210
Compact Models for Integrated Circuit Design
5.4 Substrate Current Model
The channel electrons traveling through high electric field near the drain end
of the channel can become highly energetic. These high energetic electrons
are called hot electrons and can cause impact ionization generating electrons
and holes [42–44]. The holes go into the substrate creating substrate current
I sub as shown in Figure  5.15. Some of the electrons have enough energy to
overcome the Si/SiO 2 energy barrier generating gate current I g as shown in
Figure 5.15. And, some are collected to the drain, contributing to the drain
current. The maximum electric field E m near the drain has the greatest control of hot carrier effects.
Figure 5.16 shows the detailed mechanism of hot carrier effects on nMOSFET device performance.
Figure  5.16 shows the effect of high drain bias V ds   >  V dsat on nMOSFET
devices at strong inversion, V gs  > V th . As shown in Figure 5.16, the inversion
layer electrons traveling under high electric field cause the following:
1. High energetic electrons traveling along the channel acquire energy
from the electric field and become hot;
n+ Source
n+ Drain
Hot electron
Hole
Gate
Vgs
Ig
Isub
Vgs > Vdsat
(a)
0 0.5 1.0 1.5 2.0
Length (μm)
Gate
Drain
Source
Depth
(b)
3
600
1200
1800
Temperature (K)
2400
3200
2.5 3.0 3.5 4.0 4.5 5.0
FIGURE 5.15
Hot carrier effect in MOSFETs: (a) channel hot electrons in an nMOSFET device contributing to
the drain current and generating gate current and (b) electron temperature near the drain end
of the channel of the nMOSFET.