Active conductivity of plane two-barrier resonance tunnel structure as operating element of quantum cascade laser or detector

Abstract

Within the model of rectangular potentials and different effective masses of electrons in different elements of plane two-barrier resonance tunnel structure there is developed a theory of spectral parameters of quasi-stationary states and active conductivity for the case of mono-energetic electronic current interacting with electromagnetic field. It is shown that the two-barrier resonance tunnel structure can be utilized as a separate or active element of quantum cascade laser or detector. For the experimentally studied In 0.53 Ga 0.47 As/In 0.52 Al 0.48 As nano-system it is established that the two-barrier resonance tunnel structure, in detector and laser regimes, optimally operates (with the biggest conductivity at the smallest exciting current) at the quantum transitions between the lowest quasi-stationary states.

Non-perturbation theory of electronic dynamic conductivity for two-barrier resonance tunnel nano-structure

“…The behaviour of the function is clearly explained by physical considerations. In reference [19] it was proven that the magnitude of dynamic conductivity is proportional to the electron life times in those quasi-stationary states between which the quantum transitions occur due to the interaction with electromagnetic field. If the difference between the widths of both barriers |∆ + − ∆ − | is big, the life times in all quasi-stationary states are small because the electrons rapidly quit the two-barrier RTS through the thinner barrier.…”

“…The both linearly independent exact solutions of complete Schrodinger equation with Hamiltonian H 0 (z) in the potential well are known: exp(±ikz − iω 0 t) [17,19], ω 0 = E −1 . The both linearly independent exact solutions of equation ( 3) with Hamiltonian H(z, t) = H 0 (z) + H 1 (z, t), taking into account the electron-electromagnetic field interaction in linear approximation over the electric intensity are also known:…”

“…It is evident that in linear approximation over the electromagnetic field intensity, the coefficients B ± 0 , A ± 4 are also linear. Consequently, in this approximation, (the same in PT [4][5][6][7][8][9][10][11][12][13][15][16][17][18][19]) the dynamic conductivity is independent of .…”

“…The calculations of spectral parameters of electron quasi-stationary states and dynamic conductivity of nano-structure were performed at the base of the developed NPT for In 0.52 Al 0.48 As/In 0.53 Ga 0.47 As two-barrier RTS with physical parameters: m 0 = 0.046 m e , m 1 = 0.089 m e , U = 516 meV, n 0 = 10 16 cm −3 and typical geometrical ones: b = 10.8 nm, ∆ + + ∆ − = 6 nm, ∆ + = 2 ÷ 4.5 nm. The same calculations were performed in the frames of the previously developed PT [19] in the first order over the field intensity for comparison.…”

“…The theory of dynamic conductivity established in references [16][17][18][19] for the open two-and three-barrier RTS is based, as a rule, on a more realistic model but it is so complicated compared to the δ-barrier model that it is practically impossible to leave the framework of weak signal approximation. Nevertheless, the development of experimental capabilities makes the problem of strong interaction of electronic currents and electromagnetic field in RTS more and more urgent.…”