Compact models of resonant tunneling diodes - Celino, Daniel Ricardo (2024)
Due to the growing demand for technologies capable of operating in the Terahertz (THz) frequency range, the Resonant Tunneling Diode (RTD) has attracted renewed interest from the academic community. RTD is a promising candidate for digital and analog applications due to its intrinsic negative differential resistance (NDR) characteristics, high switching speed, and flexible design requirements.  In this framework, this doctoral thesis deals with the compact modeling of the current-voltage (I-V) characteristics of double potential barrier resonant tunneling diodes. For this purpose, it is initially necessary to calculate the energy levels of the eigenstates for the quantum well of finite height present in the semiconductor structures of RTDs. However, determining energy levels for finite quantum wells is only possible through the resolution of transcendental equations using some numerical routine, thereby not allowing an exact analytical solution. Thus, fully analytical approximate solutions were developed to calculate energy levels in rectangular quantum wells of finite height, symmetric and asymmetric, with excellent agreement to exact solutions.  Next, taking the Tsu-Esaki formalism as a starting point to describe carrier transport in the RTD, we consider the general distribution of the electrical potential in the semiconductor device, including the formation of the accumulation and depletion space charge regions, as well as the charge in the quantum well. Furthermore, the scattering experienced by the carriers during the tunneling process through the double potential barrier region was also considered.  The I-V model developed encompasses two distinct cases. The first case describes RTDs, in which, due to the physical, parametric and geometric characteristics of the device, electrons in the emitter have a three-dimensional (3D) density of states. The second case occurs particularly in RTDs employing spacer layers with low doping levels. In this case, the accumulation layer formed in the RTD, adjacent to the double barrier region, is such that the electrons in the emitter have a two-dimensional (2D) density of states.  With the analytical model to calculate energy levels in a quantum well and the model developed to describe the distribution of the electrical potential profile in the RTD, compact I-V characteristic models of RTDs 3D-2D and 2D-2D were proposed. In this way, this work contributes to the compact modeling of RTDs, aiming to help on the design of integrated circuits using these devices and taking into account the main physical phenomena relevant in the description of the electrical characteristics of the RTD, thus obtaining fully analytical and explicit models. The developed models were validated with experimental and numerical data, providing very good agreement.