Characterization and modeling of DCR and DCR drift variability in SPADs

A quadratic relationship between the Dark Count Rate drift (Δ DCR) device-to-device variance
$\sigma_{\Delta\text{DCR}}^{2}$
and its mean
$\overline{\Delta\text{DCR}}$
regardless of stress conditions, architectures, and processes, is demonstrated in Single-Photon-Avalanche Diodes (SPADs). An Empirical Monte-Carlo method accounting for the stochastic diffusion of carriers in computation of the avalanche breakdown probability coupled with a nonradiative multiphonon-assisted carrier capture/emission rate (NRM) are used to simulate DCR at each defect site. Temperature measurements and simulations at different voltages allow capturing potential defect positions in the device. Convolution of uniform position distributions of uncorrelated individual defects Poisson-distributed in number from device-to-device accurately simulates the measured
$\Delta\text{DCR}$
distributions and the
$\sigma_{\Delta\text{DCR}}^{2}$
against
$\overline{\Delta\text{DCR}}$
quadratic trend along stress time.