Cryogenic Subthreshold Swing Saturation in FD-SOI MOSFETs Described With Band Broadening

In the standard MOSFET description of the drain current
$ {I}_{{D}}$
as a function of applied gate voltage
$ {V}_{{ {GS}}}$
, the subthreshold swing
${{SS(T)}}\equiv {{dV}}_{{{GS}}}/ {d}\log {I}_{ {D}}$
has a fundamental lower limit as a function of temperature
${T}$
given by
${ {SS(T)}}=\ln 10\,\, {k}_{ {B}} {T}/ {e}$
. However, recent low-temperature studies of different advanced CMOS technologies have reported
SS
(4 K or lower) values that are at least an order of magnitude larger. Here, we present and analyze the saturation of
SS(T)
in 28 nm fully-depleted silicon-on-insulator (FD-SOI) devices for both n- and p-type MOSFETs of different gate oxide thicknesses and gate lengths down to 4 K. Until now, the increase of interface-trap density close to the band edge as temperature decreases has been put forward to understand the saturation. Here, an original explanation of the phenomenon is presented by considering a disorder-induced tail in the density of states at the conduction (valence) band edge for the calculation of the MOS channel transport by applying the Fermi–Dirac statistics. This results in a subthreshold
$ {I}_{ {D}}\sim {e}^{{{ {eV}}}_{{{GS}}}/ {k}_{ {B}} {T}_{0}}$
for
$ {T}_{0}=35$
K with saturation value
${ {SS}}( {T}< {T}_{0})= \ln 10\,\, {k}_{ {B}} {T}_{0}/ {e}$
. The proposed model adequately describes the experimental data of
SS(T)
from 300 down to 4 K using
$ {k}_{ {B}} {T}_{0} \simeq 3$
meV for the width of the exponential tail and can also accurately describe
${ {SS}}( {I}_{ {D}})$
within the whole subthreshold region. Our analysis allows a direct determination of the technology-dependent band-tail extension forming a crucial element in future compact modeling and the design of cryogenic circuits.