Study of impact ionization coefficients in silicon with Low Gain Avalanche Diodes

Impact ionization in silicon devices has been extensively studied and several models for a quantitative description of the impact ionization coefficients have been proposed. We evaluate those models against gain measurements on low-gain avalanche diodes (LGADs) and derive new parameterizations for the impact ionization coefficients optimized to describe a large set of experimental data. We present pulsed infrared (IR)-laser-based gain measurements on five different types of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$50 \boldsymbol {\mu }\text{m}$ </tex-math></inline-formula>-thick LGADs from two different producers centro nacional de microelectrónica (CNM) and Hamamatsu Photonics (HPK) performed in a temperature range from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$- 15\,\,{^{\circ} }\text{C}$ </tex-math></inline-formula>to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$40 {^{\circ} }\text{C}$ </tex-math></inline-formula>. Detailed technology computer-aided design (TCAD) device models are conceived based on secondary ion mass spectrometry (SIMS) doping profile measurements and tuning of the device models to measure <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${C}$ </tex-math></inline-formula>–<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}$ </tex-math></inline-formula>characteristics. Electric field profiles are extracted from the TCAD simulations and used as input to an optimization procedure (least squares fit) of the impact ionization model parameters to the experimental data. It is demonstrated that the new parameterizations give a good agreement between all measured data and TCAD simulations which is not achieved with the existing models. Finally, we provide an error analysis and compare the obtained values for the electron and hole impact ionization coefficients against existing models.