Transmission through the Symmetrical Double Delta Barrier with a Rectangular Well in between

On Resonant Tunnelling in the Biased Double Delta-Barrier

“…In the case of the transmissions through the biased double delta-barrier, there also exists some constructive interference between the waves just transmitting through the first delta-barrier and those being reflected off the second one. Unlike the transmissions through the unbiased double delta-barrier [9][10][11], the constructive interference in the biased double delta-barrier is not strong enough to cause the ideal transmission. Thus, the applied voltage reduces the constructive interference between the waves in the double delta-barrier.…”

“…Further, δ(x) is the Dirac delta-function and g is its strength (a positive value of the strength corresponds to a barrier, while a negative value would correspond to a well), Θ(x) is the Heaviside step function (Θ(x) = 0, if x < 0; and Θ(x) = 1, if x > 0), e is the elementary charge, V is the voltage applied to the double delta-barrier, 2a is the width of the double delta-barrier. Evidently, the wave function ϕ(x) is to be sought in the form of plane waves moving from the left to the right and vice versa [5][6][7][8][9][10][11][12][13][14]. Thus,…”

“…Subjecting the wave function ϕ(x) to the connection formulae at the points x 1 = −a and x 2 = +a (vide the Appendix A) one can express it as a sum of three waves: the incident wave, the reflected wave and the transmitted wave [5][6][7][8][9][10][11][12]. Therefore, the wave function on the left-hand side of the biased double delta-barrier can be written as…”

“…ily obtains the transmission coefficient for the double delta-barrier with a rectangular well in between [11]; the well has the depth eV /2 and the width 2a,…”

“…g = w 0 U 0 . Although, the delta-function is a very simplified form of the original potential-energy function, it still enables one to get a proper insight into the transmissions through the high and narrow barrier structures [8][9][10][11]. This is also the reason why the delta--function potentials are often employed throughout many parts of the solid-state physics as a very convenient approximation to more structured and therefore more difficult, short-ranged potentials.…”