On a feature of temperature dependence of contact resistivity for ohmic contacts to n-Si with an n⁺ -n doping step
We present both theoretical and experimental temperature dependences of contact resistivity ρс(Т) for ohmic contacts to the silicon n⁺ -n-structures whose n⁺ -layer was formed using phosphorus diffusion or ion implantation. The ρс(Т) dependence was measured in the 125–375 K temperature range wi...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2014
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| Zitieren: | On a feature of temperature dependence of contact resistivity for ohmic contacts to n-Si with an n⁺ -n doping step / A.V. Sachenko, A.E. Belyaev, N.S. Boltovets, A.O. Vinogradov, V.A. Pilipenko, T.V. Petlitskaya, V.M. Anischik, R.V. Konakova, T.V. Korostinskaya, V.P. Kostylyov, Ya.Ya. Kudryk, V.G. Lyapin, P.N. Romanets, V.N. Sheremet // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2014. — Т. 17, № 1. — С. 1-6. — Бібліогр.: 15 назв. — англ. |
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irk-123456789-1177862017-05-27T03:06:22Z On a feature of temperature dependence of contact resistivity for ohmic contacts to n-Si with an n⁺ -n doping step Sachenko, A.V. Belyaev, A.E. Boltovets, N.S. Vinogradov, A.O. Pilipenko, V.A. Petlitskaya, T.V. Anischik, V.M. Konakova, R.V. Korostinskaya, T.V. Kostylyov, V.P. Kudryk, Ya.Ya. Lyapin, V.G. Romanets, P.N. Sheremet, V.N. We present both theoretical and experimental temperature dependences of contact resistivity ρс(Т) for ohmic contacts to the silicon n⁺ -n-structures whose n⁺ -layer was formed using phosphorus diffusion or ion implantation. The ρс(Т) dependence was measured in the 125–375 K temperature range with the transmission line method, with allowance made for conduction in both the n⁺ -layer and n⁺ -n doping step. 2014 Article On a feature of temperature dependence of contact resistivity for ohmic contacts to n-Si with an n⁺ -n doping step / A.V. Sachenko, A.E. Belyaev, N.S. Boltovets, A.O. Vinogradov, V.A. Pilipenko, T.V. Petlitskaya, V.M. Anischik, R.V. Konakova, T.V. Korostinskaya, V.P. Kostylyov, Ya.Ya. Kudryk, V.G. Lyapin, P.N. Romanets, V.N. Sheremet // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2014. — Т. 17, № 1. — С. 1-6. — Бібліогр.: 15 назв. — англ. 1560-8034 PACS 73.40.Ns, 73.40.Cg, 85.40.-e http://dspace.nbuv.gov.ua/handle/123456789/117786 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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| description |
We present both theoretical and experimental temperature dependences of
contact resistivity ρс(Т) for ohmic contacts to the silicon n⁺
-n-structures whose n⁺
-layer
was formed using phosphorus diffusion or ion implantation. The ρс(Т) dependence was
measured in the 125–375 K temperature range with the transmission line method, with
allowance made for conduction in both the n⁺
-layer and n⁺
-n doping step. |
| format |
Article |
| author |
Sachenko, A.V. Belyaev, A.E. Boltovets, N.S. Vinogradov, A.O. Pilipenko, V.A. Petlitskaya, T.V. Anischik, V.M. Konakova, R.V. Korostinskaya, T.V. Kostylyov, V.P. Kudryk, Ya.Ya. Lyapin, V.G. Romanets, P.N. Sheremet, V.N. |
| spellingShingle |
Sachenko, A.V. Belyaev, A.E. Boltovets, N.S. Vinogradov, A.O. Pilipenko, V.A. Petlitskaya, T.V. Anischik, V.M. Konakova, R.V. Korostinskaya, T.V. Kostylyov, V.P. Kudryk, Ya.Ya. Lyapin, V.G. Romanets, P.N. Sheremet, V.N. On a feature of temperature dependence of contact resistivity for ohmic contacts to n-Si with an n⁺ -n doping step Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Sachenko, A.V. Belyaev, A.E. Boltovets, N.S. Vinogradov, A.O. Pilipenko, V.A. Petlitskaya, T.V. Anischik, V.M. Konakova, R.V. Korostinskaya, T.V. Kostylyov, V.P. Kudryk, Ya.Ya. Lyapin, V.G. Romanets, P.N. Sheremet, V.N. |
| author_sort |
Sachenko, A.V. |
| title |
On a feature of temperature dependence of contact resistivity for ohmic contacts to n-Si with an n⁺ -n doping step |
| title_short |
On a feature of temperature dependence of contact resistivity for ohmic contacts to n-Si with an n⁺ -n doping step |
| title_full |
On a feature of temperature dependence of contact resistivity for ohmic contacts to n-Si with an n⁺ -n doping step |
| title_fullStr |
On a feature of temperature dependence of contact resistivity for ohmic contacts to n-Si with an n⁺ -n doping step |
| title_full_unstemmed |
On a feature of temperature dependence of contact resistivity for ohmic contacts to n-Si with an n⁺ -n doping step |
| title_sort |
on a feature of temperature dependence of contact resistivity for ohmic contacts to n-si with an n⁺ -n doping step |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/117786 |
| citation_txt |
On a feature of temperature dependence of contact resistivity for ohmic contacts to n-Si with an n⁺ -n doping step / A.V. Sachenko, A.E. Belyaev, N.S. Boltovets, A.O. Vinogradov, V.A. Pilipenko, T.V. Petlitskaya, V.M. Anischik, R.V. Konakova, T.V. Korostinskaya, V.P. Kostylyov, Ya.Ya. Kudryk, V.G. Lyapin, P.N. Romanets, V.N. Sheremet // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2014. — Т. 17, № 1. — С. 1-6. — Бібліогр.: 15 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2014. V. 17, N 1. P. 1-6.
© 2014, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
1
PACS 73.40.Ns, 73.40.Cg, 85.40.-e
On a feature of temperature dependence of contact resistivity
for ohmic contacts to n-Si with an n+-n doping step
A.V. Sachenko1, A.E. Belyaev1, N.S. Boltovets2, A.O. Vinogradov1, V.A. Pilipenko3, T.V. Petlitskaya3,
V.M. Anischik4, R.V. Konakova1, T.V. Korostinskaya2, V.P. Kostylyov1, Ya.Ya. Kudryk1, V.G. Lyapin1,
P.N. Romanets1, V.N. Sheremet1
1V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, 03028 Kyiv, Ukraine
Phone: 38(044) 525-61-82; Fax: 38(044) 525-83-42; e-mail: konakova@isp.kiev.ua
2State Enterprise Research Institute “Orion”, 03057 Kyiv, Ukraine
3State Centre “Belmicroanaliz”, subsidiary of R&D Centre “Belmicrosystems”
Open Joint Stock Company “Integral”, 220108 Minsk, Belarus
4Belarusian State University, 220030 Minsk, Belarus
Abstract. We present both theoretical and experimental temperature dependences of
contact resistivity ρс(Т) for ohmic contacts to the silicon n+-n-structures whose n+-layer
was formed using phosphorus diffusion or ion implantation. The ρс(Т) dependence was
measured in the 125–375 K temperature range with the transmission line method, with
allowance made for conduction in both the n+-layer and n+-n doping step.
Keywords: ohmic contact, metallization, doping step.
Manuscript received 24.10.13; revised version received 11.12.13; accepted for
publication 20.03.14; published online 31.03.14.
1. Introduction
At present there exists a fixed notion of the mechanisms
of current flow in ohmic metal-semiconductor contacts
as well as the processes of minimization of contact
resistivity and their contribution to the parameters of
semiconductor devices and integrated circuits [1]. This
notion asserts that contact resistivity ρс should be
minimal and demonstrate thermal and electrical stability,
and I – V curves of ohmic contacts must be linear and
symmetric. As a rule, ρс of such contacts is described
within either field emission (ρс does not depend on
temperature) or thermofield emission (ρс decreases with
temperature).
However, recent investigations [2-9] showed that in
some cases ρс does not demonstrate the above behavior.
To illustrate, for ohmic contacts to wide-gap
semiconductors with high dislocation density it was
shown in [2-4, 8, 9] that ρс increases with temperature.
Such growing dependences ρс(Т) were obtained in [5-7]
for ohmic contacts to lapped as well as polished n-Si, at
presence of high density of structural defects in the Si
near-contact region. In that case, calculation of the
number of defects from etching pits made for lapped
silicon gave ~107 cm–2. According to the model
proposed in [7, 8], this value turned out sufficient for
description of growing dependence ρс(Т).
Along with the above-mentioned, some other
conditions of ohmic contact formation may lead to ρс
growth with temperature. For instance, use (as an ohmic
contact) of an isotype n+-n junction (n+-n doping step) or
p+-p junction – analog of metal-semiconductor contact in
which degenerate n+-semiconductor (or p+-
semiconductor) acts as a metal. In this case, we deal
practically with a Schottky diode without a potential
barrier [10]. In what follows, we consider a model of
such ohmic contact and its experimental testing.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2014. V. 17, N 1. P. 1-6.
© 2014, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
2
2. Model of ohmic contact with a doping step
Let us consider a model of ohmic contact with an n+-n
doping step in the near-contact region, with electrons in
the heavily doped n+-layer being degenerate. This
situation is realized in manufacturing technology for
silicon devices, in particular, IMPATT diodes. In that
case, the thickness n
W of the heavily doped region
with electron concentration
1n exceeds the Schottky
layer thickness WSh, and the doping level is over the
effective density of states Nc in the conduction band. Just
this situation means that electrons in the heavily doped
region are degenerate.
In this work, we made an analytical calculation of
the ρc(T) curve for Si-based ohmic contacts with an n+-n
doping step in the limiting case when the contact band
diagram is of the form shown in Fig. 1. One can see that
the thickness n
W of the heavily doped region with
electron concentration
1n exceeds the Schottky layer
thickness WSh ( ShWW
n
), and the doping level
exceeds the effective electron density of states in the
conduction band Nc ( cNn
1 ). This means that
electrons in the heavily doped region are degenerate.
Figs 2a and 2b present band diagrams for contacts
to Si with a doping step, at two values of heavily doped
layer thickness n
W : 5 and 10 nm. In our calculations,
we used the following values: 316
2 cm10 n ,
1n =
2·1018, 5·1018, 1019, 2·1019 and 319 cm105 . To obtain
the band diagrams, we solved the Poisson equations for
the heavily doped and lightly doped regions (both with
allowance made for electron degeneracy) of the form
)(
1
0
2
2
x
dx
d
s
, (1)
where
.
exp
1exp2
8
F
21
0 F
2/1
3
2/3
kT
qEE
WxnxWn
kT
qE
z
z
dz
Tm
qx
a
nn
p
(2)
Here EF is the Fermi energy, Ea ≈ 0.005 eV, q –
elementary charge.
The barrier height at the contact (or, more exactly,
the diffusion potential φc) was preset as 0.4 V. The
electrostatic potential was considered to vanish as x.
The solutions of the Poisson equation in the heavily and
lightly doped regions were matched at the boundary
n
Wx , that is to say, the values of potentials, as well
as their derivatives (i.e., the electric field strengths),
were matched, respectively.
Naturally all the
1n values taken for calculation
obeyed the inequality cNn
1 . However, since the
Schottky layer thicknesses in the heavily doped region
met the condition ShWW
n
at all doping levels, there
0 10 20 30
-0.4
-0.2
0.0
0.2
x, nm
Fermi Energy
(
x)
, V
Fig. 1. Band diagram of ohmic contact with an n+-n doping
step; n+~ 51020 cm–3; n ~ 1016 cm–3; Wn+~ 0.01 m.
0 10 20 30
-0.4
-0.2
0.0
0.2
x, nm
2·1019
5·1020
2·1020 Fermi Energy
1020
T=300 K
W
n+
=5nm
(
x)
,
V
a)
5·1019
N
d
(x>5nm)=1016 cm-3
0 10 20 30
-0,4
-0,2
0,0
0,2 2·1019
5·1019
1020 2·1020
x, nm
5·1020
Fermi Energy
T=300K
W
n+
=10nm
(
x)
, V
b)
N
d
(x>10nm)=1016cm-3
Fig. 2. Band diagrams of contacts with a doping step for Si at
two thickness values of heavily doped layer Wn+: 5 nm (a) and
10 nm (b); n+: 51019, 1020, 21020 and 51020 cm–3 at
n2 = 1016 cm–3.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2014. V. 17, N 1. P. 1-6.
© 2014, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
3
was no portion of x independent from the coordinate
x shown in Fig. 1.
One should note that, depending on the behavior of
potential x in the near-contact region, the contact
will be either rectifying (in the case of monotonic
dependence of x on coordinate x) or ohmic (in the
case of a strongly pronounced non-monotony of x ).
In the latter case, the contact resistivity may be presented
as a sum of two terms (corresponding to series
resistances):
21 ccc . (3)
Here, ρc1 is the contact resistivity related to
thermofield passage of electrons through the barrier at
the interface between a heavily doped semiconductor
and metal, and
cn
Dc
c Nk
TAL
TnAq
Nk *
2
*2 1 (4)
is the effective contact resistance of the lightly doped
region in the limiting case of contact energy band being
of the form shown in Fig. 1. Here k is the Boltzmann
constant, A* – effective Richardson constant, μn –
electron mobility in the lightly doped region,
LD = (ε0εs kT / 2q2n2)
0.5 – Debye shielding length for the
lightly doped region. It should be noted that Eq. (4) was
obtained with allowance made for the results of [10] and
[11]: it takes into account both the diffusion and
emission terms in the current flowing through the lightly
doped region.
Thus, if the inequality ρc2 > ρc1 holds, then contact
is purely ohmic. In that case, band bending in the lightly
doped region is accumulation rather than depletion, so
the total voltage applied to the contact is dropped across
the neutral bulk, thus ensuring contact ohmicity. The
electron mobility μn in the region of light doping was
calculated with allowance made for electron scattering
by charged impurities as well as by intervalley and
acoustic phonons [12]. It was assumed that dislocation
density in the lightly doped region is sufficiently low
and does not affect electron mobility. The expressions
for μn calculation are given in [8].
Now let us dwell on an analysis of temperature
dependence of contact resistivity ρc2. If the role of
diffusion current is insignificant (that is to say, the
inequality ((LD A*T) / (k μn Nc)) <1 holds), then one
obtains with allowance made for Nc(T) = Nc0(T/300 K)3/2
that ρc2 ~ T , i.e., the contact resistivity grows with
temperature as T . It was shown in [10] that the above
inequality is valid at doping levels n2 1015 cm–3. At
lower and intermediate doping levels,
((LD A*T) / (k μn Nc)) ≥ 1, and (as analysis shows) the
degree of ρc2 growth with temperature increases as
compared with the law T .
Fig. 3 presents the theoretical ρc2(T) curves built
using Eq. (4) as well as low-temperature freeze-out of
electrons. The doping level serves as parameter of
curves. At temperatures over 125 K, all curves grow
with temperature (see curves 1-3). For the curve 1 (that
corresponds to the lowest doping level of 314 cm10 ), the
exponent of the power dependence ρc2(T) at room and
elevated temperatures is maximal (equal to 2). As the
doping level increases, that exponent goes down: it
equals 1.1 at 315
2 cm10 n and 0.8 at 316
2 cm10 n .
It should be noted that the above current
mechanism (as well as that related to current flow
through the metal shunts associated with dislocations –
see [7, 8]) ensures purely ohmic contact behavior. At the
same time, the standard mechanism that describes
slightly non-ohmic contact with low barrier height
(about kT/q), as well as the thermofield mechanism of
current flow, result in ohmic contact behavior only in the
case that Rc Rb (here Rc is the contact resistance, and
Rb is the bulk resistance). Let us assume that the
thermofield current component is predominant over wide
ranges of doping levels and temperatures. Then, it is
possible to use the following equation for determination
of VI curve for a contact of unit area:
1
)(
exp)(
0E
RJVq
JVJ b
sT , (5)
where
10 tpsT R
q
E
J ; )/(cth 00000 kTEEE ;
2/1
000 /2/ nmE ts . (6)
Here, Rtp = ρtp / S (where ρtp is contact resistivity at
realization of thermofield mechanism of current flow
through the contact), S is the contact area.
100 200 300 400
c,
·c
m
2
T, K
1
2
3
Fig. 3. Theoretical c2(T) curves built using Eq. (4) (full
curves) and with allowance made for low-temperature freeze-
out of electrons (dashed curves; n2, cm–3: 1 – 1014; 2 – 1015; 3 –
1016).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2014. V. 17, N 1. P. 1-6.
© 2014, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
4
By presenting the IV curve as
sTbb J
J
qR
E
R
V
VJ 1ln)( 0 , (7)
it is easy to make certain that the second term on the
right of Eq. (7) may be neglected as compared to the first
one if Rtp<<Rb. To this end, as it follows from Eq. (7),
the inequality J JsT has to hold. Then, using the
expression for JsT from Eq. (6), we obtain
b
tp
b R
R
VJ
R
V
VJ )()( . (8)
One can see from this that condition for contact
ohmicity is Rtp<<Rb.
3. Details of experiment
We studied two types of specimens, with an n+-n doping
step formed either by phosphorus diffusion or ion
implantation, at identical n-Si(111) wafers. The latter
were cut out of the same ingot made by the Czochralski
method. Their thickness and resistivity were ~420 m
and ~4.6 cm, respectively. The wafers were subjected
to chemo-dynamical polishing and surfaced according to
the requirements of the 14th class.
Phosphorus diffusion from vapor phase was made
at Т = 900 °С for 6 min. The depth of occurrence of the
n+-layer was ~0.065 m; the donor concentration in the
n+-layer was ~ 320 cm10 . Phosphorus ion implantation
was made using a setup “Vesuvius–5”. The ion energy
was ~60 keV; the dose was 103 C/cm2. Thermal
annealing after ion implantation was made using a setup
“SDOM 3–100” in oxygen atmosphere at Т = 850 °С for
30 min. The depth of occurrence of the n+-layer was
~0.06 m. The surface concentration of the dopant was
~ 215cm10 .
To measure ρс(Т) over the 125–375 K temperature
range, we made test structures with specimens of both
types. The configuration of test structures corresponded
to ρс measurement with the transmission line method
(TLM) [13] that was used by us earlier in [5-8]. It
enabled us to test ρс with allowance for either
conduction in the n+-layer only (planar configuration of
TLM structure) or through the n+-n doping step (vertical
configuration of TLM structure). In the latter case,
vertical TLM structure was made by n+-layer etching-off
in gaps between the test pads to a depth of ~0.5 m and
1 m, respectively, i.e., much over the thickness of n+-
layer.
Contact metallization Au(150 nm)–Ti(60 nm)–
Pd(20 nm)–n+-n was made using layer-by-layer vacuum
sputtering of metals onto the Si substrate (heated to
350 °С) with an n+-n doping step, in a single
technological cycle, in an oilless vacuum (residual
Fig. 4. SEM microphotograph of the cleavage of Au–Ti–Pd–
n+-n-Si contact structure for an n+-n doping step made using
phosphorus diffusion.
Fig. 5. Same as in Fig. 4 but for an n+-n doping step made
using phosphorus ion implantation.
pressure of ~ Pa105 4 ). The opposite wafer side was
metallized in much the same way.
For contact structures of both configurations, the
cleavage surface was studied using a high resolution
scanning electron microscope (SEM) S–4800 (Hitachi,
Japan).
The SEM photographs of cleavages for Au–Ti–Pd–
nn - -Si structures with an n -layer prepared using
phosphorus diffusion and ion implantation are shown in
Figs 4 and 5, respectively. In both photographs, one can
see n+-n doping steps with practically close n -layer
thicknesses.
4. Experimental results: Comparison with the model
Shown in Fig. 6 are the dependences ρс(Т) measured
over the 125–375 K temperature range for specimens of
two types: 1) with an n+-n doping step obtained using
phosphorus ion implantation into a silicon wafer
(ρ ~4.6 cm) and 2) with an n+-n doping step obtained
using phosphorus diffusion into the same Si wafer. The
dependences ρс(Т) presented in Fig. 6 were measured in
two ways: 1) at lateral current flow in the n -layer
and 2) at vertical current flow through the n+-n doping
step.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2014. V. 17, N 1. P. 1-6.
© 2014, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
5
One can see from Fig. 6 (curves 1 and 1) that, at
current flow in the n+-layer (regardless of the way of its
formation), the contact resistivity ρс grows with
temperature but slightly (closely to dependence ρc~Т
0.1
or ρc~Т
0.2). The ρс value for the specimen with an ion-
implanted n+-layer is about 1/3 that for the specimen
with n+-layer obtained using phosphorus diffusion. This
may be owing to the known advantages of the ion
implantation method over the diffusion one [14].
The theoretical temperature dependence of contact
resistivity is shown in Fig. 6 (curve 2), while the
experimental ρс(Т) curve (obtained for diffusion-doped
structure) is presented in Fig. 6 (curve 3); both curves
are given for vertical geometry of TLM structure. One
can see that there is no agreement between the above
two curves. In our opinion, the reason for this is related
to pronounced difference between the shunt and contact
resistances. In our case, the shunt resistance value RSh
exceeds that of contact resistance Rc = ρс / S (where S is
the contact area) by more than two orders of magnitude.
So, the relative error in determination of contact
resistance Δρс /ρс with the Cox and Strack method [15]
is close to 100%. The results of calculation for vertical
geometry of TLM structure show that, to decrease the
ratio RSh / Rc , one should use structures of smaller both
diameter (~20 m) and thickness (≤10 m). This
consideration will be taken into account later.
However, the principal result obtained in this
work is that the ρс(Т) curves for vertical structures with
a doping step are growing. This is related (as was
showed above) to realization of accumulation band
bending in a lightly doped region at the interface
between the silicon bulk and doping step. This means
that in this case we deal with purely ohmic contacts for
which linear dependence between the flowing current
and applied voltage is obeyed at any temperatures,
whatever the interrelation between the bulk and contact
resistances.
10-2
100 150 200 250 300 350 400
10-4
3
4·10
-3
2
1'
c,
·c
m
2
T, K
1
Fig. 6. Experimental temperature dependence of contact
resistivity (planar geometry of TLM structure): 1 – ion
implanted n+-layer; 1 – diffusion-doped n+-layer; theoretical
(2) and experimental (3) temperature dependences of contact
resistivity at n2= 8.5×1014 cm-3 (vertical geometry of TLM
structure).
5. Conclusions
Thus, it has been shown (both theoretically and
experimentally) for ohmic contacts formed to an n+-n
doping step of silicon that, in the case of electron
degeneracy in the n+-layer and high-resistance n-Si bulk,
contact resistivity ρс increases with temperature in the
125–375 K range. It is shown that the growing
dependences ρс(Т) are related to the accumulation band
bending in high-resistance n-Si, no matter what the way
of formation (diffusion or ion implantation) of n+-n
doping step.
Acknowledgement
The work was supported by the Project №Ф54/209-
2013 ДФФД–БРФФД–2013.
References
1. S.M. Sze, Kwok K. Ng, Physics of Semiconductor
Devices. 3rd Ed. John Wiley and Sons, Inc.,
Hoboken, New Jersey, 2007.
2. T.V. Blank, Yu.A. Gol’dberg, Mechanisms of
current flow in metal-semiconductor ohmic
contacts // Semiconductors, 41(11), p. 1263-1292
(2007).
3. Zhang Yue-Zong, Feng Shi-Wei, Guo Chun-Sheng,
Zhang Guang-Chen, Zhuang Si-Xiang, Su Rong,
Bai Yun-Xia, Lu Chang-Zhi, High-temperature
characteristics of Ti/Al/Ni/Au ohmic contacts to n-
GaN // Chin. Phys. Lett. 25(11), p. 4083-4085
(2008).
4. T.V. Blank, Yu.A. Gol’dberg, A.E. Posse, Flow of
the current along metallic shunts in ohmic contacts
to wide-gap IIIV semiconductors //
Semiconductors, 43(9), p. 1164-1169 (2009).
5. A.E. Belyaev, N.S. Boltovets, R.V. Konakova,
Ya.Ya. Kudryk, A.V. Sachenko, V.N. Sheremet,
Temperature dependence of contact resistance of
Au–Ti–Pd2Si–n+-Si ohmic contacts //
Semiconductor Physics, Quantum Electronics and
Optoelectronics, 13(4), p. 436-438 (2010).
6. A.E. Belyaev, N.S. Boltovets, R.V. Konakova,
Ya.Ya. Kudryk, A.V. Sachenko, V.N. Sheremet,
A.O. Vinogradov, Temperature dependence of
contact resistance for Au–Ti–Pd2Si–n+-Si ohmic
contacts subjected to microwave irradiation //
Semiconductors, 46(3), p. 330-333 (2012).
7. A.V. Sachenko, A.E. Belyaev, N.S. Boltovets,
A.O. Vinogradov, V.P. Kladko, R.V. Konakova,
Ya.Ya. Kudryk, A.V. Kuchuk, V.N. Sheremet, S.A.
Vitusevich, Features of temperature dependence of
contact resistivity in ohmic contact on lapped n-Si //
J. Appl. Phys. 112(6), 063703 (2012).
8. A.V. Sachenko, A.E. Belyaev, N.S. Boltovets,
R.V. Konakova, Ya.Ya. Kudryk, S.V. Novitskii,
V.N. Sheremet, J. Li, S.A. Vitusevich, Mechanism
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2014. V. 17, N 1. P. 1-6.
© 2014, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
6
of contact resistance formation in ohmic contacts
with high dislocation density // J. Appl. Phys.
111(8), 083701 (2012).
9. F. Iucolano, G. Greco, F. Roccaforte, Correlation
between microstructure and temperature dependent
electrical behavior of annealed Ti/Al/Ni/Au ohmic
contacts to AlGaN/GaN heterostructures // Appl.
Phys. Lett. 103(20), 201604 (2013).
10. R.K. Kupka, W.A. Anderson, Minimal ohmic
contact resistance limits to n-type semiconductors //
J. Appl. Phys. 69(6), p. 3623-3632 (1991).
11. G. Brezeanu, C. Cabuz, D. Dascalu, P.A. Dan, A
computer method for the characterization of
surface-layer ohmic contacts // Solid-State
Electron. 30(5), p. 527-532 (1987).
12. D.K. Ferry, First-order optical and intervalley
scattering in semiconductors // Phys. Rev. B, 14(4),
p. 1605-1609 (1976).
13. D.K. Schroder, Semiconductor Materials and
Devices Characterization. 3rd Ed., John Wiley and
Sons, Inc., Hoboken, New Jersey, 2006.
14. Ion Implantation and Beam Processing, Eds.
J.S. Williams, J.M. Poate. Academic Press, N.Y.,
1984.
15. R.H. Cox, H. Strack, Ohmic contacts for GaAs
devices // Solid-State Electron. 10(12), p. 1213-
1218 (1967).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2014. V. 17, N 1. P. 1-6.
PACS 73.40.Ns, 73.40.Cg, 85.40.-e
On a feature of temperature dependence of contact resistivity
for ohmic contacts to n-Si with an n+-n doping step
A.V. Sachenko1, A.E. Belyaev1, N.S. Boltovets2, A.O. Vinogradov1, V.A. Pilipenko3, T.V. Petlitskaya3,
V.M. Anischik4, R.V. Konakova1, T.V. Korostinskaya2, V.P. Kostylyov1, Ya.Ya. Kudryk1, V.G. Lyapin1,
P.N. Romanets1, V.N. Sheremet1
1V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, 03028 Kyiv, Ukraine
Phone: 38(044) 525-61-82; Fax: 38(044) 525-83-42; e-mail: konakova@isp.kiev.ua
2State Enterprise Research Institute “Orion”, 03057 Kyiv, Ukraine
3State Centre “Belmicroanaliz”, subsidiary of R&D Centre “Belmicrosystems”
Open Joint Stock Company “Integral”, 220108 Minsk, Belarus
4Belarusian State University, 220030 Minsk, Belarus
Abstract. We present both theoretical and experimental temperature dependences of contact resistivity ρс(Т) for ohmic contacts to the silicon n+-n-structures whose n+-layer was formed using phosphorus diffusion or ion implantation. The ρс(Т) dependence was measured in the 125–375 K temperature range with the transmission line method, with allowance made for conduction in both the n+-layer and n+-n doping step.
Keywords: ohmic contact, metallization, doping step.
Manuscript received 24.10.13; revised version received 11.12.13; accepted for publication 20.03.14; published online 31.03.14.
1. Introduction
At present there exists a fixed notion of the mechanisms of current flow in ohmic metal-semiconductor contacts as well as the processes of minimization of contact resistivity and their contribution to the parameters of semiconductor devices and integrated circuits [1]. This notion asserts that contact resistivity ρс should be minimal and demonstrate thermal and electrical stability, and I – V curves of ohmic contacts must be linear and symmetric. As a rule, ρс of such contacts is described within either field emission (ρс does not depend on temperature) or thermofield emission (ρс decreases with temperature).
However, recent investigations [2-9] showed that in some cases ρс does not demonstrate the above behavior. To illustrate, for ohmic contacts to wide-gap semiconductors with high dislocation density it was shown in [2-4, 8, 9] that ρс increases with temperature. Such growing dependences ρс(Т) were obtained in [5-7] for ohmic contacts to lapped as well as polished n-Si, at presence of high density of structural defects in the Si near-contact region. In that case, calculation of the number of defects from etching pits made for lapped silicon gave ~107 cm–2. According to the model proposed in [7, 8], this value turned out sufficient for description of growing dependence ρс(Т).
Along with the above-mentioned, some other conditions of ohmic contact formation may lead to ρс growth with temperature. For instance, use (as an ohmic contact) of an isotype n+-n junction (n+-n doping step) or p+-p junction – analog of metal-semiconductor contact in which degenerate n+-semiconductor (or p+-semiconductor) acts as a metal. In this case, we deal practically with a Schottky diode without a potential barrier [10]. In what follows, we consider a model of such ohmic contact and its experimental testing.
2. Model of ohmic contact with a doping step
Let us consider a model of ohmic contact with an n+-n doping step in the near-contact region, with electrons in the heavily doped n+-layer being degenerate. This situation is realized in manufacturing technology for silicon devices, in particular, IMPATT diodes. In that case, the thickness
+
n
W
of the heavily doped region with electron concentration
+
1
n
exceeds the Schottky layer thickness WSh, and the doping level is over the effective density of states Nc in the conduction band. Just this situation means that electrons in the heavily doped region are degenerate.
In this work, we made an analytical calculation of the ρc(T) curve for Si-based ohmic contacts with an n+-n doping step in the limiting case when the contact band diagram is of the form shown in Fig. 1. One can see that the thickness
+
n
W
of the heavily doped region with electron concentration
+
1
n
exceeds the Schottky layer thickness WSh (
Sh
W
W
n
>
+
), and the doping level exceeds the effective electron density of states in the conduction band Nc (
c
N
n
>
+
1
). This means that electrons in the heavily doped region are degenerate.
Figs 2a and 2b present band diagrams for contacts to Si with a doping step, at two values of heavily doped layer thickness +
n
W
: 5 and 10 nm. In our calculations, we used the following values:
3
16
2
cm
10
-
=
n
, +
1
n
= 2·1018, 5·1018, 1019, 2·1019 and 3
19
cm
10
5
-
×
. To obtain the band diagrams, we solved the Poisson equations for the heavily doped and lightly doped regions (both with allowance made for electron degeneracy) of the form
)
(
1
0
2
2
x
dx
d
s
r
e
e
=
j
,
(1)
where
(
)
(
)
(
)
(
)
(
)
.
exp
1
exp
2
8
F
2
1
0
F
2
/
1
3
2
/
3
ú
ú
ú
ú
û
ù
÷
ø
ö
ç
è
æ
j
-
+
-
q
+
-
q
-
ê
ê
ê
ê
ë
é
-
+
÷
ø
ö
ç
è
æ
j
-
-
p
p
=
r
+
+
+
µ
ò
kT
q
E
E
W
x
n
x
W
n
kT
q
E
z
z
dz
T
m
q
x
a
n
n
p
h
(2)
Here EF is the Fermi energy, Ea ≈ 0.005 eV, q – elementary charge.
The barrier height at the contact (or, more exactly, the diffusion potential φc) was preset as 0.4 V. The electrostatic potential was considered to vanish as x((. The solutions of the Poisson equation in the heavily and lightly doped regions were matched at the boundary
+
=
n
W
x
, that is to say, the values of potentials, as well as their derivatives (i.e., the electric field strengths), were matched, respectively.
Naturally all the
+
1
n
values taken for calculation obeyed the inequality
c
N
n
>
+
1
. However, since the Schottky layer thicknesses in the heavily doped region met the condition
Sh
W
W
n
<
+
at all doping levels, there
0
10
20
30
-0.4
-0.2
0.0
0.2
x, nm
Fermi Energy
j
(x), V
Fig. 1. Band diagram of ohmic contact with an n+-n doping step; n+~ 5(1020 cm–3; n ~ 1016 cm–3; Wn+~ 0.01 (m.
0
10
20
30
-0.4
-0.2
0.0
0.2
x, nm
2·10
19
5·10
20
2·10
20
Fermi Energy
10
20
T=300 K
W
n+
=5nm
j
(x) , V
a)
5·10
19
N
d
(x>5nm)=10
16
cm
-
3
0
10
20
30
-0,4
-0,2
0,0
0,2
2·10
19
5·10
19
10
20
2·10
20
x, nm
5·10
20
Fermi Energy
T=300K
W
n+
=10nm
j
(x), V
b)
N
d
(x>10nm)=10
16
cm
-
3
Fig. 2. Band diagrams of contacts with a doping step for Si at two thickness values of heavily doped layer Wn+: 5 nm (a) and 10 nm (b); n+: 5(1019, 1020, 2(1020 and 5(1020 cm–3 at n2 = 1016 cm–3.
was no portion of
(
)
x
j
independent from the coordinate x shown in Fig. 1.
One should note that, depending on the behavior of potential
(
)
x
j
in the near-contact region, the contact will be either rectifying (in the case of monotonic dependence of
(
)
x
j
on coordinate x) or ohmic (in the case of a strongly pronounced non-monotony of
(
)
x
j
). In the latter case, the contact resistivity may be presented as a sum of two terms (corresponding to series resistances):
2
1
c
c
c
r
+
r
=
r
.
(3)
Here, ρc1 is the contact resistivity related to thermofield passage of electrons through the barrier at the interface between a heavily doped semiconductor and metal, and
÷
÷
ø
ö
ç
ç
è
æ
m
+
=
r
c
n
D
c
c
N
k
T
A
L
Tn
A
q
N
k
*
2
*
2
1
(4)
is the effective contact resistance of the lightly doped region in the limiting case of contact energy band being of the form shown in Fig. 1. Here k is the Boltzmann constant, A* – effective Richardson constant, μn – electron mobility in the lightly doped region, LD = (ε0εs kT / 2q2n2)0.5 – Debye shielding length for the lightly doped region. It should be noted that Eq. (4) was obtained with allowance made for the results of [10] and [11]: it takes into account both the diffusion and emission terms in the current flowing through the lightly doped region.
Thus, if the inequality ρc2 > ρc1 holds, then contact is purely ohmic. In that case, band bending in the lightly doped region is accumulation rather than depletion, so the total voltage applied to the contact is dropped across the neutral bulk, thus ensuring contact ohmicity. The electron mobility μn in the region of light doping was calculated with allowance made for electron scattering by charged impurities as well as by intervalley and acoustic phonons [12]. It was assumed that dislocation density in the lightly doped region is sufficiently low and does not affect electron mobility. The expressions for μn calculation are given in [8].
Now let us dwell on an analysis of temperature dependence of contact resistivity ρc2. If the role of diffusion current is insignificant (that is to say, the inequality ((LD A*T) / (k μn Nc)) <1 holds), then one obtains with allowance made for Nc(T) = Nc0(T/300 K)3/2 that ρc2 ~
T
, i.e., the contact resistivity grows with temperature as
T
. It was shown in [10] that the above inequality is valid at doping levels n2 (( 1015 cm–3. At lower and intermediate doping levels, ((LD A*T) / (k μn Nc)) ≥ 1, and (as analysis shows) the degree of ρc2 growth with temperature increases as compared with the law
T
.
Fig. 3 presents the theoretical ρc2(T) curves built using Eq. (4) as well as low-temperature freeze-out of electrons. The doping level serves as parameter of curves. At temperatures over 125 K, all curves grow with temperature (see curves 1-3). For the curve 1 (that corresponds to the lowest doping level of
3
14
cm
10
-
), the exponent of the power dependence ρc2(T) at room and elevated temperatures is maximal (equal to 2). As the doping level increases, that exponent goes down: it equals 1.1 at 3
15
2
cm
10
-
=
n
and 0.8 at
3
16
2
cm
10
-
=
n
.
It should be noted that the above current mechanism (as well as that related to current flow through the metal shunts associated with dislocations – see [7, 8]) ensures purely ohmic contact behavior. At the same time, the standard mechanism that describes slightly non-ohmic contact with low barrier height (about kT/q), as well as the thermofield mechanism of current flow, result in ohmic contact behavior only in the case that Rc ( Rb (here Rc is the contact resistance, and Rb is the bulk resistance). Let us assume that the thermofield current component is predominant over wide ranges of doping levels and temperatures. Then, it is possible to use the following equation for determination of
V
I
-
curve for a contact of unit area:
ú
ú
û
ù
ê
ê
ë
é
-
÷
÷
ø
ö
ç
ç
è
æ
-
=
1
)
(
exp
)
(
0
E
R
J
V
q
J
V
J
b
sT
,
(5)
where
1
0
-
=
tp
sT
R
q
E
J
;
)
/
(
cth
00
00
0
kT
E
E
E
=
;
(
)
2
/
1
0
00
/
2
/
n
m
E
t
s
e
e
=
h
.
(6)
Here, Rtp = ρtp / S (where ρtp is contact resistivity at realization of thermofield mechanism of current flow through the contact), S is the contact area.
100
200
300
400
10
-6
10
-5
10
-4
10
-3
10
-2
r
c
,
W
·cm
2
T, K
1
2
3
Fig. 3. Theoretical (c2(T) curves built using Eq. (4) (full curves) and with allowance made for low-temperature freeze-out of electrons (dashed curves; n2, cm–3: 1 – 1014; 2 – 1015; 3 – 1016).
By presenting the I(V curve as
÷
÷
ø
ö
ç
ç
è
æ
+
-
=
sT
b
b
J
J
qR
E
R
V
V
J
1
ln
)
(
0
,
(7)
it is easy to make certain that the second term on the right of Eq. (7) may be neglected as compared to the first one if Rtp<<Rb. To this end, as it follows from Eq. (7), the inequality J (( JsT has to hold. Then, using the expression for JsT from Eq. (6), we obtain
b
tp
b
R
R
V
J
R
V
V
J
)
(
)
(
-
=
.
(8)
One can see from this that condition for contact ohmicity is Rtp<<Rb.
3. Details of experiment
We studied two types of specimens, with an n+-n doping step formed either by phosphorus diffusion or ion implantation, at identical n-Si(111) wafers. The latter were cut out of the same ingot made by the Czochralski method. Their thickness and resistivity were ~420 (m and ~4.6 ((cm, respectively. The wafers were subjected to chemo-dynamical polishing and surfaced according to the requirements of the 14th class.
Phosphorus diffusion from vapor phase was made at Т = 900 °С for 6 min. The depth of occurrence of the n+-layer was ~0.065 (m; the donor concentration in the n+-layer was ~3
20
cm
10
-
. Phosphorus ion implantation was made using a setup “Vesuvius–5”. The ion energy was ~60 keV; the dose was 103 (C/cm2. Thermal annealing after ion implantation was made using a setup “SDOM 3–100” in oxygen atmosphere at Т = 850 °С for 30 min. The depth of occurrence of the n+-layer was ~0.06 (m. The surface concentration of the dopant was ~
2
15
cm
10
-
.
To measure ρс(Т) over the 125–375 K temperature range, we made test structures with specimens of both types. The configuration of test structures corresponded to ρс measurement with the transmission line method (TLM) [13] that was used by us earlier in [5-8]. It enabled us to test ρс with allowance for either conduction in the n+-layer only (planar configuration of TLM structure) or through the n+-n doping step (vertical configuration of TLM structure). In the latter case, vertical TLM structure was made by n+-layer etching-off in gaps between the test pads to a depth of ~0.5 (m and 1 (m, respectively, i.e., much over the thickness of n+-layer.
Contact metallization Au(150 nm)–Ti(60 nm)–Pd(20 nm)–n+-n was made using layer-by-layer vacuum sputtering of metals onto the Si substrate (heated to 350 °С) with an n+-n doping step, in a single technological cycle, in an oilless vacuum (residual
Fig. 4. SEM microphotograph of the cleavage of Au–Ti–Pd– n+-n-Si contact structure for an n+-n doping step made using phosphorus diffusion.
Fig. 5. Same as in Fig. 4 but for an n+-n doping step made using phosphorus ion implantation.
pressure of ~
Pa
10
5
4
-
×
). The opposite wafer side was metallized in much the same way.
For contact structures of both configurations, the cleavage surface was studied using a high resolution scanning electron microscope (SEM) S–4800 (Hitachi, Japan).
The SEM photographs of cleavages for Au–Ti–Pd–
n
n
-
+
-Si structures with an
+
n
-layer prepared using phosphorus diffusion and ion implantation are shown in Figs 4 and 5, respectively. In both photographs, one can see n+-n doping steps with practically close
+
n
-layer thicknesses.
4. Experimental results: Comparison with the model
Shown in Fig. 6 are the dependences ρс(Т) measured over the 125–375 K temperature range for specimens of two types: 1) with an n+-n doping step obtained using phosphorus ion implantation into a silicon wafer (ρ ~4.6 ((cm) and 2) with an n+-n doping step obtained using phosphorus diffusion into the same Si wafer. The dependences ρс(Т) presented in Fig. 6 were measured in two ways: 1) at lateral current flow in the
+
n
-layer and 2) at vertical current flow through the n+-n doping step.
One can see from Fig. 6 (curves 1 and 1() that, at current flow in the n+-layer (regardless of the way of its formation), the contact resistivity ρс grows with temperature but slightly (closely to dependence ρc~Т0.1 or ρc~Т0.2). The ρс value for the specimen with an ion-implanted n+-layer is about 1/3 that for the specimen with n+-layer obtained using phosphorus diffusion. This may be owing to the known advantages of the ion implantation method over the diffusion one [14].
The theoretical temperature dependence of contact resistivity is shown in Fig. 6 (curve 2), while the experimental ρс(Т) curve (obtained for diffusion-doped structure) is presented in Fig. 6 (curve 3); both curves are given for vertical geometry of TLM structure. One can see that there is no agreement between the above two curves. In our opinion, the reason for this is related to pronounced difference between the shunt and contact resistances. In our case, the shunt resistance value RSh exceeds that of contact resistance Rc = ρс / S (where S is the contact area) by more than two orders of magnitude. So, the relative error in determination of contact resistance Δρс /ρс with the Cox and Strack method [15] is close to 100%. The results of calculation for vertical geometry of TLM structure show that, to decrease the ratio RSh / Rc , one should use structures of smaller both diameter (~20 (m) and thickness (≤10 (m). This consideration will be taken into account later.
However, the principal result obtained in this work is that the ρс(Т) curves for vertical structures with a doping step are growing. This is related (as was showed above) to realization of accumulation band bending in a lightly doped region at the interface between the silicon bulk and doping step. This means that in this case we deal with purely ohmic contacts for which linear dependence between the flowing current and applied voltage is obeyed at any temperatures, whatever the interrelation between the bulk and contact resistances.
10
-2
100
150
200
250
300
350
400
10
-4
3
4·10
-3
2
1'
r
c
,
W
·cm
2
T, K
1
Fig. 6. Experimental temperature dependence of contact resistivity (planar geometry of TLM structure): 1 – ion implanted n+-layer; 1( – diffusion-doped n+-layer; theoretical (2) and experimental (3) temperature dependences of contact resistivity at n2= 8.5×1014 cm-3 (vertical geometry of TLM structure).
5. Conclusions
Thus, it has been shown (both theoretically and experimentally) for ohmic contacts formed to an n+-n doping step of silicon that, in the case of electron degeneracy in the n+-layer and high-resistance n-Si bulk, contact resistivity ρс increases with temperature in the 125–375 K range. It is shown that the growing dependences ρс(Т) are related to the accumulation band bending in high-resistance n-Si, no matter what the way of formation (diffusion or ion implantation) of n+-n doping step.
Acknowledgement
The work was supported by the Project №Ф54/209-2013 ДФФД–БРФФД–2013.
References
1. S.M. Sze, Kwok K. Ng, Physics of Semiconductor Devices. 3rd Ed. John Wiley and Sons, Inc., Hoboken, New Jersey, 2007.
2. T.V. Blank, Yu.A. Gol’dberg, Mechanisms of current flow in metal-semiconductor ohmic contacts // Semiconductors, 41(11), p. 1263-1292 (2007).
3. Zhang Yue-Zong, Feng Shi-Wei, Guo Chun-Sheng, Zhang Guang-Chen, Zhuang Si-Xiang, Su Rong, Bai Yun-Xia, Lu Chang-Zhi, High-temperature characteristics of Ti/Al/Ni/Au ohmic contacts to n-GaN // Chin. Phys. Lett. 25(11), p. 4083-4085 (2008).
4. T.V. Blank, Yu.A. Gol’dberg, A.E. Posse, Flow of the current along metallic shunts in ohmic contacts to wide-gap III(V semiconductors // Semiconductors, 43(9), p. 1164-1169 (2009).
5. A.E. Belyaev, N.S. Boltovets, R.V. Konakova, Ya.Ya. Kudryk, A.V. Sachenko, V.N. Sheremet, Temperature dependence of contact resistance of Au–Ti–Pd2Si–n+-Si ohmic contacts // Semiconductor Physics, Quantum Electronics and Optoelectronics, 13(4), p. 436-438 (2010).
6. A.E. Belyaev, N.S. Boltovets, R.V. Konakova, Ya.Ya. Kudryk, A.V. Sachenko, V.N. Sheremet, A.O. Vinogradov, Temperature dependence of contact resistance for Au–Ti–Pd2Si–n+-Si ohmic contacts subjected to microwave irradiation // Semiconductors, 46(3), p. 330-333 (2012).
7. A.V. Sachenko, A.E. Belyaev, N.S. Boltovets, A.O. Vinogradov, V.P. Kladko, R.V. Konakova, Ya.Ya. Kudryk, A.V. Kuchuk, V.N. Sheremet, S.A. Vitusevich, Features of temperature dependence of contact resistivity in ohmic contact on lapped n-Si // J. Appl. Phys. 112(6), 063703 (2012).
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© 2014, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
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