Dark Current and Gain Modeling of Mid-Wave and Short-Wave Infrared Compositionally Graded HgCdTe Avalanche Photodiodes

Abstract

We present a detailed methodology for drift-diffusion (DD) modeling of gain and dark currents in mid-wave infrared (MWIR) and short-wave infrared (SWIR) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathrm {Hg}}_{{1}-{x}}$ </tex-math></inline-formula> Cd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>x</i></sub> Te <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p-around-n</i> avalanche photodiodes (APDs) based on a comprehensive analysis of experimentally obtained data from three different sets of devices. These devices are fabricated on homogeneous and compositionally-graded films with cadmium composition ranging from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${x}\,\,=0.37$ </tex-math></inline-formula> to 0.45, each with differing geometrical dimensions, and tested at operating temperatures ranging from 140 to 240 K. The temperature, composition, and electric-field dependent impact ionization (ImI) coefficients are calibrated first according to the given experimental gain data. The gain-normalized dark current (GNDC) curve, along with the presumption of electron-only multiplication, is then used to thoroughly understand and model the behavior of diffusion and generation currents. At high biases, the GNDC curve reveals contributions from tunneling, which are classified as either trap-assisted or band-to-band based on their temperature dependence. The tunneling mechanisms are modeled accordingly: trap-assisted tunneling (TAT) is scaled inversely with Shockley–Read–Hall (SRH) lifetime, while band-to-band tunneling (BTBT) is scaled with bandgap, effective mass, and an additional empirical temperature term. Finally, the comprehensive model is applied to all three experimental devices across the operating temperature range with good agreement.