Empirical Warm-Beam Child Langmuir Model Implemented in LTspice to Simulate In-Circuit Behavior of Nanoscale Vacuum Channel Transistor Arrays

An empirical warm-beam Child-Langmuir model for planar diodes is implemented in LTspice. This model generalizes the Child-Langmuir Law to account for the case of an initial electron distribution with a non-zero mean velocity and a spread in velocities (a warm beam). A warm beam electron distribution is common in physical devices such as nanoscale vacuum channel transistors (NVCTs) arrays where electrons are field emitted and subsequently accelerated before entering a diode-like gap. NVCTs have recently been experimentally demonstrated as integral components in circuits. Following the circuit design of Bhattacharya et al. [1], the warm-beam Child-Langmuir model is used in LTspice to simulate the behavior of a periodic NVCT array in a Colpitts oscillator. Further, the flexibility of the model is shown by demonstrating possible changes to the array and rapid simulation to achieve desired circuit characteristics.

[1] R. Bhattacharya, R. Hay, M. Cannon, et al., "Demonstration of a silicon gated field emitter array based low frequency Colpitts oscillator at 400 °C", J. Vac. Sci. Technol., B 41, 023201, 2023.