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.