High electron mobility transparent conductor

A transparent electrical conductor which provides relatively high electrical conductivity and transmittance in the visible/near-infrared (VNIR), relative to known transparent electrical conductors, such as tin-doped indium oxide (ITO). In one embodiment of the invention, the transparent electrical conductor is formed from a plurality of quantum wells formed between the interfaces of three layers of lattice-matched, wide band gap materials, such as AlGaN and GaN. In an alternative embodiment of the invention, a material with a band gap much larger than known materials used for such transparent electrical conductors, such as ITO, is selected. Both embodiments of the invention may be formed on a transparent substrate and provide relatively better transmittance in the VNIR at sheet electrical resistances of four or less ohms/square than known materials, such as tin-doped indium oxide (ITO).

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a transparent electrical conductor and, 
more particularly, to a transparent electrical conductor for use as an 
electrical conductor in a frequency range from DC to radio frequency (RF) 
that is transparent to visible light, formed with an electrical sheet 
conductance and a visible light transparency better than known transparent 
electrical conductors, such as tin-doped indium oxide (ITO). 
2. Description of the Prior Art 
Various opto-electronic devices require transparent electrical conductors 
that are conductive in the frequency range from DC to radio frequency (RF) 
and transparent to visible light. Such transparent electrical conductors 
are known to be applied to such opto-electronic devices in the form of a 
coating, and have become known as transparent conductive coating (TCC) 
materials. 
Various applications of such TCC materials are known. For example, such TCC 
materials are known to be used for electrically resistive heating systems 
for aircraft windshields, as well as in satellite applications. 
Solar cells are also known to use such TCC materials. In particular, in 
solar cells applications, the TCC material is used for conducting solar 
photon-generated currents from the surface of the solar cells, without 
causing the solar cell to be obscured. Such TCC materials are also known 
to be used in various other opto-electronic applications, such as liquid 
crystal displays, CCD camera sensors and photocopiers, as well as a myriad 
of other opto-electronic type devices. 
Various semiconductor coatings with a relatively wide band gap are known to 
be used for such TCC materials. 
Specifically, materials having a band gap greater than the energy of the 
photons of light passed therethrough are known to be used. For 
transparency across the entire visible/near-infrared (VNIR) band, 
materials with band gaps wider than 3eV are known to be used. 
In many known applications of such TCC materials, electrical conductivity 
for such TCC materials approaching that of metals is required. In order 
for the material to be electrically conductive, one or more of the 
electron energy bands of the material must be partially filled. In 
relatively high conductive materials, a partially filled electron energy 
band normally dominates the conduction. 
The density of carriers in the electron energy band, n, required for a 
specific conductivity, is given by Equation (1). 
EQU n=.delta./q.mu., (1) 
where q is the electronic charge, 
.mu. is the carrier mobility, and 
.delta. is the electrical conductivity. 
To obtain a sufficient density of carriers in an electron energy band for 
the desired conductivity, the material is known to be doped because the 
Fermi level of the intrinsic (pure) material is normally deep within the 
band gap. However, doping is known to reduce the transmittance of the 
material for several reasons. First, the optical absorption of free 
carriers increases with the increasing concentration of carriers, as 
generally discussed in "Optical Processes in Semiconductors", by J. I. 
Pankove, Dover Publications, 1971, p.75. Second doping is known to change 
the density of states function, producing a tail on the absorption near 
the band edge, as generally discussed in "Absorption Edge of Impure 
Gallium Arsenide", by J. I. Pankove, Physical Review A, Vol. 140, 1965, 
pp. 2059-2065. The increase in absorption as a function of the doping 
level thus causes a fundamental trade-off in such TCC materials between 
electrical conductivity and VNIR transmittance. 
Tin-doped indium oxide (ITO) is known to be used for such TCC material 
applications. As generally set forth in "Transparent Conductors--A Status 
Review", by K. L. Chopra, S. Major, and D. K. Pandya, Thin Film Solids, 
Vol. 102, 1983, pps. 1-46, such ITO coatings are known to have an electron 
mobility ranging from 15-40 cm.sup.2 /V-s. In many known commercial and 
aerospace applications, transparent electrical conductors having a sheet 
electrical conductance of 1 or less ohms per square and a visible light 
transparency of 90% or better is required. Because of the high refractive 
index of these conductive coatings, an optical anti-reflection coating 
would be needed to achieve this transparency over the visible band. A 
sheet electrical impedance of one ohm per square of the ITO coating 
requires a doping concentration of about 2.times.10.sup.21 cm.sup.-3. 
Unfortunately, such highly doped ITO coatings provide less than 
approximately 75% VNIR transmittance. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to solve various problems in the 
prior art. 
It is yet another object of the present invention to provide a transparent 
electrically conductive material having relatively high electrical 
conductivity and relatively high transmittance. 
Briefly, the present invention relates to a transparent electrical 
conductor which provides relatively high electrical conductivity and 
transmittance in the visible/near-infrared (VNIR), relative to known 
transparent electrical conductors, such as tin-doped indium oxide (ITO). 
In one embodiment of the invention, the transparent electrical conductor 
is formed from a plurality of quantum wells formed between the interfaces 
of three layers of lattice-matched, wide band gap materials, such as AlGaN 
and GaN. In an alternative embodiment of the invention, a material with a 
band gap much wider than known materials used for such transparent 
electrical conductors, such as ITO, is selected. Both embodiments of the 
invention may be formed on a transparent substrate and provide relatively 
better transmittance in the VNIR and relatively lower sheet electrical 
resistances of 4 or less ohms/square than known materials, such as 
tin-doped indium oxide (ITO). High levels of mobility can be obtained in 
quantum wells, as compared to bulk material with similar carrier 
concentration, because the dopants from which the carriers originate can 
be placed in the barrier layers. Separation of the dopants from the 
quantum wells in which the carriers accumulate reduces impurity 
scattering, resulting in increased mobility. Restricting the dopant atoms 
to the barrier layers is called modulation doping. A variety of techniques 
can be used to deposit these transparent conductors on appropriate 
substrates, both in bulk and as multi-quantum wells. These techniques are 
metal-organic vapor phase epitaxy (MOVPE), molecular beam epitaxy (MBE), 
hydride vapor phase epitaxy (HVPE), etc. which are used by researchers as 
well as the semiconductor industry to deposit crystalline semiconductor 
materials in these forms.

DETAILED DESCRIPTION OF THE INVENTION 
Two embodiments of the invention are illustrated in FIGS. 1 and 2. Both 
embodiments provide relatively higher electrical conductivity with reduced 
optical losses than known transparent electrical conductors, such as 
tin-doped indium oxide (ITO). Both embodiments utilize materials with a 
relatively wide band gap and a carrier mobility significantly larger than 
that of ITO, in order to reduce doping, while maintaining the desired 
electrical conductivity. As discussed above, the doping is required to 
achieve the desired electrical conductivity of the material. 
Unfortunately, such doping also results in optical losses, thus reducing 
the transmittance in the VNIR to unacceptable levels. 
The first embodiment of the invention is illustrated in FIG. 1. In this 
embodiment, the transparent conductive coating (TCC) is formed as a 
plurality of modulation doped quantum wells formed between the interfaces 
of three layers of lattice matched, wide band gap crystalline materials. 
The quantum well between the two lattice matched, wide band gap 
crystalline materials provides relatively higher electron mobility than 
the electron mobility in the same bulk materials for the same electron 
concentrations, as discussed in "Electron Mobility in Single and 
Multiple-Period Modulation-Doped (Al,Ga) As Heterostructures", by T. J. 
Drummond, et al., Journal of Applied Physics, Vol. 53, No. 2, Feb. 1982, 
pps. 1023-1027; and "Observation of Two-Dimensional Electron Gas in Low 
Pressure Metal Organic Chemical Vapor Deposited GaN--Al.sub.x Ga.sub.1-x N 
Heterojunction", by M. Asif Kahn, et al., Applied Physics Letters, Vol. 
60, No. 24, Jun. 15, 1992, pps. 3027-3029. For materials such as AlGaN and 
GaN, such two-dimensional quantum well structures are known to have 
electron mobilities as high as 1500 cm.sup.2 /V-s at 300.degree. K Kelvin, 
while the electron mobility of a similarly doped bulk GaN is known to be 
only 300 cm.sup.2 /V-s. As set forth in "GaN, AlN, and InN: A Review", by 
S. Strite and H. Morkoc, Journal of Vacuum Science and Technology B, Vol. 
10, No. 4, July-Aug. 1992, pps. 1237-1266, both AlGaN and GaN have 
relatively wide band gaps of 6.2 eV and 3.4 eV, respectively. Moreover, as 
set forth in "The Preparation and Properties of Vapor Deposited Single 
Crystalline GaN", by H. P. Maruska and J. J. Tietjen, Applied Physics 
Letters, Vol. 15, No. 10, Nov. 15, 1969, pps. 327-329, both AlGaN and GaN 
have high optical transparency. 
Referring to FIG. 1, the transparent electrical conductor in accordance 
with one embodiment of the invention is formed from a plurality of quantum 
wells between the interfaces of three layers of lattice-matched, wide band 
gap crystalline materials, for example, GaN and AlGaN. In this embodiment, 
the quantum wells 22 are formed by layers of GaN sandwiched between AlGaN 
barrier layers. Since the sheet resistance, R.sub.s of a plain sheet of 
materials equals 1/qN.sub.A .mu., where N.sub.A is the number of carriers 
per unit area, the sheet-charge density required for sheet resistance of 
one ohm/square would be 2.times.10.sup.14, assuming a stack of 20 quantum 
wells, as generally illustrated in FIG. 1. Alternatively, a stack of 200 
quantum wells each with a sheet charge density of 2.times.10.sup.13 
cm.sup.-2 and mobility of 1500 cm.sup.2 /V-s would also have a sheet 
resistance of 1 Ohm/Sq. Each quantum well, generally identified with the 
reference numeral 22, is formed between the interfaces of, for example, 
100 A of Al.sub.0.1 GaN.sub.0.9 N, 100 A of GaN, and 100 A of Al.sub.0.1 
Ga.sub.0.9 N. These quantum wells 22 may be formed on a buffer layer 24, 
formed, for example, of 1.5 .mu.m of GaN. The buffer layer 24 may be, in 
turn, formed on a transparent substrate 26, such as a sapphire substrate. 
The electrically conductive coating 20 illustrated in FIG. 1 is relatively 
more complex than conventional amorphous TCCs. The complexity can be 
substantially eliminated by forming a transparent electrical conductor 28, 
as shown in FIG. 2, from a bulk crystalline material, such as GaN, which, 
as mentioned above, has an electron mobility of 300 cm.sup.2 /V-s at 
300.degree. K when doped with silicon atoms at a density of 10.sup.19 
cm.sup.-3 --about ten times higher than the electron mobility of ITO. 
Thus, in accordance with an alternative embodiment of the invention, the 
transparent electrical conductor 28 is formed from a single n-type doped 
layer of a crystalline material, such as GaN, about 2 microns thick on a 2 
micron thick buffer layer, on a transparent substrate 32, such as a 
sapphire substrate. 
The transparent electrical conductor 28, illustrated in FIG. 2, outperforms 
known transparent electrical conductors, such as ITO. In particular, since 
the mobility of bulk GaN is about 10 times greater than that of ITO, an 
equal thickness of GaN will have an equal sheet resistance with one-tenth 
the carrier concentration. Since the sheet resistance, R.sub.s, of a layer 
of GaN, having a thickness of .delta. and an electron concentration of n 
per unit volume equals 1/q.mu.N.delta., 2 microns of GaN will require an 
n-type doping level of about 10.sup.20 for a sheet resistance of about 1 
ohm/square. At such a doping level, the contribution to the absorption 
coefficient from the free-carrier absorption is about 25.times. less than 
that for ITO, with the same sheet resistance. Since the absorption depends 
exponentially on the absorption coefficient, the free carrier absorption 
is substantially negligible for the structure illustrated in FIG. 2. 
The classical formula for free carrier absorption is provided in Equation 
(2) below: 
EQU .alpha.=nq.sup.2 .lambda..sup.2 /8.pi..sup.2 Nmc.sup.3 .tau.,(2) 
where .lambda. represents wavelength; 
N represents refractive index; 
m represents the electrons'effective mass in the conduction band; 
c represents the speed of light in a vacuum; 
.tau. represents the relaxation time for scattering of electrons; and 
.alpha. equals the absorption coefficient. 
As set forth in "Solid State Electronic Devices", Second Edition, by B. G. 
Streetman, Prentice-Hall, 1980, p. 83, the carrier mobility .mu. may be 
formulated in accordance with Equation 3, as follows: 
EQU .mu.=q.tau./m (3) 
Substituting Equation 3 into Equation 2 yields Equation 4 as set forth 
below: 
EQU .alpha.=nq.sup.3 .lambda..sup.2 /8.pi..sup.2 Nm.sup.2 c.sup.3 .mu.(4) 
Since m is roughly half as large for a crystalline material, such as GaN, 
as for ITO, n is 10.times. smaller for GaN, .mu. is 10.times. larger for 
GaN, while the other parameters are either identical or similar for both 
materials, the absorption coefficient .alpha. is about 25.times. smaller 
for GaN. The absorption by free carriers (i.e., transitions in which 
carriers in the partially filled band go to higher energy states in the 
same band) is ordinarily the dominant absorption mechanism in the IR(NIR) 
for conductive wide band gap materials, whereas the tail of the band edge 
absorption is dominant at visible wavelengths. The absorption for the GaN 
layer at visible wavelengths approaching the band-edge absorption, as 
illustrated in FIG. 2, is expected to be less than 10 percent for 
wavelengths to 400 nm based on the optical absorption measurements on a 
similarly doped GaN. Thus, over the visible range, 10 percent is the 
maximum absorption for GaN. 
The transparent electrical conductors 20 and 28 may be formed on 
transparent substrates 26 and 32, such as sapphire, respectively. In 
addition to sapphire, the substrates 26 and 32 may be formed from other 
substrate materials, such as SiC, which provides better lattice and 
thermal matching. Other materials are also contemplated for the substrates 
26 and 32, such as ZnO and GaN. A GaN substrate provides optimal matching 
of the lattice and the thermal expansion coefficient. 
Obviously, many modifications and variations of the present invention are 
possible in light of the above teachings. Thus, it is to be understood 
that, within the scope of the appended claims, the invention may be 
practiced otherwise than as specifically described above.