Study of Cryogenic MOSFET Sub-Threshold Swing Using Ab Initio Calculation

The abnormal subthreshold swing (SS) in Silicon Metal-Oxide Semiconductor Field Effect Transistor (MOSFET) at cryogenic temperature is commonly attributed to band tail (BT) conduction. The cryogenic SS does not scale with the temperature, T, for T
$ < 50\text{K}$
and it is observed to saturate at 10mV/dec ~ 20mV/dec at low T in most experiments. Hitherto, only analytical studies have been conducted for BT and its properties. It is not clear how much of its effect can be eliminated should there be an ideal manufacturing technology. In this letter, by using robust ab initio calculation with quantum transport, we have successfully calculated the BT in a Si nanowire (NW) and studied its characteristic length. By analyzing the transport properties of the NW with various gate lengths,
$\text{L}_{{\text {G}}}$
, at various temperatures, it is observed that for
$\text{L}_{{\text {G}}} < 20$
nm, the tunneling current dominates, and for
$\text{L}_{{\text {G}}}>$
20nm, the BT current dominates at 3K. It is found that, in a perfect nanowire (as a gedanken experimental device), an SS as low as 1.4mV/dec can be achieved at 3K for 15 orders of magnitudes of current change with a minimum of 0.42mV/dec (
$\text{L}_{{\text {G}}}$
= 50nm). This also justifies the results in a recent experiment in which a very low SS (3.4mV/dec at 5.5K) was obtained. Moreover, it is also shown that for the 2nm node (
$\text{L}_{{\text {G}}}~\sim $
15nm), direct S/D tunneling will set the ultimate limit of SS at 3K.