Analytical Inverse Solutions of the Schrödinger Equation for Closed Nanocircuits Providing a New Approach for Terahertz Devices

Conventional one-dimensional “open” tunneling circuits have a potential barrier on an axis extending to infinity in both directions. The solution has an incident and a reflected wavefunction on one side of the barrier, 2 waves within it, and a transmitted wave on the other side. Now we present ereHerehhh“closed-circuit” models with shunted square or triangular barriers. One or more of 4 parameters (electron energy, potential, and the two lengths) are specified and the others are determined. The boundary conditions require a matrix equation equivalent to 4 algebraic equations in the 4 parameters. Each equation is homogeneous because the circuit is closed. The determinant must be zero for a non-trivial solution of the parameters. Thus, one or more of the 4 parameters is varied to bring the determinant to zero, leaving a set of equations to determine the others. Specifying any one parameter gives sets of solutions for the other 3. Specifying any 2 gives sets of solutions for the other 2, and specifying 3 gives the value of the remaining parameter. Then we may calculate the coefficients for the wavefunctions. We also consider a prototype terahertz source with a ring of beryllium or silver to provide a mean-free path for coherent electron transport of 183 or 53.3 nm, with a gap for tunneling.