Previous device models for Hot Electron Bolometers (HEB) apply a lumped element approach to calculate the small signal parameters. In this work, large signal parameters are calculated using a nonlinear one-dimensional heat balance equation including critical current effects. Small signal equivalents are obtained by solving a linearized heat balance for the small signal beat term in the HEB. In this model, the absorbed bias power density is treated as a profile along the HEB bridge and the electrothermal feedback acts differently on different parts of the bridge. This model predicts more realistic conversion gain figures being about 10 dB lower than in previous ones.

A hot spot model for superconducting hot electron bolometers is presented based on a two-dimensional heat transport equation for electrons and phonons including heat trapping due to quasiparticle bandgap gradients. Skin effect concentrates the RF heating in lateral regions of the bridge and the bias current in the center. A reduction in conversion gain compared to a one-dimensional hot spot model is explained by the RF and bias heating profiles not being identical. An experimentally verified increase of the IF bandwidth from 3.5 GHz to 8 GHz when increasing bias voltage is predicted. IV curves, gain and noise are in very good agreement with measurements.