Original Russian Text © T.V . Blank, Yu.A. Gol’dberg, 2007, published in Fizika i Tekhnika Poluprovodnikov, 2007, Vol. 41, No. 11, pp. 1281–1308.
1263
1. A BRIEF HISTORY OF THE SUBJECT An ohmic contact is a metal–semiconductor contact in which a potential barrier at the interface does not manifest itself; this contact is an integral part of any semiconductor device. Studies of ohmic contacts were started ~60 years ago when it was noticed that a poten-tial barrier exists at the Ni–CdS interface while there is no such barrier at the Al–CdS interface; Schottky [1]assumed that the barrier is not formed if the work func-tion Φ m for electrons leaving the metal is smaller than the electron-affinity energy for the semiconductor X s . In 1940s–1950s, when the III–V semiconductors were developed, Bardeen [2] noted that the presence of a bar-rier is often caused by the density and energy distribu-tion of surface states in a semiconductor rather than by the work function of electrons leaving the metal; in the opinion of Spicer [3], the aforementioned states are formed due to the presence of extraneous atoms (for example, oxygen atoms) at the semiconductor surface.The early stage of studies of ohmic contacts was con-sidered in review [4].
Subsequent studies were carried out in three direc-tions.
First, technological studies were conducted with the aim of decreasing the resistance of ohmic contacts to an extent that they do not manifest themselves in the char-acteristics of semiconductor devices. The ohmic con-tacts’ resistance per unit area was as high as R c = 10 –6 –10 –8 Ω cm 2
. This was accomplished either by variation in the chemical composition of the near-contact semi-conductor’s region or by additional doping.
Second, the composition of the phases formed at the metal–semiconductor interface was studied by the X-ray spectral analysis, chemical analysis, Auger spec-troscopy, and tunneling microscopy. On the basis of these studies, the optimal chemical composition of the semiconductor’s near-contact region was defined; this composition was supposed to ensure the lowest possi-ble resistance of the contact.
Third, the methods for determining the resistance of an ohmic contact were developed; this resistance often amounts to a small fraction of the total resistance of a structure. The resistance of ohmic contacts was deter-mined from: (i) the dependence of potential difference between several contacts on the intercontact distance [5];(ii) the dependence of the resistance of the metal–semi-conductor-metal structure with two ohmic contacts on the structure’s thickness [6]; (iii) an analysis of charac-teristics of contacts with various diameters [7]; and (iv) the transmission-line method [8].
This stage of the development of ohmic contacts was represented in general reviews [6, 9–13] and also in reviews concerned with specific semiconductors: ZnO [14]; ZnS [15]; GaAs, GaN, and ZnSe [16]; SiC [17];and C (diamond) [18].
Studies of the dependences of the ohmic contacts’resistance on temperature, the charge-carrier concen-tration, the band gap of semiconductor, and other fac-
Mechanisms of Current Flow
in Metal–Semiconductor Ohmic Contacts
T. V. Blank^ and Yu. A. Gol’dberg
Ioffe Physicotechnical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 26, St. Petersburg, 194021 Russia
^e-mail: tblank@mail.ioffe.ru
Submitted January 29, 2007; accepted for publication April 2, 2007
Abstract —Published data on the properties of metal–semiconductor ohmic contacts and mechanisms of cur-rent flow in these contacts (thermionic emission, field emission, thermal–field emission, and also current flow through metal shunts) are reviewed. Theoretical dependences of the resistance of an ohmic contact on temper-ature and the charge-carrier concentration in a semiconductor were compared with experimental data on ohmic contacts to II–VI semiconductors (ZnSe, ZnO), III–V semiconductors (GaN, AlN, InN, GaAs, GaP , InP), Group IV semiconductors (SiC, diamond), and alloys of these semiconductors. In ohmic contacts based on lightly doped semiconductors, the main mechanism of current flow is thermionic emission with the metal–semiconductor potential barrier height equal to 0.1–0.2 eV . In ohmic contacts based on heavily doped semiconductors, the cur-rent flow is effected owing to the field emission, while the metal–semiconductor potential barrier height is equal to 0.3–0.5 eV . In alloyed In contacts to GaP and GaN, a mechanism of current flow that is not characteristic of Schottky diodes (current flow through metal shunts formed by deposition of metal atoms onto dislocations or other imperfections in semiconductors) is observed.PACS numbers: 73.30.+y, 73.40.Cg, 81.40.Ef DOI:
10.1134/S1063782607110012
12
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tors were started in mid-1990s with the aim of estab-lishing the mechanism of current flow through an ohmic contact. Both the current flow mechanisms char-acteristic of the Schottky barriers (thermionic emission,thermal field emission, and field emission) and other mechanisms (recombination, metal shunts) were con-sidered theoretically. The current flow mechanism was determined by comparison of experimental data with theoretical results. These studies were carried out for II–VI, III–V , and IV–IV semiconductors and for alloys based on these semiconductors. This review is dedi-cated to a systematization of the results of these studies.2. FORMATION OF AN OHMIC CONTACT As is well known, a metal–semiconductor contact can be either rectyifying (barrier) if the potential barrier between a metal and a semiconductor is tunneling-non-transparent or ohmic if the barrier is absent or is tunnel-ing-transparent for electrons.
An ohmic contact is typically formed in cases where:
(I) there is no potential barrier between a metal and a semiconductor, for example, if a metal with the work function for electrons smaller than the electron affinity in the semiconductor is chosen for an n- type semicon-ductor with a low density of surface states in the band gap (Fig. 1a);
(II) there is a potential barrier but this barrier is nar-row (tunneling-transparent) which is attained by heavy doping of the near-contact region of the semiconductor (Figs. 1b, 2c); in this case, electrons traverse the inter-face through the barrier over its entire height (the field emission); and
(III) there is a potential barrier but it is low; as a result, this barrier is easily surpassed by charge carriers.This situation is typically attained by varying the chem-ical composition of semiconductor near the contact, for example, by formation of a narrow-gap near-contact layer; in this case, electrons traverse the interface above the barrier (thermionic emission) (Fig. 2a).
Φ v
c vac
(a)
Φ c vac
v
n -GaN
Fig. 1. Energy diagrams of ohmic contacts to the n- type semiconductors: (a) the semiconductor does not have sur-face states and Φ m < X s (by the example of Mg– n- GaN);(b) the semiconductor contains high-density surface states in the band gap (by the example of Au– n- GaP); however,the near-surface region is heavily doped. E vac is the vacuum level and χ is the Fermi level.
Fig. 2.
Mechanisms of the current flow in a metal–semicon-ductor ohmic contact: (a) thermionic emission of electrons above the barrier; (b) thermal field emission of electrons through the barrier top; and (c) tunneling (field emission) of electrons through the barrier.
SEMICONDUCTORS V ol. 41 No. 11 2007
MECHANISMS OF CURRENT FLOW IN METAL–SEMICONDUCTOR OHMIC CONTACTS 1265
Combination of mechanisms II and III, in which case electrons traverse the top of the barrier (Fig. 2b), is also possible (this is the thermal field emission).
Recently, mechanisms have been seen which imply that the metal–semiconductor potential barrier is present but:
(i) the space-charge region is shunted by metal shunts formed, for example, by deposition of metal atoms onto dislocations and other imperfections in the semiconductor (this mechanism is characteristic of alloyed ohmic contacts) and
(ii) due to a large number of crystal-lattice defects near the contact, the lifetime of charge carriers is extremely short in this region, so that the ohmic contact is formed due to recombination of charge carriers (this mechanism rarely manifests itself).
3. RESISTANCE OF AN OHMIC CONTACT The main characteristic of an ohmic contact is its resistance per unit area. This resistance consists of:(I) the resistance of the near-contact region of the semiconductor and
(II) resistance related to the passage of electrons through the potential barrier.
3.1. Resistance of the Near-Contact Region
The resistance of the near-contact region is the resis-tance of the heavily doped region combined with the resistance of the n – n + and p – p + junctions. The resis-tance of the heavily doped near-contact region is typi-cally low in semiconductors with a high mobility of charge carriers. For example, the resistance of the ~1 µ m-thick n + -GaAs layer at an electron concentra-tion n + ≈ 10 19 cm –3 and a mobility of ~10 3 cm 2 /(V s) is about 6 × 10 –8 Ω cm 2 . At the same time, in the case of SiC and II–VI semiconductors, it is often the case that heavy doping of the near-contact region cannot be attained and, in addition, the charge-carrier mobility is not high (10–100 cm 2 /(V s)). In this case, the resis-tance of the near-contact region can be in the range of ~(10 –4 –10 –5 ) Ω cm 2 .
We consider the resistance of the n – n + and p – p + junc-tions by looking at the example of the n + – n junction.This resistance is inversely proportional to the electron concentration [19, 20] as
(1)
where L D is the Debye length in the n- type region, N c is the density of states in the semiconductor’s conduction band, µ n is the electron mobility in the n- type region, N and n + are the electron concentrations in the n- and n + -type regions, K is the coefficient that shows to what extent the electron concentration at the Fermi level in the n + -type region exceeds N + , and q is the elementary
R n n +–L D N c q µn KN N
+------------------------,≈ charge. In the case of an ohmic contact to GaAs, (1) makes the main contribution to the contact resis-tance at N
< 5 × 1017 cm –3.
It was shown in [21] that the n –n + junction can be considered as a Schottky diode without a potential bar-rier and with a thermionic mechanism of current flow;the resistance of this junction is given by the formula
(2)
where χ is the Fermi level energy, A * = 4πqm *k 2ប–3 =120m r A/(cm 2 K 2) is the effective Richardson constant,m r is the relative effective mass of the majority charge carriers m r = m */m 0 (m 0 is the mass of a free electron),and k is the Boltzmann constant. If in a lightly doped semiconductor we have χ ӷ kT /q , then
(3)
Estimates of the resistance of an n –n + junction for
the most widely used III–V semiconductors are listed in Table 1; the calculations were carried out on the assumption that the difference between the electron concentrations in the n- and n +-type regions amounts to at least two orders of magnitude.
3.2. Resistance Related to the Transition Through
the Metal–Semiconductor Boundary Transition of electrons through the metal–semicon-ductor interface can occur:
(i) above the barrier (thermionic emission, Fig. 2a);(ii) through the barrier top (thermal field emission,Fig 2b); and
(iii) through the barrier at the level of the Fermi energy (tunneling, field emission, Fig. 2c).
In order to determine the conditions in which a spe-cific mechanism of the current flow manifests itself,Padovani and Stratton [22] introduced the parameter E 00that depends on the semiconductor type and the degree
R n n +–R n n +–k qA *T -------------⎝⎠⎛⎞1
1χ/kT ()exp +[]
ln ---------------------------------------------,
=R n n +–kN c qA *TN -----------------⎝⎠
⎛⎞.=Table 1. Calculated reduced resistance of the n –n + junction
according to the model suggested in [21]N , cm –3
, Ω cm 2GaAs
InP GaP GaN 101610–6 1.8 × 10–610–5 4 × 10–6101710–7 1.8 × 10–710–6 4 × 10–71018
10–8
1.8 × 10–8
10–7
4 × 10–8
R n –n +
1266SEMICONDUCTORS V ol. 41 No. 11 2007
BLANK, GOL’DBERG
of its doping. In the case of an n-type semiconductor,we have
(4)
where εs is the relative permittivity of the semiconduc-tor, ε0 is the free-space permittivity, and N d is the con-centration of ionized donors in the semiconductor.In the case of a p-type semiconductor, N d is replaced by N a , the concentration of ionized acceptors in the semiconductor.
Calculations [10] show that the main mechanisms of current flow are thermionic emission at high tempera-tures (kT ӷ E 00), thermal field emission at medium tem-peratures (kT ≈ E 00), and field (tunneling) emission at low temperatures (kT Ӷ E 00).
3.2.1. Thermionic emission. We now consider the theory of thermionic emission in the example of an n-type semiconductor; all conclusions will also be valid for p-type semiconductors if the concentration of ion-ized donors is replaced with the concentration of ion-ized acceptors and the density of states in the conduc-tion band is replaced by the density of states in the valence band.
Dependence of the thermionic emission current den-sity J on the voltage V and temperature T can be written as [10]
(5)
where
(6)
Here, I s is the saturation current, n is the nonideality coefficient in the current-voltage (I–V ) characteristic,ϕb is the potential barrier height, ∆ϕb is a decrease in the potential barrier height due to the mirror-image forces and other factors, and S is the contact area. The contact resistance per unit area is in general represented as
(7)
and, if V (8)
in the case of lowering of the barrier only by the mirror-image forces, the quantity ∆ϕb is given by
(9)
where V d is the diffusion-related contact potential dif-ference and V is the applied voltage.
E 00ប
2--N d εs ε0m *
----------------,
=J J s qV
nkT ---------1–⎝⎠
⎛⎞,
exp =I s J s S A *ST 2q ϕb ∆ϕb –()
–kT
--------------------------------.==R c dV
dJ s
-------dV dI ------S
==R c k
qA *T -------------⎝⎠⎛⎞q ϕb
∆ϕb –()–kT
--------------------------------;exp =∆ϕb 2πq 2
N d εs ε0()
3------------------V d V –kT q ------–⎝⎠⎛⎞
1/4
,=Thus, if the current flow through an ohmic contact is governed by the thermionic emission, we observe the following features:
(I) the contact resistance increases exponentially as the potential barrier height ϕb is increased;
(II) the contact resistance decreases as temperature is increased; the dependence R c T = f (1/T ) should be lin-ear on a semilogarithmic scale with the slope of this dependence proportional to the barrier height ϕb and the cutoff proportional to A * at 1/T (III) the contact resistance depends on the type of semiconductor and decreases only slightly as the dop-ing level is increased (∆ϕb ∝ ).
In order to lower the ohmic-contact resistance in the
contacts under consideration, one reduces the height of the metal–semiconductor potential barrier by varying the chemical composition of the semiconductor in its near-surface region.
For example, the potential barrier height can be low-ered by forming a near-surface narrow-gap layer, since the potential barrier height typically decreases as the band gap of the semiconductor is decreased.
In particular, in the course of heat treatment of the (W/Ni + In/Ni)–GaAs contacts at T ≈ 300°C, nickel interacts with GaAs and forms Ni 2GaAs while Ni atoms mix with W and Ni 2GaAs [23]. The In 0.6Ga 0.4As phase and NiAs islands appear at the Ni 2GaAs–GaAs interface at 700°C, while an In x Ga 1 – x As layer is formed on almost 90% of the GaAs surface area at 900°C. This material features a much smaller height of the potential barrier at an interface with a metal than does GaAs since the Fermi level in n-InAs is pinned in the conduction band rather than in the band gap.
An In x Ga 1 – x P alloy is formed in the Pd/In–n-GaP contacts heated to 600°C; this alloy reduces apprecia-bly the potential barrier with Pd [24] in comparison with the height of the Pd–n-GaP barrier.
Theoretical dependences of the ohmic-contact resis-tance on the height of the metal–semiconductor poten-tial barrier in the case of thermionic mechanism of the current flow are shown in Fig. 3.
The smallest possible value of resistance of this ohmic contact is given by [25]
(10)
Here, the Fermi level energy χ is measured from the
conduction-band bottom and, for a nondegenerate n-type semiconductor in the case where χ ӷ kT /q , is equal to (11)
N d 1/4R c
min
k qA *T -------------1
1χ/kT –()exp +[]
ln -------------------------------------------------.=R c
min
k qA *T -------------χkT ------⎝⎠⎛⎞
exp = k qA *T -------------N c N d ------ = 2πm *kT qN d -------------------------.=
SEMICONDUCTORS V ol. 41 No. 11 2007
MECHANISMS OF CURRENT FLOW IN METAL–SEMICONDUCTOR OHMIC CONTACTS
1267
In the case of GaAs [26], the lowest possible value of the contact resistance is given by
(12)
At N d ≈ 1015–1017 cm –3 and T = 300 K, in which case tunneling is unimportanrt, one can form ohmic con-tacts to GaAs with the resistance = 2 × 10–5–2 ×10–7 Ω cm 2.
3.2.2. Field emission. Tunneling theory (field emis-sion theory) [10] implies that the resistance of the metal–semiconductor ohmic contact per unit area is given by
(13)
where T (E ) is the probability of passage of a charge car-rier with an energy E through the barrier with the height lower than q ϕb by the value of ∆E :
(14)
where E 00 is the Padovani–Stratton [22] parameter and V d is the diffusion-related (contact) potential differ-ence. According to [27–29], we have
(15)
R c min Ω
c m 2
[] 1.5510
5
– T 300--------10
15
N d
---------. × =R c min
1
R c -----m *q 22πប3
------------T E ()E χ–()/kT []exp 1
–-------------------------------------------------E ,d 0∞
∫
=T E ()2–∆E ()
3/2
3E 00V d
1/2
------------------------,exp ∝R c kT E 00
qA *T 2qV d -----------------------------qV d E 00--------⎝⎠⎛⎞exp ≈×χ
kT ------2εs ε0m *ប------------------------ϕb N 1/2---------⎝
⎠⎜⎟⎛⎞.exp ∝exp An analysis of this formula shows that, if the current flow through the ohmic contact is governed by the field emission, we obtain the following results:
(i) the contact resistance exponentially increases as the square root of the charge-carrier concentration is decreased (i.e., as the potential barrier width is increased);
(ii) the contact resistance increases exponentially as the potential barrier height is increased; and
(iii) the contact resistance is virtually independent of temperature.
Calculated dependence of the ohmic-contact resis-tance on the charge-carrier concentration and the metal–semiconductor barrier height is shown in Fig. 4in the case where field emission is the main mechanism of current flow.
3.2.3. Thermal field emission. According to the theory of thermal field emission [30], the dependence of the forward current density J on the voltage V is exponential
(16)
where
(17)in this case, the saturation current density J s depends on
temperature as
(18)
J J s qV
E 0------⎝⎠
⎛⎞,
exp =E 0E 00E 00kT -------⎝⎠
⎛⎞;coth =J s AT πE 00q ϕb qV –χ+()
k E 00/kT ()
coth ------------------------------------------------------------=×χkT ------ϕb χ+T 0--------------–⎝⎠
⎛⎞
.exp 150
200
250300400
T , K
100
10 0 10 –1 10 –2 10 –3 10 –4 10 –5 10 –6 10 –7 10 –8
R c , Ω cm 2 q ϕ b = 0.025
e V
q ϕ
b =
0.05 e V
q ϕ b = 0.075 e
V
q ϕ b = 0.1 e V q ϕb =
0.1
25
e V
q ϕb
= 0
.15 e V
q ϕ
b =
0.
2 e V
q ϕ
b =
0.25 e V
q ϕ
b
= 0.3 e
V Fig. 3. Calculated temperature dependences of the resis-tance R c of the ohmic contact to GaAs at various values of the height ϕb of the metal–semiconductor potential barrier in the case of the current flow according to the theory of thermionic emission.1010101010
N d , cm –3
101010101010101010R c , Ω cm 2Fig. 4. Calculated dependence of the ohmic-contact resis-tance R c on the concentration of uncompensated donors N d and the height ϕb of the metal–semiconductor potential bar-rier in the case of the current flow according to the theory of field emission [29].
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Analysis of the formulas for thermal field emission shows the following data:
(I) the dependence of the forward current on voltage is exponential;
(II) at each temperature, the slope of this depen-dence on the semilogarithmic scale is equal to 1/E 0; this quantity depends on the intrinsic parameters of the semiconductor at a given temperature rather than on the barrier’s properties; and
(III) the cutoff on the vertical axis in the dependence of current on voltage on the semilogarithmic scale yields the value of saturation current, while the depen-dence of
is linear on the semilogarithmic scale; the slope of this
dependence corresponds to the height of the metal–semiconductor potential barrier.
J s E 00/kT ()coth T
-------------------------------------on
1E 0
-----The contact resistance R c = dV /dJ s per unit area at V (19)
Thus, if the current flow through an ohmic contact is controlled by thermal field emission, then
(i) the contact resistance increases exponentially as the potential barrier height ϕb is increased and
(ii) the contact resistance decreases as temperature is increased but to a much lesser extent than in the case of thermionic emission.
The contact resistance for nonalloyed Au/Ti-GaAs(2–10 nm)–n +-GaAs(n + = 1020 cm –3)–n-GaAs(n = 1018 cm –3)–GaAs ohmic structures in rela-tion to temperature and electron concentration in GaAs was calculated by Nien-Po Chen et al. [31] taking into account both the thermal field emission and field emis-sion (Fig. 5).
We note a particular case of the ohmic contact to a heterostrucrure with two-dimensional (2D) electron gas [32], for example, to GaN/Al x Ga 1 – x N. In this case,the current flowing from the metal to the semiconductor consists of the thermal emission current, longitudinal tunneling current, and the tunneling current caused by quantum wells with the latter current being predomi-nant. The probability of electron tunneling in the i th subband with the energy E i is given by
(20)
while the contact resistance is equal to
where (21)
In particular, the contact resistance of the Al/Ti/Ta–n-GaN/Al x Ga 1 – x N structures with a 2D electron gas decreases with temperature according to a law close to exponential, from ~10–4 Ω cm 2 at 77 K to ~10–6 Ω cm 2at 300 K.
Table 2 lists the parameters of semiconductors and metals used in calculations of the contact resistances.3.2.4. Metal shunts. It was shown in our recent studies [33, 34] that another mechanism of current flow (current via metal shunts) can manifest itself in alloyed metal–semiconductor contacts in the case where disso-lution of semiconductor in metal and recrystallization
R c ϕb
E 00E 00/kT ()coth ----------------------------------------⎝⎠
⎛⎞.exp ∝T E i ()q ϕb qV –E i χ–()
–E 00
----------------------------------------------–,
exp =R c 2qm *kT
π2ប
3--------------------Σ1Σ2+()1
–,
=Σ1E i /E 00i 1+--------------1E 002kT ---------+⎝⎠
⎛⎞q ϕb E i χ–()–E 00---
------------------------------–,exp E i χ
<∑
=Σ2E i /E 00i 1+--------------E i χ+kT -----------
---⎝⎠⎛⎞q ϕb E i χ–()
–E 00
---------------------------------–.
exp ln E i χ
>∑
=
T , K 10101010101010R c , Ω cm 21010N d , cm –3
1010101010101010Fig. 5. Resistance R c of the ohmic contact as a function of (a) temperature T for various concentrations of uncompen-sated donors N d in GaAs and (b) the concentration N d at var-ious heights of the metal–semiconductor potential barrier ϕb by the example of nonalloyed Au/Ti–n-GaAs ohmic struc-tures. The lines represent the calculated dependences based on theory of thermal field and field emission, while the points represent the experimental data [21].
occur in the course of heat treatment. These shunts are represented by metal atoms deposited onto the imper-fection lines (for examples, dislocations) and shunt the space-charge layer. In this case, the electric field is con-centrated at the edges of these “needles” and the current flow is realized owing to field emission.
The presence of metal shunts in semiconductor devices was also assumed previously, in studies of the resistance of epitaxial films based on TiN [35] and in gaining insight into the mechanism of the reverse-cur-rent flow in the Ni-GaN Schottky diodes [36, 37]. It was noted recently [38] that indium diffuses over disloca-tions during thermal annealing of GaN light-emitting diodes (LEDs) with contacts formed of an alloy of the indium and tin oxides (ITO). These shunts of indium atoms were observed directly. Wang et al. [39] used a transmission electron microscope to study the interface reactions in the Ti/Al/Mo/Au ohmic contacts to the Al/GaN heterostructures and showed that the reaction product is TiN. In this case, a correlation was observed between the appearance of TiN islands and the density of dislocations in the semiconductor; these dislocations acted as short circuit diffusion channels.
The current–voltage (I–V) and capacitance–voltage (C–V) characteristics of Schottky diodes based on GaAs and GaP under conditions of continuous heating were studied in [40–42]. It was established that the In-GaAs and In-GaP barrier contacts are transformed into ohmic contacts at temperatures that are much lower than the melting points for the metal or metal–semicon-ductor eutectic and prior to formation of any recrystal-lized layers (heavily doped or with graded-gap struc-ture); in this case, the ohmic contact is retained even after cooling of the structures.
One may assume that, in the course of heating, metal (for example, indium) atoms diffuse over disloca-tions or other imperfections; as a result, metal shunts are formed. It is these shunts that give rise to an ohmic contact.
In the case under consideration, if the atomic radius of metal is smaller than the semiconductor’s lattice con-stant, the ohmic-contact resistance is given by
(22) Here, ρ0 is the resistivity of the metal at T0;
α is the temperature coefficient of resistivity; W is the thick-ness of the space-charge layer; r is the atomic radius of the metal; and P is the density of dislocations or other imperfections onto which metal atoms can be deposited.
In Fig. 6, we show the calculated dependences of the ohmic-contact resistance on the dislocation density in the semiconductor in the case where shunts are respon-sible for formation of an ohmic contact. It can be seen that, at a low dislocation density (104–106 cm–2) charac-teristic, for example, for GaAs crystals, the mechanism of current flow over metal shunts is unimportant. At the same time, at a high dislocation density (108–1010 cm–2) characteristic, for example, for GaN [43], the resistance
R c
ρ0αT
+
()W
πr2P
-----------------------------.
=
Table 2. Work functions Φm for electrons leaving the metal and the electron-affinity energies X s in the semiconductor with energy gap E g and density of surface states D s for various semiconductors [10, 12, 44–49]
MetalΦm, eV Semiconductor E g, eV X s, eV D s, eV–1 cm–2
Ag 4.42ZnO 3.46–
Al 4.18ZnS 3.6–
Au 5.1–5.2ZnSe 2.7 4.09–
Co 4.97CdS 2.43 4.77 1.6 × 1013
Cr 4.4–4.6AlN 6.20.6–
Cu 4.59GaN (wurtzite) 3.39 4.1(1–2) × 1011 (for SiO2–GaN) Fe 4.46InN0.7–
In 3.97GaAs 1.425 4.0712.5 × 1013
Mg 3.61InAs0.354 4.9–
Mo 4.21GaP 2.26 3.8 2.7 × 1013
Ni 5.15–5.2InP 1.344 4.38–
Pb 4.04GaSb0.726 4.06–
Pd 5.17InSb0.17 4.59–
Pt 5.43–5.65C 5.46–5.6––
Sb 4.56Si 1.12 4.05 2.7 × 1013
Sn 4.43Ge0.661 4.0–
Ta 4.24H-SiC 3.23 4.05~1013
Ti 3.83–4.336H-SiC 3.0 4.07~1013
related to the metal shunts can become predominant in the total contact resistance.
In addition, in alloyed contacts to semiconductors with a fairly low dislocation density, the mechanism of shunting can also become important since the density of imperfections (in particular, dislocations) increases drastically in the case of alloying metal to a semicon-ductor due to the difference between lattice constants of the materials in contact.
Thus, if the current in an ohmic metal–semiconduc-tor contact flows over metal shunts, the contact resis-tance increases as temperature is increased, which is characteristic of the metallic type of conductivity.
4. EXPERIMENTAL RESULTS 4.1. Ohmic Contacts to II–VI Semiconductors In II–VI semiconductors (and also in the GaN and AlN nitrides), the surface-state density is low and an ohmic contact is formed with the metals for which either the work function of electrons Φm is smaller than the electron affinity X s for an electron in an n-type semi-conductor or the work function for electrons from metal
Φm is larger than the sum of electron affinities X s for the
semiconductor and the band gap E g (a p-type semicon-ductor); thus, we have
Φm < X s in the case of an n-type semiconductor,(23)Φm > E g + X s in the case of a p-type
semiconductor.(24)
The values of the work function for electrons escap-ing from metals Φm , the electron affinity of the semi-conductor X s , the band gap of the semiconductor E g ,and the density of surface states D s for various semicon-ductors are listed in Table 2 [10, 12, 44–49].
In recent years, ZnSe and alloys based on this com-pound began to be used in the fabrication of photode-tectors for blue and ultraviolet optical radiation, mainly for detection of laser radiation; the above materials can be easily grown on GaAs substrates.
Ohmic contacts to n-ZnSe can be produced, for example, with the use of In or a Ti-Pt-Au alloy (Φm =4.3 eV); in order to form the contact, it is only neces-sary to remove possible intermediate layers, which is accomplished by heat treatment at T > 200°C [50].At the same time, in the case of p-ZnSe, there are no metals with a work function Φm that exceeds the sum of the electron affinity X s and the band gap E g ; as a result,the potential barrier always exists. Therefore, in order to form an ohmic contact, one typically changes the composition of the near-surface region, for example, by growing a graded-gap p-ZnSe x Te 1 – x layer on the sur-face or using HgSe (X s = 6.1 eV) as the metal film; as a result, the barrier height is reduced to 0.4 eV [51].Examples of ohmic contacts to ZnSe and ZnO are given in Table 3 [52–65].
The mechanism of current flow in ohmic contacts to ZnSe and ZnO has not been studied in detail; however,the tunneling mechanism of current flow is assumed since the resistance of the contact to heavily doped n-ZnSe [52] and n-ZnO [] is typically temperature-independent. Yang and Schetzina [66] assumed that tunneling combined with thermionic emission takes place in p-ZnSe (p = 1017–1019 cm –3) with the barrier height surmounted by electrons estimated at ϕb =0.3 eV (for structures with p = 1017 cm –3).
4.2. Ohmic Contacts to Semiconductor Nitrides A similar situation is also observed in the case of an ohmic contact to n-GaN; the latter is a promising mate-rial for production of LEDs and photodetectors that operate in the short-wavelength visible and ultraviolet spectral regions. The Fermi level is almost not pinned at the surface [67]; however, conventional chemically stable metals have a work function larger than the elec-tron affinity for GaN (Table 4); the resistance of ohmic contact to GaN increases drastically with an increasing work function for electrons leaving the contact metal (Fig. 7) [68]. Therefore, in order to form an ohmic con-tact to the n-type semiconductors, multicomponent
40030020010010010–110–210–310–410–510–6
10–7
R c , Ω × cm 2P = 106 cm –2
107 cm –2108 cm –2109 cm –21010 cm –21011 cm –21012 cm –2
(a)
400300
200100
10010–110–210–310–410–510–610–7
(b)
P = 105 cm –2106 cm –2
107 cm –2
108 cm –2
109 cm –2
1010 cm –2
1011 cm –21012 cm –2
T , K
Fig. 6. Calculated dependences of the resistance R c of the metal–semiconductor ohmic contact on temperature T at various densities of defects (dislocations) P in the semicon-ductor in the case of the current flowing through the metal shunts in (a) GaAs and (b) GaN.
Low resistance of the metal-GaN ohmic contact (as low as 10–6–10–7Ω cm2 at high concentrations of charge carriers in the semiconductor) [70–72] is typi-cally related to the formation of nitrogen vacancies due to interaction of GaN with the contact material, for example, Ti. Such nitrogen vacancies form a damaged layer under the contact; this layer acts as a heavily doped layer.
In the case of p-GaN, there are also no metals with Φm > X s + E g = 7.5 eV; in this situation, either com-pounds with a high work function are used or a nar-row-gap near-surface layer is formed in the semicon-ductor [73].
For example, in the case of alloying Au/Ni to GaN at 600°C, several binary intermetallic phases are formed; these phases lower the potential barrier [74]. Alloying of Au/C/Ni makes it possible to additionally dope the near-surface layer [75] since C atoms act as acceptors. The Ru/Ni contact with annealing in the O2 atmosphere can also be used for p-GaN. The formed RuO2 compound reduces the effective height of the potential barrier, while NiO acts as a barrier to diffusion of released Ga and N atoms. This contact features a high transmission of light (84.6%) and low resistance (4.5 × 10–5Ω cm2) [76].
Table 3. Ohmic contacts to II–VI semiconductors
Metal Semicon-
ductor
Carrier
concentration,
cm–3
Annealing
temperature,
°C
Contact
resistance,
Ω cm2
Notes Refe-
rences
Ti/Pt/Au ZnSe n = 2 × 1019250 1.1 × 10–4[52] In ZnSe n = 2 × 1018250–300Compounds are not formed, In diffusion[54] In/Au ZnSe n = 101710–2[55] Si-As/BeTe ZnSe p The metal/Si-As/BeTe-ZnSe structure[56] BeTe ZnSe p = 1018104Formation of Be x Zn1 – x Te y Se1 – y[57] BeTe ZnSe p = 2 × 1017 6 × 10–2[58] Cu/Au ZnSe p = 4.5 × 10180.167[55] Pd ZnSe p250Formation of the Pd-Zn-Se phase[59, 62] p+-ZnTe ZnSe p = 7 × 1016 5 × 10–2Resonance tunneling of holes[53] Ti/Au ZnO n = 1019300 6 × 10–8Roughening of the surface[] Cu x O CdTe 2.2 × 10–2[65]
Table 4. Ohmic contacts to n-GaN
Metal Carrier concent-
ration, cm–3Annealing tem-
perature, °C
Contact resis-
tance, Ω cm2Note References
Ti/Al n = 10178 × 10–6[77] n = 10178 × 10–6[71]
n = 3.67 × 10188.63 × 10–6[78] Ti, TiN, Ti/TiN n = 7 × 1017400–900 4 × 10–6Reaction of Ti and GaN[79] Ti/Al/Ni/Au n = 2 × 1017 1.19 × 10–7
n = 4 × 10178.9 × 10–8[80] Ti/Al/Pt/Au Nanotubes700–800 1.8 × 10–2[81] Ti/Al/W2B/Ti/Au8007 × 10–6[82]
Si/Ti900 3.86 × 10–6Lowering of the SiTi barrier
and doping with donors [83]
[84]
Ge/Cu/Ge10–5Donor-like V N vacancies[85] In-Sn oxide n = 1019 5 × 10–4[86]
The most widely used contacts to n-GaN are given in Table 4 [71, 77–86], and contacts to p-GaN are listed in Table 5 [79, 87–105].
In Table 6, data on the current flow mechanisms in ohmic contacts to n- and p-GaN are given [34, 83, 84,
88, 91, 106–112]. In the case of heavily doped GaN, the resistance of an ohmic contact is nearly independent of temperature (Fig. 8b, curve 1) and decreases as the con-centration of the majority charge carriers is increased (Fig. 8a), which substantiates the assumption that the main mechanism of the current flow is field emission (tunneling) [80, 106–108]. In the case of medium-doped GaN, the contact resistance decreases as temper-ature is increased, which makes it possible to assume that the main mechanism of the current flow is the ther-mionic emission 69, 109, 110, 112]. It was shown by Kwak et al. [112] that the ohmic-contact resistance decreases as temperature is increased; however, the dependence of R c on T was slight, and it was assumed that the main mechanism of current flow is hopping conductivity with involvement of deep-level centers.Thus, the resistance of an ohmic contact to GaN either is temperature-independent or decreases as temperature is increased. Only Lu et al. [107] observed an increase in the contact resistance as temperature was increased from 50 to 300°C. This behavior was attributed to orig-ination of imperfections in the GaN layer as tempera-ture was increased; these imperfections presumably brought about an increase in the height of the metal–semiconductor potential barrier.
Φm , eV
101010101010R c , Ω cm 2Fig. 7. Experimental dependence of the resistance R c of the metal–n-GaN ohmic contact on the work function Φm for electrons leaving the contact metal.
Table 5. Ohmic contacts to p -GaN
Metal Carrier concentration, cm –3Annealing tem-perature, °C Contact resis-tance R c , Ω cm 2Notes
References Pd p = (0.28–2.5) × 1017
Formation of acceptor-like states
[87]Pd/Ru p = 3 × 1017500
2.4 × 10–5[88]Pd/Au p = 3 × 1017 10–4[]PdAu
p = 1018 1.5 × 10–6[]Pd/Au/InGaN p
1.1 × 10–6Formation of p -In 0.19Ga 0.18N [90]Ni
p > 1.7 × 1019750, 950Heavy doping [91]Ni/Au/InGaN p
No annealing
(12–6) × 10–3Heavy doping
[92]Ni/In p = 2 × 1017(8–9) × 10–3[93]Ni/Pt/Au p = 9.4 × 1016 2.1 × 10–2[94]Ni/Au p = 2 × 1017 4 × 10–6[95]Pt/Ni p = 1.7 × 10178 × 10–3
[96]Ni/Au p 500Formation of NiO or a -Ni-Ga-O [97][98]Ni/Au
p 600 6 × 10–4Formation of Ga vacancies
[79]In–Sn oxide p
500
4.5 × 10–2Formation of p -In 0.1Ga 0.9 and Ga vacancies
[99]Pt/Ru p = (2–3) × 1017 2.2 × 10–6[100]Ta/Ti p = 7 × 1017 3 × 10–5[101]Ni/Cr/Au p = 5 × 1017
1.6 × 10–2[102]Ni/Pd/Au 4.6 × 10–6[103]In 0.19Ga 0.18N 1.1 × 10–6[104]Ag/Pd
p = 5 × 1017
330–530(4–6) × 10–5
A decrease in the barrier height
[105]
We previously observed [34] an increase in the resistance of the In–n-GaN ohmic contact with temper-ature, which is characteristic of metallic conductivity (Fig. 9); it was assumed that the ohmic contact of alloyed In to GaN, during the formation of which dis-solution of semiconductor in metal occurs, can be formed due to the appearance of metallic shunts that thread through the space-charge layer as a result of dep-osition of In atoms onto the near-surface dislocations and other imperfections of the semiconductor. The den-sity of dislocations in conventional GaN crystals is 107–108 cm–2. The dislocation density determined from the temperature dependence of the ohmic-contact resis-tance was estimated at ~108 cm–2; i.e., it was close to the dislocation density in ordinary GaN crystals.
Alloys in the GaN-AlN system are very promising for ultraviolet photoelectronics; however, fabrication of ohmic contacts to Al x Ga1 – x N alloys and, in particular,to n-GaN, encounters serious difficulties since the elec-tron affinity in n-AlN is very small (0.6 eV), while the Fermi level is virtually not pinned at the surface. Ohmic contacts to GaN–AlN alloys are typically formed using the same scheme as in the case of GaN.
In Table 7, we list examples of ohmic contacts to GaN–AlN alloys [113–119].
Blank et al. [120] studied the mechanism of current flow in the Pd–p-Al1 – x Ga x N ohmic contact at composi-tions close to GaN (x = 0.94). It was found that, at a concentration of uncompensated acceptors of 3 ×1018 cm–3, the ohmic-contact resistance decreases exponentially as temperature is increased, which is accounted for by the thermionic mechanism of current flow. The potential barrier height determined from the dependence of R c on T was found to be equal to 0.05 eV. However, at N a – N d = 3 × 1018 cm–3, the value of R c is already independent of temperature, which makes it possible to assume that the main mechanism of the cur-rent flow at the concentrations under consideration is tunneling.
Table 6. The current flow mechanisms in ohmic contacts to n- and p-GaN
Contact Carrier concen-
tration, cm–3Temperature
dependence
Concentration
dependence
Barrier
height
Current flow
mechanism
Refe-
rences
n-GaN (theory)Decreases
superlinearly
[108]
Decreases
sublinearly
Tunneling
Ti/Ag–n-GaN(1.5–1.7) × 1018Decreases
∝
Tunneling[106]
Ti/Ag/Ni/Au–n-GaN(4–30) × 1017The same Tunneling[77] Ti/Ag/Pd/Au–n-GaN 6 × (1017–1020)Increases Decreases Tunneling[107] Ti/Al/W2B/Ti/Au–n-GaN Does not
depend
Tunneling[82] Ni–p-GaN>1.7 × 1019The same Tunneling[91]
Pt–n-GaN 2 × 1017Decreases
∝ exp(T–1/4)Thermionic emission
at T≥ 200 K
[109] Tunneling at T≤ 200 K
Pt–n-GaN(1.8–10) × 1017Decreases
∝ exp(1/T)
0.13Thermionic emission[110]
Si/Ti–n-GaN Decreases
∝ exp(1/T)
Thermionic emission[111]
Au/Ti/Si/Ti–n-GaN Decreases
∝ exp(1/T)
Thermionic emission[83]
[84] In–n-GaN1017Increases Metal shunts[34] Pd/Ru–p-GaN 3 × 1017Thermionic emission before
annealing, tunneling after
annealing at 500°C
[88]
Pd/Pt/Au–p-GaN(2–22) × 1017Decreases
∝ exp(T–1/4)
Hopping conductivity[112] 1/n
Guse œnov [115] studied the resistance of ohmic con-tacts to (AlN)x (SiC)1 – x heterostructures; it was shown
that, as the heterostructure’s band gap E g increases, the
contact resistance increases as
(25)This dependence functionally corresponds to the dependence of R c on E g for GaAs 1 – x P x alloys; this dependence was reported previously [121].
In semiconductor devices, high-resistivity AlN lay-ers are often used as substrates for the formation of active layers in devices. Formation of thin-film ohmic contacts to this semiconductor encounters serious diffi-culties; in this case, one can use the formation of
alloyed ohmic contacts with the mechanism of current flow through metal shunts [34].
R c Ω c m 2 [] 2.710 9– E g eV [] 0.28----------------- ⎝⎠
⎛⎞ .exp × = InN is also promising for medium-wavelength opto-electronics. Since the band gap of InN is about 0.7 eV ,the InN–GaN–AlN alloys can be used in solar cells and photodetectors in the infrared, visible, and ultraviolet spectral regions. Examples of ohmic contacts to InN and InGaN alloys are given in Table 8 [49, 122–127].
4.3. Ohmic Contacts to Semiconductor Arsenides,
Phosphides, and Antimonides
Semiconductors of Group IV and III–V semicon-ductors (aside from nitrides and n- InAs) have a high concentration of surface states at the free surface; these states are located deep in the band gap, which brings about a rigid pinning of the Fermi level at the surface.Therefore, in order to form an ohmic contact to the semiconductors under consideration, one has to:(i) reduce the density of surface states,(ii) reduce the potential barrier height by varying the chemical composition of the near-contact region, or
(iii) increase the charge-carrier concentration in the
near-contact region.
At present, gallium arsenide is widely used in semi-conductor electronics and optoelectronics as a material
for high-speed integrated circuits, microwave devices,detectors of nuclear particles, LEDs, and lasers. At the same time, gallium arsenide is a direct-gap model semi-conductor suitable for studies of electrical and optical phenomena. The density of surface states in GaAs is
very high (higher than 10 14 cm –2 eV –1 ), and the height of the metal–GaAs potential barrier (the Schottky bar-rier) is nearly independent of the metal’s nature, due to pinning of the Fermi level at the surface, and equals approximately 0.9 eV .
The density of surface states in a semiconductor can be reduced by passivating the surface in solutions that
contain sulfur ions. In the course of treatment of GaAs
10 10 –2 10 –3 10 –4 10 –5 R c , Ω cm 2 10 3 / T , K –1
10 10 10 10 10 10
Fig. 8. (a) Dependence of the resistance of the Ti/Ag– n- GaN ohmic contact on the concentration of uncompensated
donors N d at 300 K. The mechanism of current flow: tunnel-ing ( q ϕ b = 0.067 eV) [106]. (b) Dependence of the resis-tance R c of the Pt– p- GaN ohmic contact on temperature:
( 1 ) Concentration of uncompensated acceptors N a =
10 18 cm –3 and the current flow mechanism is tunneling
( q ϕ b = 0.42 eV); ( 2 ) N a = 1.8 × 10 18 cm –3 and the current flow
mechanism is thermionic emission ( q ϕ b = 0.53 eV) [110].
T , K
R c –3 2 Fig. 9. The resistance R c of the alloyed In– n- GaN ohmic contact on temperature. The current predominantly flows through metal shunts [34].
in the Na2S or (NH4)2S solutions, the near-surface impurity O atoms (responsible for the surface states) are replaced with S atoms that are kept at the surface because of chemical adsorption. The energy released as a result (lower than 40 kJ/mol) is lower than the energy released during chemical adsorption (higher than 100 kJ/mol) and is not high enough for formation of intrinsic defects that give rise to pinning of the Fermi level [128–131]. The density of surface states D s in GaAs decreases to 2 × 1013 cm–2 eV–1 as a result of treatment in (NH4)2S and to 1013 cm–2 eV–1 as a result of treatment in (NH4)2S x. A still lower density of sur-face states D s in GaAs (7.6 × 1012 cm–2 eV–1) was obtained in the case where a thin (3.5 nm) n-GaAs:Be layer was grown on the surface (n = 5 × 1016 cm–3) [132], as a result of which the Fermi level nearly was not pinned at the surface of the GaAs semiconductor.
It is noteworthy that passivation of semiconductors in solutions containing ions of sulfur or other elements kept at the surface due to chemical adsorption reduces the density of surface states for other materials as well. For example, treatment of the GaN surface in (NH4)2S x brought about a decrease in the density D s from 1012 to 8.3 × 1010 cm–2 eV–1 [133]; in this case, the height of the Ni/Cu–n-GaN Schottky barrier was 1.099 eV, which is close to the theoretical limit (1.10 eV). Passivation of
the Ti/Al–n-GaN:Si ohmic structures (n = 3 × 1018 cm–3) reduced the contact resistance approximately by two orders of magnitude owing to removal of oxide from the GaN surface and to a shift of the Fermi level towards the conduction-band bottom [134]. Passivation of 4H-SiC in solutions containing the NO and NH3 ions brought about a decrease in the density D s from ~1013 to ~ 2 × 1012 cm–2 eV–1 [135].
Table 7. Ohmic contacts to alloys in an AlN–GaN system
Metal Semiconductor Annealing tem-
perature, °C Contact resis-
tance, Ω cm2Note
Refe-
rences
Ti/Al/Ti/Au n-AlGaN/AlN700 5.6 × 10–5[113] Al/In n-AlGaN/AlN[114] Al, Al/Cr, Al/N, Al/Pt(AlN)x(SiC)1 – x120010–4–10–2[115] Ti/Al/Mo/Au/Si AlGaN/AlN80010–6Formation of TiSi and a dec-
rease in the barrier height
[116] Ti/Al/Mo/Au AlGaN/GaN Formation of TiN[117] Ni/Au Superlattice
p-Al0.15Ga0.85N/GaN
(p = 1018 cm–3)
650 4 × 10–6[118]
Ni Superlattice
p-AlGaN/GaN
400–5009.3 × 10–4[119] Al/Ti n-AlGaN/GaN900–950 5.6 × 10–6[114] Table 8. Ohmic contacts to InN and to InN-based alloys
Metal Semiconductor Carrier concen-
tration, cm–3Annealing tempe-
rature, °C
Contact resis-
tance, Ω cm2Note
Refe-
rences
Ti, Al, N n-InN(1.5–2.3) × 1018Without annealing 1.4 × 10–7–10–6[122] Ti/Pt/Au n-InN 5 × 1020300–420 1.8 × 10–7[123] Ti/Pt/Au InN380(5–6) × 10–7[123] W n-In0.17Ga0.83N 1.63 × 1019950 2.7 × 10–8Formation of β-W2N[124] Si0.44, Ti/Al n+-In0.65Ga0.35N Without annealing(1–4) × 10–7[125] n-InN Without annealing(1–10) × 10–7Field emission[125]
n+-In0.75Ga0.25N Without annealing10–4[125] W, WSi0.44n+-In0.65Ga0.35N Without annealing(1–4) × 10–7Field emission[126] n-InN Without annealing(1–10) × 10–7[126] W, WSi0.44, Ti/Al n+-In0.65Ga0.35N900(1–4) × 10–7Field emission[127] n-InN600(1–10) × 10–7[127]
n+-In0.75Ga0.25N10–4[127]
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The Al–n-GaAs ohmic contact with the resistance of (1–3) × 10–4 Ω cm 2 was prepared by treating the surface in H 2S solutions in order to reduce the density of sur-face states in n-GaAs (n = 1018 cm –3) [136]; however,this method has not been widely recognized.
The most widely used method of forming the ohmic contacts to GaAs consists in formation of a heavily doped (with the carrier concentration as high as 1020–1021 cm –3) surface layer, which narrows appreciably the metal–semiconductor potential barrier. Most often, this layer is formed owing to interfacial chemical reactions that bring about dissociation of GaAs and origination of a new layer of heavily doped GaAs [74].
For example, in the course of heat treatment of the widely used Al/Ge/Ni contact, the latter at first reacts with GaAs at T < 250°C and forms Ni x GaAs; this phase decomposes at T > 250°C with resulting formation of NiGa y and NiAs z compounds. In this case, Ni reacts also with Ge (giving rise to NiGe compound) and with Al (giving rise to Ni x Al y compound); in the course of cooling, the n +-GaAs:Ge layer grows with the electron concentration in this layer being as high as 1020–1021 cm –3 [137].
In the case of the Ni/[Au + Ge(27%)]/Ni/Au–n-GaAs contacts, Ge first diffuses from the Au + Ge alloy to the upper layer, while Ni reacts with GaAS and forms Ni x GaAs. At temperatures of 375–400°C, Au reacts with Ga and forms the β-AuGa phase, while Ge pene-trates into Ni x GaAs and replaces Ga. The contact acquires the β-AuGa/NiAs:Ge/GaAs structure, while a new heavily doped GaAs layer is formed as a result of cooling [138]. The resistance of these contacts to n-GaAs is as low as 3.6 × 10–6 Ω cm 2 at n = 1016 cm –3
[139], 10–6 Ω cm 2 at n = 2 × 1016 cm –3 [140], 5 ×10−7 Ω cm 2 at n = 1.5 × 1017 cm –3 [141], and 4 ×10−7 Ω cm 2 ar n = 2.2 × 1018 cm –3 [141].
As the technology was improved, the resistance of the ohmic contact to GaAs was reduced by approxi-mately an order of magnitude in the decade [6]; the contact resistance was inversely proportional to the charge-carrier concentration [142].
The other method for attaining the ohmic contact to GaAs consists in the formation of a narrow-gap (most often, Ga 1 – x In x As) near-surface layer. In InAs, the sur-face Fermi level is pinned in the conduction band, which appreciably reduces the height of the metal–semiconduc-tor potential barrier in the alloys of a GaAs–InAs system compared to the height of the metal–GaAs barrier. The In contact to p- and n-GaAs can serves as an example of the above contact. This contact is formed as a result of heating to 300°C; the lowest resistance of the contact is observed after heating at 500°C. At higher annealing temperatures, evaporation of As atoms becomes notice-able and increases the contact resistance.
Various types of ohmic contacts to n-GaAs are described in Table 9 [143–172]; the data on ohmic con-tacts to p-GaAs are given in Table 10 [173–182]; and ohmic contacts to ternary alloys based on GaAs are rep-resented in Table 11 [174, 181, 183–197]. Results of the studies carried out in the last decade are given; earlier studies were analyzed in reviews [6, 14].
As a result of technological efforts, the resistance R c of ohmic contacts to GaAs has attained very small val-ues (10–6–10–8 Ω cm 2; see, for example, [21, 198–202]);the mechanism of current flow in ohmic contacts to GaAs was analyzed in [111, 203–211].
The contacts in which appreciable dissolution of semiconductor in the metal does not occur were studied in [111, 148, 151, 154, 208–211] (Table 12): the con-tacts were either nonalloyed, or thin-film, or were sub-jected to a heat treatment at comparatively low temper-atures (~300°C). Contacts to GaAs with a high concen-tration of doping impurity (1018–1020 cm –3) were mainly studied in the aforementioned publications. The potential barrier height in the above contacts was fairly large: 0.14–0.26 eV [205], 0.5 eV [209], and 0.3–0.5 eV [206]; the main current flow mechanism was tunneling,with the low contact resistance ensured by pronounced narrowing of the potential barrier (Fig. 10).
At the same time, attempts to form a heavily doped near-contact region failed for a lightly doped GaAs (the electron concentration lower than 1017 cm –3); therefore,the potential barrier height was reduced as a result of interfacial reactions and was as low as 0.068 eV [111]and 0.09 eV [204]. This circumstance ensured a sub-stantial above-barrier current and thermionic mecha-nism of its flow. The thermionic mechanism of current flow was also detected in the case of the In 0.53Ga 0.47As alloy (Fig. 11); it is noteworthy that the current flow mech-anism changed to that of thermal field emission [207].
N d 1/2
–1010–cm
3/2,1010101010R c , Ω cm 2Fig. 10. Dependences of the resistance R c of the ohmic con-tact to p-GaAs on the concentration of uncompensated acceptors N a in the initial material at 300 K. The current flow mechanism is tunneling (q ϕb = (0.4–0.6) eV). The lines represent calculated dependences, while triangles,squares, and circles represent the experimental data [209].
Table 9. Examples of ohmic contacts to n-GaAs
Metal
Carrier
concentration,
cm–3
Annealing
temperature,
°C
Contact
resistance,
Ω cm2
Note References
Au/Ti 5 × 1018– 2 × 10–6[143] Au/Ti Nonalloyed
contact
2 × 10–6 (40 K)[151]
Au/Al/Ti 2 × 1018Without
annealing 3.7 × 10–3Intermediate GaAs eliminates
pinning
[144]
Au/Pt/Ti– 3 × 10–4[148] Au/Ti/W/Ti400 5.5 × 10–6Treatment of the surface in
(NH4)2S
[146] Au/Ge/Ni/Au 4 × 1017 5.6 × 10–6[147] Au/Pt/Ti/GaS 2 × 1018300 4.1 × 10–6Formation of TiGaS[157] Ni/In/Ge650Formation of In x Ga1 – x As[150] Ni/Ge/Au Ni is used for wetting[156] In375 3 × 10–6Formation of an In x Ga1 – x As
graded-gap layer
[158]
n+-In x Ga1 – x As Nonalloyed
contact
10–7Tunneling[154] In0.7Ga0.3As/Ni/W2Ni/W550[170]
[171] Pd/In(1.6–1.8) × 101860010–6Formation of In x Ga1 – x As[172] Pd/Ge 4 × 10–7[169] Pd/Sn360 3 × 10–5[145] Pd/Sn, Pd/Sn/Au360–4308 × 10–6–3 × 10–5[163]
[1]
[165]
[166] Pd/Sn, Pd/Sn/Au Nonalloyed
contact
[153] Pd/Ge/Ti/Au340 2.8 × 10–6Formation of the AuGa phase[160]
[161] Pd/Ge/Ti/Pt400 2.4 × 10–6Formation of Ga5Pd[149] Pd/Ge/Ti/Pt380–450(2.4–5.3) × 10–6[152] Pd/Ge/Au/Pd/Au400 2 × 10–6[155] Pd/Ge/Au/Pd/Au400 2.1 × 10–6Formation of AuGa and
Pd5Ga2
[159] Pt/Ti/Ge/Pd 5 × 1018450–600Formation of Ge8Pd21[162] Ge/Cu7 × 10174007 × 10–7Formation of a heavily doped
GaAs : Ge layer
[167]
WSi400 6 × 10–6Formation of β-AuGa and
WSi2
[168]
SEMICONDUCTORS V ol. 41No. 112007
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as temperature was increased (the same as for nonal-loyed contacts), and the main mechanism of current flow was the thermionic emission.
Gallium phosphide is another III–V semiconductor with a high density of surface states. The Fermi level at the GaP surface is pinned practically at the midgap.Gallium phosphide is widely used in LEDs for red, yel-low, and green lights and in photodetectors of UV radi-ation [212, 213]. Ohmic contacts to GaP were fabricated in many studies (the examples are given in Table 13)
[33, 214–221]; however, the current flow mechanism has been studied in these contacts very little.
An anomalous temperature dependence of the ohmic-contact resistance R c for the In–n-GaP contacts was detected by Blank et al. [33]; this resistance increased as temperature was increased; it was con-cluded that the main mechanism of current flow in an ohmic contact is the current flow through metallic shunts (Fig. 13). As a result, it becomes understandable why In forms an ohmic contact to GaP. In the case of In contact to GaAs, a graded-gap In x Ga 1 – x As phase can be formed; it is noteworthy that it is not only a solid solution but also n-InAs in which the Fermi level is pinned in the conduction band. At the same time, in the
Table 10. Ohmic contacts to p -GaAs
Metal Carrier concen-tration, cm –3Annealing tem-perature, °C Contact resis-tance, Ω cm 2
Note References Au/Ti
1017
9 × 10–6
[173]Au/Ge, Au/Ti Semi-insulating GaAs : Cr ρ = 106–107 Ω cm 2
300–320[181]Au/Ti/Pd
320–380[180]Au : Cu/Pt : Ir/Ti p +
400 1.47 × 10–6Pt–Ti barrier for the deep-level Cu impurity
[174]Ni/Pd/Au 300
2 × 10–6
[175]In
Semi-insulator
Laser-assisted deposition [182]In x Ga 1 – x As Can be used for both n - and
p -GaAs
[178]PdIn
<40010–7
Convenient contact for micro-wave devices
[176]Pd/Ge/Ti/Pt, Ti/Pd p +550[179]ε1-Cu 3Ge
7 × 1018400
5 × 10–6
[177]
10–4
10–5
10–6
R c ,
2Fig. 11. Dependences of the resistance R c of the Pt/Ti–p -In 0.53Ga 0.47As on temperature T at various conditions of contacts’ treatment. The mechanism of current flow for the contacts not subjected to heat treatment is thermionic emis-sion (q ϕb = 0.13 eV). As the annealing temperature is increased, the current flow mechanism transforms into ther-mal field emission [207].
103/T , K –1
R c , Ω cm 2Fig. 12. The resistance R c of the alloyed In–n-GaAs ohmic contact on temperature T . The current flow mechanism is thermionic emission (q ϕb = 0.03 eV) [203].
Metal Semiconductor Annealing tem-
perature, °C Contact resis-
tance, Ω cm2Note References
AuBe/Au,
Pd/AuBe/Pt/Au
AlGaAs/GaAs400 4 × 10–6[193] Au/Pt/Ti/WN x n-InGaAs250–45010–8–10–7[187] Au/Pt/Ti/WSiN n+-InGaAs 2 × 10–7[190] Au/Ni/Au/Ge/Pd n-InGaAs400[186] Au/Ni/Au/Ge/Pd n-InGaAs40010–6[1] Pd/Ge AlGaAs/GaAs[197] Pd/Ge n-InGaAs400[191] Pd/Si/Ti/Pt n-InGaAs425(1–2) × 10–6[183] Pd/Ge/Ti/Pt n-InGaAs400 3.7 × 10–6Formation of PdGe and dif-
fusion of Ge
[184]
Pd/Pt/Au/Pd p-InGaP
p = 3 × 1019 cm–3415–440Formation of PdGa, PdAs2,
and In x Ga1 – x P
[192]
Pd/Ga/Ti/Au n-AlGaAs/InGaAs(2.3–95) × 10–6The contact is formed owing
to Au2Al and β-AuGa
[195]
Pd/Si/Pd/Ti/Au n-InGaAs300–400 4.3 × 10–7Formation of the Pd2Si
phase
[188] Pd/Ge(Si)/Pd/Ti/Au n-InGaAs425(0.9–1.1) × 10–6[174]
[181]
Ti/Pt/Au GaAs with vertical
InGaAs layers (1–10) × 10–6Formation of a superlattice,
ϕb = 0.14–0.26 V
[196]
Be–In/As/Au AlGaAs–p-GaAs
p = 3 × 1019 cm–3
[194] WN x/WN0.5x/W n-InGaAs400 2 × 10–7[185] Table 12. Mechanisms of current flow in ohmic contacts to GaAs
Contact Charge-carrier
concentration, cm–3Current flow mechanisms Potential barrier
height, eV References
In–n-GaAs n = 4 × 1015Thermionic emission0.03[203] Au/Pt/Ti–n-GaAs n > 1018Thermionic emission0.09[148] Pt/Ti/p-GaAs p = (5–10) × 1018Thermionic emission0.068[111] InAs/n-GaAs n = 1020Tunneling0.14–0.26[205] Au/Ti–GaAs>5 × 1018Tunneling<0.7[151] n+-In x Ga1 – x As–n-GaAs Tunneling[154] Ti/Pd, NiGeAu–GaAs Tunneling[208] Ti/Pt/Ag–p-GaAs p = 4 × 1020Tunneling0.5[209]
Au/Ti–n-GaAs (theory)n = 1020Tunneling between metallic state
and the conduction band 0.3–0.5[210]
n = 1018
Ni/In x Ga1 – x As/n-GaAs–0.13[211]
case of GaP, formation of a graded-gap phase can only bring about the appearance of InP on the surface. It is noteworthy that the latter semiconductor has a fairly wide band gap with the Fermi level pinned deep in this gap. We may assume that, in this case, In is deposited on dislocations and other imperfections and forms metal shunts. The density of metal shunts in GaP crys-tals, determined from the temperature dependence of the contact resistance, was found to be nearly tempera-ture-independent and equaled 107 cm–2, which is close to the dislocation density in GaP. In the case of GaAs, the dislocation density is usually lower by three–four
SEMICONDUCTORS V ol. 41No. 112007orders of magnitude, so that the shunts do not play an important role in the current flow mechanism. As a result, thermionic emission is the main mechanism of current flow in the In–GaAs contact, while metallic shunts are related to the main mechanism of current flow in the In–GaP alloyed contact.
The InP compound and, especially, the InGaP alloys grown on the InP substrates are used for the fabrication of field-effect transistors with a 2D electron gas and a high electron mobility. Examples of ohmic contacts to n-InP are given in Table 14 [222–236], while examples of similar contacts to p-InP are given in Table 15 [226, 237–248]. In Table 16 [249–257], we give the examples of ohmic contacts to the InGaAs/InP and InAlAs/InP alloys.
The main mechanism of current flow in ohmic con-tacts to p-InP is the thermionic emission through the barrier with qϕb < 0.2 eV [258], whereas tunneling rep-resents the main mechanism of current flow through the AuZn(Ni) contact to heavily doped n-InP (n = 1.4 ×1020 cm–3) [259].
The GaSb compound and alloys on its basis are used as materials for LEDs and photodetectors in the mid-IR spectral region [260]. The Fermi level at the GaSb sur-face is pinned near the valence-band edge [261]. Exam-ples of ohmic contacts to GaSb and alloys on its basis are given in Table 17 [261–272].
In Table 18 [273–278], we give examples of ohmic contacts to narrow-gap InAs and HgCdTe semiconduc-tors. The current flow mechanism in these contacts was studied inadequately.
4.4. Ohmic Contacts to Semiconductors of Group IV
Ohmic contacts to Si and Ge have been already stud-ied for several decades and were considered in detail in the monographs by Milnes and Foight [9] and by Rod-erick [10]; therefore, we will not consider those struc-tures and will restrict ourselves to dealing with ohmic contacts to new semiconductors, diamond and silicon carbide.
Diamond is the semiconductor with the widest band gap among semiconductors used in optoelectronics (E g = 5.5 eV, E0≈ 7.3 eV). Diamond can be used in pho-todetectors for the short-wavelength, especially, the vacuum (ultraviolet) spectral region. Ohmic contacts to diamond are typically formed on the basis of the Ti, Mo, or Ta metals that form carbides in the course of annealing. Examples of ohmic contacts to diamond are given in Table 19 [279–298]. Detailed studies of the current flow mechanisms in these contacts have not been carried out. In heavily doped diamond crystals of p- and n-type, the main current flow mechanism is believed to be tunneling [280, 282, 291, 294, 298] on the basis of the fact that the contact resistance is inde-pendent of temperature.
Table 13. Ohmic contacts to GaP
Metal Semiconductor Carrier concen-
tration, cm–3Annealing tem-
perature, °C
Contact resis-
tance, Ω cm2Note References
Ai/Si/Pd n-GaP55010–5Solid-phase epitaxy of
Si onto GaP
[214]
Si/Pd n-GaP 5 × 1017350–650 2 × 10–4Solid-phase epitaxy of
Si onto GaP [215] [216]
In n-GaP 3 × 1017Metal shunts[33]
Pd/Zn/Pd p-GaP 2 × 1017550 6 × 10–5Formation of the p-p+-ZnP2
and Zn3P2 phases [217] [218] [219] [220]
Ni, Ti + Au n-GaP : Be 5 × 1019400[221] p-In0.49Ga0.51P 2 × 1019
T, K
R c, 10–4 Ω cm2
Fig. 13. Dependence of the resistance of the In–n-GaP
ohmic contact on temperature T. Current flows through the
metal shunts [33].
SEMICONDUCTORS V ol. 41No. 112007
Silicon carbide is a semiconductor that is actively used in the fields of high-temperature, high-frequency, and high-power electronics. This semiconductor has several polytypes; the most widely encountered of these are 4H-SiC (E g = 3.23 eV, E0≈ 5 eV) and 6H-SiC (E g = 3.0 eV, E0≈ 5.5 eV). Silicon carbide is a semicon-ductor with predominantly covalent bonding and the surface states caused by the presence of carbon vacan-cies. The height of the potential barrier at the metal–SiC interface depends heavily on the work function for elec-trons that leave the metal [299, 300].
Ohmic contacts to n-4H-SiC and n-6H-SiC are often fabricated on the basis of Ni (ΦNi = 5.15–5.2 eV). These contacts can be formed both without annealing and using a heat treatment, as a result of which oxides and
Table 14. Ohmic contacts to n-InP
Metal Carrier concentra-
tion, cm–3Annealing tem-
perature, °C
Contact resis-
tance, Ω cm2Note
Refe-
rences
Au/Ge/Ni8 × 101845010–8[226] Au/Ge/Ni1017250–40010–7Formation of Ni2P + Al10In3[230] Au/Ge/Pd350 2.5 × 10–6Heavy doping with Ge[233] Au/Pd/Te 4 × 101510–4Formation of In2Te3[231]
4 × 101810–6
Au/Si/Pt550 2.77 × 10–5[225] Au/Ru/Au-Ge/Ni40010–7[236] Au/Pt/Au/Ge500 2.15 × 10–6[232] Ni/AuGe/Au300[224] Ni/Au/Pt/Au/Pt/Ti/Ni Formation of the Ni–P phase[234] Pd/Ge350 4.2 × 10–6[233] Ge/Pt/Ge/Pt5007.71 × 10–7Doping with Ge[235] Al/Ti600Formation of Al/Ti/In/Ti–p-InP[228] Ti/Pt/Au Nonalloyed
contact
3.4 × 10–6Formation of InN[222]
W–Sb40010–6P diffuses into W, and the In–Sb
phase is formed
[223] W/Sb, W–In–Sb40010–6[227] WS0.79 1.4 × 1020 (InP : Te)10–6[229] Table 15. Ohmic contacts to p-InP
Metal Carrier concen-
tration, cm–3Annealing tem-
perature, °C
Contact resis-
tance, Ω cm2Note References
Au/Zn 5 × 10187 × 10–6[226] Au-Be/Ru/Au(1–4) × 1018280(2–7) × 10–4[246] Au/Zn/Au/Ti/Au Formation of Au x In y and Au2P3[242] Ni, Pd/Zn/Ni, Pd7 × 10–5Formation of Nd2.7InP and Pd2InP[240]
[241] Pd/Zn/Pd/Au7 × 10–5Formation of Pd2InP–PdP2[237] Pd/Zn/Pd(Pt)4007 × 10–6[238] Pd/Sb/Zn/Pd500 2 × 10–6Formation of the InSb phase[239] Ge/Pd(Zn)40010–5–10–4[247] Sb/Zn/Pd375Formation of Pd2InP[243]
Sb/Zn/Au/Nb325 4 × 10–5Removal of oxide; diffusion of Au
and Zn into InP [244] [245]
Zn3P2/InP10–5The Zn3P/InP heterojunction[248]
SEMICONDUCTORS V ol. 41No. 112007other layers are removed from the semiconductor sur-face. Examples of ohmic contacts to 4H-SiC are given in Table 20 [301–328], while Table 21 lists examples of ohmic contacts to 6H-SiC [329–339].
Fabrication of contacts to p-SiC encounters serious difficulties due to the wide band gap of the semiconduc-tor. To this end, metals with a high work function (Ni, Pt, Pd, and Au) can be typically used; these metals, as a result of heating to 800–1000°C, form compounds (of the Ti3SiC2 type) that reduce considerably the height of the metal–semiconductor barrier (see Table 20).
The mechanism of current flow through ohmic con-tacts to silicon carbide was studied recently [314, 316, 334, 340]. On the basis of temperature dependences of the contact resistance, it was assumed that the main mechanism of current flow is the thermionic emission. The heights of the metal–SiC potential barrier as deter-
Table 16. Ohmic contacts to the InGaAs/InP and InAlAs/InP alloys
Metal Semiconductor Annealing tem-
perature, °C Contact resistance,
Ω cm2References
Ti/Pt/Cu InGaAs350[250] AuGe/Ni/Au InGaAs[251] TiN x InGaAs/InP500[253] Pt/Zn/Pt/ZrB2/Au p-InGaAs/InP[252] W(Zn)p-InGaAs/InP (p = 1018 cm–3) 5 × 10–6[254] PdGe n-In0.53Ga0.47As/InP425 6.6 × 10–8–1.4 × 10–6[255] Pd/Zn/Pd/Au p-In0.47Ga0.53As/InP5007.5 × 10–6[256] Pd/Zn/Pd/Au p-InGaAsP/InP (p = (1–1.5) × 1019 cm–3)400 2 × 10–6[257] Ge/Ag/Ni n-InAlAs/InP425 2.26 × 10–7[249]
Table 17. Ohmic contacts to GaSb
Metal Semiconductor
Carrier
concentra-
tion, cm–3
Annealing
temperature,
°C
Contact resis-
tance, Ω cm2Note References
Au/Ge/Pd n-GaSb 4.9 × 10–6Formation of poly-
crystalline AuSb2
[265]
Au/Ge/Ni,
Ag/Au/Ge/Ni
n-GaSb4008 × 10–4–8 × 10–3[269] Pd(Ge, S)n-GaSb 1.2 × 1018 4 × 10–5[267] Pd/Ge/Pd/In/Pd n-GaSb 5.6 × 1017350 1.4 × 10–6[261] Pd/Ge/Pd 1.8 × 1018 3.8 × 10–6
Pd/Ge/Au/Pt/Au n-GaSb 1.3 × 1018 2 × 10–6–10–5[262] n-GaInAsSb/GaAs 3 × 1018 2 × 10–6[263]
Pd, Pd/Sb,
Ge/PbGe/Pd/Sb n-GaSb300–325(1–10) × 10–4Formation of
the n-Ge/n-GaSb
heterojunction
[266]
Pd3In7/Pt(W,
WSi2, WSiN)
n-GaSb 2 × 1018325–35010–6Tunneling[2] Te–Au n-GaSb10–6[268] Ti/Pt/Au n-GaAs1 – x Sb x250–500 3 × 10–7[270] Au, Ag p-GaSb1018250–350 5 × 10–5[272]
1019 5 × 10–6
Zn–Au p-GaSb10–5[268]
Ti/Au, Pt/Au, Pd/Au, Ni/Au p-GaSb Nonalloyed
contact
2.6 × 10–7[271]
Ti/Pt/Au p-GaSb 6.6 × 1016[267]
SEMICONDUCTORS V ol. 41No. 112007mined from the above dependences differed by an order of magnitude: from 0.097 eV for 4H-SiC [316] to 0.97 eV for 6H-SiC [334]. In [314], temperature depen-dences of the contact resistance were not exactly con-sistent with the thermionic-emission theory, so it was assumed [314] that, in these cases, the main current flow mechanism is thermal field emission.
Crofton et al. [340] studied the dependence of the contact resistance on the hole concentration in 4H-SiC. Experimental data are consistent with theoretical results if we assume that the tunneling effective mass and the effective mass of the density of states are equal to the mass of a free electron; in this case, the height of the barrier overcome by electrons was found to be equal
Table 18. Ohmic contacts to InAs and HgCdTe
Metal Semiconductor Carrier concen-
tration, cm–3Annealing tem-
perature, °C
Contact resis-
tance, Ω cm2Note
Refe-
rences
Ti/Pt/Au n-InAs3509.8 × 10–7[273] Au/Ge, Au/Te n-InAs325 2.3 × 10–7[274]
Super-lattice graded-gap n-InAs–n-GaAs1019Nonalloyed
contact
5 × 10–8[275]
conventional10–8–10–5The barrier height
0.14–0.26 eV
Ti HgCdTe Nonalloyed
contact 10–4Thermal field
emission
[276]
Pd/Pt/Au p-InAs9.6 × 10–7[277] Ti 2.6 × 10–7
Pd/Pt/Au AlSb/InAs175[278] Table 19. Ohmic contacts to diamond
Metal Semicon-
ductor Carrier concen-
tration, cm–3
Annealing tem-
perature, °C
Contact resis-
tance, Ω cm2Note
Refe-
rences
Au, Cu n-C : B 5 × 1017[279] Ti, Au n+-C : B Tunneling[280] Al2O3 C nanotubes[281] Au p-C<10–3[285] Au/Ti p-C1020 1.2 × 10–6Formation of TiC[290] Au/Ti p-C500 1.6 × 10–6Tunneling[291] Au/Ti p-C 2 × 10–4Formation of TiC[292] Au/Ti p-C : B102050010–4Tunneling[298] Au/Pt/Ti p-C[293] Au/Pt/Ti p-C : B600 1.3 × 10–5[286] Au/Ta p-C : B Formation of TaC[288]
[2] Al/Si p-C : B450Tunneling[294] Al/Si p-C : B45010–7[297]
Al/Si, Ti/Au, TiWN/Au p-C Tunneling, R c
decreases ~ 1/T
[282]
Ti, Mo p-C 3 × 1018–3 × 1020400–600As low as 10–6Formation of α-Mo2C,
field and thermal field
emission
[296]
Ti/Au p-C : B7 × 102085010–6–10–5[283] Ti/Au p-C : B85010–5Formation of TiC[284] TiC/Au, TaSi2/Au p-C : B85010–5[295] Pt/Ti/Au p-C : B101845010–4[287]
SEMICONDUCTORS V ol. 41No. 112007to 0.37 eV (Fig. 14a). Temperature dependences of the contact resistance [334] showed that the main current flow mechanism in p-4H-SiC and p-6H-SiC (p≈1019 cm–3) is thermal field emission (Fig. 14b).
5. MAIN CONCLUSIONS CONCERNING
THE CURRENT FLOW MECHANISMS
5.1. From the standpoint of the formation of ohmic contacts, all main semiconductors can be separated into two groups:
(i) Semiconductors with a low density of surface states located deep in the band gap (for example, ZnSe, GaN, and SiC) or with the surface states located in the conduction band. Ohmic contacts to these semiconduc-tors can be obtained by choosing the work function for electrons Φm lower than the electron affinity X s for the n-type semiconductors (Φm < X s) or by choosing the contact metals with the electrons’ work function Φm larger than the sum of the band gap E g and the electron affinity X s for the p-type semiconductors (Φm > E g + X s). If such metals are available, fabrication of the ohmic
Metal Carrier concen-
tration (cm–3) or
the conductivity
type
Annealing
temperature,
°C
Contact
resistance,
Ω cm2
Note Refe-
rences
Ni n Without
annealing 1.3 × 10–5The use of a Si layer[304]
[305]
Ni n1000[306] Ni n1000Formation of the Ni31Si12 and Ni2Si
layers and formation of donor-like
C vacancies; the barrier height 0.38 eV
[309]
Ni n+10–6[310] Ni/Ti/Au n = 101980010–4[320] Ni, Ni/W, Ni/Ti/W n1000–1050Formation of Ni2Si or a Cr3C2 layer[311] Ni/Cr/W, Cr/MoW
Cr n[303]
[318] Pt/Ti/WSi/Ni n950–1000[301] Co/Si/Co n800 1.5 × 10–6Formation of a CoSi2 layer[307]
[308] Al/Ti p10–4Formation of the Ni2Si and TiC layers[313] Al/Ti p+ (>1020)10–4[327] Al/Si p750 3.8 × 10–5Thermionic emission[314] Al/Si p700–9509.6 × 10–5[315] Al/Si p9509.5 × 10–5Formation of Al4C3[317] Al/Ti/Ni p = 10199 × 10–5Thermal–field emission through
the 0.097-eV barrier
[316] Au/Al/Si, Au/Ti/Al p700(1.4–8.3) × 10–5[322] Au/Ti/Au, Ti/Au p1000(2–7) × 10–5Formation of Ti3SiC2[323] Au/Ti/Al, Au/Pd/Al p850–95010–5Formation of Ti3SiC2[325] Ti/Al p100010–5Formation of Al3Ti, Ti3SiC2, Al4C3,
and Ti3Si3
[319] Ti/Al/Ge p60010–4[324] Ni/Ti/Au p = 4.5 × 101880010–3[320] Pd p750 5.52 × 10–5[312] Pd p600–700 5.5 × 10–5Formation of PdSi2[326] Si/Pt p110010–4Diffusion of C into metal layers[328] Ge/Ti/Au p80010–4Formation of Ti3SiC2[321]
SEMICONDUCTORS V ol. 41No. 112007
SEMICONDUCTORS V ol. 41 No. 11 2007
contacts amounts to the removal of the near-surface dam-aged or oxide layer (for example, Ti/Pt/Au–n-ZnSe).If such metals are not available, fabrication of these con-tacts consists in formation of a compound with a low work function between the metal and semiconductor (for exam-ple, the Si/Ti–n-GaN structure with formation of the tita-nium oxide in the course of heat treatment).
(ii) Semiconductors with a high density of surface states located near the midgap (for example, Si, Ge,GaAs, GaP, and InP).
In these materials, the Fermi level is pinned at the surface and the work function for electrons leaving the contacting metal affects only slightly the contact’s properties.
Fabrication of ohmic contacts to these semiconduc-tors amounts to either heavy doping of the near-surface region, which ensures the tunneling-like passage of electrons through the interface (for example, the level of doping of GaAs with Ge is as high as 1021 cm –3 in the Ni/Au + Ge/Ni/Au–n-GaAs contact); or formation of chemical compounds in the near-surface region that reduce appreciably the height of the metal–semicon-ductor potential barrier, which makes it possible for electrons to pass the interface due to thermionic emis-sion (for example, in the In–GaAs structure); or passi-vation of the semiconductor surface, which leads to a decrease in the density of surface states (for example,the treatment of the GaAs surface in (NH 4)2S x brings about a decrease in the density of surface states by an order of magnitude).
5.2. Nonalloyed ohmic contacts (thin-film contacts and the contacts formed at low temperatures) can be considered as Schottky barriers with a low or thin potential barrier. Therefore, the following current flow mechanisms are characteristic of the Schottky diodes:(I) thermionic emission (the contact resistance decreases exponentially with increasing temperature and the height of the metal–semiconductor potential barrier);
(II) field emission and tunneling (the contact resis-tance decreases exponentially as the doping level is increased and is virtually independent of temperature);and
Metal
Carrier concen-tration, cm –3Annealing tem-perature, °C Contact resis-tance, Ω cm 2
Note
References Ni, Ni/W, Ni/Ti/W, Ni/Cr/W, Cr/MoW n
1000–1050Formation of Ni 2Si or a Cr 3C 2 layer
[333]NiSi n
60010–5
[330]TiSi x n = 5 × 1019900–1100(4–7) × 10–6[332]Re
n = 1.28 × 101810007 × 10–5[329]W/WC/TaC n 1000[331]Al/Ti p 1000 2 × 10–4[336]Al/Ti p 1000[335]Pt, W
p No annealing
2.8 × 10–4[338]W/Ti, Al/Ti p [337]TiN
p
4.4 × 10–5[339]
101010101010R c , Ω × cm 2T , °C
101010Fig. 14. Dependences of the ohmic-contact resistance R c on (a) the concentration N a of uncompensated acceptors at 300 K for Al/Ti–p-4H-SiC [340] and (b) temperature T for the Al/Ti–p-6H-SiC (1) and Al/Ti–p-4H-SiC contacts (2). The mechanism of the current flow is thermionic emission (q ϕb =0.53 eV for 6H-SiC and q ϕb = 0.82 eV in 4H-SiC) [334].
Thermionic emission manifests itself in contacts to lightly doped n- and p-GaAs, n-GaN. p-InP, and p-In0.53Ga0.47As, in which chemical composition was changed in the near-contact region. This mechanism was identified on the basis of exponential decrease in the contact resistance as temperature was increased. The height of the metal–semiconductor potential bar-rier determined from comparison of theoretical results with experimental data was found to be equal to 0.068–0.09 eV for GaAs, 0.13 eV for GaN, lower than 0.2 eV for InN, and 0.13 eV for InGaAs. These values are much smaller than the height of the Shottky potential barrier at the metal–semiconductor interface or the height of the potential barrier at the free semiconduc-tor’s surface.
Tunneling (field emission) manifests itself in struc-tures based on GaAs, InP, GaN, AlGaN, and SiC, in which the surface region was subjected to heavy dop-ing. This mechanism was identified on the basis of independence of the contact resistance on temperature and exponential decrease in the contact resistance as the charge-carrier concentration was increased. The doping level in the near-contact region was as high as 1020–1021 cm–3, which resulted in an appreciable nar-rowing of the metal–semiconductor potential barrier. In this case, the potential barrier height was fairly high: 0.3–0.5 eV for p-GaAs, ~0.5 eV for GaN, and ~0.4 eV for SiC structures. In this case, the contact resistance was fairly low due to a small thickness of the potential barrier.
5.3. For alloyed ohmic contacts (especially in the case of semiconductors with a high density of imper-fections), another mechanism, noncharacteristic of the Schottky diodes, can manifest itself; this mechanism consists in the current flow over the metal shunts. Based on experimental data on the increase in the resistance of ohmic contacts with increasing temperature, this mech-anism was verified for In contacts to lightly doped GaP and GaN. The number of shunts (per unit contact area) determined from the temperature dependence of the contact resistance correlated well with the dislocation density in the near-surface region of the semiconductor (the density of shunts was 107–108 cm–2 for GaN and (4.5–8) × 107 cm–2 for GaP). At the same time, this mechanism becomes unimportant at low dislocation density (for example, for GaAs); as a result, other (tra-ditional) mechanisms manifest themselves).
ACKNOWLEDGMENTS
We thank Professor O.V. Konstantinov for discus-sion of this study.
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Translated by A. Spitsyn
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