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Analysis and simulation of Au/InSb/InP diode C–V characteristic:
modeling and experiments
B. Akkal a,b,*, Z. Benamara b, B. Gruzza a, L. Bideux a, N. Bachir Bouiadjra b
aLaboratoire des Sciences des Materiaux pour l’Electronique et d’Automatique, Universite Blaise Pascal de Clermont II,
Les Cezeaux, 63177, Aubiere Cedex, FrancebLaboratoire de Micro-electronique Appliquee, Universite Djillali Liabes de Sidi Bel Abbes, 22000, Sidi-Bel-Abbes, Algeria
Abstract
The effects of the energy density distribution and relaxation time of the interface state on electric parameters of Au/InSb/InP(100)
Schottky diodes were investigated, in the latter diode, InSb forms a fine restructuration layer allowing to block P atoms migration to surface.
To be sure of the disappearance of the In droplets, a high quantity of Sb was evaporated and the excess was eliminated by heating the
substrate surface at 300 jC before evaporating Au onto it. The current–voltage I(VG) and capacitance–voltage C(VG) characteristics are
measured as a function of frequency (100 Hz–1 MHz). Typical Ln[I/(1� e� qVG/kT)] versus VG characteristics of Au/heated InSb/InP(100)
Schottky diode under forward bias show two linear regions separated by a transition segment. From the first region, the slope and the
intercept of this plot on the current axis allow to determine the ideality factor n and the saturation current Is evaluated to 1.79 and
1.64� 10� 7 A, respectively. The mean density of interface states estimated from the C(VG) measurements was 1.57 1012 cm� 2 eV� 1. The
interface states were responsible for the non-ideal behavior of the I(VG) characteristics, the capture cross-section rn for the fast slow varies
between 2.16� 10� 11 and 7.13� 10� 12 cm2 for the relaxation times range 7.9� 10� 3–2.4� 10� 2s.
D 2002 Elsevier Science B.V. All rights reserved.
Keywords: Energy density distribution; Relaxation time; Au/InSb/InP(100) Schottky diodes
1. Introduction
During the elaboration of semiconductor devices of the
MS and MIS types, defects appear which lead to electronic
states with energies located in the forbidden band, the band
gap. These states are known as surface states and alter the
functioning of such devices.
The relationship between the admittance of the interface
state charging process above and the capacitance and con-
ductance of the MIS structure measured in the external
circuit has been described and analyzed by Nicollian and
Goetzberger [1]. They have observed that the capacitance
decreases with increasing frequency. This effect is obtained
at low and intermediate frequencies. The interface states can
follow the AC signal and yield an excess capacitance, which
depends on the relaxation time of the interface states and the
frequency of the AC signal. This model can be applied to
determine the interface state of a metal-interface layer-
semiconductor Schottky diode.
The purpose of this paper is to characterize interface
states in Au/heated InSb/InP(100) Schottky diode and
determine the energy density distribution and relaxation
time of the interface states. The density of interface states
and relaxation time are determined using capacitance meas-
ured at different frequencies.
2. Experimental procedure
The used InP(100) substrates were n-type wafers doped
with antimony at different levels (1015–1017 atoms cm� 3).
They were chemically cleaned according to a method based
on successive baths of H2SO4 solution, methanol solution
3% bromine, and deionized water [2]. Then, they were in-
troduced into an ultra-high-vacuum (UHV) chamber at a
pressure of 10� 9–10� 10 Torr. The sample surface was
controlled using an Auger electron spectroscopy (AES) with
a retarding field analyzer. A low rate of carbon and oxygen
contamination atoms was detected. These impurities were
removed in situ by cleaning with low energy Ar+ ions bom
bardment (ions energy = 300 eV, ionic current = 2 AA cm� 2).
This operation has induced metallic In formation in the
0928-4931/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved.
PII: S0928 -4931 (02 )00083 -8
* Corresponding author. Laboratoire des Sciences des Materiaux pour
l’Electronique et d’Automatique, Universite Blaise Pascal de Clermont II,
Les Cezeaux, 63177, Aubiere Cedex, France.
www.elsevier.com/locate/msec
Materials Science and Engineering C 21 (2002) 291–296
shape of submicroscopic droplets [3]. The surface can be
stabilized by creating an established number of InSb mono-
layers before depositing the gold atoms. To be sure of the
disappearance of the In droplets, a high quantity of Sb was
evaporated and the excess was eliminated by heating the
substrate at 300 jC so that the metallic Sb desorbed from the
surface.
To realize a metallic gate, we have used a mask with
molybdenum. This mask allows to achieve electrical meas-
urements with a gold gate of 1-mm diameter and thick
layers of about 1000 A. Hence, the homogeneity studiesand
cleanliness of these deposits were possible. Lastly, let us
note that the current–voltage I(VG) characteristic measure-
ments were measured using a standard set-up (two 616
electrometer). The capacitances C, as a function with bias
voltage VG plotted at the frequency in the range between
100 Hz and 1 MHz, were measured with a PAR 129 A two-
phase Lock-in amplifier.
3. Computational model
The I(V) relation for non-ideal Schottky contact is given
by [4,5].
I ¼ Is 1� e�qV=kTh i
eqV=nkT ð1Þ
where q and T are the magnitude of the electron charge, the
temperature in Kelvin, respectively, and n is the ideality
factor. Is is the saturation current expressed by:
Is ¼ SA*T2exp � q
kT/Bn
h ið2Þ
A*, S and /Bn are the Richardson constant, the area of the
rectifying contact, the barrier height, respectively, and V is
the voltage drop across the rectifying barrier.
The energy of the interface states Ess, relative to the
conduction band edge Ec at the semiconductor surface, is
given by [6]:
Ec � Ess ¼ qð/Bn � V Þ ð3Þ
The density of the interface state Nss related to the interface
state capacitance Css is given by [1]:
Css ¼SqNss
wsarctgðwsÞ ð4Þ
where s is the relaxation time of the interface state and is
defined as follow [7]:
s ¼ 1
VthqnNd
eqVd=kT ð5Þ
where Nd, Vd are the doping concentration and the diffusion
potential, respectively, rn represents the cross-section of the
interface states and Vth is the thermal velocity of the carriers
(Vthc 107 cm s� 1).
For a Schottky diode with a thin interfacial layer between
the metal and the semiconductor (MIS), and at sufficiently
high frequencies such that the interface states cannot follow
the AC signal, the slope of the C� 2(V) relationship obtained
by Fonash [8] is given by:
dC�2
dV¼ 2
qesNd
Csc þ Ci
Csc þ ð1þ aÞCi
� �ð6Þ
where Ci and Csc are the interfacial layer and depletion zone
capacitances, respectively. The parameter a is given by:
a ¼ qNssdei
ð7Þ
The presence of a thin interfacial layer d implies that
CiHCsc, Eq. (6) can be reduce to:
dC�2
dV¼ 2
esq1
Ndð1þ aÞ
� �ð8Þ
According to relation (8), the slope of the high frequency
C � 2(V) is constant if the interfacial states density Nss is
Fig. 1. Ln[I/(1� e� qVG/kT)] variations versus bias.
B. Akkal et al. / Materials Science and Engineering C 21 (2002) 291–296292
constant. We have a other behavior when Nss varies sig-
nificantly in the semiconductor energy band gap.
The extrapolated intercept, V0, of the high frequency
C� 2(V) curve is given by:
V0 ¼ V1=21 ðVd � kT=qÞ1=2 þ ð1þ aÞðVd � kT=qÞ
þ ð1� aÞ V1
4ð9Þ
where V1 is defined by :
V1 ¼2qesNdd
2
e2ið10Þ
For low values of d and Nd, the intercept, V0 of the C� 2(V)
plot with the V-axis can be reduced to:
V0 ¼ ðVd � kT=qÞð1þ aÞ ð11Þ
and the barrier height /Bn is described by the relation:
/Bn ¼ Vd þkT
qLn
Nc
Nd
ð12Þ
where Nc is the effective states density in the conduction
band.
4. Results and discussion
Typical Ln[I/(1� e� qVG/kT)] versus VG characteristics of
Au/heated InSb/InP(100) Schottky diode under forward
bias is reported in Fig. 1. This curve shows two linear
regions separated by a transition segment. From the first
region, the slope and the intercept of this plot on the current
axis allows to determine the ideality factor n and the
saturation current Is evaluated to 1.79 and 1.64� 10� 7
A, respectively.
At forward voltage considerably higher (VG > 0.4 V), the
Ln[I/(1� exp(� qVG/kT)] curves become straight lines and
thereby permit the determination of the series resistance Rs
from the slope of the second region [6]. The values of Rs so
obtained are equal to 230 V.
Fig. 2 shows clearly a low backward current and great
barrier height values equal to 0.63 eV. This is calculated by
substituting the Is value in Eq. (2).
The non-ideal I–VG characteristics indicate that the
diode is not intimate metal–semiconductor (MS) contacts
but instead have a metal-interface layer-semiconductor
(MIS) configuration. The DC current densities of several
AA even under low forward bias is too high for a thick
MIS and indicates that the interface layer thickness, dV 50
Fig. 2. I(VG) characteristic of the Au/heated InSb/InP structure.
Fig. 3. Variation of C(VG) characteristics with frequency.
B. Akkal et al. / Materials Science and Engineering C 21 (2002) 291–296 293
A [9]. The lack of humps in the I–VG characteristics under
forward bias indicates that dz 30 A. If we take d = 40 A, it
gives a reasonably good fit to our data.
The plot of C(VG) characteristics with frequency is
shown in Fig. 3. In the high frequency, the interface states
cannot follow the AC signal and consequently do not
contribute appreciably to the junction capacitance. Hence,
the junction capacitance in the high frequency CHF, is
equal to the space charge capacitance, Csc. The situation
may be different at low and intermediate frequencies,
depending on the relaxation time of the interface states
and the frequency of the AC signal. Then, the interface
state capacitance Css(V, w/2p) can be expressed with the
measured values of C(V, 1 MHz) and C(V, w/2p) as follow[10].
CssðV , w=2pÞ ¼ CðV , w=2pÞ � CðV , 1 MHzÞ ð13Þ
Fig. 4 shows the evolution of Css(VG) curves as a
function of frequency. Similar curve for Css(w/2p) has beenobtained by Laflere and Van Meirhargher [11], and Morant
et al. [12] for Au/GaAs an Al/GaAs Schottky diodes,
respectively.
Fig. 4. Css(VG) variation versus frequency (Solid line Simulation, Symbol
Experimental).
Table 1
Experimental parameters obtained of Au/InSb/InP
Fast states Slow states
VG (V) Ec�Ess
(eV)
Nss
(eV� 1 cm� 2)
s (s) Nss
(eV� 1 cm� 2)
s (s) rn cm2
0.25 0.38 1.1�1011 10�4 2.6�1012 7.9�10� 3 2.16�10� 11
0.2 0.43 1.5�1011 1.5�10� 4 2.2�1012 1.1�10� 2 1.55�10� 11
0.14 0.49 1�1011 1.9�10� 4 1.6�1012 1.4�10� 2 1.22�10� 11
0.1 0.53 8.96�1010 2.3�10� 4 1.15�1012 1.9�10� 2 9�10� 12
0.05 0.58 9.3�1010 3.2�10� 4 9.9�1011 2.2�10� 2 7.78�10� 12
0.01 0.62 8�1010 3.9�10� 4 9.1�1011 2.4�10� 2 7.13�10� 12
Fig. 5. Cp(VG) variation versus frequency (Solid line Simulation, Symbol
Experimental).
B. Akkal et al. / Materials Science and Engineering C 21 (2002) 291–296294
The data for diode Au/InSb/InP show a plateau in the
frequency range between 300 Hz and 1 kHz. We fitted the
theoretical formula (4) to the Css(V, w/2p) curve shown in
Fig. 4 in the frequency range between 1 and 20 kHz and
found good agreement between experiment and theory. To
obtain the dependence of s and Nss on the bias voltage VG,
the fitting procedure was repeated for various values of VG.
The dependence of Nss versus VG, obtained by the above
method was converted to function of Ess using Eq. (3). The
values of s and Nss as function of Ec�Ess for the ‘fast
states’ are shown in Table 1.
For low frequencies, a new quantity of the interface
states capacitance Cp(V, w/2p) is defined by:
CpðV , w=2pÞ ¼ CssðV , w=2pÞ � CsoðV Þ ð14Þ
where Cso(V) is the height of the plateau shown in Fig. 4.
We have fitted Eq. (4) to the experimental values of Cp(V,
w/2p) for frequencies w/2pV 1 kHz shown in Fig. 5 to
obtain the density of interface Nss and their relaxation time sfor the ‘‘slow states’’. These values of Nss, s and rn as
function of bias voltage are also shown in Table 1. A similar
distribution of capture cross-section rn has been reported in
the literature [13] and is probably due to the scatter of
interface state over a few atomic layers across the interface
layer-semiconductor boundary.
Fig. 6 gives a variation of C� 2(VG) with frequency. The
slope at high frequency (1 MHz) is constant, and is identical
to the slope of an ideal metal–semiconductor contact. For
frequencies w/2pV 20 kHz, the C � 2(VG) curves at reverse
voltage greater than 0.1 V show a curvature (concave
downwards), are attributed to the deep donor level in the
bulk.
The value of a equal to 0.25 is obtained using Eq. (7)
with ei = 4.5e0 [14] and the mean value of Nssc 1.57� 1012
eV � 1 cm � 2 obtained from the analysis of Cp(V) data.
Substituting this value into Eq. (8) and using the values of
dC � 2/dV at (1 MHz) (in Fig. 6) and es = 12.1e0 [15], we
have evaluated Nd to 4.65� 1015 cm� 3.
The intercept, V0 of C� 2(VG) plot at (1 MHz) with the
axis equal to 0.71, and the value of V1 calculated from Eq.
(10) allow to evaluate Vd which is equal to 0.58 V. (see Eq.
(11))
The calculated values of Nd and Vd were substituted in
Eq. (12) to determine the value of /Bn which is equal to
0.66 eV.
The value of /Bn obtained from the analysis of I(VG) data
is in good agreement with the one obtained from the C(VG)
measurement at height frequencies.
Our computation of the interface state density based on
the high frequency I(VG) and C(VG) characteristics is more
accurate than those obtained at low frequency [16].
In our case, we cannot plot the electrical characteristics at
the frequencies less than 100 Hz and consequently cannot
study the interface state computation for slow states. This is
due to the instability of the used set-up.
5. Conclusion
The studied Au/InSb/InP Schottky diode is an MIS
structure with interface states in thermal equilibrium with
the semiconductor. The I(VG) curve is not ideal and the ideal
factor n is controlled by the interface states density.
The linearity of the C � 2(VG) characteristic is due to the
uniform distribution of the interfacial states density Nss and
the dopage Nd in the band gap.
The peak value of the capacitance has been found to be
strongly dependent on the values of interface state density
and the frequency of the AC signal.
The heating treatment before Au deposition gives good
results in electrical measurements, so, we have obtained a
high quality Schottky type contact with elevated barrier
height values of 0.63 eV. These improvements can be
explained by the passivation of the substrate, using Sb
atoms, which prevent any migration of the semiconductor
components during the alumina and gold deposition.
The relaxation times shown in Table 1 is found to be
independent of bias VG or energy of interface states Ess.
The capture cross-section, rn, decreases exponentially
and it is independent of the bias. It varies between 2.16�10� 11 and 7.13� 10� 12 cm2.Fig. 6. C� 2(VG) variations versus bias VG.
B. Akkal et al. / Materials Science and Engineering C 21 (2002) 291–296 295
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