148
Strain-Engineered MOSFETs
current is generated at low frequencies when the electrons cross the barrier
independently and randomly. At higher frequencies it transforms to white
noise. The shot noise current fluctuates with a PSD of [10]
S
qI
2
I =
(6.4)
The physics behind shot noise is closely related to the thermal noise phenomenon. A p-n junction has a nonlinear resistance; the spectral density of
the noise current is half the thermal noise for the dynamic resistance associated with the p-n junction. The reason behind the factor 1/2 is basically that
the current is essentially flowing in one direction across the p-n junction.
In bipolar transistors, the sources of shot noise are located at the depletion
region of each junction. The recombination (at the base-emitter junction) of
minority carriers generated at the base contributes to the shot noise, whereas
in the collector-base junction, the minority carriers generated at the emitter
and base contribute to the shot noise. Shot noise in FETs, on the other hand,
is attributed to the gate leakage current.
6.2.3 Generation–Recombination Noise
Generation–recombination (g-r) noise in semiconductors originates from random capture or emission of carriers by localised charge centres (or traps),
thereby causing random fluctuation in the carrier number. If carriers are trapped
at some critical spots, the trapped charge can also induce fluctuations in the
mobility, diffusion coefficient, electric field, barrier height, space charge region
width, etc. Localised defect states within the forbidden band gap are referred to
as traps, the physical origin of which are due to the presence of various defects
or impurities in the semiconductor bulk or at the surface. In MOSFETs the inversion charge may be trapped or de-trapped in these defect states, causing current
or voltage level to fluctuate. The carrier transitions in a semiconductor mainly
consist of generation of an electron/hole pair, recombination of a free electron
and hole, and trapping of electrons and holes in empty traps.
A trap may be neutral or charged in its empty state (depending on whether
it is a donor trap or acceptor trap). From the Langevin differential equation
governing how the number of carriers N depend on time,
d N
dt
N H t
( )
= − τ
+
(6.5)
where H(t) is a random noise term, ΔN is the fluctuation in the number of
carriers, and τ is the time constant. The PSD of the carrier fluctuation can be
derived [11]:
S f
N
f
( )
4
[1 (2 ) ]
N
2
2
=
τ
+ π τ
(6.6)
Strain-Engineered MOSFETs
current is generated at low frequencies when the electrons cross the barrier
independently and randomly. At higher frequencies it transforms to white
noise. The shot noise current fluctuates with a PSD of [10]
S
qI
2
I =
(6.4)
The physics behind shot noise is closely related to the thermal noise phenomenon. A p-n junction has a nonlinear resistance; the spectral density of
the noise current is half the thermal noise for the dynamic resistance associated with the p-n junction. The reason behind the factor 1/2 is basically that
the current is essentially flowing in one direction across the p-n junction.
In bipolar transistors, the sources of shot noise are located at the depletion
region of each junction. The recombination (at the base-emitter junction) of
minority carriers generated at the base contributes to the shot noise, whereas
in the collector-base junction, the minority carriers generated at the emitter
and base contribute to the shot noise. Shot noise in FETs, on the other hand,
is attributed to the gate leakage current.
6.2.3 Generation–Recombination Noise
Generation–recombination (g-r) noise in semiconductors originates from random capture or emission of carriers by localised charge centres (or traps),
thereby causing random fluctuation in the carrier number. If carriers are trapped
at some critical spots, the trapped charge can also induce fluctuations in the
mobility, diffusion coefficient, electric field, barrier height, space charge region
width, etc. Localised defect states within the forbidden band gap are referred to
as traps, the physical origin of which are due to the presence of various defects
or impurities in the semiconductor bulk or at the surface. In MOSFETs the inversion charge may be trapped or de-trapped in these defect states, causing current
or voltage level to fluctuate. The carrier transitions in a semiconductor mainly
consist of generation of an electron/hole pair, recombination of a free electron
and hole, and trapping of electrons and holes in empty traps.
A trap may be neutral or charged in its empty state (depending on whether
it is a donor trap or acceptor trap). From the Langevin differential equation
governing how the number of carriers N depend on time,
d N
dt
N H t
( )
= − τ
+
(6.5)
where H(t) is a random noise term, ΔN is the fluctuation in the number of
carriers, and τ is the time constant. The PSD of the carrier fluctuation can be
derived [11]:
S f
N
f
( )
4
[1 (2 ) ]
N
2
2
=
τ
+ π τ
(6.6)