Semiconductor device manufacturing: process – Electron emitter manufacture
Reexamination Certificate
2000-08-05
2004-01-20
Mulpuri, Savitri (Department: 2812)
Semiconductor device manufacturing: process
Electron emitter manufacture
C216S040000, C216S054000, C216S066000, C216S067000, C430S199000, C430S296000, C430S302000, C430S310000
Reexamination Certificate
active
06680214
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention is concerned with methods for fabricating nanostructures to develop a band gap, and elementary particle emission properties.
2. Description of Related Art
Semiconductors, or semiconducting materials, have a small energy band gap (about one eV or less) between the conduction band and the valence band associated with the solid. This gap in energy distribution is useful for microelectronics such as lasers, photodetectors, and tunnel junctions. Intrinsic semiconductors (not doped by another element) conduct due to the effect that raising the temperature will raise the energy of some electrons to reach the conduction band. Intrinsic semiconductors usually have a very low conductivity, due to the difficulty of exciting an electron by approximately one eV.
Silicon is a commonly used semiconducting material and has limited electrical conductivity. In using silicon, designers of semiconductor devices are bound by the inherent material limitations of silicon.
The electrical conductivity of a semiconducting material is enhanced by adding small amounts of impurities, such as gallium arsenide. However, the process by which dopants are implanted in a semiconductor substrate of a semiconductor device is expensive and time-consuming. Also, the designing of semiconductor devices using doped materials currently known in the art, such as silicon and gallium arsenide, often requires a lengthy and expensive trial and error process to achieve the desired band gap.
From the foregoing, it may be appreciated that a need has arisen for a band gap material that does not require doping, or materials having other characteristics, to produce a desired band gap, and a method for making such a band gap material.
A. Quantum Mechanics and the De Broglie Wave
It is well known in quantum mechanics that elementary particles have wave properties as well as corpuscular properties. The probability of finding an elementary particle at a given location is |&psgr;|
2
where &psgr; is a complex wave function and has form of a de Broglie wave, as follows:
&psgr;=
A
exp[(−
i
2
&pgr;/h
)(
Et−pr
)] (1)
where h is Planck's constant; E is an energy of the particle; p is an impulse of the particle; r is a vector connecting initial and final locations of the particle; and t is time.
There are well known fundamental relationships between the parameters of this probability wave and the energy and the impulse of the particle.
The wave number k related to the impulse of the particle as follows:
p
=(
h
/2&pgr;)
k
(2)
The de Broglie wavelength, &lgr;, is given by:
&lgr;=2
&pgr;/k
(3)
At zero time, t=0, the space distribution of the probability wave may be obtained. Accordingly, substituting (2) into (1) gives:
&psgr;=
A
exp(
ikr
) (4)
FIG. 1
shows an elementary particle wave moving from left to right perpendicular to a surface
104
dividing two domains. The surface is associated with a potential barrier, which means the potential energy of the particle changes as it passes through it.
Incident wave
101
Aexp(ikx) moving towards the border will mainly reflect back as reflected wave
103
&bgr;Aexp(−ikx), and only a small part leaks through the surface to give transmitted wave
102
&agr;(x)Aexp(ikx) (&bgr;≈1>>&agr;). This is known as quantum mechanical tunneling. The elementary particle will pass the potential energy barrier with a low probability, depending on the potential energy barrier height.
B. Electron Interference
Usagawa in U.S. Pat. No. 5,233,205 discloses a novel semiconductor surface in which interaction between carriers such as electrons and holes in a mesoscopic region and the potential field in the mesoscopic region leads to such effects as quantum interference and resonance, with the result that output intensity may be changed. Shimizu in U.S. Pat. No. 5,521,735 discloses a novel wave combining and/or branching device and Aharanov-Bohm-type quantum interference devices which have no curved waveguide, but utilize double quantum well structures.
Mori in U.S. Pat. No. 5,247,223 discloses a quantum interference semiconductor device having a cathode, an anode and a gate mounted in vacuum. Phase differences among the plurality of electron waves emitted from the cathode are controlled by the gate to give a quantum interference device operating as an AB type transistor.
C. Tunneling Through Potential Barriers
In U.S. patent application Ser. No. 09/020,654, filed Feb. 9, 1998, entitled “Method for Increasing Tunneling through a Potential Barrier”, Tavkhelidze teaches a method for promoting the passage of elementary particles at or through a potential barrier comprising providing a potential barrier having a geometrical shape for causing de Broglie interference between said elementary particles.
Referring to
FIG. 2
, two domains are separated by a surface
201
having an indented shape, with height a. An incident probability wave
202
is reflected from surface
201
to give two reflected waves. Wave
203
is reflected from top of the indent and wave
204
is reflected from the bottom of the indent. The reflected probability wave will thus be:
A
&bgr;exp(−
ikx
)+
A
&bgr;exp[−
ik
(
x
+2
a
)]=
A
&bgr;exp(−
ikx
)[1+exp(−
ik
2
a
)] (5)
When k2a=&pgr;+2&pgr;n, exp(−i&pgr;)=−1 and equation (5) will equal zero.
Physically this means that for k2a=(2&pgr;/&lgr;)2a=&pgr;+2&pgr;n and correspondingly a=&lgr;(1+2n)/4, the reflected probability wave equals zero. Further this means that the particle will not reflect back from the border. Leakage of the probability wave through the barrier will occur with increased probability and will open many new possibilities for different practical applications.
Indents on the surface should have dimensions comparable to the de Broglie wavelength of an electron. In particular the indent height should be:
a=n&lgr;/2+&lgr;/4 (6)
Here n=0,1,2, etc., and the indent width should be on the order of 2&lgr;. If these requirements are satisfied, then elementary particles will accumulate on the surface.
For semiconductor material, the velocities of electrons in an electron cloud is given by the Maxwell-Boltzman distribution:
F
(
v
)
dv=n
(
m
/2
&pgr;K
B
T
)exp(−
mv
2
/2
K
B
T
)
dv
(7)
where F(v) is the probability of an electron having a velocity between v and v+dv.
The average velocity of the electrons is:
V
av
=(3
K
B
T/m
)
½
(8)
and the de Broglie wavelength corresponding to this velocity, calculated using formulas (2), (3) and the classical approximation p=mv is:
&lgr;=
h
/(3
mK
B
T
)
½
=62 Å for
T
=300
K.
(9)
This gives a value for a of 62/4=15.5 Å. Indents of this depth may be constructed on a surface by a number of means known in the art of micro-machining. Alternatively, the indented shape may be introduced by depositing a series of islands on the surface.
In metals, free electrons are strongly coupled to each other and form a degenerate electron cloud. Pauli's exclusion principle teaches that two or more electrons may not occupy the same quantum mechanical state: their distribution is thus described by Fermi-Dirac rather than Maxwell-Boltzman. In metals, free electrons occupy all the energy levels from zero to the Fermi level (&egr;
f
).
Probability of occupation of energy states is almost constant in the range of 0−&egr;
f
and has a value of unity. Only in the interval of a few K
B
T around &egr;
f
does this probability drop from 1 to 0. In other words, there are no free states below &egr;
f
. This quantum phenomenon leads to the formal division of free electrons into two groups: Group 1, which comprises electrons having energies below the Fermi level, and Group 2, comprising el
Cox Isaiah Watas
Edelson Jonathan Sidney
Harbron Stuart
Tavkhelidze Avto
Borealis Technical Limited
Mulpuri Savitri
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