3.1.4 Quantum Mechanical Effects

The following bias-independent calculations are for the threshold voltage shift and bias dependence of the inversion charge centroid due to quantum mechanical confinement. See Section 3.4 and Section 3.7 for more details.

$m_x = 0.916 \cdot m_e \qquad (3.56)$

$m_x^{\prime} = 0.190 \cdot m_e \qquad (3.57)$

$m_d = 0.190 \cdot m_e \qquad (3.58)$

$m_d^{\prime} = 0.417 \cdot m_e \qquad (3.59)$

$g^{\prime} = 4.0 \qquad (3.60)$

$g = 2.0 \qquad (3.61)$

$MT_{cen}$ and $T_{cen0}$ are defined as follows in the UFCM formulation. Note that this formulation reduces to those used in BSIM-CMG 108.0.0 if $ACH\_UFCM$ and $W\_UFCM$ are replaced by their definitions:

$MT_{cen} = 1.0 + AQMTCEN \cdot exp \Big[ -\Big( \dfrac{2 \cdot ACH\_UFCM}{W\_UFCM} \Big) \cdot \dfrac{1}{BQMTCEN} \Big] \qquad (3.62)$

$T_{cen0} = \Big( \frac{2 \cdot ACH\_UFCM}{W\_UFCM} \Big) \cdot MT_{cen} \qquad (3.63)$

If $GEOMOD = 0$ then

$MT_{cen} = 1 + AQMTCEN \cdot exp \Big( -\frac{TFIN}{BQMTCEN} \Big) \qquad (3.64)$

$T_{cen0} = TFIN \cdot MT_{cen} \qquad (3.65)$

If $GEOMOD = 1$ then

$MT_{cen} = 1 + AQMTCEN \cdot exp \Big[-\frac{min(HFIN, TFIN)}{BQMTCEN} \Big] \qquad (3.66)$

$T_{cen0} = min(TFIN, HFIN) \cdot MT_{cen} \qquad (3.67)$

If $GEOMOD = 2$ then

$MT_{cen} = 1 + AQMTCEN \cdot exp \Big[ -\frac{min(HFIN, TFIN)}{BQMTCEN} \Big] \qquad (3.68)$

$T_{cen0} = min(TFIN, HFIN) \cdot MT_{cen} \qquad (3.69)$

If $GEOMOD = 3$ then

$MT_{cen} = 1 + AQMTCEN \cdot exp \Big( -\frac{R}{BQMTCEN} \Big) \qquad (3.70)$

$T_{cen0} = R \cdot MT_{cen} \qquad (3.71)$