In order to perform quantum computations, the quantum states, or qubits, must remain coherent. The spin of an electron bound to a shallow donor in silicon is a promising candidate as a qubit. Some of the advantages which have led researchers to consider electrons' spins in silicon as qubits are that the electrons can be moved and controlled with biases applied to gates, a huge technological base already exists for controlling electrons in conventional silicon devices, and data had been obtained in the late 1950's showing spin coherence in isotopically enriched ²⁸Si of close to a millisecond - probably the longest electron spin coherence observed until the last few years. this part of our research is aimed at understanding the physical mechanisms limiting spin coherence in silicon, and identifying ways of reducing the decoherence. This figure illustrates how the measured coherence (T₂) has increased over the last few years, and the processes which were causing the decoherence. Ultimately the coherence time is limited by the “spin flip time” (T₁), which means that we can potentially increase spin coherence by another two orders of magnitude.

This picture shows a portion of a Charge-Coupled Device (CCD) which can transport electrons across the surface of superfluid helium. It has been suggested that electrons spins will remain coherent for long times (seconds, or longer) when the electrons are floating on helium. A small portion of the device is shown, consisting of a series of channels (the darker gold areas) about 2 microns deep and filled with helium. This device is based on silicon integrated circuit technology, and was fabricated by colleagues at Sandia National Laboratory. The brighter gold areas are a metal layer at the top of the channels, and there is also metal at bottom of the channels, but the lower metal is patterned into gates. The green dots represent electrons, and by applying appropriate voltages to them, the electrons can be moved left and right (as shown by the arrow through the bottom electron). There is also one channel which is vertical in this picture, to move electrons between the horizontal channels. Each horizontal channel has two short stubs where electrons can be stored (memories). In this CCD three gates make up a pixel. Single electrons have been transported back and forth over a billion pixels at 250,000 pixes/second without any evidence of errors (an electron ending on the wrong pixel). We have recently designed newer, more advanced CCD structures, which have been fabricated through MOSIS. These devices are being prepared for testing.

As discussed above, one promising qubit is the spin of an electron bound to a donor in silicon, but those electrons are tightly bound and difficult to manipulate with gates. An alternative approach, which still uses an electron's spin in silicon as the qubit, is to confine individual electrons by gates in a Si layer. These electrons are confined to move in a plane by a heterostructure, typical either a metal-oxide-silicon (MOS) interface, or a silicon quantum well embedded in an alloy semiconductor, SiGe. We have measured spins in both types of heterostructure, though most recently we have used the Si/SiGe heterostructures because the electron mobility is very high. As shown schematically on the figure, we currently are using dual-gated structures, with the gates insulated using atomic-layer deposited (ALD) Al₂O₃. The SiGe is not intentionally doped, and thus a gate must be made positive to pull electrons in from the electrical contacts to the quantum well. We use electron-beam lithography to define a large number (about 10⁸) of nanoscale holes in the lower gate. First both gates are made positive, to bring electrons in from the contacts, and then the lower gate is made more negative, to push electrons out of the quantum well, except beneath the holes. By adjusting the two gate voltages we change from having large numbers of electrons everywhere, to having one electron beneath each hole. With many electrons we use pulsed ESR to measure spin coherence and find that is is relatively short, a few microseconds. When the gate voltages are adjusted to leave one electron in each quantum dot (under each hole in the lower gate) the spin coherence increases by a factor of 30 or more. Recent data suggest that smaller dots will have even longer spin coherence times.

Detecting the spin of large numbers of electrons can be readily done using ESR techniques. However, detecting the spin of a single electron, or single nucleus, is more challenging. Many schemes for measuring an electron's spin involve bringing up a second electron, of known spin, and tuning the energy levels so that a potential will bind both electrons only if they form a singlet state (so are opposite spin). Thus the problem of measuring a spin becomes one of measuring a charge. Reliably measuring charge, at the level of a single electron, is still a challenging task. We are investigating the possibility of measuring the charge of a donor in silicon using the IQHE. The picture is a cartoon of how such a device might operate. When a large magnetic field (about 4.5T in these experiments) is applied perpendicular to a 2-dimensional electron system, the usual band states form Landau levels. The resistance along the direction of current flow (R_xx) goes nearly to zero at certain magnetic fields, while the transverse Hall resistance (R_xy) has a quantized plateau. This behavior was discovered by Klaus von Klitzing, for which he received the Nobel Prize in Physics in 1984, and it forms the basis for the international resistance standard. The current flows in “edge states” along the edge of the sample. In the diagram, the green area represents the 2D electrons, the blue regions represent gates, which are biased negatively to repel the electrons and deplete the region below them, and the black lines represent two edge states. The current is flowing from left to right, with electrons in the edge states along the bottom moving one direction (shown by the arrows), while those along the top move the other direction. As long as these edge states are far apart, it is difficult to scatter an electron all the way across the sample to the states moving the other direction, and thus the resistance goes nearly to zero at low temperature. However, with the blue depletion gates biased to bring the edge states close together, as shown, the resistance will increase. By placing a donor (the ”+” at the tip of the lower depletion gate) in the gap between the two blue depletion gates, if it is charged it can scatter electrons across the small remaining gap, and cause an increase in resistance. A neutral donor can capture a second electron, becoming negatively charged, but only when the two electrons form a singlet (opposite spin). Thus, measuring R_xx becomes a means for measuring the spin of the electron on the donor. (This is a new project, and is just getting underway.)

As we make more complicated quantum devices and systems, measuring their properties is becoming increasingly difficult. Since many of these devices operate at very low temperatures, the heat conducted to them by their many control wires becomes a limiting factor. We are also typically detecting very small voltages and currents (for example the voltage induced on a gate by a single electron), and it is difficult to avoid degrading these small signals while bringing them out to room-temperature measuring equipment. One way to reduce the number of wires and improve our ability to measure small signals is to build preamplifiers into the same chips on which we build the quantum devices. An example of an early preamplifier design is shown in the picture. This preamp was designed to detect individual electrons for the electrons-on-helium experiments. While those already use a low-temperature preamp, it is a separate chip (a GaAs HEMT), and is is difficult to get the parasitic capacitance of the bondpads and bond wire much below 1pF. The circuit pictured here was designed to have a 30 times smaller input capacitance (meaning a 30 times larger induced voltage from one electron), and our current designs are another 10 times smaller input capacitance (~3fF). However, the circuits must be designed to operate at extremely low power (nanowatts) to avoid heating, and at very low noise levels.

In addition to analog detection circuits, we are also designing digital circuits to control the devices. This work is starting with the electrons-on-helium structures, where we are already using CMOS chips so the circuits come “free”. These systems also utilize many control lines for complex clocking of the electrons. However, we are looking into the possibility of adding control and measurement circuits onto some of the silicon spin qubit devices, where it is advantageous to be able to test multiple devices in a single cooldown. As with the analog circuits, ultra-low power dissipation is essential. There is also very little, if any, modeling data for operation at liquid helium temperature for most of the foundry processes, making it difficult to rely on circuit simulations to any significant degree. (This is a new project, and is just getting underway.)

Projects are in a constant state of flux, morphing into new ones as we learn and develop new ideas. We attempt to keep this page reasonably up to date.