238
Strain-Engineered MOSFETs
and mechanical effects [15]. It is well known that H plays a critical role in the
fabrication of high-quality Si/SiO 2 interfaces where these dangling bonds
are compensated by hydrogen atoms. The experimental data for the kinetics
of interface trap formation show that the time dependence of trap generation
can be described by the relation
−
= + γ
α
N
N
N
t
it
it
hb
1 ( )
0
0
(8.11)
where N it is the concentration of the interface, and N 0 hb and N 0 it are the
initial concentrations of the Si-H bonds and interface traps, respectively.
Considering
=
+
N N
N
hb
it
0
0 total Si bonds at the interface, the remaining
number of Si-H bonds at the interface after stress is
= −
N
N N
hb
it , given by
1 ( )
0
N
N
t
hb
hb
= + γ
α
(8.12)
and the Si-H concentration during stress is given by
= −γ
dN
dt
N
hb
hb
.
(8.13)
where γ is a reaction constant and is given by γ = γ
−ε k T
A
B
exp(
/ )
0
in the
Arrhenius approximation. ε A is the Si-H activation energy and T is the temperature. The activation energy needed to release hydrogen from the interface can be expressed as
ε = ε + + β
−
−
kT
N N
N N
A
A
hb
hb
(1 ) ln
0
0
(8.14)
where ε A is the energy needed to break a Si-H bond and the last term represents the potential energy needed to go over the potential barrier of the 2D
potential system with prefactor β.
8.4 Simulation of HCI in n-MOSFETs
In the following, simulation results for the strain-engineered n-MOSFETs
after hot-carrier stressing are presented. The constant voltage stress (electrical stress) conditions for which the simulations are performed are gate
voltage (V gs ) range of 1.5 to 2.8 V, and the device is kept under the stress for
10 5 s. When the degradation simulation is finished, the device is set to normal
Strain-Engineered MOSFETs
and mechanical effects [15]. It is well known that H plays a critical role in the
fabrication of high-quality Si/SiO 2 interfaces where these dangling bonds
are compensated by hydrogen atoms. The experimental data for the kinetics
of interface trap formation show that the time dependence of trap generation
can be described by the relation
−
= + γ
α
N
N
N
t
it
it
hb
1 ( )
0
0
(8.11)
where N it is the concentration of the interface, and N 0 hb and N 0 it are the
initial concentrations of the Si-H bonds and interface traps, respectively.
Considering
=
+
N N
N
hb
it
0
0 total Si bonds at the interface, the remaining
number of Si-H bonds at the interface after stress is
= −
N
N N
hb
it , given by
1 ( )
0
N
N
t
hb
hb
= + γ
α
(8.12)
and the Si-H concentration during stress is given by
= −γ
dN
dt
N
hb
hb
.
(8.13)
where γ is a reaction constant and is given by γ = γ
−ε k T
A
B
exp(
/ )
0
in the
Arrhenius approximation. ε A is the Si-H activation energy and T is the temperature. The activation energy needed to release hydrogen from the interface can be expressed as
ε = ε + + β
−
−
kT
N N
N N
A
A
hb
hb
(1 ) ln
0
0
(8.14)
where ε A is the energy needed to break a Si-H bond and the last term represents the potential energy needed to go over the potential barrier of the 2D
potential system with prefactor β.
8.4 Simulation of HCI in n-MOSFETs
In the following, simulation results for the strain-engineered n-MOSFETs
after hot-carrier stressing are presented. The constant voltage stress (electrical stress) conditions for which the simulations are performed are gate
voltage (V gs ) range of 1.5 to 2.8 V, and the device is kept under the stress for
10 5 s. When the degradation simulation is finished, the device is set to normal