Noise models for diodes and transistors
Noise models for diodes and transistors
V.Vasudevan,
Department of Electrical Engineering,
Indian Institute of Technology Madras
Noise models for diodes and transistors
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pn junctions and BJTs - shot noise, flicker noise, burst noise
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MOSFETs - flicker noise, thermal noise in strong inversion,
shot noise in weak inversion, burst noise
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Shot noise occurs due to various reasons - random emission of
carriers across a barrier, random tunneling of carriers,
generation/recombination processes in bulk and depletion
region, thermal fluctuations triggering a relaxation current
through diffusion. The PSD of shot noise is proportional to
the current
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Some controversy on origin of flicker noise - whether it occurs
due to number (of carriers) or mobility fluctuations. Models
are empirical models.
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Burst noise (or random telegraph signal) is seen as random
“bursts” of noise in the time domain - occurs due to
charging/discharging of a single defect
Noise models for diodes and transistors
Diodes
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Shot noise occurs because the minority carrier density in the
bulk fluctuates due to thermal motion and
generation/recombination of carriers. This triggers a
relaxation current - the current flow is by diffusion
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The noise spectral density is given as
SI (f ) = 2q(I + 2Is )
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A more accurate expression includes a frequency dependent
term
Noise models for diodes and transistors
Bipolar Junction transistor
B
2qIB ∆ f
C
rBE
CBE
gm vBE
2qIC ∆ f
E
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Shot noise - mechanism is similar to diodes (narrow diodes)
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The spectral densities are given by
SIE = 2qIE , SIB = 2qIB , SIC = 2qIC
Noise models for diodes and transistors
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The three noise current sources are correlated
√
SCE = −2qIC ⇒ cCE = − α
r
α
SBE = −2qIB ⇒ cBE = −
β
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The collector base correlation occurs due to charging and
discharging of the diffusion capacitance
SCB = −2qIC
p jωτt
jωτt
⇒ cCB = − β
3
3
where τt is the base transit time
Noise models for diodes and transistors
MOSFET - strong inversion
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I
I
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Random thermal motion of carriers in the inversion layer
Modelled as a voltage dependent nonlinear resistor
The noise in the drain current is
µ
id2 = 4kT 2 |Qinv |∆f
L
where Qinv is the total inversion charge in the MOSFET
In a simple model, ignoring channel length modulation,
Qinv
=
2
1 + α + α2
WLCox (VGS − VT )
3
1+α
where
VDS
VGS − VT
More complex models take into account velocity saturation
α=1−
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Noise models for diodes and transistors
Induced gate noise
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Voltage fluctuations in the channel coupled to the gate
through Cg
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Induced gate noise correlated to the drain noise
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A potential fluctuation at v (x) causes a gate current ig given
by
Z L
Cg (x)v (x)dx
ig = −jωW
o
Noise models for diodes and transistors
Long channel transistor in saturation
G
ig2
D
Cgs
gm vgs
id2
S
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For long channel devices in saturation (VDsat = VGS − VT ),
the PSDs of the drain current and induced gate current are
2
Sid = 4kT gm ,
3
Sig = 4kT
16 ω 2 (WLCox )2
135
gm
Noise models for diodes and transistors
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The drain and gate noise are correlated and the cross spectral
density is
1
Sig id ∗ = 4kT jωCox WL
9
The correlation coefficient (coherence function) is therefore
Si i ∗
c= pgd
≈ 0.395j
Sid Sig
Noise models for diodes and transistors
1/f Noise
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Fluctuations in the curent due to trapping/detrapping by
interfacial defects
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A simple model is
2
idf
=
I
2 1
Kgm
∆f
2 f
WLCox
Often just modelled as
2
idf
= K0
a
IDS
f
where a is left as a parameter
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K depends on device type and processing
Noise models for diodes and transistors
Other noise sources
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Thermal noise due to the distributed gate resistance (Rg )
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Thermal noise due to source and drain resistances Rs and Rd
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Shot noise due to gate tunneling current and junction diodes
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Noise due to hot electrons (in submicron devices)
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Substrate noise
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RTS noise
Noise models for diodes and transistors
References
1. A.van der ziel “Noise in solid state devices and circuits”
2. A good introduction to noise in MOSFETs is contained in the book
“Analysis and modelling of MOS transistors” by Y.Tsividis
3. A.J.Scholten et al, “Noise modelling for RF CMOS circuit
simulation”, IEEE trans. Elec. Devices, vol.50, no.3, pp 618-632,
Mar. 2003
4. A.Van der ziel, “Unified presentation of 1/f noise in electronic
devices: Fundamental 1/f noise sources”, Proc. IEEE, vol.76, no.3,
Mar 1988