177
Compact Models for Small Geometry MOSFETs
5.2.1.1 Threshold Voltage Modeling for Nonuniform
Vertical Channel Doping Profile
Due to nonuniform channel doping, the body effect coefficient γ depends
on the body bias, V bs . For the simplicity of mathematical formulation, let us
approximate the nonuniform vertical channel doping profile by a high–low
step function as shown in Figure 5.3 with uniform concentration N CH from
Spacer
S p ac er
Gate
Body (B)
(a)
SDE
DSD
Halo
Halo
L g
T ox
L eff
X jd
X j
S
G
1.4e+18
5.31e+18
5.31e+18
1e+18
1e+18
1.4e+18
1.8e+18
2.2e+18
2.6e+18
3e+18
3.4e+18
3.8e+18
4.2e+18
4.6e+18
5.31e+18
P-type
linear
4.2e+18
D
(b)
FIGURE 5.1
2D cross-section of a MOSFET device: (a) threshold adjust and halo implant causing nonuniform channel doping profile and (b) simulated 2D-doping contours of a typical double-halo
nMOSFET device with laterally and vertically nonuniform p-type channel doping generated
using device CAD MEDICI; 2D cross-section shows S, G, and D are the source, gate, and drain
terminals, respectively, and the outline of SDE and deep source-drain (DSD) junctions. (Data
from S. Saha, Proc. SPIE Conf., 5042, 172–179, 2003.)