 eV for
palladium.
Forward Current versus Voltage
Typical curves of forward current density versus
forward voltage are presented in Fig. 2 for gold
and
palladium barriers on chemically prepared zinc oxide.
The
area of each device is given in the figure. Current
measurements were made with a three-lead configura-
tion
to
eliminate errors due to potential drop
at
the bulk
crystal contact.
The
current-voltage characteristic, for thermiomic
current
and
voltages in excess
of
a few
kT/q
is given
by
J = J 0 exp
(q
V /
nk
T) ,
(2a)
where
J is the current density, V is the applied voltage,
k is
the
Boltzmann constant, T is the absolute tem-
perature,
and
J
o
=A*T2exp(-qcf>/kT), (2b)
where
cf>
is the surface barrier energy, A * is the Richard-
son constant corresponding to the effective mass of the
material,
and
(2c)
where
m* is the effective mass taken as O.38m. after
Ref. 5,
m. is the rest mass
of
the electron,
and
h is
Planck's constant divided by
271'.
The
factor (n) in
Eq.
(2) is treated in Henish
8
and
in
Sze.H
It
arises here from the change in
cf>
with applied
voltage.
n=l+(ilcf>/ilV),
where after Ref.
9,
I1n(image force)
=acf>/av
=
t(
q
3N
d/
t03871'2eop2tDO)
1/4
(3)
X[cf>- V
-t-
(kTjq)
]-3/4,
(4)
where
I1n
is
the
deviation
of
n from unity,
EO
is the
permittivity
of
free space,
and
top
is the relative
permittivity of zinc oxide
at
optical frequencies. After
Ref.
12
this
is
set
at
4.
fDO
is the low-frequency relative
permittivity
of
zinc oxide. After Collins
and
Kleinman
(Ref. 4) this is taken
at
8. V is the applied voltage
and
r is the Fermi energy below the conduction
band
edge.
r is given
by
r=kT/q
lnNoIND,
(Sa)
where
No
is the conduction band effective density
of
states and where
N
c
=
(Jr
1
/
2
/2/7I'
2
'/i
3
)
(m.*)3/2(kT) 312. (Sb)
Combining Eqs. (3)
and
(4) one can write for the
diode nonideality factor
n=
1
+An(image
force).
(6)
The
value
of
n for forward voltages between 0.05
and
0.15 V is found to be 1.05±0.05. This value is in agree-
ment
with
that
expected as a result
of
image force
lowering from the Eqs. (4)
and
(6) using the carrier
concentration determined from resistivity and Hall
effect measurements.
Using Eq. (2a) the surface barrier energies were
calculated from current-voltage
data
taken on some
10"
/0
j
/
°
I
I
J
/0
10-
2
/ °
J
I
/
J
/ °
omp/cm'
/
/
I
10-
3
/
I
GOLD
PALLADIUM
0
I
".~
0
0.1
0.2
0.3
v
(volts)
FIG.
2.
Typical forward current density as a function of
applied voltage for gold and palladium surface barriers on zinc
oxide
at
300
0
K.
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SURFACE
BARRIERS
ON
ZINC
OXIDE
3797
40 individual barriers on 4 crystals.
The
energies ob-
tained in this manner are
0.66±0.03
eV
for gold
and
0.60±0.04
eV
for palladium on zinc oxide.
Thermal Activation Energy
A
third
measurement
of
the surface barrier energy
was obtained from the measurement
of
reverse current
as a function
of
the temperature
at
fixed bias voltage.
A Peltier cooler was employed
and
the results
of
the
measurement are presented in Fig. 3.
The
activation
energy was determined from the relationship:
CPA=
(-k/q)[o
InI.(V)/al/T]-
(2kT/q) , (7)
where
I.(V)
is the current
at
some fixed bias
V.
The
thermal activation energies obtained on chemi-
cally treated zinc oxide for 40 individual barriers on
four crystals are
0.70±0.04
eV for gold
and
0.63±0.04
eV for palladium.
The
thermal activation energy determined from
Eq.
(7) is expected
to
be higher
than
the barrier energy due
to
the change in barrier energy with temperature.
In
general,
the
barrier energy is
not
constant with tem-
perature,
but
over a small temperature range IS ex-
pected to
vary
approximately as follows:
(8)
where
CPo
is
the
barrier energy
at
the
measurement
temperature
and
Al
is the temperature coefficient of
the
barrier energy in
the
vicinity
of
the measurement
temperature.
T
(OC)
10_
260
,--
___
4,°_-'3,.:.°_.,.:23'---_;.;:.13
__
°;....,
i".
10-
3
'"
~
GOLD
PALLADIUM
0
J
R
i"-'\.
"',
(A/cm
2
)
'\.
'"
'\.
'"
\'",
0
"-
'\.
'0
0",
'"
'"
'"
10-
5
'::-----:f-:------:L-_L-_-'--_""----L_--...l.---I
3.0
3.1
3.2 3.3 3.4
3.5
3.6
1000/T
(OKf
l
FIG.
3. Current density as a function of temperature for a
reverse bais
of
1
V.
GOLD
PALLADIUM
0
·8
I °
l;--~--.-k-----;,L;--!n--,L,-----,l
.8 .9
1.0
1.1
1.2
1.3
1.4
Yv+vo
(vI/
4
)
FIG.
4. Reverse current as a function of applied voltage for gold
and
palladium surface barriers on zinc oxide.
In
covalent semiconductors
the
presence
of
surface
states fixed the Fermi level,
at
the
surface, relative
to
one
band
edge.
In
such instances
it
has been found
that
the
barrier energy varies in temperature as does the
bandgap.13 An ionic semiconductor has virtually no
surface states.
The
Fermi level,
at
the
surface,
is
free
to
move between conduction
and
valence
band
edges,
depending upon
the
work function
of
the
metal em-
ployed.
Zinc oxide is an ionic semiconductor with no
surface states.
6
,14
The
variation of surface barrier energy
with temperature is then expected
to
be proportional
to
that
fraction
of
the forbidden gap occupied
by
the
barrier.
A
I
=acp/aT=
(cp/
Eg)(aEg/aT)
<0,
(9)
where
Eu
is
the
forbidden gap.
The
bandgap energy for zinc oxide
is
3.435 eV
at
1.2°K.15
The
barrier energy for gold and palladium on
zinc oxide has been determined
by
photoresponse and
forward current versus voltage techniques.
The
change
in the forbidden gap with temperature has been meas-
ured
by
Watanabe
and
Wada
I6
to
be
-8X
10--4
eV;oK
in the vicinity
of
room temperature.
From
Eq.
(9) Al
is -1.57XIQ--4 eV for gold
and
-1.43XIQ--4 eV for
palladium. Use
of
these values in Eq. (8) together with
the barrier values
attained
from
Eq.
(7) results in
substantial agreement for values of
cP
as determined
bv
photoresponse, forward current,
and
thermal
activatio~
energy (see Table
I).
Reverse Current
The
voltage dependence
of
the reverse current charac-
teristic,
at
fixed temperature, as a function
of
the fourth
root
of
the applied voltage
is
displayed in Fig.
4.
At
a
fixed temperature
the
reverse current as a function
of
the
applied voltage
is
expected
to
be nonconstant.
The
ideal, constant reverse current, independent
of
applied
bias,
of
the Bethe diode theory is modified
by
the
presence
of
the image force field lowering which causes
the barrier energy
to
change with applied voltage.
9
The
theoretical slope
of
the logarithm
of
the
reverse current
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3798
R.
C.
NEVILLE
AND
C.
A.
MEAD
TABLE
1.
Measured barrier energies
on
zinc oxide.
Barrier energy (electron volts)
Metal Photoresponse
J-
V characteristic Activation energy Capacitance
Gold
Palladium
O.64S±O.04
O.59±O.04
O.66±O.03
O.60±O.04
O.6S±O.04
O.S9±O.04
O.67±O.03
O.61±O.OS
versus voltage
is
given
by
[0
lnIs(V)/o(V
o
-
V)
1/4]
=
(q/kT)
(qWa/81r2E03Eop2EDC)
1/4,
(10)
where
Vo
is
rp-r-kT/q.
The
slope as given
by
Eq. (10)
is
also plotted in
Fig.
4.
The
agreement between theory
and
experiment
for both gold and palladium surface barriers
is
seen to
be good over a range in bias between
0.1
and
3
V.
Capacitance Studies
The
fourth measurement of the surface barrier
energies was made using the variation
of
barrier capac-
itance with applied voltage
at
a frequency
of
1 MHz.
In
Fig. 5
we
present
1/C2
versus applied voltage for two
typical surface barriers under the conditions
of
darkness
and illumination with
0.5-,u
light.
This technique
not
only yields the surface barrier
energy
but
allows determination
of
the effective donor
concentration
of
that
part
of
the crystal directly under
the individual barrier. Following Goodman
17
the effec-
tive donor concentration is
N
a
=
(-2/qEDCEO)
[oV/O(S/C)2], (11)
where
S is the barrier area
and
C
is
the measured
capacitance
at
the applied voltage.
The
extrapolated intercept
Vo
of
a plot
of
1/
C2
versus
the applied voltage is related to the surface barrier
energy
by
the equation
vo=rp-r-kT/q.
(12)
In
the derivation of Eqs. (11)
and
(12) the absence
of trapping was assumed.
The
effect
of
empty
traps
is
to increase the measured donor concentration. Thus the
measurement
of
capacitance under illumination of
sufficiently short wavelength
is
expected to yield values
of donor concentration in excess
of
the true value. The
measured intercept will be lower than the true value
of
barrier energy
by
the Fermi level
and
a thermal term.
Table
II
presents, in summary form, the donor
concentrations
and
extrapolated intercepts
Vo
for the
several zinc oxide crystals studied. An average
of
seven
barriers of each type were measured and both the av-
erages
and
scatter for each sample
is
given.
The sample marked palladium-A was a crystal
possessing a much higher impurity concentration level
than
did the other crystals. The surface barrier energies
as determined
by
all four techniques on this heavily
doped sample were in agreement with the barrier
energies obtained from the other, less heavily doped,
samples. No systematic relationship between surface
barrier energy and impurity concentration was found.
The
values
of
carrier concentration obtained from the
capacitance-voltage
data
on individual surface barriers
under conditions
of
no illumination are in good agree-
ment with the values obtained
by
Hall
and
resistivity
measurements. For example, sample number 3 was
found earlier to have an effective donor concentration
of 2.9X
10
16
/cc.
The
capacitance-voltage technique
yields a value
of
(3±0.3)
X
10
16
/cc.
The Fermi level was calculated to be
0.135 eV below
the conduction band using Eqs. (Sa)
and
(5b) with a
capacitance derived carrier concentration
of
3 X
10
16
/
cc.
From this and Eq. (12) the barrier energies were
calculated to be
0.67±0.03 eV for gold
on
zinc oxide and
0.61±0.OS eV for palladium.
Capacitance and Traps
The capacitance
of
the surface barriers measured was
a function
of
the wavelength
and
intensity
of
the
illumination. The samples were illuminated
by
a strong
fluorescent source with a number
of
filters
of
a differing
cutoff wavelength. An increase in the capacitance was
experienced for wavelengths in the l-1.S-,u range. From
this
data
the
trap
level energy depth was estimated to
be between
0.8
and
1.2
eV.
The deep
trap
density can be estimated
by
comparing
the donor density under illumination and no illumina-
tion. A lower bound for the
trap
density
Nt
can be
estimated
by
using
N
t
';::5Nd(illuminated)
-N
d
(
dark).
(13)
The lower bound
trap
densities are estimated from
Table
II
to be 2 X
10
15
/ cc for all samples except palla-
dium-A. For palladium-A the
trap
density is estimated
to be
at
least
2XI0
16
/cc. Based on limited
data
it
appears
that
the
trap
density fluctuates with the carrier
concentration and has a magnitude approximately one-
tenth
the donor concentration.
Further
investigation of
the trapping site will be required to determine the
exact nature
of
the trap, its er,ergy level, cross section,
and origin.
Barrier
Energy
Summary
In
Table I the values
of
surface barrier energy result-
ing from the four measurement techniques are presented.
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