In this thesis, I present the work performed towards a proposal to couple a piezoelectric, nanomechanical beam to a radio frequency single electron transistor (RF-SET). Lumped element RF circuit theory is applied to 50 kOhm single electron transistors acting as the resistor in an RLC circuit. It is shown that for the expected inductances and stray capacitances, at an operating frequency of 1.25 GHz, the RF-SET is expected to have a usable half-bandwidth of 175-200 MHz and a charge sensitivity on the order of 10^(−5) e/√Hz. A fabricated RF-SET device is cryogenically cooled and used to find experimental values of the stray capacitance. A heterostructure made of gallium arsenide and aluminum gallium arsenide from which piezoelectric beams can be made is designed to contain a 2-dimensional electron gas (2DEG). Quantum Hall effect samples are fabricated from the wafer, and magnetoresistance measurements for each sample are presented. It is shown that the 2DEG has a high electron concentration of about 8 × 10^11 cm−2 but a low mobility of about 3.5 × 10^4 cm^2/(V·s) for this type of heterostructure. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2010-03-01 22:55:56.427

In the past decade, nanomechanical resonators have found use in the work towards understanding mesoscopic quantum systems and the necessary validation of quantum mechanics on this scale. In 2010, the observation and state manipulation of a nanomechanical quantum system was achieved for the first time by O'Connell et al.. In 2002, Knobel and Cleland proposed to use a radio frequency superconducting single-electron transistor (RF-SSET), a fast and sensitive charge amplifier, to sense the quantum-limited motion of a piezoelectrically coupled nanomechanical resonator. The work presented in this thesis is towards the realization of the RF-SSET component of this device. An in-house fabrication recipe for making SETs with tunnel junction areas < 100^2 nm^2 and resistances between 20 kΩ and 150 kΩ was developed, in the end producing six SETs with resistances (36 ± 8) kΩ that were not susceptible to aging effects. Three measurement circuits were designed and used to characterize one of these SETs in the superconducting state (SSET) and operated in the DC and RF modes in a cryostat at a base temperature of 320~mK. Lock-in measurements revealed the SSET junction capacitances as 206 and 305 aF, contributing to a charging energy of (296 ± 11) x 10^(-6) eV. The resonant LC tank, which permitted RF operation, was also characterized at base temperature. The charge sensitivity of the RF-SSET was 6.8 x 10^(-5) e/√Hz (with uncertainty between 9.6 x 10^(-4) e/√Hz and 3.5 x 10^(-5) e/√Hz). With moderate improvements to the impedance matching network formed with the LC tank and greater junction resistances, an RF-SSET charge sensitivity on the order of 10^(-6) e/√Hz, required for sensing the quantum-limited motion of the nanomechanical resonator, should be achieved. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2010-08-10 17:38:43.798