LOW-RESISTANCE ELECTRON TRANSPORT IN SOLIDS

Abstract

Voltage-controlled, resistance-free electric current conduction in 2-dimensional electron gases (2DEG) and its technical application at temperatures (T) up to above room temperature can be achieved by electrons with energies E<(E.sub.F-k.sub.BT) (E.sub.F=Fermi energy, k=Boltzmann constant) of a completely filled conduction band of a 2DEG which are exposed to a magnetic field B.sub.z in the z-direction and an electric field E.sub.y in the y-direction, which forces all of them to move in cyclotron motion in the x-y-plane with a common drift velocity v.sub.Dx in the x-direction. The resulting electric drift current J.sub.x has no resistance, as the electrons involved can neither be accelerated in a sole electric field nor disturbed by scattering from defects, impurities or phonons, as all possible final states of these processes are occupied by other electrons in the 2DEG. Minor losses only occur due to J.sub.y currents of the normally conducting electrons of the 2DEG with energies between E=E.sub.Fk.sub.BT which are necessary for the generation of the E.sub.y field in the 2DEG.

Claims

1. Low-resistance to resistance-less electrical conductance at temperatures up to above room temperature, wherein a fraction of the electrons of high mobility >20 /B.sub.z m.sup.2/Vs located in the conduction band of a solid cannot be accelerated by an electric field and cannot be scattered by ions, defects, impurities or phonons, since all possible final states of these processes are occupied for these electrons, so that this fraction of electrons when exposed to crossed magnetic B.sub.z-fields in the z-direction and electric E.sub.y-fields in the y-direction provide a resistance-free cyclotron drift current in the x-direction, which reduces the overall electrical resistance of this solid.

2. Low-resistance to resistance-less electrical conductance of claim 1, wherein electrons of high mobility occupy all energy-states from the ground-state energy E.sub.0 to the Fermi-Energie E.sub.F>E.sub.0 of the conduction band and are exposed to a magnetic field B.sub.z in the z-direction and an electric field E.sub.y in the y-direction which leads despite the energy between E.sub.0 and E.sub.FkT of the electrons in the conduction band to a cyclotron-drift current of these electrons in the x-direction which is resistance-less since it is neither perturbed by thermal excitations of the electrons nor perturbed by scattering of the electrons on crystal-defects, on impurities, or on phonons, since all possible final states of these processes are occupied.

3. Low-resistance to resistance-less electrical conductance of claim 1, wherein solid-state structures are produced by MBE (Molecular Bearn Epitaxy) or similar methods that enable completely filled conduction bands of electrons with high mobility >200 /B.sub.z, with energies between E.sub.0 and E.sub.F, and with the property (E.sub.FE.sub.0)>kT.

4. Low-resistance to resistance-less electrical conductance of claim 1, wherein solid-state structures or specifically semiconductor heterostructures with quantum wells are produced which enable the existance of 2DEG (two-dimensional electron gases) in the x-y plane with, for example, the length L.sub.x and the width L.sub.y, and with the properties specified in claim 1, whereby electrodes attached on both sides at L.sub.y/2 and the voltage difference U.sub.y between these two electrodes can generate the electric field E.sub.y in the 2DEG.

5. Low-resistance to resistance-less electrical conductance of claim 1, wherein solid-state structures are produced by layering films of different materials so that different quantum well shapes for 2DEG can be produced or series of quantum wells for series of 2DEG in the three spatial directions become possible.

6. Low-resistance to resistance-less electrical conductance of claim 1, wherein the quantum well depth E.sub.F0=E.sub.FE.sub.0 is conditioned by various methods such as, for example, with the gate voltage of a HEMT, or with special doping concepts and/or with infrared radiation in such a way that E.sub.F0 is greater than kT at room temperature so that more than half of the electrons in the 2DEG can participate in the loss-less cyclotron drift current J.sub.x.

7. Low-resistance to resistance-less electrical conductance of claim 1, wherein the 2DEG produced in the x-y plane are exposed to a not necessarily homogeneous magnetic field in the z-direction B, over the entire area L.sub.xxL.sub.y of the 2DEG, which is generated, for example, by external permanent magnets or by intrinsic magnetic structures adapted to the area L.sub.xxL.sub.y of the 2DEG, the latter comprising, for example, micro-permanent magnets, of permanent magnetic layers in the closest possible proximity to the 2DEG or of doping some of the layers defining the 2DEG with magnetizable nanoparticles (atoms) with which very high local magnetic fields B.sub.z can be achieved.

8. Low-resistance to resistance-less electrical conductance of claim 1, wherein MOSFET (Metal Oxide Semiconductor Field Effect Transistor, see FIG. 10.36 in Ref. [5])-, or HEMT (High Electron Mobility Transistor, see FIG. 5.54 in Ref. [6]), or similar solid-state structures with 2DEG in the x-y plane comprising B.sub.z-generation can be produced, in which the voltage U.sub.yfor the generation of the electric field E.sub.y=U.sub.y/L.sub.y can be applied in the 2DEG over the width L.sub.y of the 2DEG by corresponding electrodes, so that by action of the magnetic field in the z-direction B.sub.z the supercurrent of all electrons of the 2DEG in the x-direction can be tapped at the drain electrode, which can be controlled with the gate voltage and/or with U.sub.y.

9. Low-resistance to resistance-less electrical conductance of claim 1, wherein MOSFET-or HEMT-like solid-state structures are formed by several thin-film films (see FIG. 2b of Ref. [7] as an example) so that 2DEG comprising B.sub.z generation with the greatest possible mobility of the electrons and E.sub.F0>kT can be realized in supercurrent-conducting or supercurrent-producing microelectronic components, which can possibly be conditioned by infrared radiation.

10. Low-resistance to resistance-less electrical conductance of claim 1, wherein such microelectronic components, connected in series, provide a supercurrent conductor or, connected in parallel, a supercurrent generator.

11. Low-resistance to resistance-less electrical conductance of claim 1, wherein 2DEG with >20 /B.sub.z, E.sub.F0<kT and B.sub.z-generation, in large length L, are manufactured in an electronics component as voltage-controlled supercurrent conductors.

12. Low-resistance to resistance-less electrical conductance of claim 1, wherein integrated parallel circuits are manufactured of many 2DEG with >20 /B.sub.z, E.sub.F0<kT and B.sub.z-generation in one electronic component as a voltage-controlled super current generator.

13. Low-resistance to resistance-less electrical conductance of claim 1, wherein 2DEG microstructures with >20 /B.sub.z, E.sub.F0<kT and B.sub.z-generation are incorporated into integrated circuits, thereby significantly reducing their thermal losses.

14. Low-resistance to resistance-less electrical conductance of claim 1, wherein all electronic components mentioned so far are operated at lower temperatures than room temperature, which improves the condition E.sub.F0>kT.

Description

SUMMARY

[0008] An embodiment may have a low-resistance to resistance-less electrical conductance at temperatures up to above room temperature, wherein a fraction of the electrons of high mobility >20 /B.sub.z m.sup.2/Vs located in the conduction band of a solid cannot be accelerated by an electric field and cannot be scattered by ions, defects, impurities or phonons, since all possible final states of these processes are occupied for these electrons, so that this fraction of electrons when exposed to crossed magnetic B.sub.z-fields in the z-direction and electric E.sub.y-fields in the y-direction provide a resistance-free cyclotron drift current in the x-direction, which reduces the overall electrical resistance of this solid.

[0009] The task of the invention is to utilize these noble electrons with energies E.sub.1zEE.sub.FkT for electric current conduction without impairing their special properties and thus to generate a loss-free electron current. The prerequisites for this are a) the generation of an 2DEG and b) a method for imposing a drift velocity v.sub.D on the noble electrons of the 2DEG.

[0010] Ad a) A typical 2DEG is confined in a potential well of energetic depth E.sub.0, length L.sub.x, width L.sub.y<L.sub.x, and height L.sub.z. L.sub.z is made so small that quantum mechanically only the ground state E.sub.1z>E.sub.0 can exist. In the following, such a potential well is referred to as a quantum well (QW). With a constant electron energy density D(E)=L.sub.x.Math.L.sub.y.Math.4.Math..Math.m*/h.sup.2 (see Eq. 7.1.22 in Ref. [1] with h=Planck's quantum of action and m*=reduced mass of the electrons), the 2DEG fills all energy states of this QW from E.sub.1z to E.sub.FkT. The number of electrons N.sub.e in the 2DEG results in N.sub.e=D(E).Math.(E.sub.FE.sub.F1z)=D(E).Math.E.sub.F1z. The z-wave function of the E.sub.1z state has exponential tails into the walls at z=0 and z=L.sub.z. All other energy states of the 2DEG have the same z-wave function and differ only in the x-y wave functions. This means that all electrons of the 2DEG are exposed to the quality of the walls at z=0 and z=L.sub.7. However, this only limits the free mobility of the N.sub.e.sup.leit=D(E).Math.k.Math.T electrons participating in the normal electric conduction, as they can be accelerated or scattered into free final states. For the N.sub.e.sup.edel=D(E)(E.sub.F1zkT) noble electrons, these final states of possible disturbances are not available, so that they fulfill the conditions for a perfect free electron gas, which is therefore referred to as a 2-dimensional free electron gas (2DFEG).

[0011] Until now, the aim has been to improve the quality of the walls of a 2DFEG in order to increase the electric current J.sub.x of the N.sub.e.sup.leit electrons in MOSFETs and HEMTs, for example. The current J.sub.x=(N.sub.e.sup.leit/L.sub.x.Math.L.sub.y).Math.e.Math..Math.E.sub.x.Math.L.sub.y through a HEMT from the source electrode at x=0 to the drain electrode at x=L.sub.x is proportional to . The electric field E.sub.x=U.sub.x/L.sub.x with the voltage difference U.sub.x between source and drain. In GaN-HEMTs, mobilities of =1.Math.10.sup.3 to 2.Math.10.sup.3 cm.sup.2/Vs are achieved at room temperature with electron surface densities of n.sub.lei=N.sup.leit/(L.sub.x.Math.L.sub.y)2.Math.10.sup.13 cm.sup.2 [5]. For the values L.sub.x=5 mm, L.sub.y=1 mm, U.sub.x=5 V, =1000 cm.sup.2/Vs and n.sub.leit=1.Math.10.sub.leit.sup.13 cm.sup.2, this results in a current of J.sub.x=1.6 mA, for example.

[0012] Ad b) All noble electrons of the conduction band with energies E<(E.sub.F1zkT) do not participate in normal electric conduction.

[0013] As shown above, by applying a magnetic field B.sub.z in the z direction, it is possible to set the noble electrons into cyclotron motion in the x-y plane. If these noble electrons are exposed to an additional electric field E.sub.y in the y-direction, they experience a cyclotron drift movement in the x-direction with the drift velocity v.sub.Dx=E.sub.y/B.sub.z. The frequency and the drift velocity are independent of the energy of the electrons. All N.sub.e.sup.edel=D(E)(E.sub.F1zkT) noble electrons therefore have the same drift velocity v.sub.Dx. This allows the desired drift current density j.sub.Dx=n.sub.edel.Math.e.Math.V.sub.Dx to be calculated. Assuming that the surface density of the noble electrons n.sub.edel=N.sup.edel/(L.sub.x.Math.L.sub.y) is at least as large as n.sub.leit, this results in a drift current J.sub.Dx=160 mA with U.sub.y=10 V and B.sub.z=1 Tesla, for example. As all the noble electrons involved are not subject to any perturbation, because all the final states of such perturbations are occupied, this drift current is loss-less and passes through the 2DFEG with the electric resistance R.sub.xx=0. It is therefore referred to from here as the super drift current J.sub.Dxsuper. This J.sub.Dxsuper=160 mA is an excellent result, but it has to be set in relation to the thermal loss of the current J.sub.y=n.sub.leit.Math.e.Math..Math.E.sub.y.Math.L.sub.x, which is necessary to generate the field E.sub.y in the 2DFEG. With the example values used so far, J.sub.y=80 mA with a thermal loss W.sub.y=J.sub.y.Math.U.sub.y=800 mW. This loss is too high and has to be reduced. The answer is provided by the ratio (J.sub.Dxsuper/J.sub.y)=(n.sub.edel/n.sub.leit).Math.(L.sub.y/L.sub.x)/(B.sub.z), which was previously equal to 2. Accordingly, (n.sub.edel/n.sub.leit) jas to be made large and (.Math.B.sub.z) small.

[0014] The requirement for a small (.Math.B.sub.z) can easily be met for B.sub.z, because a B.sub.z=0.01 Tesla is easier to generate in the 2DFEG than B.sub.z=1 Tesla. However, it is accepted that the minimum width L.sub.ymin of the 2DEG has to be increased by a factor of 10. The requirement for small mobility u is completely contrary to all previous efforts, but is understandable, as the smallest possible current J.sub.y is to be used here with the sole aim of producing the field E.sub.y. In view of the development of HEMTs by modulation doping from MOSFETs in order to make u larger, a return to HEMT-2DEG structures but without modulation doping is an obvious way of reducing . This means that =200 cm.sup.2/Vs at T=300 K can be expected for the N.sub.e.sup.leit electrons, while the N.sub.e.sup.edel noble electrons are not affected. This has already been shown with a MOSFET in Ref. [6] with the first proof of R.sub.xx=0. However, in that experiment the temperature had to be cooled down to 1.5 K in order to reduce the width kT of the Fermi edge so that the QHE could be resolved. With these smaller example values =200 cm.sup.2/Vs and B.sub.z=0.01 Tesla, a J.sub.Dxsuper=16 A with U.sub.y=10 V is achieved while the thermal loss is reduced to W.sub.y=160 mW. Compared to the thermal loss of W.sub.x=160 W of a hypothetical current of 16 A through a HEMT with U.sub.x=10 V, this is an excellent result. This demonstrates the clear advantage of the invention over existing HEMTs. A further reduction of is possible by increasing the temperature to T>300 K, which, however, also slightly worsens the ratio n/n.sub.edelleit.

[0015] Increasing n.sub.edel/n.sub.leit is more complex, because the electron surface density n=n.sub.leit+n.sub.edel is initially unknown, as only n.sub.leit is measured directly. In addition, in an asymmetric triangular QW, the energy states E.sub.mz are closer and closer with increasing m (E.sub.2z=1.67.Math.E.sub.1z, E.sub.3z=2.34.Math.E, E.sub.1z 24z=2.88.Math.E.sub.1z, etc.). This leads to the occupation of several 2DFEG bands E.sub.F1z, E.sub.F2 z, E.sub.F3z, etc. with the same D(E). An analysis of this situation results. for example, for n=1.Math.10.sub.leit.sup.13 cm.sup.2 in the occupation of 5 2DFEG bands with E.sub.1z=22.6 meV, E.sub.F1z=65.2 meV and n.sub.edel=0.885n.sub.leit. This corresponds with good approximation to the previous assumption of n.sub.edel=n.sub.leit. The ratio n.sub.edel/n.sub.leit can therefore hardly be improved with asymmetric triangular QW. This changes with symmetrical rectangular QWs, because in these QWs the energy states E.sub.pz=E.sub.1z.Math.p.sup.2 are further and further apart with increasing p, whereby E.sub.1z=h.sup.2/(8.Math.e.Math.m*.Math.L.sub.z.sup.2)=1.88.Math.10.sup.18/L.sub.z.sup.2 [m]. With a semiconductor heterostructure with a symmetrical structure and, as an example, GaN as the QW material with a height of L.sub.z=7 nm, n.sub.leit=1.Math.10.sup.13 cm.sup.2 results in a single filled 2DFEG band with E.sub.F1z=115.2 meV. Of these, 27 meV would be occupied by N.sub.leit=n.sub.leit.Math.L.sub.x.Math.L.sub.y and 88.2 meV by N.sub.edel=n.sub.edel.Math.L.sub.x.Math.L.sub.y. This corresponds to a ratio n.sub.edel/n.sub.leit=3.26. Under the simplifying assumption that n.sub.edel remains n.sub.edel=1.Math.10.sup.13 cm.sup.2 as an example in this rectangular QW, n.sub.leit is reduced to n.sub.leit=3.Math.10.sup.12 cm.sup.2. With this value of n.sub.leit, W.sub.y is reduced to W.sub.y=48 mW for a loss-free current transport of J.sub.Dxsuper=16 A. Compared to the thermal loss of the W.sub.x=160 W of a hypothetical current J.sub.x=16 A through a HEMT with U.sub.x=10 V, this is an excellent result. This clearly demonstrates the advantage of the invention over existing HEMTs.

[0016] For practical application, the QWs of 2DEG heterostructures havz to be equipped with electrodes along L.sub.x on both sides of the 2DEG at y=0 and y=L.sub.y. According to the above discussion, these electrodes are needed to generate the electric field E.sub.y=U.sub.y/L.sub.y in the 2DFEG with the voltage difference U.sub.y between them.

[0017] In addition, the entire surface L.sub.xxL.sub.y has to be exposed to a magnetic field B.sub.z in the z-direction. For this purpose, the entire heterostructure can be exposed to an external magnetic field B.sub.z. However, internally produced magnetic fields with adaptation to the surface L.sub.xxL.sub.y are more suitable. This can be realized by permanent magnetic layers of size L.sub.xxL.sub.y of various types above or below or above and below the 2DFEG in the layered structure of the heterostructure. In this context, a 2DFEG in a symmetrical rectangular QW is advantageous because the heterostructure layers to be applied above and below the 2DFEG, including the permanent magnetic layers, can be made mirror-symmetrical.

[0018] A 2DFEG equipped in this way, which is arranged between the source electrode at x=0 and the drain electrode at x=L.sub.x, can also be used directly as an almost loss-less transistor without a gate electrode. With a constant magnetic field B.sub.z, the super current J.sub.Dxsuper is only dependent on U.sub.y, so that a perfectly linear current-voltage curve is obtained when controlled with U.sub.y. For the above example with L.sub.x=5 mm and L.sub.y=1 mm, J.sub.Dxsuper=1.6.Math.U.sub.y A with a thermal loss of only W.sub.y=1.6U.sub.y.sup.2 mW. Since the cyclotron frequency at B=0.01 Tesla, for example, is equal to v=2.210.sup.9 s.sup.1, it can be assumed that the transistor allows switching frequencies of up to 1 GHz. These are all excellent prerequisites for the technical application of this new type of transistor, which deserves to be called a drift transistor.

[0019] By additionally attaching the usual gate electrodes as in HEMTs, the super current J.sub.Dxsuper of a drift transistor can be controlled with a second, independent input signal U.sub.Gate=U.sub.G. The electron density n in the 2DFEG is changed non-linearly by U.sub.G, which leads to a non-linear J.sub.Dxsuper/U.sub.G characteristic. An almost loss-less transistor with two independent control inputs U.sub.G and U.sub.y is a novelty that is becoming interesting for applications.

[0020] The almost loss-free super current can be increased by connecting drift transistors in parallel. The most effective method of increasing the current of a transistor in the micro range can be achieved by stacking q of the same QW in the z direction. Such structures are known as superlattices of QWs (see FIG. 10.34 in Ref. [1]). In addition to the semiconductor layers required to generate the QWs, an additional permanent magnet layer between the QWs is then sufficient to generate the magnetic field B.sub.z in the entire superlattice. If the width L.sub.y=1 mm is maintained, a supercurrent of J.sub.Dxsuper=160 A with U.sub.y and U.sub.G can be controlled with q=10 parallel QWs in the superlattice. The loss of q QWs is then simply the loss of one QW multiplied by q.

[0021] While this invention has been described in terms of several advantageous embodiments, there are alterations, permutations, and equivalents, which fall within the scope of this invention. It should also be noted that there are many alternative ways of implementing the methods and compositions of the present invention. It is therefore intended that the following appended claims be interpreted as including all such alterations, permutations, and equivalents as fall within the true spirit and scope of the present invention.

REFERENCES

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