161
Noise in Strain-Engineered Devices
with a low background noise. RTS noise can be observed over the mobility
1/f noise in MOSFETs with small gate area (usually below 1 μm 2 ) if the following criterion on the number of carriers (N) in the channel is fulfilled [29]:
N < 1/4πα H
(6.31)
With increasing N (increasing gate voltage overdrive), the visibility of RTS
over the mobility 1/f noise becomes very small. On the other hand, when
the 1/f γ noise and the RTS noise are originated from the same oxide traps,
the occurrence of RTS noise depends on gate area but not on bias. The number of traps that can generate 1/f γ noise can be estimated according to
Number of traps = 4 kTWLN t z
(6.32)
where z is the tunneling distance of a carrier from the gate oxide/channel
interface, maximum ~3 nm, N t is the trap density, and 4 kT is the energy
around the Fermi level where the traps are distributed. RTS noise can be
observed if the number of active traps is very small. The relative drain current amplitude is related to the trap position inside the oxide z t as [30]
I
I
q
WL
g
I
z t
C
1
/
D
D
m
D
t
o x
ox
eff
=
−
+ αµ
(6.33)
The trap depth can also be extracted from the variation of the characteristic time constants with gate voltage [31]. For a two-level RTS, considering
electrons as the charge carriers and assuming a acceptor trap, the high current level time τ + is the time when the trap is filled (emission time τ e ) and the
low current level time τ – is the time when the trap is empty (capture time τ c )
Statistical measurement of τ + and τ – reveals two exponential distributions.
The RTS exhibits a Lorentzian spectrum in the frequency domain with a
corner frequency in excellent agreement with the harmonic mean of the two
transition times.
From the principle of detailed balance, one can write the ratio of the mean
emission time τ e and mean capture time τ c as [31]
g
E E
kT
exp
c
e
T
F
τ
τ
=
−
(6.34)
where g is a degeneracy factor usually considered as 1, (E T – E F ) is the energy
level of the trap relative to the Fermi level, T is the absolute temperature, and
K is the Boltzmann constant.
In an n-MOSFET, when the gate bias is increased, the trap occupancy is
expected to increase, and hence the c e
τ τ ratio should change. This change
would indicate capture or emission of an electron, and hence provide an
insight into the type of trap. With the high current level (charged trap state)
Noise in Strain-Engineered Devices
with a low background noise. RTS noise can be observed over the mobility
1/f noise in MOSFETs with small gate area (usually below 1 μm 2 ) if the following criterion on the number of carriers (N) in the channel is fulfilled [29]:
N < 1/4πα H
(6.31)
With increasing N (increasing gate voltage overdrive), the visibility of RTS
over the mobility 1/f noise becomes very small. On the other hand, when
the 1/f γ noise and the RTS noise are originated from the same oxide traps,
the occurrence of RTS noise depends on gate area but not on bias. The number of traps that can generate 1/f γ noise can be estimated according to
Number of traps = 4 kTWLN t z
(6.32)
where z is the tunneling distance of a carrier from the gate oxide/channel
interface, maximum ~3 nm, N t is the trap density, and 4 kT is the energy
around the Fermi level where the traps are distributed. RTS noise can be
observed if the number of active traps is very small. The relative drain current amplitude is related to the trap position inside the oxide z t as [30]
I
I
q
WL
g
I
z t
C
1
/
D
D
m
D
t
o x
ox
eff
=
−
+ αµ
(6.33)
The trap depth can also be extracted from the variation of the characteristic time constants with gate voltage [31]. For a two-level RTS, considering
electrons as the charge carriers and assuming a acceptor trap, the high current level time τ + is the time when the trap is filled (emission time τ e ) and the
low current level time τ – is the time when the trap is empty (capture time τ c )
Statistical measurement of τ + and τ – reveals two exponential distributions.
The RTS exhibits a Lorentzian spectrum in the frequency domain with a
corner frequency in excellent agreement with the harmonic mean of the two
transition times.
From the principle of detailed balance, one can write the ratio of the mean
emission time τ e and mean capture time τ c as [31]
g
E E
kT
exp
c
e
T
F
τ
τ
=
−
(6.34)
where g is a degeneracy factor usually considered as 1, (E T – E F ) is the energy
level of the trap relative to the Fermi level, T is the absolute temperature, and
K is the Boltzmann constant.
In an n-MOSFET, when the gate bias is increased, the trap occupancy is
expected to increase, and hence the c e
τ τ ratio should change. This change
would indicate capture or emission of an electron, and hence provide an
insight into the type of trap. With the high current level (charged trap state)