Single-Electron Parametron

We have suggested a novel family of wireless single-electron digital devices, based on the parametric excitation principle. The basic cell is a short array of small conducting islands separated by tunnel barriers with relatively low capacitance and conductance. External rf (clock) field creates conditions for spontaneous breaking of the charge symmetry of the cell. The symmetry may be broken by the signal field provided by the neighboring cell(s). This mode ensures robust operation of the parametron-based logic circuits. Moreover, these devices may be reversible, dissipating energy well below kBT ln2 per logic operation.


INTRODUCTION
The effects of correlated single-electron tunneling may be used for implementation of ultradense (n> 100 Gb/cm2) digital circuits of several types ]. Circuits based on Single-Electron-Transistor (SET) logic [2] may be close in design to the usual CMOS circuits, but their static power consumption is too high to allow room-temperature operation. This drawback may be avoided in devices of Single-Electron Logic (SEL) ], which use trapping of single electrons in conducting islands to present digital bits and hence do not have static power dissipation.
Since 1987, several families of SEL devices have been suggested (see Ref. [1] and references therein). In the recently suggested Wireless Single-Electron (WISE) logic [3] which is a SEL-type logic, the necessary energy is supplied by the time-depending electric field Em(t), which also serves as a global clock. When the field Era(t) exceeds some threshold value E t, it induces electric polarization of short one-dimensional arrays serving as basic cells. Field E s of this 43 electric dipole may lower the polarization threshold of the neighboring cell and thus pass the data bits electrostatically. However, orientation of fields Em(t and E s is almost the same, leading to small (about 5 %) parameter margins.
The goal of this work is to suggest a new version of wireless SEL devices, where perpendicular orientation of the fields Em(t) and E s allows more robust operation. As a byproduct of this improvement, the resulting device (which we call Single-Electron Parametron) allows physically-reversible operation, i.e. may be switched between its stable states with dissipation of energy W<<ktT In 2. When the clock field Em(t), which is perpendicular to axis y, is larger than a certain threshold value E t, it keeps the extra electron inside the middle island (top frame in Fig. b). As E m is reduced below the thresh- well trapped inside one of the edge islands, even if the signal field E now favors its transfer into the opposite edge island (bottom frame in Fig. b). This transfer may be only achieved via a higher-order tunneling process; probability of this process may be made negligibly small by either decreasing the tunnel conductance or by inserting a few additional islands into the cell [1 ]. If this parasitic process is suppressed, the cell has a fixed dipole moment and may serve as a source of signal for neighboring cells. It is evident that the principle of operation of this device is similar to that of the well-known Josephsonjunction device called Parametric Quantron (PQ) [4]. The only substantial difference between these devices is that the PQ is described by a continuous degree of freedom (Josephson phase difference ) while the single-electron parametron is characterized by a discrete charge (or the dipole moment P). It is easy to show, however, that both devices share the same basic property: they may operate reversibly. It means that slowly changing external fields may switch the device from one stable state into another adiabatically, with the total energy dissipation much below the apparent limit kBT ln2. As a result, the single-electron parametron may be used as a basic cell of reversible computers, provided that their structure supports the informational reversibility (see Ref. [4] and references therein).

BASIC CELL
Practically, it is more convenient to avoid electric charging of each parametron cell. The device may operate equally well with excitation of electron-hole pairs ("excitons"). old, it becomes energy advantageous for the electron to tunnel from the middle island into one of the edge islands, either right or left one. If the system is completely symmetric along axis y, this symmetry breaking is spontaneous, and the direction of the resulting electric dipole moment of the system is random: P=+_Pony. If, however, the symmetry is broken by some external field E with a component along axis y, i.e. by dipole field of a similar neighboring cell, the direction of the electron tunneling and hence of P will be predetermined by this field (middle frame in Fig.  b). Finally, when E m is well below E t, the electron is 3. SHIFr REGISTER The middle island of each cell of offset from its axis by the same distance; in each following cell of the structure the direction of this offset is rotated by angle re/3 within plane (x,z). As a result, the rotating clock field switches each cell from an OFF state into one of ON states with the rt/3-phase delay with respect to its upper neighbor. In this moment the upper neighbor is already in a certain ON state, and its field is applied to the decision-making cell. In the same time, the lower neighbor is still in one of its OFF states with the "neutral" value of P, not affecting the decision. Thus the data bits are propagating from. the top to the bottom of the structure, shifted by 6 cells during one clock period.
Our analysis has shown that the single cell may operate correctly within at least _+25%wide window of the clock field amplitude. Optimization of the shift register as a whole is still in progress, but we expect that it operates reliably within a relatively wide window of basic parameters.
Logic cells may be designed similarly to the shift register. For example, Fig. 2b shows a possible structure of a 2-input logic gate. In this case an additional dc field (parallel to axis y) should be applied to the decision-making cell marked by arrow. The direction of this field will determine the function (OR or AND) performed by this (irreversible) gate. A majority gate (which does not require the additional bias field) and reversible gates of this type [4]  sunysb.edu) is currently a Research Scientist at SUNY, Stony Brook. His research interests include physics and applications of single-electron tunneling and transport properties of semiconductor heterostructures.