Theory for a quantum modulated transistor

We present a theoretical study of semiconductor T-structures which may exhibit transistor action based on quantum interference. The electron transmission through a semiconductor quantum wire can be controlled by an external gate voltage that modifies the penetration of the electron wavefunction in a lateral stub, affecting in this way its interference pattern. The structures are modeled as ideal two-dimensional electron waveguides and a tight-binding Green's function technique is used to compute the electron transmission and reflection coefficients. The calculations show that relatively small changes in the stub length can induce strong variations in the electron transmission across the structure. Operation in the fundamental transverse mode appears to be important for applications. We also show that a bound state of purely geometrical origin nucleates at the intersection between waveguide and stub. The performance of the device can be improved by inserting additional stubs of slightly different lengths. Taking into account the applicable scaling rules, we give estimates of the experimental parameters that optimize the transmission characteristics and speed of operation of the proposed transistor.