Electron wave deflection in modulation doped and other doped semiconductor structures

The present invention relates to semiconductor devices which incorporate doped semiconductor elements or modulation doped devices wherein ballistic electrons in these elements or in a two-dimensional electron gas (2-DEG) are deflected by shaped potential barriers. A shaped potential barrier is formed by depositing a shaped electrode on the surface of the device and applying a potential to it. The electrode may take the shape of a biconcave lens which induces a potential barrier of that shape in the underlying device. Upon transiting the potential barrier induced by the shaped electrode, the phases of the exiting electrons are different across the width of the electrode and the beam of electrons is focused. By changing the applied potential, the focal point of the exiting electrons may be moved in a direction parallel to the axis of the lens-like electrode. Other electrode configurations such as a biconvex shape will cause incident electrons to diverge from their original paths. In another embodiment, a triangular electrode, depending on the potentials applied to it, reflects, transmits or deflects incident electron waves.

DESCRIPTION 
1. Field of the Invention 
This invention relates generally to doped semiconductor devices and more 
specifically to modulation doped structures wherein carriers introduced 
into a doped semiconductor or into a two-dimensional carrier gas are 
controlled both by the shape of an overlying electrode and by the 
magnitude and polarity of a potential applied to the electrode. To the 
extent that ballistic electrons can be described in terms of their 
wave-like characteristics, they have wavelength and phase and, as such, 
both of these parameters can be controlled by the action of a potential 
barrier applied by an electrode having the desired morphology. Thus, a 
metal or doped semiconductor gate electrode having a biconcave shape will 
focus electron waves impinging on one side thereof to a point upon 
transiting the shaped potential barrier provided by the shaped electrode. 
By changing the magnitude of the voltage applied to the gate electrode, 
the focal point will be moved along the axis of the lens-like electrode. 
An electrode having a biconvex shape, on the other hand, causes carriers 
to diverge away from their original path when they encounter a potential 
barrier shaped by an electrode of that kind. Other electrode shapes, like 
a triangular electrode, influence the path in which carriers travel and, 
with the proper potentials applied to such gate electrodes, current may be 
directed to one or more collector electrodes or totally reflected. In this 
way, circuits connected to such collector electrodes may be selectively 
activated to provide what may be termed logic inputs to such circuits. 
BACKGROUND OF THE INVENTION 
In the prior art, the propagation of electron waves in modulation doped 
structures is well-known. U.S. Pat. No. 4,550,330, filed Jun. 29, 1984 
shows an interferometer structure wherein a bifurcated branch conductive 
path coplanar with a heterojunction in a semiconductor has a 
two-dimensional electron gas (2-DEG) formed adjacent the heterojunction so 
that electron waves can be launched into and travel in the 2-DEG. In 
addition, the reference shows a means for inducing a potential barrier 
such that the wavelength and phase of the electron waves transiting it are 
changed. In this arangement, all the electron waves which exit the 
potential barrier have the same wavelength and phase. There is no 
indication in this reference that electron waves traversing a potential 
barrier may be acted on in such a way that the phases and wavelengths of 
the exiting electron waves may be different. Similarly, in a copending 
application, Ser. No. 06/854,635 filed Apr. 22, 1986 and assigned to the 
same assignee as the present application, a tunable stub is shown in which 
a potential barrier is induced in an underlying heterojunction 
semiconductor arrangement by a gate structure, such that the wavelength 
and phase of electron waves transiting the barrier are all affected the 
same way. There is no indication in this reference that the phase and 
wavelength of the impinging electron wavesd may be controlled by 
controlling the slopes of the potential barrier at the points where the 
electron waves impinge. 
IBM Technical Disclosure Bullentin, Vol. 31, No. 8, Jan. 1989, page 150, in 
an article entitled "Heterostructure Traveling Wave Transistor" by F. Fang 
and T. P. Smith, III, there is shown an interdigitated comb gate disposed 
over a 2-DEG. When the comb gate has a potential applied to it, potential 
barriers are induced in the underlying heterostructure such that electron 
waves launched in the 2-DEG encounter periodically varying potential 
barriers. These barriers are all aligned in such a way that electron waves 
transiting a given barrier all exdperience the same change in wavelength 
and phase across the width of the induced barrier. There is no indication 
in this reference of how the wavelength and phase of the electron waves 
may be varied across the width of a potential barrier. 
It is, therefore, an object of the present invention to provide a ballistic 
transport semiconductor device in which a shaped electrode induces a 
shaped potential barrier such that electron waves transiting the potential 
barrier are each affected differently. 
Another object is to provide a ballistic transport semiconductor or quantum 
mechanical effect device in which the slopese of the induced potential 
barrier affect different electron waves differently such that the electron 
waves are deflected from their original paths. 
Still another object is to provide a ballistic transport semiconductor 
quantum mechanical device wherein gate electrodes having curved edges 
induce similarly curved potential barriers such that parallel electron 
waves impinging on the curved potential barriers are focused or diverge 
from their initial paths. 
Yet another object is to provide a ballistic transport semiconductor 
quantum mechanical device wherein, relative to the path of an impinging 
electron wave, the slope of an induced potential barrier at the point of 
impingement determines the amount of deflection and, therefore, the 
ultimate destination of the electron wave. 
These and other objects, features and advantages of the present invention 
will become more apparent from the following particular description of the 
preferred embodiments taken in conjunction with following briefly 
described drawings.

BRIEF SUMMARY OF THE INVENTION 
The present invention relates to smeiconductor device which incorporate 
droped semiconductor elements or modulation doped devices wherein 
ballistic electrons in these elements or in two-dimensional electron gas 
(2-DEG) are deflected by shaped potential barriers. In a preferred 
approach, a sandwich of GaAs and GaAlAs forms a 2-DEG adjacent the 
heterojunction in a well-known way. A lens is formed by depositing or 
growing a shaped electrode on the surface of the sandwich. The electrode 
may take the shape of a biconcave lens which includes a potential barrier 
of that shape in the underlying sandwich. When the electrons encounter the 
potential barrier, the excess energy of the ballistic electrons changes 
and so does their wavelength. Upon transiting the potential barrier 
induced by the shaped electrode, the phases of the exiting electrons are 
different acrosss the width of the electrode and the beam of electrons is 
focused into a tight region. By changing the applied potential, the focal 
point of the exiting electrons may be moved in a direction parallel to the 
axis of the lens-like electrode. If the incidence of the electron beam is 
displaced off-axis, the focal point will also be displaced off-axis. Other 
electrode configuration like a biconvex shape will cause incident 
electrons to diverge from their original paths. In both of the above 
described embodiments, the potential barrier induced may be of such 
magnitude that the impinging electron waves are totally reflected. 
In another embodiment, the lens-like electrodes are replaced by triangular 
electrode through which electron waves are injected from an injector 
contact where, depending on the potentials applied to the triangular 
electrode, the incident electron waves are reflected, transmitted along 
their orginal path or transmitted and deflected from their original path. 
Then, depending on the positioning of collector electrodes, one of a 
plurality of such electrodes, either in the original path or in a 
different path displaced from the original path, will be intercepted by 
the exiting electron beam. 
The above structures can be fabricated using well-known photolithographic 
and etching techiques in spite of the fact that the dimensions involved 
are of the order of mean free path of an electron in a semiconductor such 
as GaAs. At cryogenic temperatures, like the temperature of liquid helium 
(4.2.degree. K ), the mean free of such electrons is in the micrometer 
range and, as such, the diminensions involved are larger than at ehr 
higher temperatures. The carriers involved are not limited to electrons. 
Holes whick form a two-dimensional hole gas instead of a 2-DEG, through 
their mean free path is much smaller, may also be used with the 
appropriately shaped electrode and potential polarity in the practice of 
the present invention. 
DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring FIG. l, there is shown therein a plan view of a semiconductor 
structure in which injected electron waves are subjected to a shaped 
potential barrier such that the electron waves are focused. The shaped 
potential barrier is provided by an electrode having the same morphology 
as the shaped potential barrier. 
In FIG. 1, a semiconductor substrate 1 has a metallic or doped 
semiconductor electrode 2 desposited on its surface. Electrode 2 is 
connected to a voltage source 3 such that a potential barrier having the 
same shape as electrode 2 is induced in substrate 1. In FIG. 1, electrode 
2 has a biconcave shape. Electrons injected into substrate 1 from a source 
(not shown) have wave-like characteristics represented in FIG. 1 by arrows 
4 are directed through the shaped potential barrier in a direction 
parallel to axis 5. Because of the shape of the potential barrier, the 
electron waves are incident on the potential barrier at different angles 
depending on their position along the lens, and exit from it at different 
angles such that the overall effect is to focus the electron waves at a 
focal point on axis 5. If the potential from voltage source 2 is changed 
so that the velocity of the electron waves under electrode 2 is changed, 
the focal point of the structure will be changed from F1 to F2 or F3. By 
locating ohmic collector contacts at focal points F1-F3 and by changing 
the potential on electrode 2, current may be applied to any selected 
electrode. This result is opposite from Snell's Law for photons which 
shows that a biconcave lens causes light to diverge. 
In FIG. 1, if no potential is applied from voltage source 3, injected 
electrons in their wave-like regime will pass under electrode 2, encounter 
no potential barrier and pass with no velocity changes to an output 
electrode (not shown). If the applied potential is very high and the 
resulting potential barrier is higher than that of the energy of the 
injected electrons, the electron waves will be totally reflected from the 
potential barrier. Under such circumstances, the device is essentially 
nonconducting. Thus, by controlling the potentials on electrode 2, high 
speed switching can take place since all the elements involved take up a 
path length which is less than the mean free path of a carrier (electron 
or hole) in a semiconductor such as gallium arsenide. The passage of a 
carrier to a collector electrode is essentially ballistic under these 
conditions and switching speeds can be in the subnanosecond range. Also, 
by changing the angle at which electrons are injected, electron waves will 
encounter the interface of the potential barrier at different angles of 
incidence than when they were injected parallel to axis 5. The electron 
waves, under such circumstances, have their focal point on an axis which 
is disposed at an angle with respect to axis 5. Then, by changing the 
potential on electrode 2, the focal point will move along the thus 
displaced axis. 
FIG. 2 shows a cross-sectional view taken along line 2--2 of FIG. 1 of a 
structure which is preferably used in the practice of the present 
application. While a single doped semiconductor layer disposed on a 
substrate may be utilized in the practice of the present application, 
constraints, such as scattering which limit the length over which 
electrons are ballistic, form structures which include a two-dimensional 
carrier gas; the preferred medium because of the resulting advantages in 
mobility and speed. 
Thus, FIG. 2 shows a layer 10 of a semiconductor, such as undoped gallium 
arsenide. Layer 11 is an epitaxial layer of semiconductor, such as undoped 
gallium arsenide, which forms a heterojunction 12 with an epitaxially 
deposited layer 13 of gallium aluminum arsenide. Layer 13 has a highly 
doped upper portion 14 which is doped with Si to a concentration of 
10.sup.18 atom cm.sup.-3. The properties of the structure are such that a 
potential well containing a two-dimensional electron gas (2-DEG) exists 
adjacent heterojunction 12 in undoped layer 11. An electrode 15 having a 
shape similar to electrode 2 in FIG. 1 is disposed atop layer 13. The 
2-DEG adjacent heterojunction 12 has the form of a sheet of electrons 
which acts as a channel for injected electrons. The latter can travel 
ballistically from injection to collection under shaped electrode 15 
provided the distance traveled is of the order of the mean free path of an 
electron in gallium arsenide or less. While gallium arsenide and gallium 
aluminum arsenide have been shown hereinabove as preferred semiconductor 
materials, it should be appreciated that other Group III-V compound 
semiconductor materials may be used utilized to form layers 11 and 13 
provided that layer 13 has a higher bandgap than layer 11. The 2-DEG is 
formed at the interface between the two materials in the lower bandgap 
material, GaAs, due to the separation of electrons from their parent 
impurities. The higher band gap material AlGaAs, doped with n-type 
impurity has an excess of electrons which are transferred to and collected 
at heterojunction 12 in GaAs layer 11. At this juncture, it should be 
appreciated that the two-dimensional carrier gas may be either a 2-DEG or 
a two-dimensional hole gas. To obtain a two-dimensional hole gas adjacent 
heterojunction 12 in layer 11, layer 13 need only be doped with a p-type 
dopant to provide the excess holes needed. 
FIG. 3 shows a portion of the cross-sectional view of FIG. 2 further 
including a source of potential and an energy diagram correlated with the 
structure illustrating the principles of the invention. The reference 
characters utilized in FIG. 2 identify the same elements in FIG. 3. 
In FIG. 3, a source of negative voltage, -V.sub.G, is shown applied to 
shaped electrode 15 and the 2-DEG disposed adjacent heterojunction 12 in 
GaAs layer 11. The associated energy diagram shows the Fermi level, 
E.sub.F, and the conduction band edge energy, E.sub.C, correlated with the 
structure immediately above it. When a negative voltage is applied to 
electrode 15, the conduction band edge under electrode 15 is raised by a 
height, .PHI., toward the Fermi level, E.sub.F 
The height, .PHI., is proportioned to the potential, V.sub.G, applied to 
electrode 15. Electrons at the Fermi energy, E.sub.F, or others injected 
at higher energy, E, will pass through a potential barrier as they enter 
the region under electrode 15. Their kinetic energy and thus their 
velocity is reduced and they will follow the rules described hereinbelow 
in conjunction with FIG. 4. 
The biconcave electrode 2 of FIG. 1, for example, deposited over the 2-DEG 
of FIG. 3 focuses the ballistic electrons passing underneath electrode 2 
in the manner discussed hereinabove in connection with FIG. 1. As 
indicated above, the focal length is changed as a function of the voltage 
on electrode 2 which changes the barrier height, .PHI., and consequently, 
the "effective index of refraction". Thus, the index of refraction 
n.about..sqroot.E.sub.K, where E.sub.K is the kinetic energy of the 
electrons. 
If an electron with an energy E, traverses the potential barrier from left 
(L) to right (R) in FIG. 3, the total energy, E, and the tranverse 
momentum, k.sub.y, are conserved in their passage. 
Thus, k.sub.y.sup.L =k.sub.y.sup.R and 
##EQU1## 
where E=Total energy 
h=Reduced Planck's constant 
k=wave vectors at the Fermi surface 
m=effective mass of an electron 
.PHI.=Potential Energy on the Right 
Then, because k.sub.y.sup.L =k.sup.L sin .theta..sub.L, k.sub.y.sup.R 
=k.sup.R sin .theta..sub.R, from equation (1) k.sup.L sin .theta..sub.L 
=k.sup.R sin .theta..sub.R. 
Also, from equation (1) above, 
##EQU2## 
therefore, 
##EQU3## 
but E-.PHI.&lt;E 
and hence 
EQU .theta..sub.L &lt;.theta..sub.R (2) 
This relationship can be more clearly understood by considering FIG. 4 in 
which an electron wave 30 of given energy is shown travelling toward an 
interface 31 of an induced potential barrier provided by an electrode 32. 
Electron wave 30 can be resolved into components v.sub.y and v.sub.x and 
the angle of the resultant is .theta..sub.1 =v.sub.y.sup.l /v.sub.x.sup.1. 
Electron wave 30 impinges on interface 31 at the angle .theta..sub.L with 
respect to an axis 33 drawn perpendicularly to interface 31. The resolved 
components v.sub.y.sup.l, v.sub.x.sup.l are each acted on in a different 
way as they encounter potential barrier interface 31. Upon impingement, 
the v.sub.y.sup.l component which is parallel to interface 31 is left 
unchanged while, the v.sub.x.sup.l component which is perpendicular to 
interface 31 has its energy reduced. The resultant of the new components 
which is the now modified electron wave 30' leaves interface 31 at an 
angle tan .theta..sub.2 =v.sub.y.sup.2 /v.sub.x.sup.2, which is greater 
than the angle of incidence .theta..sub. l and conforms to the result 
shown in (2) hereinabove. To the extent that the foregoing will hold true 
for any electron wave impinging on an interface wherein the interface is a 
potential barrier, if the potential barrier presents exactly the same 
conditions to each impinging electron wave, the v.sub.y and v.sub.x 
components thereof will each be affected in the same way and the only 
effect will be that all the electron waves will have their directions 
changed by the same amount. To the extent that it is the energy component 
perpendicular to the interface which is always reduced when an electron 
wave encounters a potential barrier while the component parallel to the 
interface remains substantially unchanged, the tangent .theta..sub.2 
=v.sub.y.sup.2 /v.sub.x.sup.2 is always greater than tangent .theta..sub.1 
=v.sub.y.sup.1 /v.sub.x.sup.l. 
Once the electron wave is in the region of the potential barrier, its 
kinetic energy and velocity are reduced. The wave then passes out from the 
potential barrier via interface 34 and its kinetic energy and velocity are 
thereby increased. Under such circumstances, the rule developed for 
electron waves entering a potential barrier reverses and the angle 
.theta..sub.4 at which a wave leaves the potential barrier via interface 
34 is always smaller than the angle .theta..sub.3 at which wave encounters 
the potential barrier at interface 34. This can be understood by 
appreciating that the component v.sub.y parallel to the barrier interface 
again remains unchanged while the component v.sub.x perpendicular to the 
barrier interface, now experiences an increase in energy and, as a result, 
the angle of the electron wave departing from the potential barrier 
interface is always less then the angle at which it impinged upon the 
potential barrier interface. From the foregoing then, it can be seen, for 
example, that a biconvex gate will cause electron waves travelling 
parallel to the axis of the gate to diverge since, the tangents to the 
points at which the waves strike the first potential barrier interface are 
aligned in such a way that waves on either side of the axis are deflected 
away from the axis. These waves, in turn, impinge on the oppositely curved 
interface, leaving the second potential barrier interface and are further 
deflected away from the axis porviding an arrangement which causes the 
incoming electron waves to diverge. 
With a biconcave gate like that shown in FIG. 1, electron waves travelling 
parallel to the axis of the gate encounter a first potential barrier 
interface. The tangents to points on the barrier are such that waves on 
either side of the axis are deflected toward the axis. These waves, in 
turn, impinge on the oppositely curved second barrier potential interface 
and are further deflected toward the gate axis providing an arrangement 
which causes the incoming electron waves to converge. By controlling the 
slopes of the tangents to points on the potential barriers where electron 
waves impinge, the electron waves may be focused to a point. Then, by 
adjusting, the height of the potential barrier by adjusting the voltage on 
the gate, the point at which the electron waves focus may be changed. If 
the height of the potential barrier is sufficiently great, the impinging 
electron waves will, of course, be totally reflected. 
From the foregoing, it should be clear that electron waves can be caused to 
converge or diverge by simply controlling the slopes of the potential 
barriers induced in the semiconductor materials by a gate electrode which 
has a shape similar to the shape of the potential barrier it induces. 
Since different points across the width of the potential barrier have 
different slopes, the variation in slope determines the curvature of the 
potential barrier which, in turn, is determined by the curvature of the 
overlying barrier inducing electrode. 
FIG. 5 shows a top view of a metallic electrode 40 having a biconvex shape 
which may be substituted for the biconcave shaped electrode of FIG. 1. in 
FIG. 5, arrows 41 which represent electron waves injected into 
semiconductor layer 1 or into an underlying 2-DEG like that shown in FIG. 
2, are oriented parallel to the axis 42 of biconvex electrode 40 and 
impinge on the potential barrier interface of the same biconvex curvature 
in that manner. However, instead of focusing like light rays in a biconvex 
lens, the electron waves diverge from axis 42 at angles which are a 
function of the voltage applied from voltage source 3 and the slopes of 
the various points of the potential barrier at which waves impinge. An 
electrode, like biconvex electrode 40, may be used to supply current 
simultaneously to a plurality of collector electrodes which are disposed 
on the end of semiconductor substrate 1 and, switching may be accomplished 
by applying a potential greater than the energy of the electron waves to 
cause their complete reflection. In applications where a number of outputs 
must be served, ohmic contacts 43 may be lined up as shown in FIG. 5 so 
that a plurality of outputs may be obtained from a single input. 
At this point, it should be clear that using electrodes of a desired shape 
will provide a potential barrier of the same shape and that electron waves 
impinging on such a shaped field will be focused, diverged, refracted or 
diffracted depending on the shape of the potential barrier induced and the 
magnitude and polarity of the applied voltage. 
FIG.6 shows a plan view of another embodiment of the present invention 
which incorporates a triangular potential barrier provided by a triangular 
electrode. By applying appropriate potentials to the electrode, elctron 
waves may be transmitted without deflection, transmitted with deflection 
or totally reflected. In this way, currents may be applied to 
appropriately positioned collector electrodes which act as inputs to other 
circuits. 
In more detail FIG. 6 is similar to FIG. 1 except that the electrode 50 has 
the shape of a triangular instead of the biconcave shaped electrode 2 of 
FIG. 1. Also shown in FIG. 6 is a collimator arrangement 51 consisting of 
an ohmic contact 52 from which electron waves emanate in radial fashion. A 
pair of electrodes 53 disposed adjacent contact 52 collimates the electron 
waves such that they form a plurality of parallel electron waves 54. The 
latter impinge on the potential barrier interface 55 provided by a source 
of voltage 56 connected to electrode 50. To the extent that the potential 
barrier has an energy value lower than that of the electron waves, waves 
54 will be deflected pursuant to the rule described hereinabove in 
connection with FIG. 4, for electron waves in that waves 54 encounter a 
shaped potential having at least one interface 55 with a slope sufficient 
to deflect impinging electron waves 54. The thus deflected electron waves 
54 pass under electrode 50 and, in exiting from it, encounter another 
potential barrier interface 56 which, depending on its slope, further 
deflects electron waves 54 to an ohmic collector contact 57. The latter is 
an ohmic contact which is connected to the 2-DEG in the instance of a 
heterojunction device or to the doped semiconductor in a single 
semiconductor layer device. Restrictor electrodes 58 disposed adjacent 
contact 57 have a potential applied thereto which depletes the underlying 
doped semiconductor region or 2-DEG of carriers to insure that current 
flows to contact 57. 
FIG. 6 also shows another ohmic contact 59 positioned on the same side of 
electrode 50 as collimator electrodes 53, which responds to electron waves 
54 which are reflected from interface 55 when the potential barrier is 
higher than the energy of electron waves 54. Contact 59 also includes 
restrictor electrodes 60. Still another ohmic contact 61 including 
restrictor electrodes 62 is shown in FIG. 6 which is disposed in such a 
way that when not potential is applied to electrode 50, waves 54 pass 
directly from contact 52 to collector contact 61 without deflection. From 
the foregoing, it should be clear that electron waves may be deflected or 
reflected or permitted to pass undeflected depending on the potential 
applied from a variable votlage source 63 connected to electrode 50. The 
potential applied to restrictor electrodes 53, 58, 62 from a source (not 
shown) should be of sufficient magnitude to insure that the regions 
beneath them are depleted of carriers. 
FIG. 7 is plan view showing an arrangement which permits electron waves 
emanating from a point source to become parallel. 
In FIGS. 1, 5, electron waves 4, 41, respectively, are shown as a plurality 
of electron waves moving in parallel before encountering the potential 
barrier formed by shaped electrodes 1, 40, respectively. FIG. 7 shows a 
structure 70 which may be a single layer of a dopted semiconductor or a 
heterojunction structure having a cross section like that shown in FIG. 2. 
An ohmic contact 71 connected to a source of current (not shown) has a 
pair of restrictors 72 connected to a source of potential (not shown). The 
latter deplete the semiconductor regions beneath them so that electron 
waves 73 emanate from the former in radial fashion. Waves 73 are directed 
to the interfaces of a biconcave potential barrier provided by biconcave 
shaped electrode 75. The interaction deflects waves 73 such that they exit 
from the potential barrier as a plurality of parallel electron waves. The 
potential applied from source 74 can be of fixed value. From the 
foregoing, it should be clear that the arrangement of FIG. 7 can be 
coupled with the arrangements of FIGS. 1, 4 to provide the desired 
parallel electron waves as inputs to the lens-like shaped potential 
barriers. 
All of the FIGS. showing the various embodiments are schematic to some 
extent in that they do not suggest the scale of the various elements 
involved. All of the lengths, widths and thickness involved can be 
characterized in angstrom units and fabrication is carried out using 
integrated circuit techniques. Thus, deposition of the various 
semiconductor layers may be carried out by the well-known Molecular Beam 
Epitaxy (MBE) technique. The shaped electrodes and restrictor electrodes 
may be of any appropriate metal such as gold-germanium nickel which is 
deposited on the GaAs surface by evaporation. The deposited layer is 
shaped as desired by well-known photolithographic masking and etching 
techniques which may include metal lift-off. Restrictor electrodes of 
aluminum or titanium-gold may be formed in a similar fashion. Finally, 
ohmic contacts such as the well-known gold-germanium-nickel (AuGeNi) 
contacts may be used in conjunction with III-V compound semiconductors 
like gallium arsenide. Operations of the devices may be carried out at 
liquid helium temperatures to maximize the mean free path length of 
carriers in the semiconductors used. 
In a typical device such as that shown in FIG. 1, biconcave electrode 2 
would vary from 5000 Angstroms at its thickest 2000 Angstroms at its 
thinnest. A typical distance from input to output would be about 2 microns 
at 4.2.degree. K. A voltage of between -0.2--0.5 volts would be applied to 
gate electrode.