Momentum filter using resonant Zener tunneling

We consider the formation of a double barrier structure which includes both the valence and conduction bands in an $\mathrm{In}\mathrm{Sb}∕\mathrm{In}\mathrm{Al}\mathrm{Sb}$ quantum well system and demonstrate basic features of the transport process through this structure, which exhibits Zener tunneling. In particular, we employ an eight-band model and the Landauer-Büttiker formalism [Phys. Rev. B 31, 6207 (1985)] to investigate the transport process which under high confinement involves resonant energy levels due to the induced quasibound states in the valence bands. The mechanism of momentum filtering, taking advantage of resonant Zener tunneling, is shown to give improved performance at elevated temperatures compared with a unipolar double barrier resonant tunneling structure.

Figure 1

(a) Schematic illustration of a possible gate design to induce the ZDBS. The gates $G_1$ and $G_2$ control transverse confinement in the plane of the 2DEG and the gate $G_3$ controls confinement along the transport $z$ direction. (b) Simplified schematic illustration of the potential landscape of the ZDBS in the plane of the 2DEG and along the transport direction (for a detailed description of the band structure, see the text). The solid lines represent conduction $\left(E_c\right)$ and valence band $\left(E_v\right)$ edges. The dotted line indicates the Fermi energy $\left(E_F\right)$, and the dashed lines indicate quantized energy levels in the valence band due to the strong confinement. The energy levels above the conduction band edge, which correspond to quasibound states, allow resonant Zener tunneling.

Figure 2

Conductance (in units of $G_o=2e^2∕h$) as a function of energy derived from the eight-band model, for an electric field of $\mathcal{E}=0.47\mathrm{MV}∕\mathrm{cm}$.

Figure 3

(Color online) Conductance versus transverse momentum $k_{\perp }=k_{\perp }(n_x,n_y)$ for $T=0\mathrm{K}$ and three different electric fields. These results are obtained from the eight-band model with Fermi energy fixed to give maximum conductance $G_o$ for the lowest mode $n_x=n_y=1$ (light hole resonance).

Figure 4

(Color online) Conductance versus Fermi energy for the ZDBS at temperature $T=77\mathrm{K}$. Note that any extra resonances due to the heavy hole band are averaged out at finite temperatures. The curves correspond to different values of $n_y$, whereas in all cases $n_x=1$.

Figure 5

(Color online) Conductance versus Fermi energy for the DBS at temperature $T=77\mathrm{K}$. For all the resonances, $n_x=1$ and different values of $n_y$ are considered.

Figure 6

(Color online) Dependence of normalized conductance $G∕G_{\mathit{\text{lowest}}}$ on transverse momentum $k_{\perp }$ in an InSb channel for various temperatures. Results for (a) the ZDBS for an electric field $\mathcal{E}=0.47\mathrm{MV}∕\mathrm{cm}$ and (b) the unipolar DBS.