Physical modelling and self-oscillations in double barrier quantum well resonant tunnelling diodes

We present a unified quantum-mechanical and circuit-level modelling approach for double-barrier quantum well resonant tunnelling diodes (DBQW RTDs), centered on the derivation of a voltagedependent differential conductance function. Using the effective mass approximation and transfer matrix formalism, a ballistic quantum transport model is developed that captures key features of RTD behavior, including resonant energy levels, thermal broadening, and negative differential conductance. While our model neglects scattering effects and space charge accumulations for analytical tractability, it can be viewed as a natural conductance counterpart of the classical Schulman formulation by embedding explicit physical parameters linked to the quantum structure of the device in the coherent (ballistic) regime. Numerical simulations for representative III-V heterostructures such as AlGaAs/GaAs/AlGaAs, AlAs/InGaAlAs/AlAs, and InAs/AlSb/GaSb yield transmission, T DBQW (E z ), current, I RTD (V) and conductance, G RTD ( V ) characteristics consistent with existing experimentally observed RTD behavior. To demonstrate the interplay between quantum transport and nonlinear circuit dynamics, the conductance model is incorporated into a Liénard-type oscillator framework to elucidate how resonant tunnelling induces self-oscillations and complex behaviours relevant to high-frequency and THz applications. This work provides a robust and generalizable foundation for the design and analysis of RTD-based quantum electronic and optoelectronic devices.