Progress Towards the Quantum Limit: High and Low Frequency Measurements of Nanoscale Structures
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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.