Temperature Dependence Modeling of Grain Boundary Barrier Height in Macaroni MOSFETs

In this article, a physically based grain boundary (GB) barrier height (
$\psi _{B}$
) model with temperature (
${T}$
) dependence is developed for poly-Si channel macaroni MOSFETs. Experimental data of 3-D NAND flash string current are employed to calibrate a computer aided design (TCAD) simulation tool.
$\psi _{B}$
is then extracted from the macaroni MOSFETs with a single GB located at the center of the channel as a simulation structure, which is used to verify the
$\psi _{B}$
model. In order to model the temperature dependence,
$\psi _{B}$
is derived without approximation of Fermi-Dirac distribution function. The
$\psi _{B}$
model is compared with simulated
$\psi _{B}$
to validate the model over a wide temperature range as well as a gate bias (
${V}_{\text {GS}}$
), and a good agreement between them is achieved. In addition, we investigate the contributions of the surface potential inside grain,
$\psi _{S}$
, and the surface potential at GB,
$\psi _{\text {GB}}$
, to the reduction of
$\psi _{B}$
with increasing temperature.