Time-dependent electron tunneling through time-dependent tunnel barriers

Abstract

A plane electron wave incident on a tunnel-transparent potential barrier formed by the potential V(x,t)=V0(x)+V1(x)cos ωtV(x,t)=V0(x)+V1(x)cos ωt generates, in addition to the usual stationary transmitted and reflected stationary waves, also “transmitted” and “reflected” electron waves oscillating with the same frequency ωω. The transmitted oscillating wave can serve as the basis for transit-time microwave generators oscillating in the terahertz range. (Such oscillators are ballistic analogs of the tunnel-emission transit-time diode oscillators suggested almost half a century ago.) In the special case of a rectangular potential barrier, we describe the dependence of a small transmitted oscillating wave amplitude on the frequency ωω and the value of V1(x)V1(x). We consider two forms of V1(x)V1(x): (1) homogeneous oscillation of the height of the rectangular barrier and (2) V1(x)=aδ(x−x1)V1(x)=aδ(x−x1) [where δ(x)δ(x) is the Dirac delta function and 0<x1<w0<x1<w; ww is the barrier thickness]. For sufficiently high frequencies ωω determined by the time for tunneling, a much higher emission of the transmitted oscillating wave takes place in comparison with the results of quasistatic calculations.