151
Noise in Strain-Engineered Devices
6.2.5 1/f Noise
1/f noise, also called flicker noise or pink noise, is the low-frequency noise
with fluctuations with a PSD proportional to 1/f γ , with γ close to 1, usually in
the range 0.7–1.3. The PSD for 1/f noise takes the general form
S f
KI
f
( )
I
=
β
γ
(6.10)
where K is a constant and β is a current exponent. There are so many
theories regarding the 1/f noise mechanisms, of which most prominent
are the carrier number fluctuation (surface phenomenon) and mobility
fluctuation (bulk phenomenon) theories. The mechanisms behind flicker
noise are still a long-debated topic and an interesting research topic. The
generally accepted origins of the 1/f noise are attributed to conductivity fluctuations, damage in crystal structures, and traps due to defects in
semiconductors. 1/f fluctuations in the conductance have been observed in
the low-frequency part of the spectrum (10 –6 to 10 6 Hz) in most conducting materials and a wide variety of semiconductor devices [11, 13]. From
Equation (6.7) also, it is clear that there are essentially two physical mechanisms behind any fluctuations in the current: fluctuations in the mobility
or fluctuations in the number of carriers (g-r noise). G-r noise from a large
number of traps can produce 1/f noise if the time constants of the traps are
distributed as [14]
g
g
o therwise
( ) 1/ln( / ) ,
( ) 0,
2
1
2
1
τ =
τ τ τ τ < τ < τ
τ =
(6.11)
The factor ln(τ 2 /τ 1 ) is for normalisation purposes. The total noise PSD
(S tot (f)) from superposition of the g-r noise from many traps distributed
according to g(τ) yields, combining Equations (6.6) and (6.11),
S f
g S
d
K
f
d
or S f
K
f
for
f
( )
( )
( )
1
ln( / )
1
1 (2 )
, ( ) 4ln( / )
, 1 /2
1/ 2
tot
g r
tot
0
2
1
2
2
1
2
1
1
2
∫
∫
=
τ
τ τ =
τ τ
τ
τ
+ π τ
τ
≈
τ τ
πτ << <<
πτ
−
∞
τ
τ
(6.12)
An illustration is shown in Figure 6.3, where g-r noise from four individual traps with different time constants adds up to a 1/f γ spectrum, with γ
approximately 1. Some remarks are necessary about the addition of g-r noise
spectra. The superposition of g-r noise in producing a 1/f spectrum assumes
Noise in Strain-Engineered Devices
6.2.5 1/f Noise
1/f noise, also called flicker noise or pink noise, is the low-frequency noise
with fluctuations with a PSD proportional to 1/f γ , with γ close to 1, usually in
the range 0.7–1.3. The PSD for 1/f noise takes the general form
S f
KI
f
( )
I
=
β
γ
(6.10)
where K is a constant and β is a current exponent. There are so many
theories regarding the 1/f noise mechanisms, of which most prominent
are the carrier number fluctuation (surface phenomenon) and mobility
fluctuation (bulk phenomenon) theories. The mechanisms behind flicker
noise are still a long-debated topic and an interesting research topic. The
generally accepted origins of the 1/f noise are attributed to conductivity fluctuations, damage in crystal structures, and traps due to defects in
semiconductors. 1/f fluctuations in the conductance have been observed in
the low-frequency part of the spectrum (10 –6 to 10 6 Hz) in most conducting materials and a wide variety of semiconductor devices [11, 13]. From
Equation (6.7) also, it is clear that there are essentially two physical mechanisms behind any fluctuations in the current: fluctuations in the mobility
or fluctuations in the number of carriers (g-r noise). G-r noise from a large
number of traps can produce 1/f noise if the time constants of the traps are
distributed as [14]
g
g
o therwise
( ) 1/ln( / ) ,
( ) 0,
2
1
2
1
τ =
τ τ τ τ < τ < τ
τ =
(6.11)
The factor ln(τ 2 /τ 1 ) is for normalisation purposes. The total noise PSD
(S tot (f)) from superposition of the g-r noise from many traps distributed
according to g(τ) yields, combining Equations (6.6) and (6.11),
S f
g S
d
K
f
d
or S f
K
f
for
f
( )
( )
( )
1
ln( / )
1
1 (2 )
, ( ) 4ln( / )
, 1 /2
1/ 2
tot
g r
tot
0
2
1
2
2
1
2
1
1
2
∫
∫
=
τ
τ τ =
τ τ
τ
τ
+ π τ
τ
≈
τ τ
πτ << <<
πτ
−
∞
τ
τ
(6.12)
An illustration is shown in Figure 6.3, where g-r noise from four individual traps with different time constants adds up to a 1/f γ spectrum, with γ
approximately 1. Some remarks are necessary about the addition of g-r noise
spectra. The superposition of g-r noise in producing a 1/f spectrum assumes