Quantum-well charge and voltage distribution in a metal–insulator–semiconductor structure upon resonant electron Tunneling

The prerequisites for electron storage in the quantum well of a metal–oxide–$p^+$-Si resonant-tunneling structure and the effect of the stored charge on the voltage distribution are theoretically investigated. Systems with SiO$_2$, HfO$_2$, and TiO$_2$ insulators are studied. It is demonstrated that the occurrence of a charge in the well in the case of resonant transport can be expected in structures on substrates with an acceptor concentration from (5–6) $\times$ 10$^{18}$ to (2–3) $\times$ 10$^{19}$ cm$^{-3}$ in the range of oxide thicknesses dependent on this concentration. In particular, the oxide layer thickness in the structures with SiO$_2/p^+$–Si(10$^{19}$ cm$^{-3}$) should exceed $\sim$3 nm. The electron density in the well can reach $\sim$10$^{12}$ cm$^{-2}$ and higher. However, the effect of this charge on the electrostatics of the structure becomes noticeable only at relatively high voltages far above the activation of resonant transport through the first subband.