Calculation and design of GaAs quantum dot devices where the vibrational modes can be frozen out at cryogenic temperatures

Abstract We calculate how the frequencies of the vibrational modes in a free-standing GaAs bar are changed as a function of the bar’s geometrical features such as length, thickness and shape. After understanding the effect of the physical characteristics we add finger gates that will be used to define quantum dots on the bar and study the system as a function of the length of the suspended finger gates, and their material properties. Finally, we strengthen the bridges in order that the first vibrational modes occur at a temperature of 100 mK or more, so that all modes can be frozen out when operated in a dilution refrigerator.