Schottky diode formation and characterization of titanium tungsten to n- and p-type 4H
silicon carbide
S.-K. Lee, C.-M. Zetterling, and M. Östling
Citation: Journal of Applied Physics 87, 8039 (2000); doi: 10.1063/1.373494
View online: http://dx.doi.org/10.1063/1.373494
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Schottky diode formation and characterization of titanium tungsten
to n- and p-type 4H silicon carbide
S.-K. Lee,a)
C.-M. Zetterling, and M. Östling
KTH, Royal Institute of Technology, Department of Electronics, Electrum 229, S-164 40, Kista, Sweden
共Received 2 December 1999; accepted for publication 29 February 2000兲
Titanium tungsten (Ti0.58W0.42) Schottky contacts to both n- and p-type 4H silicon carbide were
fabricated using sputtering. The n- as well as p-type Schottky contacts had excellent rectifying
characteristics after vacuum annealing at 500 °C with a thermally stable ideality factor of 1.06
⫾0.03 for n-type and 1.08⫾0.01 for p-type. The measured Schottky barrier height 共SBH兲 was
1.22⫾0.03 eV for n-type and 1.93⫾0.01 eV for p-type in the range of 24–300 °C. Our results of
Ti0.58W0.42 Schottky contacts to both n- and p-type can be explained perfectly by thermionic
emission theory and also satisfy the Schottky–Mott model in contrast to earlier works.
Capacitance–voltage measurements were also performed and the results were in good agreement
with those of current–voltage measurements. In addition, the inhomogeneous behavior with higher
ideality factor and lower SBH of p-type Ti0.58W0.42 contacts for as-deposited contacts is explained
by using a model with contribution of recombination current originated by lattice defects to
thermionic emission current. © 2000 American Institute of Physics. 关S0021-8979共00兲05911-9兴
I. INTRODUCTION
Silicon carbide has received remarkable attention during
the last decade as a promising device material for high tem-
perature, high frequency, and high power devices.1,2
Metal–
semiconductor contacts have many device applications such
as the gate electrode of a field-effect transistor 共MESFETs兲,
the source and drain contacts in metal–oxide–semiconductor
field-effect transistors 共MOSFETs兲, and the electrodes for
high-power impact ionization avalanche transit time
共IMPATT兲 oscillators.3
Many previous studies have mainly
been concerned with n-type silicon carbide,4
but investiga-
tion is also needed for complementary MESFETs and MOS-
FETs. Complementary devices are used in a variety of power
electronic applications.5
Raghunathan and Baliga6
also
pointed out that p-type Schottky contacts are definitively
useful for power electronic applications with the advantage
of low current density operation. In the literature, there is
very little on p-type Schottky contacts to SiC 共3C–SiC, 6H–
SiC, and 4H–SiC兲. In our group Lundberg et al.7,8
have in-
vestigated cobalt 共Co兲 and tungsten 共W兲 Schottky contacts
for both n- and p-type 6H–SiC. Recently, Raghunathan and
Baliga6
reported Ti/Al Schottky contacts to p-type 4H–SiC
and 6H–SiC. They have achieved a Schottky barrier height
of 1.4–1.5 and 1.8–2.0 eV for p-type 4H and 6H–SiC, re-
spectively using both current–voltage (I–V) and
capacitance–voltage (C–V) measurements, but with high
ideality factors 共2.2 for 4H–SiC and 1.9 for 6H–SiC兲 com-
pared to n-type Schottky contacts. They suggested that the
reason for the high ideality factor for p-type Schottky con-
tacts was because thermionic emission is not the dominant
mechanism. Using Schottky–Mott theory9
it is expected that
the sum of the barrier heights to n- and p-type semiconduc-
tors would be equal to the energy band gap of a semiconduc-
tor for any set of semiconductor and metal, that is
Eg⫽⌽Bn⫹⌽Bp . 共1兲
Unfortunately, most of the earlier works have not satisfied
Eq. 共1兲. TiW has been used extensively as a diffusion barrier
for Al based metallization in silicon technology.10
They are
also used for ohmic contacts to 3C–SiC11
and 6H–SiC.12,13
However, there is no previous work on the performance of
TiW Schottky diodes to n- and p-type 4H–SiC.
In this article, we have investigated the characteristics of
Schottky contacts using sputtered titanium tungsten
(Ti0.58W0.42) as a basic metal for studying n- and p-type 4H-
SiC, and compared the results to Schottky–Mott theory.
II. EXPERIMENTAL DETAILS
Both n- and p-type Si face 4H–SiC substrates
(⬃1018
cm⫺3
) with 4 ␮m thick lightly doped epitaxial layers
(1.2–1.4⫻1016
cm⫺3
) were purchased from CREE Research
Inc.14
The wafers were cleaned sequentially with two differ-
ent cleaning recipes 共so called oxidation and etching兲 such as
H2SO4:H2O2 共2.5:1兲 with temperature ⬎80 °C during 5 min
and H2O:CH3CH共OH兲CH3:HF 共100:3:1兲 during 100 s prior
to the sputtering process. After each cleaning process, the
wafers were rinsed with deionized 共DI兲 water during 5 min.
The cleaning was completed by a dip in 5% diluted HF so-
lution and a DI water rinse to ensure that the native oxide
was kept to a minimum prior to loading a wafer in the sput-
tering chamber. The metallization was done by sputtering
with a compound TiW target 共nominally 30:70 weight per-
cent ratio兲. The sputtering was performed in a dc magnetron
sputter under deposition conditions of 3 kW power, 120 °C
substrate temperature, 69 sccm of Ar gas flow, 5.2
⫻10⫺7
Torr base pressure, and 5 mTorr deposition pressure.
About 1250 Å Ti0.58W0.42 metal was deposited on n- and
p-type 4H–SiC and a blanket piece was also deposited si-
multaneously for Rutherford backscattering spectrometry
a兲
Electronic mail: lee@ele.kth.se
JOURNAL OF APPLIED PHYSICS VOLUME 87, NUMBER 11 1 JUNE 2000
8039
0021-8979/2000/87(11)/8039/6/$17.00 © 2000 American Institute of Physics
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共RBS兲 measurement. Different sizes of circular Schottky
contacts 共diameter 50, 100, 200, 400, and 1000 ␮m兲 were
fabricated using a standard photolithography procedure with
photoresist mask. Ti0.58W0.42 was wet etched using a mixture
of NH3:H2O2 共1:5兲 with an etching rate of 300 Å/min. After
Ti0.58W0.42 deposition, a 1 ␮m thick aluminum film was also
deposited on the highly doped backside substrate to form a
large area backside ohmic contact, using sputtering under
similar conditions. Some of the samples were annealed in a
low pressure (2⫻10⫺6
Torr) vacuum chamber during 30
min at 500 °C. Both I–V and C–V measurements were per-
formed on different diodes for each temperature 共24, 100,
200, and 300 °C兲 using a Hewlett Packard 共HP兲 4156 A
semiconductor parameter analyzer in the range of 20 fA–100
mA and a HP 4284A inductance capacitance resistance
共LCR兲 meter with four different frequencies 共1 MHz, 100
kHz, 10 kHz, and 1 kHz兲 at room temperature, respectively.
RBS measurements were also performed to investigate exact
composition, thickness of TiW metal, and reaction at the
interface.
III. RESULTS AND DISCUSSION
A. C–V characteristics
The Schottky barrier height can be determined from the
voltage intercept in plotting 1/C2
versus the reverse voltage.
Using the following3
⌽B⫽Vi⫹Vn⫹
kT
q
⫺⌬␾, 共2兲
where Vi is the voltage intercept, Vn the depth of the Fermi
level below the conduction band, ⌬␾ is the image force low-
ering of the Schottky barrier, and kT is the thermal energy.
All of the data in the C–V measurements was measured at
room temperature without any sample heating. From C–V
measurements in the range of 1 kHz to 1 MHz, the average
doping concentration of the epilayer under metal for as-
deposited and after annealing was determined to be 1.0
⫾0.13⫻1016
cm⫺3
for n-type and 7.76⫾0.05⫻1015
cm⫺3
for
p-type, respectively. All of our results in the frequency range
1 kHz–1 MHz were consistent, we did not see any frequency
dependence. For as-deposited contacts to n- and p-type, the
Schottky barrier height was 1.23 and 2.11 eV for n-type and
p-type, respectively. The C–V results for as-deposited
Ti0.58W0.42 contacts are shown in Fig. 1 and Table I. From
Fig. 1 and Table I, the sum of the ␾Bn and ␾Bp at room
temperature was about 3.34 eV which was 0.14 eV higher
than the ⬇3.2 eV of the energy band gap (Eg) of 4H–SiC at
room temperature.15
A possible reason for a high Schottky
barrier height 共SBH兲 for our as-deposited Schottky contacts
in C–V measurements can be explained by adding a capaci-
tance in series with depletion capacitance. This additional
capacitance might be created by lattice defects in the silicon
carbide, by a nonuniform interface creating inhomogeneity
in the barrier height, or a thin oxide layer in the interface
region between silicon carbide and the metal layer which
was also reported by Lundberg et al.8,16
The lattice defects
result in a highly resistive region between the metal and the
space charge region. The capacitance in a highly resistive
region will decrease and consequently the determined barrier
height will be higher. Another possible reason is that during
sample preparation a thin oxide layer was created at the in-
terface, which can also act as additional capacitance in C–V
measurements. After annealing at 500 °C the Schottky bar-
rier height from the C–V measurement was estimated to be
1.19 eV for n-type and 1.66 eV for p-type contacts shown in
Fig. 2. The SBH of p-type was decreased ⬇0.45 eV com-
pared to the results of the as-deposited Schottky contacts,
and the sum of the SBH of n- and p-type contacts was 2.85
eV, which is lower than the ideal energy band gap of 4H-
SiC. It might be explained by recovering lattice defects, or
breaking up of the thin oxide at the interface due to the
annealing process at 500 °C during 30 min. It is also indi-
cated that the annealing process for Schottky contacts is
helpful to make better contacts.
B. I–V characteristics
The forward I–V characteristics of a Schottky diode
obey the thermionic emission model given by9
J⫽JS冋exp冉 qV
␩kT冊⫺1册, 共3兲
JS⫽A*T2
exp关⫺q␾B /kT兴, 共4兲
where Js is the saturation current density, ␩ is the ideality
factor, and A* is effective Richardson’s constant 共146
FIG. 1. 1/C2
vs reverse bias voltage (VR) for as-deposited Ti0.58W0.42
Schottky contacts to 共a兲 n-type and 共b兲 p-type 4H–SiC in the frequency
range of 1 kHz–1 MHz at room temperature. The contact area is 3.14
⫻10⫺4
cm2
.
8040 J. Appl. Phys., Vol. 87, No. 11, 1 June 2000 Lee, Zetterling, and Östling
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A cm⫺2
K⫺2
兲.17
The ideality factor 共␩兲 and the saturation cur-
rent density (Js) can be extracted from the experimentally
obtained forward current density–voltage (J–V) character-
istics. By rearranging Eqs. 共3兲 and 共4兲, the Schottky barrier
height (␾B) and ideality factor 共␩兲 are obtained from follow-
ing equations:
␾B⫽
kT
q
ln冉A*T2
JS
冊, 共5兲
␩⫽
q
kT 冉 ⳵V
⳵共ln J兲
冊. 共6兲
1. Forward I–V characteristics
The typical J–V characteristics of as-deposited and
500 °C annealed Ti0.58W0.42 Schottky diodes to both n- and
p-type 4H–SiC as a function of measurement temperature
are shown in Figs. 3 and 4, respectively. For as-deposited
contacts, the average Schottky barrier height was 1.22 and
1.61 eV for n- and p-type in the range of 24–300 °C. The
Schottky barrier height increased slightly for both n- and
p-type with increasing temperature, as shown in Fig. 3. The
ideality factor for the n-type as-deposited contacts was 1.09,
slightly increasing with temperature, indicating that thermi-
onic emission is dominant. For p-type contacts, we obtained
a high ideality factor decreasing from 3.11 to 1.16 with in-
creasing temperature. Our results for p-type having a high
ideality factor are consistent with results reported by Raghu-
nathan et al.6
They suggest that the ideality factor for p-type
contacts cannot be explained with ordinary thermionic emis-
sion theory, although the high value of the ideality factor and
low value of the Schottky barrier height can be explained
with recombination current.9
Recombination current is a
common cause of departure from ideal behavior at low for-
ward voltage regions of Schottky diodes, and the same
mechanism can be used in C–V analysis.9
Lattice defects
created by surface preparation and deposition processes will
serve as a carrier recombination center, adding a recombina-
tion current to the thermionic emission current, and conse-
quently the ideality factor is extremely high and SBH is low.
As shown in Figs. 4 and 5, after annealing at 500 °C in a low
pressure vacuum chamber the Schottky barrier height was
1.22⫾0.03 eV for n-type and 1.93⫾0.01 eV for p-type con-
tacts, respectively. The estimated ideality factors are constant
with value of 1.06 and 1.08 for n- and p-type contacts, re-
spectively in the temperature range 24–300 °C. The annealed
n- and p-type Ti0.58W0.42 Schottky contacts revealed excel-
TABLE I. Results of Schottky barrier height ␾B and ideality factor 共␩兲 measurement of Ti0.58W0.42 contacts to
n- and p-type 4H–SiC using C–V and I–V measurements as a function of the annealing and measurement
temperature; also included is the reverse current density Jrev(A/cm2
) at 100 V of reverse bias voltage.
Annealing
temp.
共°C兲
Measurement
temp.
共°C兲
n-type p-type
C–V
␾B
共eV兲
I–V
␾B
共eV兲 ␩
Jrev
共A/cm2
兲
C–V
␾B
共eV兲
I–V
␾B
共eV兲 ␩
Jrev
共A/cm2
兲
As- 24 1.23 1.22 1.05 8⫻10⫺9
2.11 1.41 3.11 7⫻10⫺8
deposited 100 1.21 1.08 4⫻10⫺8
1.38 3.12 5⫻10⫺7
200 1.22 1.10 5⫻10⫺5
1.66 2.24 2⫻10⫺6
300 1.24 1.12 7⫻10⫺3
2.01 1.16 5⫻10⫺5
500 °C, 24 1.19 1.18 1.10 7⫻10⫺7
1.66 1.91 1.08 4⫻10⫺7
30 min 100 1.22 1.05 5⫻10⫺7
1.93 1.07 6⫻10⫺6
200 1.24 1.03 5⫻10⫺5
1.93 1.08 1⫻10⫺4
300 1.25 1.06 4⫻10⫺3
1.94 1.10 1⫻10⫺3
FIG. 2. 1/C2
vs reverse voltage (VR) for 500 °C annealed Ti0.58W0.42
Schottky contacts to 共a兲 n-type and 共b兲 p-type 4H–SiC in the frequency
range of 1 kHz–1 MHz at room temperature. The annealing was performed
in a low pressure (2⫻10⫺6
Torr) vacuum chamber during 30 min. The
contact area is 3.14⫻10⫺4
cm2
.
8041
J. Appl. Phys., Vol. 87, No. 11, 1 June 2000 Lee, Zetterling, and Östling
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lent rectifying behavior as shown in Fig. 4. One possible
explanation is that the 500 °C annealing process reduces the
barrier inhomogeneities on silicon carbide and improves the
aluminum backside ohmic contacts. From our results, we
observed that the vacuum annealing process helps to im-
prove interface quality, and to reduce the contribution of
recombination current, so that thermionic emission current is
the dominating mechanism. Figure 5 also shows that our
Schottky diodes after annealing at 500 °C support perfectly
the thermionic emission theory. After annealing the average
sum of Schottky contact height was determined to be 3.15
⫾0.04 eV having a slightly increasing tendency in the range
of 24–300 °C. The temperature dependence of SBH for as-
deposited and annealed Ti0.58W0.42 Schottky contacts to n-
and p-type 4H–SiC are plotted in Fig. 6. To our knowledge,
the temperature dependence of the energy band gap in 4H–
SiC has not been published, instead we will use the value
obtained for 6H–SiC.15,18
The dotted line in Fig. 6 was fitted
with energy band gap of 4H–SiC using temperature depen-
dent energy band gap given by the following equation:
Eg共4 H–SiC兲共T兲⫽3.19⫺3.3⫻10⫺4
共T⫺300 K兲 eV. 共7兲
The sum of ␾Bn and ␾Bp are in good agreement with the
fitted energy band gap of 4H silicon carbide as shown in Fig.
6 and perfectly satisfy the Schottky–Mott model after an-
nealing. Figure 6 also shows that our J–V measurements are
in good agreement with C–V measurement for both n- and
p-type at room temperature.
2. Reverse leakage current characteristics
The results of reverse leakage current density (Jrev) at
100 V bias voltage for n- and p-type are summarized in
Table I. For as-deposited contacts at room temperature, the
FIG. 3. Current density (log J) vs forward bias voltage (VF) for as-
deposited Ti0.58W0.42 Schottky contacts to 共a兲 n-type and 共b兲 p-type 4H–SiC
with measurement temperature from 24 to 300 °C.
FIG. 4. Current density (log J) vs forward bias voltage (VF) of Ti0.58W0.42
Schottky contacts to 共a兲 n-type and 共b兲 p-type 4H–SiC with measurement
temperature from 24 to 300 °C. All samples are annealed at 500 °C tempera-
ture for 30 min.
FIG. 5. Ideality factor 共␩兲 distribution of Ti0.58W0.42 Schottky contacts as a
function of temperature for as-deposited and 500 °C annealed contacts to n-
and p-type 4H-SiC.
8042 J. Appl. Phys., Vol. 87, No. 11, 1 June 2000 Lee, Zetterling, and Östling
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reverse leakage current density at a reverse bias voltage of
100 V was determined to be less than 8⫻10⫺9
A/cm2
for
n-type and 7⫻10⫺8
A/cm2
for p-type Schottky contacts. The
reverse leakage current density increased with elevating tem-
perature from 24 to 300 °C for both n- and p-type contacts
and was 7⫻10⫺3
and 5⫻10⫺5
A/cm2
for n- and p-type at
300 °C, respectively. For both n- and p-type annealed con-
tacts the reverse leakage currents were found to be 10–100
times higher than those of as-deposited contacts, which is
consistent with the reduction of barrier height after anneal-
ing. For our contacts the reverse current density increases as
a function of temperature indicating the presence of thermi-
onic emission.
3. Forward voltage drop and on resistance „Ron…
results
The forward voltage drop of the n-type contacts at a
current density of 100 A/cm2
was 1.42 and 1.39 eV for as-
deposited and after annealed contacts at room temperature,
respectively. The temperature dependence of forward voltage
drops for n-type contacts with varying forward current den-
sity 共300, 100, 10, 1 A/cm2
兲 with temperature up to 300 °C is
shown in Fig. 7. For p-type contacts, we have around 100
times lower current density for the same voltage drop used in
n-type contacts due to the higher Schottky barrier height and
much poorer ionization of Al dopants in backside contacts of
4H–SiC. The forward voltage drop is given by5
VF⫽
␩kBT
q
ln冉 JF
A*T2冊⫹␩␾B⫹Ron JF , 共8兲
where VF is the forward voltage drop, ␩ is the ideality factor,
kB is Boltzman’s constant, T is absolute temperature, JF is
the forward current density, A* is the effective Richardson’s
constant 共in our case 146 A cm⫺2
K⫺2
兲,17
␾B is the Schottky
barrier height, and Ron is the series or on-resistance. Using
Eq. 共8兲, we have estimated the on-resistance (Ron) to be 4.3
m⍀ cm2
for n-type and 580 m⍀ cm2
for p-type at 24 °C,
respectively, obtained in high current regions where series
resistance is dominant.
C. RBS measurements
RBS measurements, utilizing 2.4 MeV 4
He⫹
ions, were
performed to investigate TiW film thickness, composition
ratio of Ti and W metal, and interface reaction between TiW
and SiC epilayers. The RBS spectra for both as-deposited
FIG. 8. RBS spectra of the as-deposited and 500 °C annealed Ti0.58W0.42
Schottky contacts to n-type 4H-SiC 共2.4 MeV, 4
He⫹
ion, 7° tilt兲. The arrows
indicate the surface position of the respective elements.
FIG. 6. Temperature dependence of SBH for Ti0.58W0.42 Schottky contacts
to n- and p-type 4H silicon carbide for 共a兲 as-deposited and 共b兲 500 °C
annealed samples. The SBH was extracted from both C–V and I–V mea-
surements. The dotted line shows the energy band gap of 4H-SiC using the
experimental Eq. 共7兲: Eg(4 H–SiC)(T)⫽3.19⫺3.3⫻10⫺4
(T⫺300), where T
is temperature in kelvin 共see Ref. 18兲.
FIG. 7. Temperature dependence of the forward voltage drop at various
forward current densities up to 300 °C for n-type Ti0.58W0.42 Schottky con-
tacts for as-deposited and after annealing at 500 °C.
8043
J. Appl. Phys., Vol. 87, No. 11, 1 June 2000 Lee, Zetterling, and Östling
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and annealed n-type TiW are shown in Fig. 8. From the
results of the RUMP™ simulator19
the composition ratio
Ti:W was 0.58–0.42 and the thickness was 1250 Å. It can be
noted that the nominal composition of the sputter target was
30/70 in weight percent which corresponds to Ti0.59W0.41 in
atom percent. As shown in Fig. 8, no detectable reaction
between silicon carbide and Ti0.58W0.42 contacts happened
after anneal at 500 °C at 30 min.
IV. CONCLUSIONS
Ti0.58W0.42 Schottky contacts have been fabricated using
sputtering and investigated on n- and p-type 4H silicon car-
bide. A summary of our experimental results is given in
Table I. The thermally stable ideality factor of 1.06⫾0.03 for
n-type and 1.08⫾0.01 for p-type was achieved after low
pressure vacuum annealing at 500 °C. The Schottky barrier
height was 1.22⫾0.03 and 1.93⫾0.01 eV for n- and p-type,
respectively in the temperature range of 24–300 °C. I–V
characteristics show that Ti0.58W0.42 Schottky contacts on
both n- and p-type can be perfectly explained by the thermi-
onic emission mechanism after annealing. The Schottky bar-
rier results of C–V measurements also are in good agree-
ment with I–V characteristics of Ti0.58W0.42 Schottky
contacts at room temperature. The sum of the Schottky bar-
rier heights 共␾Bn⫹␾Bp⬇Eg in our case 3.15⫾0.04 eV兲 is in
good agreement with the fitted temperature dependence of
the energy band gap of 4H-SiC and perfectly support the
Schottky–Mott model. Our results also show that there is no
Fermi-level pinning in sputtered Ti0.58W0.42/4H–SiC
Schottky diodes after annealing. We believe that the anneal-
ing process reduces the barrier inhomogeneities of Schottky
contacts and improves the aluminum backside contact.
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8044 J. Appl. Phys., Vol. 87, No. 11, 1 June 2000 Lee, Zetterling, and Östling
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1.373494 ti w

  • 1.
    Schottky diode formationand characterization of titanium tungsten to n- and p-type 4H silicon carbide S.-K. Lee, C.-M. Zetterling, and M. Östling Citation: Journal of Applied Physics 87, 8039 (2000); doi: 10.1063/1.373494 View online: http://dx.doi.org/10.1063/1.373494 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/87/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Deep levels induced by reactive ion etching in n- and p-type 4H–SiC J. Appl. Phys. 108, 023706 (2010); 10.1063/1.3460636 Electrical properties and microstructure of ternary Ge Ti Al ohmic contacts to p -type 4H–SiC J. Appl. Phys. 96, 4976 (2004); 10.1063/1.1797546 Mechanism of ohmic behavior of Al/Ti contacts to p-type 4H-SiC after annealing J. Appl. Phys. 95, 5616 (2004); 10.1063/1.1707215 Ternary TiAlGe ohmic contacts for p-type 4H-SiC J. Appl. Phys. 95, 2187 (2004); 10.1063/1.1643772 Microscopic mapping of specific contact resistances and long-term reliability tests on 4H-silicon carbide using sputtered titanium tungsten contacts for high temperature device applications J. Appl. Phys. 92, 253 (2002); 10.1063/1.1481201 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 146.201.208.22 On: Fri, 26 Sep 2014 04:01:41
  • 2.
    Schottky diode formationand characterization of titanium tungsten to n- and p-type 4H silicon carbide S.-K. Lee,a) C.-M. Zetterling, and M. Östling KTH, Royal Institute of Technology, Department of Electronics, Electrum 229, S-164 40, Kista, Sweden 共Received 2 December 1999; accepted for publication 29 February 2000兲 Titanium tungsten (Ti0.58W0.42) Schottky contacts to both n- and p-type 4H silicon carbide were fabricated using sputtering. The n- as well as p-type Schottky contacts had excellent rectifying characteristics after vacuum annealing at 500 °C with a thermally stable ideality factor of 1.06 ⫾0.03 for n-type and 1.08⫾0.01 for p-type. The measured Schottky barrier height 共SBH兲 was 1.22⫾0.03 eV for n-type and 1.93⫾0.01 eV for p-type in the range of 24–300 °C. Our results of Ti0.58W0.42 Schottky contacts to both n- and p-type can be explained perfectly by thermionic emission theory and also satisfy the Schottky–Mott model in contrast to earlier works. Capacitance–voltage measurements were also performed and the results were in good agreement with those of current–voltage measurements. In addition, the inhomogeneous behavior with higher ideality factor and lower SBH of p-type Ti0.58W0.42 contacts for as-deposited contacts is explained by using a model with contribution of recombination current originated by lattice defects to thermionic emission current. © 2000 American Institute of Physics. 关S0021-8979共00兲05911-9兴 I. INTRODUCTION Silicon carbide has received remarkable attention during the last decade as a promising device material for high tem- perature, high frequency, and high power devices.1,2 Metal– semiconductor contacts have many device applications such as the gate electrode of a field-effect transistor 共MESFETs兲, the source and drain contacts in metal–oxide–semiconductor field-effect transistors 共MOSFETs兲, and the electrodes for high-power impact ionization avalanche transit time 共IMPATT兲 oscillators.3 Many previous studies have mainly been concerned with n-type silicon carbide,4 but investiga- tion is also needed for complementary MESFETs and MOS- FETs. Complementary devices are used in a variety of power electronic applications.5 Raghunathan and Baliga6 also pointed out that p-type Schottky contacts are definitively useful for power electronic applications with the advantage of low current density operation. In the literature, there is very little on p-type Schottky contacts to SiC 共3C–SiC, 6H– SiC, and 4H–SiC兲. In our group Lundberg et al.7,8 have in- vestigated cobalt 共Co兲 and tungsten 共W兲 Schottky contacts for both n- and p-type 6H–SiC. Recently, Raghunathan and Baliga6 reported Ti/Al Schottky contacts to p-type 4H–SiC and 6H–SiC. They have achieved a Schottky barrier height of 1.4–1.5 and 1.8–2.0 eV for p-type 4H and 6H–SiC, re- spectively using both current–voltage (I–V) and capacitance–voltage (C–V) measurements, but with high ideality factors 共2.2 for 4H–SiC and 1.9 for 6H–SiC兲 com- pared to n-type Schottky contacts. They suggested that the reason for the high ideality factor for p-type Schottky con- tacts was because thermionic emission is not the dominant mechanism. Using Schottky–Mott theory9 it is expected that the sum of the barrier heights to n- and p-type semiconduc- tors would be equal to the energy band gap of a semiconduc- tor for any set of semiconductor and metal, that is Eg⫽⌽Bn⫹⌽Bp . 共1兲 Unfortunately, most of the earlier works have not satisfied Eq. 共1兲. TiW has been used extensively as a diffusion barrier for Al based metallization in silicon technology.10 They are also used for ohmic contacts to 3C–SiC11 and 6H–SiC.12,13 However, there is no previous work on the performance of TiW Schottky diodes to n- and p-type 4H–SiC. In this article, we have investigated the characteristics of Schottky contacts using sputtered titanium tungsten (Ti0.58W0.42) as a basic metal for studying n- and p-type 4H- SiC, and compared the results to Schottky–Mott theory. II. EXPERIMENTAL DETAILS Both n- and p-type Si face 4H–SiC substrates (⬃1018 cm⫺3 ) with 4 ␮m thick lightly doped epitaxial layers (1.2–1.4⫻1016 cm⫺3 ) were purchased from CREE Research Inc.14 The wafers were cleaned sequentially with two differ- ent cleaning recipes 共so called oxidation and etching兲 such as H2SO4:H2O2 共2.5:1兲 with temperature ⬎80 °C during 5 min and H2O:CH3CH共OH兲CH3:HF 共100:3:1兲 during 100 s prior to the sputtering process. After each cleaning process, the wafers were rinsed with deionized 共DI兲 water during 5 min. The cleaning was completed by a dip in 5% diluted HF so- lution and a DI water rinse to ensure that the native oxide was kept to a minimum prior to loading a wafer in the sput- tering chamber. The metallization was done by sputtering with a compound TiW target 共nominally 30:70 weight per- cent ratio兲. The sputtering was performed in a dc magnetron sputter under deposition conditions of 3 kW power, 120 °C substrate temperature, 69 sccm of Ar gas flow, 5.2 ⫻10⫺7 Torr base pressure, and 5 mTorr deposition pressure. About 1250 Å Ti0.58W0.42 metal was deposited on n- and p-type 4H–SiC and a blanket piece was also deposited si- multaneously for Rutherford backscattering spectrometry a兲 Electronic mail: lee@ele.kth.se JOURNAL OF APPLIED PHYSICS VOLUME 87, NUMBER 11 1 JUNE 2000 8039 0021-8979/2000/87(11)/8039/6/$17.00 © 2000 American Institute of Physics [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 146.201.208.22 On: Fri, 26 Sep 2014 04:01:41
  • 3.
    共RBS兲 measurement. Differentsizes of circular Schottky contacts 共diameter 50, 100, 200, 400, and 1000 ␮m兲 were fabricated using a standard photolithography procedure with photoresist mask. Ti0.58W0.42 was wet etched using a mixture of NH3:H2O2 共1:5兲 with an etching rate of 300 Å/min. After Ti0.58W0.42 deposition, a 1 ␮m thick aluminum film was also deposited on the highly doped backside substrate to form a large area backside ohmic contact, using sputtering under similar conditions. Some of the samples were annealed in a low pressure (2⫻10⫺6 Torr) vacuum chamber during 30 min at 500 °C. Both I–V and C–V measurements were per- formed on different diodes for each temperature 共24, 100, 200, and 300 °C兲 using a Hewlett Packard 共HP兲 4156 A semiconductor parameter analyzer in the range of 20 fA–100 mA and a HP 4284A inductance capacitance resistance 共LCR兲 meter with four different frequencies 共1 MHz, 100 kHz, 10 kHz, and 1 kHz兲 at room temperature, respectively. RBS measurements were also performed to investigate exact composition, thickness of TiW metal, and reaction at the interface. III. RESULTS AND DISCUSSION A. C–V characteristics The Schottky barrier height can be determined from the voltage intercept in plotting 1/C2 versus the reverse voltage. Using the following3 ⌽B⫽Vi⫹Vn⫹ kT q ⫺⌬␾, 共2兲 where Vi is the voltage intercept, Vn the depth of the Fermi level below the conduction band, ⌬␾ is the image force low- ering of the Schottky barrier, and kT is the thermal energy. All of the data in the C–V measurements was measured at room temperature without any sample heating. From C–V measurements in the range of 1 kHz to 1 MHz, the average doping concentration of the epilayer under metal for as- deposited and after annealing was determined to be 1.0 ⫾0.13⫻1016 cm⫺3 for n-type and 7.76⫾0.05⫻1015 cm⫺3 for p-type, respectively. All of our results in the frequency range 1 kHz–1 MHz were consistent, we did not see any frequency dependence. For as-deposited contacts to n- and p-type, the Schottky barrier height was 1.23 and 2.11 eV for n-type and p-type, respectively. The C–V results for as-deposited Ti0.58W0.42 contacts are shown in Fig. 1 and Table I. From Fig. 1 and Table I, the sum of the ␾Bn and ␾Bp at room temperature was about 3.34 eV which was 0.14 eV higher than the ⬇3.2 eV of the energy band gap (Eg) of 4H–SiC at room temperature.15 A possible reason for a high Schottky barrier height 共SBH兲 for our as-deposited Schottky contacts in C–V measurements can be explained by adding a capaci- tance in series with depletion capacitance. This additional capacitance might be created by lattice defects in the silicon carbide, by a nonuniform interface creating inhomogeneity in the barrier height, or a thin oxide layer in the interface region between silicon carbide and the metal layer which was also reported by Lundberg et al.8,16 The lattice defects result in a highly resistive region between the metal and the space charge region. The capacitance in a highly resistive region will decrease and consequently the determined barrier height will be higher. Another possible reason is that during sample preparation a thin oxide layer was created at the in- terface, which can also act as additional capacitance in C–V measurements. After annealing at 500 °C the Schottky bar- rier height from the C–V measurement was estimated to be 1.19 eV for n-type and 1.66 eV for p-type contacts shown in Fig. 2. The SBH of p-type was decreased ⬇0.45 eV com- pared to the results of the as-deposited Schottky contacts, and the sum of the SBH of n- and p-type contacts was 2.85 eV, which is lower than the ideal energy band gap of 4H- SiC. It might be explained by recovering lattice defects, or breaking up of the thin oxide at the interface due to the annealing process at 500 °C during 30 min. It is also indi- cated that the annealing process for Schottky contacts is helpful to make better contacts. B. I–V characteristics The forward I–V characteristics of a Schottky diode obey the thermionic emission model given by9 J⫽JS冋exp冉 qV ␩kT冊⫺1册, 共3兲 JS⫽A*T2 exp关⫺q␾B /kT兴, 共4兲 where Js is the saturation current density, ␩ is the ideality factor, and A* is effective Richardson’s constant 共146 FIG. 1. 1/C2 vs reverse bias voltage (VR) for as-deposited Ti0.58W0.42 Schottky contacts to 共a兲 n-type and 共b兲 p-type 4H–SiC in the frequency range of 1 kHz–1 MHz at room temperature. The contact area is 3.14 ⫻10⫺4 cm2 . 8040 J. Appl. Phys., Vol. 87, No. 11, 1 June 2000 Lee, Zetterling, and Östling [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 146.201.208.22 On: Fri, 26 Sep 2014 04:01:41
  • 4.
    A cm⫺2 K⫺2 兲.17 The idealityfactor 共␩兲 and the saturation cur- rent density (Js) can be extracted from the experimentally obtained forward current density–voltage (J–V) character- istics. By rearranging Eqs. 共3兲 and 共4兲, the Schottky barrier height (␾B) and ideality factor 共␩兲 are obtained from follow- ing equations: ␾B⫽ kT q ln冉A*T2 JS 冊, 共5兲 ␩⫽ q kT 冉 ⳵V ⳵共ln J兲 冊. 共6兲 1. Forward I–V characteristics The typical J–V characteristics of as-deposited and 500 °C annealed Ti0.58W0.42 Schottky diodes to both n- and p-type 4H–SiC as a function of measurement temperature are shown in Figs. 3 and 4, respectively. For as-deposited contacts, the average Schottky barrier height was 1.22 and 1.61 eV for n- and p-type in the range of 24–300 °C. The Schottky barrier height increased slightly for both n- and p-type with increasing temperature, as shown in Fig. 3. The ideality factor for the n-type as-deposited contacts was 1.09, slightly increasing with temperature, indicating that thermi- onic emission is dominant. For p-type contacts, we obtained a high ideality factor decreasing from 3.11 to 1.16 with in- creasing temperature. Our results for p-type having a high ideality factor are consistent with results reported by Raghu- nathan et al.6 They suggest that the ideality factor for p-type contacts cannot be explained with ordinary thermionic emis- sion theory, although the high value of the ideality factor and low value of the Schottky barrier height can be explained with recombination current.9 Recombination current is a common cause of departure from ideal behavior at low for- ward voltage regions of Schottky diodes, and the same mechanism can be used in C–V analysis.9 Lattice defects created by surface preparation and deposition processes will serve as a carrier recombination center, adding a recombina- tion current to the thermionic emission current, and conse- quently the ideality factor is extremely high and SBH is low. As shown in Figs. 4 and 5, after annealing at 500 °C in a low pressure vacuum chamber the Schottky barrier height was 1.22⫾0.03 eV for n-type and 1.93⫾0.01 eV for p-type con- tacts, respectively. The estimated ideality factors are constant with value of 1.06 and 1.08 for n- and p-type contacts, re- spectively in the temperature range 24–300 °C. The annealed n- and p-type Ti0.58W0.42 Schottky contacts revealed excel- TABLE I. Results of Schottky barrier height ␾B and ideality factor 共␩兲 measurement of Ti0.58W0.42 contacts to n- and p-type 4H–SiC using C–V and I–V measurements as a function of the annealing and measurement temperature; also included is the reverse current density Jrev(A/cm2 ) at 100 V of reverse bias voltage. Annealing temp. 共°C兲 Measurement temp. 共°C兲 n-type p-type C–V ␾B 共eV兲 I–V ␾B 共eV兲 ␩ Jrev 共A/cm2 兲 C–V ␾B 共eV兲 I–V ␾B 共eV兲 ␩ Jrev 共A/cm2 兲 As- 24 1.23 1.22 1.05 8⫻10⫺9 2.11 1.41 3.11 7⫻10⫺8 deposited 100 1.21 1.08 4⫻10⫺8 1.38 3.12 5⫻10⫺7 200 1.22 1.10 5⫻10⫺5 1.66 2.24 2⫻10⫺6 300 1.24 1.12 7⫻10⫺3 2.01 1.16 5⫻10⫺5 500 °C, 24 1.19 1.18 1.10 7⫻10⫺7 1.66 1.91 1.08 4⫻10⫺7 30 min 100 1.22 1.05 5⫻10⫺7 1.93 1.07 6⫻10⫺6 200 1.24 1.03 5⫻10⫺5 1.93 1.08 1⫻10⫺4 300 1.25 1.06 4⫻10⫺3 1.94 1.10 1⫻10⫺3 FIG. 2. 1/C2 vs reverse voltage (VR) for 500 °C annealed Ti0.58W0.42 Schottky contacts to 共a兲 n-type and 共b兲 p-type 4H–SiC in the frequency range of 1 kHz–1 MHz at room temperature. The annealing was performed in a low pressure (2⫻10⫺6 Torr) vacuum chamber during 30 min. The contact area is 3.14⫻10⫺4 cm2 . 8041 J. Appl. Phys., Vol. 87, No. 11, 1 June 2000 Lee, Zetterling, and Östling [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 146.201.208.22 On: Fri, 26 Sep 2014 04:01:41
  • 5.
    lent rectifying behavioras shown in Fig. 4. One possible explanation is that the 500 °C annealing process reduces the barrier inhomogeneities on silicon carbide and improves the aluminum backside ohmic contacts. From our results, we observed that the vacuum annealing process helps to im- prove interface quality, and to reduce the contribution of recombination current, so that thermionic emission current is the dominating mechanism. Figure 5 also shows that our Schottky diodes after annealing at 500 °C support perfectly the thermionic emission theory. After annealing the average sum of Schottky contact height was determined to be 3.15 ⫾0.04 eV having a slightly increasing tendency in the range of 24–300 °C. The temperature dependence of SBH for as- deposited and annealed Ti0.58W0.42 Schottky contacts to n- and p-type 4H–SiC are plotted in Fig. 6. To our knowledge, the temperature dependence of the energy band gap in 4H– SiC has not been published, instead we will use the value obtained for 6H–SiC.15,18 The dotted line in Fig. 6 was fitted with energy band gap of 4H–SiC using temperature depen- dent energy band gap given by the following equation: Eg共4 H–SiC兲共T兲⫽3.19⫺3.3⫻10⫺4 共T⫺300 K兲 eV. 共7兲 The sum of ␾Bn and ␾Bp are in good agreement with the fitted energy band gap of 4H silicon carbide as shown in Fig. 6 and perfectly satisfy the Schottky–Mott model after an- nealing. Figure 6 also shows that our J–V measurements are in good agreement with C–V measurement for both n- and p-type at room temperature. 2. Reverse leakage current characteristics The results of reverse leakage current density (Jrev) at 100 V bias voltage for n- and p-type are summarized in Table I. For as-deposited contacts at room temperature, the FIG. 3. Current density (log J) vs forward bias voltage (VF) for as- deposited Ti0.58W0.42 Schottky contacts to 共a兲 n-type and 共b兲 p-type 4H–SiC with measurement temperature from 24 to 300 °C. FIG. 4. Current density (log J) vs forward bias voltage (VF) of Ti0.58W0.42 Schottky contacts to 共a兲 n-type and 共b兲 p-type 4H–SiC with measurement temperature from 24 to 300 °C. All samples are annealed at 500 °C tempera- ture for 30 min. FIG. 5. Ideality factor 共␩兲 distribution of Ti0.58W0.42 Schottky contacts as a function of temperature for as-deposited and 500 °C annealed contacts to n- and p-type 4H-SiC. 8042 J. Appl. Phys., Vol. 87, No. 11, 1 June 2000 Lee, Zetterling, and Östling [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 146.201.208.22 On: Fri, 26 Sep 2014 04:01:41
  • 6.
    reverse leakage currentdensity at a reverse bias voltage of 100 V was determined to be less than 8⫻10⫺9 A/cm2 for n-type and 7⫻10⫺8 A/cm2 for p-type Schottky contacts. The reverse leakage current density increased with elevating tem- perature from 24 to 300 °C for both n- and p-type contacts and was 7⫻10⫺3 and 5⫻10⫺5 A/cm2 for n- and p-type at 300 °C, respectively. For both n- and p-type annealed con- tacts the reverse leakage currents were found to be 10–100 times higher than those of as-deposited contacts, which is consistent with the reduction of barrier height after anneal- ing. For our contacts the reverse current density increases as a function of temperature indicating the presence of thermi- onic emission. 3. Forward voltage drop and on resistance „Ron… results The forward voltage drop of the n-type contacts at a current density of 100 A/cm2 was 1.42 and 1.39 eV for as- deposited and after annealed contacts at room temperature, respectively. The temperature dependence of forward voltage drops for n-type contacts with varying forward current den- sity 共300, 100, 10, 1 A/cm2 兲 with temperature up to 300 °C is shown in Fig. 7. For p-type contacts, we have around 100 times lower current density for the same voltage drop used in n-type contacts due to the higher Schottky barrier height and much poorer ionization of Al dopants in backside contacts of 4H–SiC. The forward voltage drop is given by5 VF⫽ ␩kBT q ln冉 JF A*T2冊⫹␩␾B⫹Ron JF , 共8兲 where VF is the forward voltage drop, ␩ is the ideality factor, kB is Boltzman’s constant, T is absolute temperature, JF is the forward current density, A* is the effective Richardson’s constant 共in our case 146 A cm⫺2 K⫺2 兲,17 ␾B is the Schottky barrier height, and Ron is the series or on-resistance. Using Eq. 共8兲, we have estimated the on-resistance (Ron) to be 4.3 m⍀ cm2 for n-type and 580 m⍀ cm2 for p-type at 24 °C, respectively, obtained in high current regions where series resistance is dominant. C. RBS measurements RBS measurements, utilizing 2.4 MeV 4 He⫹ ions, were performed to investigate TiW film thickness, composition ratio of Ti and W metal, and interface reaction between TiW and SiC epilayers. The RBS spectra for both as-deposited FIG. 8. RBS spectra of the as-deposited and 500 °C annealed Ti0.58W0.42 Schottky contacts to n-type 4H-SiC 共2.4 MeV, 4 He⫹ ion, 7° tilt兲. The arrows indicate the surface position of the respective elements. FIG. 6. Temperature dependence of SBH for Ti0.58W0.42 Schottky contacts to n- and p-type 4H silicon carbide for 共a兲 as-deposited and 共b兲 500 °C annealed samples. The SBH was extracted from both C–V and I–V mea- surements. The dotted line shows the energy band gap of 4H-SiC using the experimental Eq. 共7兲: Eg(4 H–SiC)(T)⫽3.19⫺3.3⫻10⫺4 (T⫺300), where T is temperature in kelvin 共see Ref. 18兲. FIG. 7. Temperature dependence of the forward voltage drop at various forward current densities up to 300 °C for n-type Ti0.58W0.42 Schottky con- tacts for as-deposited and after annealing at 500 °C. 8043 J. Appl. Phys., Vol. 87, No. 11, 1 June 2000 Lee, Zetterling, and Östling [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 146.201.208.22 On: Fri, 26 Sep 2014 04:01:41
  • 7.
    and annealed n-typeTiW are shown in Fig. 8. From the results of the RUMP™ simulator19 the composition ratio Ti:W was 0.58–0.42 and the thickness was 1250 Å. It can be noted that the nominal composition of the sputter target was 30/70 in weight percent which corresponds to Ti0.59W0.41 in atom percent. As shown in Fig. 8, no detectable reaction between silicon carbide and Ti0.58W0.42 contacts happened after anneal at 500 °C at 30 min. IV. CONCLUSIONS Ti0.58W0.42 Schottky contacts have been fabricated using sputtering and investigated on n- and p-type 4H silicon car- bide. A summary of our experimental results is given in Table I. The thermally stable ideality factor of 1.06⫾0.03 for n-type and 1.08⫾0.01 for p-type was achieved after low pressure vacuum annealing at 500 °C. The Schottky barrier height was 1.22⫾0.03 and 1.93⫾0.01 eV for n- and p-type, respectively in the temperature range of 24–300 °C. I–V characteristics show that Ti0.58W0.42 Schottky contacts on both n- and p-type can be perfectly explained by the thermi- onic emission mechanism after annealing. The Schottky bar- rier results of C–V measurements also are in good agree- ment with I–V characteristics of Ti0.58W0.42 Schottky contacts at room temperature. The sum of the Schottky bar- rier heights 共␾Bn⫹␾Bp⬇Eg in our case 3.15⫾0.04 eV兲 is in good agreement with the fitted temperature dependence of the energy band gap of 4H-SiC and perfectly support the Schottky–Mott model. Our results also show that there is no Fermi-level pinning in sputtered Ti0.58W0.42/4H–SiC Schottky diodes after annealing. We believe that the anneal- ing process reduces the barrier inhomogeneities of Schottky contacts and improves the aluminum backside contact. 1 K. M. Geib, C. Wilson, R. G. Long, and C. W. Wilmsen, J. Appl. Phys. 68, 2796 共1990兲. 2 R. J. Trew, Phys. Status Solidi A 162, 409 共1997兲. 3 S. M. Sze, Physics of Semiconductor Devices, 2nd ed. 共Wiley, New York, 1981兲. 4 L. M. Porter and R. F. Davis, Mater. Sci. Eng., B 34, 83 共1995兲. 5 B. J. Baliga, Modern Power Devices 共Wiley, New York, 1987兲. 6 R. Raghunathan and B. J. Baliga, IEEE Electron Device Lett. 19, 71 共1998兲. 7 N. Lundberg, C. M. Zetterling, and M. Östling, Appl. Surf. Sci. 73, 316 共1993兲. 8 N. Lundberg, M. Östling, P. Tägtström, and U. Jansson, J. Electrochem. Soc. 143, 1662 共1996兲. 9 E. H. Rhoderick and R. H. Williams, Metal-Semiconductor Contacts, 2nd ed. 共Clarendon, Oxford, 1988兲, Vol. 19. 10 V. Hoffman, Semicond. Sci. Technol. 26, 119 共1983兲. 11 J. Kriz, K. Gottfried, T. Scholz, C. Kaufmann, and T. Gebner, Mater. Sci. Eng., B 46, 180 共1997兲. 12 J. Crofton, J. R. Williams, M. J. Bozack, and P. A. Barnes, Inst. Phys. Conf. Ser. 137, 719 共1994兲. 13 J. Crofton, J. M. Ferrero, P. A. Barnes, J. R. Williams, M. J. Bozack, C. C. Tin, C. D. Ellis, J. A. Spitznagel, and P. G. McMullin, in Amorphous and Crystalline Silicon Carbide IV, edited by C. Y. Yang, M. M. Rahman, and G. L. Harris 共Springer, Berlin, 1992兲, p. 163. 14 CREE Research Inc., Durham, NC. 15 W. J. Choyke and L. Patrick, Phys. Rev. 105, 1721 共1957兲. 16 N. Lundberg and M. Östling, Solid-State Electron. 39, 1559 共1996兲. 17 A. Itoh, T. Kimoto, and H. Matsunami, IEEE Electron Device Lett. 16, 280 共1995兲. 18 M. Ruff, H. Mitlehner, and R. Helbig, IEEE Trans. Electron Devices 41, 1040 共1994兲. 19 Computer Graphic Service Ltd., Ithaca, NY. 8044 J. Appl. Phys., Vol. 87, No. 11, 1 June 2000 Lee, Zetterling, and Östling [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 146.201.208.22 On: Fri, 26 Sep 2014 04:01:41