Noise in Materials and Components

Noise in Materials and ComponentsLow frequency noise as a diagnostic tool for reliability and quality assessment of devices

L.K.J. VandammeEindhoven University of Technology (EH 9.13)

5600 MB Eindhoven, The [email protected]

Toulouse, 26 February 2004

mailto:[email protected]

mailto:[email protected]

L.K.J. Vandamme / Noise / 26-02-2004

2

I. Introduction1. Objectives To give an introduction on definitions, noise measuring set-upsand to give an overview of noise sources such as: thermal-, shot-, generation recombination-, RTS noise and 1/f noise.

A better understanding of different types of noise can learn uswhat types of noise are inevitable and what can be reduced.

Some emphasis on sensitivity in the omnipresent conductance 1/f noise.

The noise in devices: resistance, resistance- type (MOSTs), diodes, and diode–type devices is discussed.


3

From the analysis of RTS-, 1/f- and thermal-noise in MOSTs we explain that faster devices are noisier.

Explain why low frequency noise is a good diagnostic tool andshow how current crowding will enhance 1/f noise. The shot noise, 1/f noise and generation-recombination (RTS-) noise are important for quality assessment in e.g., diode type devices like: solar cells, laser diodes, LEDs, avalanche photo diodes and bipolar transistors

Applications are e.g.,: contacts, conductive adhesive joints, thick and thin film resistors, parasitic series resistance or parallelconduction paths in devices like in: submicron MOS-, MES-,and MODFET and poly silicon emitter BJT and HBT.


4

Why knowledge of the physical origin of noise is important?

a. Stochastic fluctuations set a detection limit to measuring systems and telecommunication systems

b. Noise can be used for reliability assessment of devices.

c. Knowing the physical origin of noise can help to reduce noise: Thermal noise, Brownian motion (resistance-type devices: T↓, W↑)

Shot noise, stochastic emission (diode –type devices: avoid micro-plasma due to non uniform fields in reverse biased (FET) junctions)

Generation recombination-, and RTS noise (∆N→∆σ→∆R: avoid traps)

1/f noise (∆µ→ ∆σ →∆R: N or Neff not too low)


5

2. Some definitions and remarks [1-4]

Electrical noise is a real stochastic signal often described in terms of variance (σ2), rms values or standard deviation (σ), average absolute amplitudes (∆I ) or relative absolute amplitudes, e.g., ∆I / I, correlation function, C (τ), amplitude distribution function (pdf) or spectral noise density (Sx(f)). There is a difference between: amplitude spectrum [x] and power spectrum [x2], both are line spectra for periodic functions. The power density spectrum [x2 / Hz] of the noise is continuous . Power often means x2, not Watt.”x” can be a fluctuation in time of voltage V, current I, resistance R, optical power P [Watt], magnetization (Ni / Fe), extinction coefficient of an optical fiber, or height along a line (surface roughness) [x2/(1/x)].Spectral density, Sx (f) and correlation functions C(τ) of physical quantities are real and we use positive frequencies.


6

Correlation functions: C2 (τ) is a two-point correlation function [x2]

C2 (τ) = <x(t). x(t+ τ)>,C(τ) = C2 (τ) and S (f) are two different representations of x (t). The cosine transform or the Wiener-Khintchine theorem or the so- called Fourier transform of C(τ) gives S(f):

ττπτ d.f2cos)(C4)f(S0∫∞

=

Spectral density Sx (f) is also defined as the variance of a band pass filtered x (t), that becomes <xf (t)2> per bandwidth ∆f at frequency f

Variance 22

0 x σ)()( =∆=∫∞

xdffS


7

3. Analogue noise measurement set-up [5, 5a, 5b]

AC amplifier and sample in a cage of Faraday and output at A is monitored with oscilloscope for 50Hz, 150Hz parasitic, do we have “normal Gaussian noise”, clipping or oscillations? At B, the signal looks like amplitude modulated carrier at frequency f with random envelope if ∆f is small enough, ∆Vf (t). Variance of band pass filtered noise divided by ∆f gives the power spectral density:

A

B

)t(V2f∆f

SV ∆≡


8

FFTFast Fourier Transform (FFT) systems (Spectrum analyzer) are based on:

“periodic” in a time block of duration T, it will give a line spectrum.

sampling on x(t)

Power spectrum / ∆f = power spectrum x T Power densityspectrum in e.g., V2/Hz or V2s

On the next slide some FFT artefacts with rectangular windowing

"")(2

)( 22 harmonicsTnfwithbaTfS anna =+≈


9

FFT of a sine wave of 1Hz, T = 1s; 1.25s; 1,5s → f1=1, 0.8, 0.66 Hz


10

10-16

10-15

10-14

10-13

10-12

100 101 102 103 104 105 106 107f (Hz)

SV (V2/Hz)

10-11

figuur 2

)RR.(IV ∆+=

thVVVV ++= ∆

f)t(VS

2f

V ∆∆

≡

Thermal- and 1/f noise, in time- and frequency domain, decomposition

Top: thermal noise, bottom left and below: the 1/f noise in time and frequency domain, at high frequencies the thermal noise always becomes visible and can be used for calibration


11

II. Noise Sources [6-11]

1. Thermal noiseJohnson or Nyquist-noise: Phys Rev, 32 (1928)no 1, pp 97-113.

R→ Real [Z] and 1/R→ Real [Y] white noise for 0 < f < 3x1012 Hz

Physicists avoid problems at f →∞ by replacing “kT ” with

Engineers and material scientists multiply SV by

with f0 = 1/2πRC; τ = RC is a circuit time constant or the dielectric time constant τdiel : with 0.1s > τdiel > 10-12 s for most dielectrics and for metals.

We observe in a bandwidth ∆f a variance of the voltage or current fluctuations given by <en

2 > = 4kTR ∆f or <in2 >= (4kT/R) ∆f

RkTSandkTRS Iv /44 ==

1ehfkT/hf −

))f/f(1/(1 2o+

nqrodiel µεετ /=


12

Equivalent circuit for network analysis ( SPICE ) with test sources

A noise free resistor with a noise voltage in series or a noise current in parallel. The open circuit resistance is not heated by the current noise source. The short circuited resistor is not heated by the noise voltage! Equivalent, means equal to a certain level !

22n

21n

2n

2n1nn

2n1n

2n1n

eee

eee0e.e

0ee

+=

+≠=

==

Independent noise sources are added in squarred values, not in nV/√Hz


13

Origin of thermal noise

Brownian motion (1827) of free charge carriers (electrons 1897) Random motion of particles in a fluid (1827-1900) in plants, organic and inorganic material; due to light?; due to evaporation?; persist after a year!; smaller particles move faster; motion increases with temperature; molecular impact;

In analogy: electrons within a conductor’s lattice make a randomwalk at T > 0K. Average kinetic energy of an electron:

kTvmE th )2/3(*21 2 == KTatscm

mkTvth 300/10

*3 72 =≈=

17nm < λ = vth τ < 300 nm for 50 < µ ( cm2 /Vs ) < 16000


14

For f < fc holds: for the short circuit current fluctuations SI = 4kT/R

and for the open circuit voltage fluctuations SV = SI R2 = 4kTR

Thermal noise is independent of dc or ac current passed throughthe resistor. A temperature raise due to power dissipation can be taken into account by adapting T in the above equations. Ohms law, and the simple SV = 4kTR holds if collision time τ is not influenced by the field (vdrift < vth).

We can expect deviations, if there are no collisions, (e.g. at 0 K at f > fc (THz) in very short time intervals and for resistors with a length L < λ and transit time of electron τtransit < τ ( ballistic transport; not enough collisions in L)

collisiontransit VL τµ

τ <=2


15

Remarks on thermal noise:

Thermal noise is reduced by lowering the temperature, e.g., cryogenic applications in satellites. In MOSFET design, very often wide and short channels are chosen to reduce equivalent input thermal noise voltage.

Thermal noise and resistance measurements are used to measure the temperature in hostile environments (neutron flux and other ionizing radiation).

Equivalent voltage noise at the input of amplifier (SVin = SVout/ G2 ) are often expressed in an equivalent noise resistance(@ 289K) or equivalent noise temperature (has nothing to do with the real device temperature). Req and Teq are equivalent noise parameters defined by

TkR

kTRSTTfT vsystem

eq >+

=∆+=4

4)(andfkTRS eqvin

)(4=


16

2. Shot noise [8]

Stochastic emission of electrons is often like a Poisson process. If the average transit time is t0 = τ and G is the generation rate (s-1) of electrons at the cathode, then we have at the average <N> = G. t0crossing electrons underway. The noise is in the emission-time and also in the transit-time due to initial velocity fluctuations.

C(t) = 0 for t > t0 (no overlap in populations) and for 0 < t < τ

τNqI =

τNqI ∆

=∆ 2

222 )()(

τqNI ∆=∆

NNPoisson =∆⇒ 2)( ττqIqNI ==∆ 2

22)(

)/t1()I()t(C 2 τ−∆=


17

πτ/12)( <= fforqIfS I

ττω >=⇒= ∫∞

tforCdtttCSo

I 0)(.cos)(42

0

)sin(2.cos)1(4∫

=−=

τ

τπτπω

ττ ffqIdtttqISI

0.001

0.01

0.1

1

0.01 0.1 1 2 3

Log [ f τ ]

Log [ SI /2qI ] Fano- factor

4/л2 2

0.04

0.016

0.5

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

fτ

SI/2qI


18

3. Generation Recombination Noise [10]

τ/)0()( teNtN −∆=∆

andf

NfS n 22

)2(14)()(

τπτ

+∆=

?)( 2 NN =∆ Is the smallest value of N, the number of full traps and the number of empty traps. It depends on EF.

∫∞

=+0

2 1)2(1

4 dffτπ

τ

Conduction band

bandgap

traps

Generation-recombination from traps

electener

G RN is number of free electrons, not concentration, τ is lifetime of ∆N


19

10-2

10-1

1

10

10-1 1 10

Lorentzian-spectrum

f -2

SN / (4τ 2N∆ )

10-2

0.5

2πfτ

26 10][10 −− << sτ

One single trap (∆N=1) and low N ==> RTS-noise; ∆I/I = ∆G/G = ∆N/N = 1/N

τ can be read from the spectrum

1.6 105 > fc = 1/2πτ [Hz] >16


20

4. Burst noise, popcorn noise, RTS noise [9,11-14]

RTS-noise is a special case of generation recombination noise with one single trap, ∆N = 1, if τe = τc then <∆N2> = ¼ , has its highest value

Two level noise and superimposed 1/f noise in time domain and its amplitude propability density function (pdf)


21

Pure RTS without 1/f noise component has a Lorentzian spectrum.

RTS is a problem of submicron devices with traps, e.g., in diode type devices with dislocations in sensitive areas and submicron MOSFETs with a low number of carriers. RTS is a poor (traps) device indicator. For strong asymmetric noise holds <∆N>2 → 0. Symmetric traps can become asymmetric in a MOSFET, by applying switching bias, but asymmetric ones can become symmetric

cepp

pNvI

fK

NS

VS

IS τττ

τπτ

/1/1/1)2(1

42222 +=⇒

+===

⇒∆

≡ 2

2

NNK 222 )(

.1

ce

ce

ce

p

NNKor

ττττ

τττ

+=

+=

Nττττ //2

12

++=>∆<

ecce


22

Analysis of RTS in time and frequency domain [13,14]

-10-4 -5⋅10-5 0 5⋅10-5 10-4 2⋅10-4 0

2⋅104

4⋅104

6⋅104

8⋅104 pdf

U, Volt

Solid line: Id=2.15⋅10-6 A Doted line: Id=1.53⋅10-4 A

LED#4k pdf examples V(t)

t

a

-b

V0

0

ϑi

τ i

The waveform of the measured noise displayed by the oscilloscope

The probability density function of the raw noise


23

Detection of noise in noise

Total noise: V(t) = V1/f(t) + VRTS(t)

State “1” (V(t) > V0):V1/f(t) = V(1)(t) – a ; VRTS(t) = +a

State “0” (V(t) < V0):V1/f(t) = V(0)(t) + b ; VRTS(t) = −b

V0 threshold voltage to be found using the standard signal detection theory in the noise background

V(t)

t

a

-b

V0

0

ϑ i

τ i


24

Noise reconstruction The pdf of the raw noise:

−−+

+−= 2

2

22

2

2 2)(exp

22)(exp

2)(

σπσσπσ

aVpbVqVWV

-10-4 -5⋅10-5 0 5⋅10-5 10-4 2⋅10-4 0

2⋅104

4⋅104

6⋅104

8⋅104 pdf

U, Volt

Solid line: Id=2.15⋅10-6 A Doted line: Id=1.53⋅10-4 A

LED#4k pdf examples

p = <τ>/(<ϑ> +<τ>)

q = <ϑ>/(<ϑ> +<τ>)Probabilities for states “1” and “0”

+−

−−=Λ 2

2

2

2

2)(exp

2)(exp)(

σσbVqaVpV

ba

babaV ln

2

2

0 ++

−=

σ

V(t)

t

a

-b

V0

0

ϑ i

τ i

Likelihood relation:

1=Λ


25

Obtained results after detection reconstruction

t

V

a

V 0

0

- b

t

V 1/f

0

t

V RTS

0

a

- b

10 102 103 10410-16

10-15

10-14

10-13

10-12 SV, V2/Hz

f, Hz

RAW

1/f

RTSIf 1/f and RTS have a different dependence on bias, then there is a different physical origin

Raw noise spectrum and its decomposition in a 1/f and RTS


26

5. 1/f Noise [15-19]For metal-, semiconductor-, organic- samples with perfect contacts, holds an empirical relation for the 1/f conductance fluctuations. Spectra are 1/fγwith 0.8< γ <1.2 and have been observed between 10-7 to 107 Hz. If samples are homogeneous, also in current density then Hooge’s empirical relation holds:

C is a dimensionless parameter for the amount of 1/f noise, independent of bias and frequency, with values 10-16 < C < 10-6 .Smaller C-values are not detectable due to thermal noise. Samples with higher C-values often show burst noise on top of the 1/f noise. N is the number of free electrons, α is a dimensionless parameter of the order of 10-4 for metals and 3x10-7< α < 3x10-3 in semiconductors, itrepresents the relative 1/f noise at 1 Hz from one carrier.Contacts are notorious for 1/f noise due to current crowding, Neff low!

NffC

RS R α

==2 suggesting a bulk origin,


27

a) Experimental facts on 1/f noise1. For I = 0 → SR ∝ 1/f already exists as a conductance fluctuation in equilibrium.2. For I (dc) → SV = I 2 SR ∝ 1/ f (Ohm, ∆V = I∆R).

3. I (ac)→ SV ∝ 1/( fc ± f ) ∝ 1/∆f-noise (up conversion of 1/f noise→phase noise in RF) (best values depend on fo,-100 dB < dBc @ 10 kHz < -90 dB for 10-14 < C < 10-13 ).

4. Observable in homogeneous samples with a number of carrier N between 107

and 1014 . For N < 107 often homogeneity problems, RTS-noise on top of 1/f, for N >10 14 detection problems, always 4kTR.

210c

Pc P

SLogdB =

∆f = 10kHz


28

5. ∆ρ is not due to ∆T: because samples with a negligible small temperature coefficient have the same 1/f noise as samples with a normal ∆R/R∆T=∆ρ/ρ∆T=-∆µ/µ∆T

6. omnipresent as a bulk phenomenon (SV /V2 ∝ 1/N) in:metals (solid-liquid), semiconductors, polymers (homogeneous,contacts) in dielectrics like optical fibers as a 1/f fluctuation in theattenuation coefficient, in magnetization fluctuations in magneto-resistive sensors (NiFe) and in devices like: (photo) diodes, laserdiodes, BJT, HBT, JFET, MESFET, MODFET and MOSFET.Exist also in non electronic systems: loudness in music; heartbeat fluctuations; electro encephalic-graphs during sleep or in the state of attention

00.→∆⇒→⇒

∆=

∆ ρδδρρ

TT

⇒∝ −δµ T ⇒+−= ATloglog δµ


29

7. Hooge’s empirical relation, [19] “1/f noise is no surface effect”…Au samples, no oxide, no traps, no ∆ N

2// lNqlnAqG µµ ==

?NN

GGor

GG ∆

=∆∆

=∆

µµ ( ) ( )22 //// GGRRGGRR ∆=∆⇒∆−=∆

Experimental results on homogeneous samples submitted to homogeneous fields are often well described by

2222 IS

GS

NffC

RS

VS IGRV =====

α 21 by applying a current sourceby applying a voltage source

1

2

is the number of carriers with Ω volume of the sampleΩ= nN


30

About the 1/N dependence, N in the empirical relation does not suggest number fluctuations → noise source is distributed uniformly in the volume

?or bothorNNN µ

µµ

σσ

∆∆⇒∆

+∆

=∆ ∑

=

∝⇒N

iiG

1µ

µNG ∝ 22iNG µ∆∝∆

2i

22

2i

2

N1

NN

GG

µµ∆

=µ

µ∆=

∆

⇒∝ µNG22

NN

GG

∆

=

∆

Mobility fluctuations

Number fluctuations

Or traps at interface, FermiPoisson, or sub-Poissonian in bulk

tt PNNNwith 1111

2++=

∆orpwithpNN 12 ==∆

Np

GG 2

=

∆

]1p[pNN2 <=∆2

22

NN

GG ∆

=

∆


31

About Neff [17, 20,21]1/f noise is only detectable above thermal noise for N < 1014 [71] (MOST; tox = 2nm, L = 0.2µm, W = 2 µm, VG

* = 46mV N = 2x103 )Inhomogeneous current density (current crowding) in homogeneous material: N must be replaced by Neff << N. Hence, contacts (current crowding) are notorious for huge 1/f noise. In inhomogeneous samples with current crowding holds [4,6]:

[ ]∫∫

Ω

Ω=

dJ

dJnNeff 4

22

∫∫ Ω∝Ω=Ω

dnJdJ

nfISV 3

44

2

21 αρ

Hence, non-uniform native oxides (at interfaces) can increase the 1/f noise with decades (n low and J high in punched native oxides)


32

Experimental facts in favor of a bulk origin for the 1/f noise [19,22-24]

← metals, Au, Pt, GaSb; Si ↑ holds over more than 5 orders of magnitude in volume

The relative 1/f noise at 1 Hz normalised versus N for Pt (dots), Au (full line) and GaSb (solid triangles). The dotted line is calculated with α=10-4 and the full line [19, 22,23] (Au and GaSb) with α=10-3

α-values for silicon samples with different volume. α is not a strong function of temperature and is volume independent. Open circles: n-Si at 300 K; dots:p-Si at 300 K; black squares: p-Si at 77 K; open squares : n-Si at 77 K [24]


33

8. ∆µ→∆ρ, 1/f-fluctuations are in the lattice scattering → ∆µ and α-value is a parameter [25-27]

Experimental values of α versus µ/µlatt at 300 K. Circles denote p-type Ge with resistivities in the range of 4.5x10-4

Ωcm < ρ< 50 Ωcm.Crosses (+) denotes n-type GaAs with ρ= 2.7x10-3 Ωcm.Squares denote MBE grown GaAslayers with thickness between 3.2 µmand 10 µm and electron concentration between 2.5x1014 cm-3 < n < 1017 cm-3. Solid line: α proportional to µ2


34

Physical origin for ∆µ due to 1/f fluctuations in lattice scattering [25]

Hypothesis: ∆µlatt ≠ 0 and ∆µCoul = 0 ⇒+=Coullatt µµµ111

⇒

∆

=

∆222

latt

latt

latt

andµµ

µµ

µµ

22

dd

latt

latt

µµ

µµ

=⇒

NfS

NfRS latt

latt

measR αµ

µµ

α µ2

22

===⇒

DD

qkTDand ∆

=∆

⇒

=

µµ

µ( ) lattlattmeas αµµα 2/=


35

9. 1/f noise is in the lattice scattering [25]

latt

2

latt

= αµ

µα ⋅

A low α-value can mean a lot of impurity scattering, hence a low µbut an acceptable crystal quality.

α-values can be low in semiconductors with a high crystal quality even if µ ≈ µlatt.

On top of the ubiquitous lattice scattering there may be number fluctuations of the McWhorter-type or several generation recombination contributions. This often leads to 1/f-like spectra~1/fγ with a frequency exponent 1.15 < γ <1.45 or 0.55 < γ< 0.85


36

α is not a constant, and not predictable with a high precision [23, 60]

α versus thickness ton bismuth samples1/λ = 1/λb + 1/t [28]

α vs VG [29], in n-type Si layer. α is high if carriers are at the surface inaccumulation. In depletion (carriers away from surface) low α-values are observed


37

log

T an (K -1)-1

-4

-3

-5

-68 x10 -4 1 .5 x10-3

10. α depends on

crystal quality

α versus versus proton flux in irradiated n-GaAs. α-values at T = 78 K (•) and at T = 295 K (0) versus irradiation doses Φ. The solid line shows proportionality between the low temperature α-values and proton irradiation dose Φ. The dose-independent α-values @300K (broken line)[32]

α vs reciprocal anneal temperature in boron implanted Si. The dots are obtained at T = 300K, the squares indicate results at T = 77K. The dotted line through the results at 300K show the proportionality with activation energy of 1.1eV. [30, 31]


38

Remedies to reduce 1/f noise

1/f noise is inherent in the conduction and cannot be avoided. Devices can be designed in such a way that 1/f noise is reduced at the cost of device area and speed. Avoid that the current is carried by a small number of electrons. Avoid submicron devices," the faster, the noisier ”. Faster devices have shorter channel lengths and smaller N. For a given I, N is small in fast diodes due to a small τ (Au killers) and transit time.

Avoid current crowding, like in granular materials (poly silicon, thick film resistors consisting of touching grains, too thin film resistors), high tech conductive adhesives, Neff << N.

Avoid lattice damage due to lattice mismatch (SOS, silicon on sapphire) and due to implantation followed by poor annealing (SOI).


39

b) Some 1/f Noise problems

SV is divergent for f → 0 and the variance

is logarithmic divergent for fl → 0 and fh →∞ . This can be solved by introducing two corner frequencies: one where SV levels off for f < flc and a second cut off frequency fhc where holds that SV becomes proportional to 1/f2 for f > fhc . However, flc and fhc have never been observed. The 1/f noise component disappears in the thermal or shot-noise at high frequencies. A finite measuring time (10 periods of 10-7

Hz in 3 years) and thermal stability problems set a limit at the lowest frequencies. The variance of 1/f noise increases logarithmically with measuring time. A plot of the measured variance (linear) over a time tmeas versus the logarithm of tmeas is an other way to measure 1/f noise with a drift free and sensitive dc voltmeter [71]

∫ =h

l

f

f l

h

ffCVdf

fVC ln2

2

meashtt tfCVVmeasmeas

ln222 =>∆=<σ


40

Controversy about physical origin: surface or bulk; ∆N or ∆µ?∆N: Surdin-model → 1/f = Sum of independent g-r noises with a 1/τdistribution with 10-7 s < τ < 107 s ; McWhorter model → 1/τ distribution explained by tunneling into traps at the surface of a MOST or 1 /ffluctuations in surface velocity recombination time in short diodes

•∆µ: empirical relation, no theory to explain the value of α and the 1/fdependence of the spectrum. Better no theory than a wrong theory.

•arguments for ∆µ : (i) 1/f fluctuations in the Seebeck (thermo-voltage) coefficient, Hall voltage, magneto-resistance, injection diodes, hot carrier mobility, diffusion coefficient in diodes, and α~µ2 by changing the ratio of lattice scattering and Coulomb scattering changes µ, but also α. It can only be explained by ∆µlatt ≠ 0 and ∆µCoul= 0.


41

Fluctuation in Spectrum Remedy

Thermal V,I: resistance-type devices, MOS-FETS, MOD-, MES-, J-FETS

Sv=4kTR No, low R and T, high µsensors

Shot I: diode type devices, BJT, HBT

SI=2qI No, Fano- factor

G-R N, conductance: semiconductors Fermi level position dependent

2

2

)2(14

τπτ

fNSN +

>∆<=

Lorentzian

No traps No noise

1/f R: in metals, liquids polymers and semiconductors

∝ 1/f ? Avoid sub micron. It is not dependent on Fermi level

Summary


42

III. Sensitivity coefficient for current crowding [17, 17a, 33, 34, 72]

Important for conductance fluctuations with inhomogeneous current densities. A distributed system is considered as a limit case of a network. A local change in the resistivity will provoke a voltage fluctuation if a constant current is applied. In a arbitrarily-shaped sample holds for resistance R and conductance G between two contacts

The total dissipated power is the sum over the whole sample volume Ωof the power density multiplied by sub volumes dΩ. For a homogeneous sample submitted to uniform electric field E (J is constant) the well know equation is obtained,

∫∫ΩΩ

Ω=⇒Ω= dEV

GdJI

R .11 22

22 σρ ∆Ω∑==⇒ )(22 PdensityGVRI

G/1A/LR =ρ=


43

The sensitivity coefficient is taken from the derivative in the sub area where the resistivity increase occurs, Ωl

For a homogeneous increase in resistivity over the complete volume, the integral must be taken over Ω . The voltage or current fluctuation is given by the product of the sensitivity coefficient and ∆ρ or ∆σ

If the 1/f noise source is spatial uncorrelated and distributed homogeneously over the sample the empirical relation can be applied on a sub volume which results in

δρδ /V

⇒Ω= ∫ dJI

V 21 ρ ]/[dimensionwith1 2 cmAdJI

V∫Ω

Ω=lδρ

δ

Ωρ∆=∆ ∫ΩdJ

I1V 2

lΩσ∆=∆ ∫Ω

dEV1I 2

l


44

2

22

22

22

2 1

Ω=

Ω= ∫∫

ΩΩ

dJI

dJI

Vand ρρΩαρ

= ∫Ω

dn

JfI

1S42

2v

In homogeneous samples: α, ρ and the concentration of free carriers n can be in front of the integral. The relative voltage fluctuation becomes

fndJnf

dJ

VS

eff2

2

4

2v

Ωα

≡

Ω

Ωα=

∫

∫

Ω

Ω the effective number of carriers Neff = nΩeff is given by the effective volume Ωeff that seems to be concentrated at the spots of the highest current density.

Only for uniform current density (J constant) holds Ω = Ωeff

Ω<Ω

Ω

=Ω∫

∫

Ω

Ω

dJ

dJ

4

22

eff


45

Some applications, contacts and sensors [17, 17a, 33, 35, 36]


46Contact noise (constriction dominated, no interface or multispot)

Top: Qualitative shape of current and equipotentiallines of a circular contact on a thick homogeneous sample.Bottom:Simplified model of a point contact on. The semi circles represent hemispherical equipotentialsurfaces

C1/f vs R at T=300 K for two alloys with negligible temperature coefficient [34] • Manganin; o Constantan. The lines are drawn using a bulk 1/fnoise origin. The full line is for manganin with α = 6 × 10-4, the dotted line is for constantan with α = 1.2 × 10-4. ∆ρ/ρ∆T→0, 1/f not caused by temperature fluctuations

3/12

3

/

RNf

C

RS

aN

aR

eff

fR

eff

∝==

∝

∝

α

ρ


47

Point contacts between InSb rods ( native oxide interface alwayspresent, but not always dominant) [70]

Bulk or interface dominated relative 1/f noise C vs R and R vs force at 77 and 300K, with and without H2O2 treatment, (native oxide thickness). p-type InSb, @ 300K, intrinsic ”n-type”, dope 1015 cm-3 and ρ77K/ ρ300K= 103


48

Remarks on current crowding and interfacesDeviations from homogeneity in electric field and current density in samples with homogeneous properties in ρ,n, and noise result in an increase in excess noise e.g.:

• electrical contacts, vias and conductive adhesives (multi spot contacts)

• granular thin layer with thickness 10 nm < t < 100 nm

• granular thick layers (poly silicon, thick film resistors (RuO))

• trim cuts in precision resistors always lead to an increase in noise

• Interfaces are notorious for the excess noise, because the local value of J is much higher at weak spots. Due to a poor local crystal quality, depletion at crystal boundaries or a native oxide, and the 1/f noise is higher.

γρα fn/ i2ii


49

For samples with 4 contacts: [33,35] a pair of current contacts, D1, D3(drivers) and 2 voltage contacts, Q4, Q2,(sensors) holds for the 1/f noise

represents the dot product of the two current densities with the current density in the ad joint situation by interchange of the current source I from the driver contacts to the sensor contacts. Areas with conductivity fluctuations where the J and are perpendicular do not contribute to the observed voltage noise at the sensor contacts. For a given current I at the driver contacts, we always find higher voltage fluctuations at the current contacts, than at the sensors [36]

JJ ~•J~

J~

Ω•= ∫ dJJnfI

SQV

22

2 )~(1 αρ

Hall sensor


50

IV. Noise in devices: resistors, diodes, BJT, MOST1. Resistors [5b]

1/f Noise only exceeds thermal and amplifier noise above a certain minimum power dissipated in the sample:

If Req << R then the eq. can be written as an electric field criterion E = V/Lfor homogeneous samples and fields

Dielectrics, low (hopping) µ, Ecrit >> Ebreak down → ”no” 1/f noise, it is not detectable. Dielectrics with soft or hard breakdow show high 1/f and RTS noise

+

µ=+>

αeq

2

eq

2

RNq

LkT4)RR(kT4fNV

µα> q/kTf4E2 [ ]21

/4 µαqkTfEcrit =⇒Field criterion:


51

Power density criterion for metals and semiconductors

kTnJfcrit 4

2αρ=⇒α>ρ /kTfn4J2

26max /102 cmAxJJ =<In thin metal layers (ρ ≈ 3.10-6 Ωcm ):

damagerationelectromigavoidcmWJPP dd ⇒==< 372maxmax /10ρ

Metals, high n ≈ 3. 1022 cm-3 , 1/f noise only for f < fcrit ≈ 100 Hz, for α=4x10-3 and J > 2x106 A/cm2 . Electromigration damage, drift and current induced non stationary 1/fγ –noise (with γ>2) will occur for J>3x106 A/cm2.


52

τα4max

=cf⇒== τρ /2maxmax

kTnJPd

τ = 10-12 s, collision time

fmax for homogeneous semiconduc. resistors at highest current density

⇒≅ thqnvJmax

N < 1014 criterion: from the choice fcrit=100 Hz (to be able to judge a 1/f spectrum from 1Hz on) and a maximum power dissipated in a samplevolume Ω at T=300K, Pd Ω < 0.1 Watt, and an α = 1.6x10-3 follows

crit

d

critcrit kTf

PN

kTfJn

kTnJf

444max

22 Ω==

Ω=Ω⇒=⇒

αραρα

A sample resistance R larger than Req and with N < 1014 is always a safe start to be able to detect 1/f conductance fluctuations above the thermal noise under reasonable bias conditions.


53

1/f noise of m resistors in series or in parallel

∑∑∑

=

==

≠=⇒=⇒= m

ii

m

j j

jRm

ii

ii

R

N

fNR

RfRSRR

fNRS

i

1

1

2

221

2

/αααFor m resistors in series holds:

jijiji NNandGGorRRforonly ====⇒≠

For m conductors in parallel holds:

∑∑∑

=

==

≠=⇒=⇒= m

ii

m

j j

jGm

ii

ii

G

N

fNG

GfGSGG

fNGS

i

1

1

2

221

2

/ααα

Proof is based on the empirical relation and uncorrelated noise sources: <∆Ri ∆Rj> = 0 for i≠j


54

The 1/f noise can be quite different for resistors with the samethermal noise

Thin film resistors all having the same thickness and width, length ratio: W/L, will show the same thermal noise but a different 1/f noise: SR ~ 1/WL.

Resistors with the same ratio of length over cross section : L/Wt with t the thickness, will show the same thermal noise but a different 1/f noise: SR ~ 1/WLt

A noisy but small series resistance in series or a small but noisy leakage conductance in parallel can be very annoying.

This makes 1/f noise a very useful diagnostic tool


55

Overlooking a small, but noisy series resistance or small leakage conductance in parallel can result in apparently high α-values. That is one of the reasons of a wide spread in 1/f noise and α-values.

m resistors in series and n lines in parallel

For a resistance with value R consisting of a network of n branches in parallel, with each branch consisting of m resistances in series; all with the same average value r and 1/f noise value Sr results a resistance and in a relative 1/f noise given by:

22

1rS

nmRS

nrmR rR =⇒=

For m=n, R=r, and the thermal noise remains 4kTR, but the 1/f noise of the network is the 1/f-noise of one resistance r reduced by n2.


56

log f(Hz)

log SV (V2/Hz)

1/f

G-R

1/2πτ

4kTR

Decomposition of a spectrum for frequency index analysis in three independent components

The precision in the calculated frequency index of 1/fγ noise is reduced by a lack off or a poor decomposition of spectra.

At low bias, a competition of thermal noise, white background noise gives too low γ-values and at strong bias often an additional non-stationary current induced noise and drift with a 1/f2 dependence results in too high γ-values


57

2. 1/f noise in long and short diffusion dominated diodes [37-39]

If V > kT/q then I ∝ I0 exp(qV/kT) and I ∝ I0 ∝ D/L and with D/µ= kT/q holds I ∝ (µ/τ)1/2 with I0 the saturation current, D the diffusion coefficient of the dominant carriers, L the diffusion recombination length defined by (Dτ)1/2, τ the minority carrier lifetime, and µ the mobility. Hence holds: ln I = 1/2 ln µ + constant, thus: ∆I/I = ½ ∆µ / µ and SI / I2 = ¼ Sµ / µ2 and I=qN/τ (charge control) [37-39]

f

IqS

fI

q

Nf

S

I

S fI

fI

τ

α

τ

αα

µ

µ44424

1 /1/1

2=⇒===

τα8

)()( /1 =⇒= cf

IshotI ffSfS

At the corner frequency fc holds SIshot = 2qI = S1/f(fc)


58

Corner frequency fc in long diodes, is current independent only when the 1/f noise only stems from one type of current (with e.g,, ideality factor =1) and α is homogeneous

τα8

=cf

τ is large, slow device ; low 1/f noiseτ is small, fast device; high 1/f noisefc independent of current and device area

fc is a real figure of merit, if there is 1/f and shot noise onlyτ in III-V direct band gap semiconductors << τ in Si indirect band gapHence III-V will show higher 1/f noise than Si (has nothing to do with poor material quality) because of smaller value for N=Iτ/q outside the depletion region, for a given current.

10-25

10-24

10-23

10-22

10-21

10-20

100 102 104 106 108

SI [A2/Hz]

f [Hz]

fc


59

1+=∝ xkifAIS x

k

INo edge effects in diodes if

A A A≡

)()(

)()()()(

)(2

)(1

)(21

2

2

1

1

21

21

xkxkk

I

xkk

I

x

k

x

k

I

k

x

k

I

AAfJS

fAAJS

AJA

AJAS

AAfAAJS

−−−

+∝≡+

∝

+∝≡⇒++

∝

γγ

γ

A = A1 +A2

Holds only for any A1 and A2 if: k-x=1


60

If there is no perimeter effect (in mature technology) then

γγ fAJ

AfIS

k

k

k

I =∝⇒ −1

Comparing noise at the same current leads to SI∝ 1/Ak-1 or at the same current density (junction voltage) leads to SI∝ A.

shot noise: γ = 0, k = 1 (no perimeter effect)

1/f noise: γ =1, and 1 ≤ k < 2 ( for η1and η2 contributions, or series resistance noise gives k = 2)k = 1 then holds for S1/f = αqI/4τf often observed in Si


61

k > 1 often observed in poly-emitter BJTs, HBTs (III-V) and SiGe BJTs can be explained by either an α-profile increasing towards the junction, or by different contributions of the current components with ideality factor η1, η2 to I and SI;

I=I1(η=1) +I2(η=2) and SI = SI1+ SI2

If, I ≅ I1 ∝ I22 ; and if SI ≅ SI2∝ I1/2 or I ≅ I2 ∝ I1

1/2 ;and SI ≅ SI1∝I2

1/1 −∝ k

k

I fAIS

f τ ττ

1

1

1 −

−

−

∝∝k

k

k

cJ

AIf

for the same A, current dependentfor the same current, fc ∝ 1/Ak-1

for the same J, independent of A

⇒

and fc becomes

figure of merit, fc without mentioning I or J becomes doubtful.


62

3. Noise in BJTs and HBTs [40-44]

1 2

3

4 5W W

p pn

~I

I

I

I

II

I

• re , rb, rc: 3x3 (thermal, 1/f-, and g-r noise) = 9• e-b, b-c junctions (short diode) 2x3 (shot, 1/f, g-r) =6In total: 15 possible independent noise sources (15 = 9+6)

4 3 5

1 2


63

1/f noise in series resistances (high dope, low noise)

effectivebe

ber Nf

rS

be,

2,

,

α=

effectivebe

bebeV Nf

rIS

ber,

2,2

,,

α=

dominated by I1 or I2IB dominated by

kTqV

kTqV

eIeIIB2

2010 +=j

IW

DISe

Ibτ

221 +∝

⇒+= 21 III B ⇒bIS

About (1/2 ≤ k ≤ 2)kBI IS b ∝

I2→

I1→ 221; IIII BB ∝∝

2/112; IIII BB ∝∝

2e

BIbWDIS ∝

22

eBIb

WDIS ∝

j

BIb

ISτ

2/1∝

j

BIb

IS

τ∝


64

fc / fT a new figure of merit [42] Highest fT, highest fc

SiGe MBE (Daimler-Benz)1.9x10-7500010

SiGe Motorola1.9x10-770030

SiGe epitaxial polysilicon emitter

6x10-8

6x10-7

3003x10340

InGaAs (NEC)>1.7x10-4> 10646

AlGaAs/GaAs (NEC)

>1.4x10-5> 10554

GaInP/GaAs (Thompson)

8x10-53x10530

AlGaAs/GaAs (TI)

1.5x10-5

1.3x10-5

≈ 4x104

≈ 4x104

2225

SiGe (IBM)1.3x10-750030

Commentαfc(Hz)

fT(GHz)Unit current gain approximated

)(21

21

cBloadjcjeecTf τττττππτ ++++

≈=

)(21

cBTf ττπ +

≤

8α

≅T

cff

If 1/f noise is dominated by native oxide than 8

α>>

T

cff

A new empirical relation if fcand fT ∝ 1/(τB+τc)


65Experimental results: poly-emitter Si BJTs [42]

7.5 Å oxide, SIband Sre fully correlated

1/f tunnel transmission fluctuations modulate SIb

and Sre

k = 2Markus et. al. (1997) Eindhoven

low oxide dosehigh oxide dose AE = 20x20 µm2

k = 1k = 1.8

Simoen et. al. (1996) IMEC

AE = 10x103 µm2, 2x10-17 < fSIb/IB <

5x10-16k = 1.3Mounib et.al. (1996) Grenoble

7.5 Å oxide, SIb ∝ IB

2/A (no perimeter effect)

k = 2Markus & Kleinpenning (1995) Eindhoven

no oxidethin oxidethick oxide

k = 11.2 < k < 1.8

k = 2

Quon et. al. (1994) California

10-16, 330 Hz (AE = 10x103 µm2)k = 1Mounib et.al. (1993) Grenoble

3x10-16-5x10-15, 2x10-6 < α < 2x10-5k = 1Kleinpenning & Holden (1992) Eindhoven

2x10-17-5x10-16, 2kHzk ≈ 1.5 Pong-Fei Lu (1987) IBM

Comments onfSIb

/Ib [A], fc, α, area Ak in

SIb∝ Ib

k

Author, publication year, affiliation


66

Experimental results III-V HBTs npn – GaAs/GaAlAs

SIb

[A2/Hz]

IB [µA]

100 101 102 103

10-19

10-18

10-17

10-16

10-15

, , Kleinpenning – Holden (1993) [73]

, Tutt et al. (1990, 1992)

Jue et. al. (1989)

Costa et. al. (1992,1994)

Plana et. al. (1992);

SIb ∝IB3/2

→∆µ

SIC

[A2/Hz]

IC [µA]

100 102 104

10-20

10-18

10-16

10-14

∆µ – model with 2x10-5 < α < 3x10-3

fI

SkC

Ic∝ 1.3 < k < 1.4


67

Discussion and conclusions [40, 42]

•1/f noise is unavoidable / RTS- or g-r noise on top of the 1/f noise with 1/(1+(2πfτ)2) can be avoided by avoiding traps. Some III-V HBT have an “inherent” g-r noise, e.g., GaAlAs with Al > 20%, often shows τ ≤ 10-4

s and a fg-r ≥ 1.6 kHz.A new figure of merit is proposed: fc / fT ≈ α /8 useful to compare technologies. The lowest values of fc/fT are from SiGe devices.Native oxide at the poly-emitter results in more 1/f noise (SV ∝ αiJ4/ni

3dΩ ). This is not a proof for the ∆N origin of the 1/f noise [20].•Current crowding at contacts will increase the 1/f noise and can dominate the 1/f noise of the junction.


68

•Contact noise, SIBE∝ IB

2, IE2 visible at higher currents contributions of

∆re, ∆rb and on top of the 1/f noise, often GR noise with τ ≤ 10-4 s

•SIb∝ Ib

k 1 ≤ k < 2 can be understood as ∆µ noise either by a non-uniform α-profile increasing towards the junction or noise and current dominated by different areas (depletion layer or outside space charge layer) k ≈ 1 in Si devices 1.3 < k < 1.6 in III-V devices

•Physical origin of 1/f noise in diodes and diode type devices are mobility fluctuations: D/µ = kT/q ⇒ ∆µ/µ= ∆D/D.

•For long diodes τ is the minority carrier lifetime at the low doped side of the junction. For a short diode it is the transition time W2 /D(W = emitter or base width, D diffusion coefficient.)


69

S G D

p-type

oxiden

L

n+ n+

• Substrate dope: 1014 < NA (cm-3 )<1018

• Fields: 2x105 < EpSiO2 (V/cm) <5x106

• Peak mobility @ Ep = 0.4 MV/cm

• 104 V/cm < ESi// < 105 V/cm

• Ebreak down SiO2 : 107; Si: 3x105 V/cm

•Surface concentration of charge and electrons: 1.6x10-8 < C/cm2 < 8x10-8

103 < n (µm -2 ) <104 EpSi = (εSio2 /εSi) EpSio2 → 65KV/cm < EpSi < 1MV/cm

4. MOSFET [45-55]

Scaling laws: l/K; W/K; tox /K; K x Cox , Cgate /K; V/K → Ebreak down criterion; I/K (power density, current density I/W constant). “0,1 µm technology” has an oxide thickness of about 2nm: tox x 50 = lmin


70

1/f noise in MOSFETs (Geometry and bias dependence) [48-50]

NLEV=2,3 Sveq ≡ KF/CoxWlf or

NLEV=0 (SPICE)

trial and error_________________________________________NLEV=1

Saturation region Vd ≥ VG*

HSPICE noise parameters version (release) 9 1.1NLEV = 0, 1, 2, 3 with NLEV2 (default) with 10-25 V2F < KF (Coulomb V) < 10-19 V2F

Ohmic region Vd << VG* (MOST = resistor)

Weakness of Circuit-oriented equationsEquations in terms of α

WlfWlVCq

NfIS

Gox

I 1*2 ∝==

αα

( )( ) lfWlC

qIS

VIgVCl

WI

fWlVCq

ox

sIs

GsmGoxs

Gox

2/1

2/32/1

*2*

*

2

holds/2and2/

with2

αµ

µ

α

=

==

==Nf2α

IS

2s

Is[ ]

( )2/1

2/1

1/22

2

AFarad2/3for hence

=

=≡

WLCqKF

KFAFfLC

IKFS

ox

ox

AFs

Is

αµ

[ ]( ) 2/1

1/2

/2

/VA2/3for

LWCqKF

KFAFWLfCIKFS

ox

ox

AFs

Is

µα=

=≡

gox

oxG

m

IsVeq

oxGm

Gox

GmsIs

CWlt

WlfCqV

gSS

WlfCqVg

fWlVCqVg

NfIS

12

2422

*

2

*2

*

2*22

∝∝==

===

α

ααα

[ ][ ]))10( 10 problems,r -g (102/

FVV Coulombhence

6-25-19*

22

≈=

≡

− αα qVKF

KFWLfC

gKFS

G

ox

mIs


71

NLEV = 2,3

η 2 ≈ 2 (85 mV / decade in sub threshold current increase)

Sub threshold [52]

Circuit-oriented parameters, bias…. dependent

Equations in terms of α

g

ox

ox

G

m

IsVeq

ox

Gm

Gox

GmsIs

CWlt

WlfCqV

gSS

WlfCqVg

fWlVCqVg

NfIS

12

2422

*

2

*2

*

2*22

∝∝==

===

α

ααα

[ ]2/

/mCoulomb

o

*

22

22

2

oxGa

a

ox

aVeq

ox

maIs

CqVK

K

WlfCKSr

WlfCgKS

α=

≡≡

kTqVGeI η/∝

( )qqkTWlCN

NNfNfNNI

SkTIqg

ox

I

m

/)/(

)(

/

0

000

2

=

<≈+

=

=αα

η

WlfCKFSox

veq =

WlfCkTS

oxveq

2αη= [ ]V Coulomb 2kTKF αη=

qkTVd >>


72

Experimental Results vs Wl, VG and Isat [50, 51, 54,55]

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-12 10-11 10-10 10-9 10-8 10-7 10-6

f SVeq

(V2)

W x L (m 2)

"1""2"

"4"

"3"

"5"

The equivalent 1/f noise SVeq at 1 Hz (f SVeq) versus the area W × L. The extrapolated values at 1 Hz (f SVeq) of the 1/f noise measured for “1” tox = 600 nm and “2” tox = 150 nm, at f = 1 kHz, 25 µm technology; αp = 1.7 × 10-4; SVeq ∝ toxfor “3” and “4” tox = 100 nm, at f = 10 Hz, αn = 10-4 @ VG = 1V; αp = 10-6;for “5” tox = 12 nm, 0.6 µm technology,

at f = 100 Hz, αn = 10-4 [54]

10-7

10-6

10-5

10-4

10-3

10-1 100 101

α

VG

* (V)

Surface channel

Bulk channel

The 1/f noise parameter α versus VG* for a surface(p+poly) and bulk

(n+poly) p-MOST. The α–values are calculated with eq. (2) from experimental results obtained in the ohmic region [50,51] : ∆ surface channel with L = 5 µm, surface channel with L = 0.8 µm, ο bulk channel with L = 5 µm, bulk channel with L = 0.8 µm

10-24

10-23

10-22

10-21

10-20

10-19

10-7 10-6 10-5 10-4

f SIsat

(A2)

Isat

(A)

slope = 3/2 The quantity fSIsat versus the saturation current Isat. The results obtained on n-type MOSFETs show a power low with exponent 3/2 [54]

WltS ox

veq ∝


73

n-MOSTs often show a surface origin, tunneling (∆N), Experimental facts in favor and at variance with ∆N, 1/f ∝ Nss? [47, 48]

The equivalent input noise at 1 Hz and VG

* = 1V versus x0D0 [cm2 eV-1]. The dotted line follows the McWhorter model. [48]

The equivalent input noise at 1 Hz and 1carrier (α values) versus x0D0 [cm2 eV-1]. [47] The dotted line follows the McWhorter model.1…6 are n- channels, b,c,d,e,f are p- channels


74

Independent verification of traps with there characteristic low values of time constants responsible for the 1/f noise at f < 10 Hz and at a given value VG

*, corresponding to MOST bias condition is often lacking.n-MOSTs : a ∝ 1/VG

* ⇒ in favor of a ∆N interpretation, but a ∆µinterpretation is also possiblep-MOSTs : a = const. ⇒ in favor of a ∆µ interpretation

tNI NNNNNNSIS ∝∆∝∆∝= ∆222222 if/1///

Unsolved problem: α-values are not predictable with a high precision, only trend can be given. There is no theory for the shape of the 1/f spectrum


75

Faster MOSFETs are noisier [54], [56]

• Resistance:

• MOSFETs: SI th = SI 1/f ⇒

• “Highest” frequency fT

• New figure of merit for MOSFETs

kT = 1/40 eV, VG* = 1V fc = 47 × α fT ,; α= 2x10-5 fc = fT /103

2

2

/1

2

44

kTlVqfS

NfVkTRS cfVVth

µαα=⇒===

22

2*

/116

3l

lkTVq

f Gc ∝=

µα

22

*

/12

2/ ll

VCgf GgmT ∝==

πµπ

kTqV

ff G

T

c8

3 *πα=


76

αn = 1 × 10-4

αp = 6 × 10-6

2 < L < 100 µm3 < W < 300 µm

25Alcatel /Eindhoven Univ. 1989

αp = 9.6 × 10-510 × 0.50.2 < L < 2 µm

4.5IMEC /Eindhoven Univ. 1998

αp,n ≈ 1.9 × 10-6

SVeq ∝ tox ⇒ ∆µ0.18 < L < 0.5 µm

3 < tox < 16comparing different tox

STMicroelectronics2001

αn = 9 × 10-5

αp = 4.4 × 10-6

0.8 < L < 5 µm1.5 < W < 10 µm

17.5Univ. of Singapore

2001

αn = 5.7 × 10-5

without F implant 10 × 4

1.8multiple gate oxide process

Philips Research2001

αn = 1 × 10-410 × 101.5 nm < tox < 3.5 nmLeti /Grenoble

2001

α fromS I / I 2 = α / N f

W × lµm2

tox

nmSupplier/Group

Year

Some a values (10-6 < a < 3×10-4)


77

α-values from sub threshold bias

2.5 × 104αp = 5 × 10-52 × 10-910 × 24.5IMEC1998

1 × 1041.5 × 10-41.5 × 10-820 × 2.426Grenoble

1991

1.4 × 105

3.6 × 104

1.8 × 10-4

7 × 10-6

1.3 × 10-9 (T=300K)2 × 10-10 (T=77K)

200 × 15120Thomson

1984

2.9 × 1052.7 × 10-41 × 10-91040 × 10200Hitachi1977

N0α from

SI/I2 = α/N0f

Experimental plateau value

f SIs / Is2

W × lµm2

tox

nmSupplier

Year

fNISinqkTWlCN I

ox0

22

0 )/( α==


78

RTS noise is not 1/f noise [9, 11, 12, 13,14]

( )01or 1/

41

//21

)2(141

2

2

2

222

→⇒<>=

≤++

=∆

+=⇒

+∆

==

RTSIce

ecce

ce

ceNI

SKK

N

fN

NNS

IS

ττ

ττττ

ττττ

ττπ

τ

(RTS ∝ 1/N2) Small devices will suffer from RTS on top of the 1/f noise if : N < 1/αe.g., for α ≈ 3 × 10-4 ; N ≈ 3.2 × 103 NNfI

SI 12 ∝=

α

Prediction: “0.15 µm technology” tox = 3 nm , l = 0.15 µm, W = 1µm,VG

* ≤ 0.9 V or lW < 1µm2 : RTS problems on top of the 1/f noise


79

Misunderstandings [53]

1.1/f noise is different from RTS noise (uniformly distributed and local)•uniformly distributed 1/f noise source in device SI / I2 = α/Nf•RTS noise is due to one trap (local) close to Fermi level very bias and temperature sensitive (in contrast to 1/f )•RTS noise can be reduced (or increase) by switching bias techniques making τe / τc << 1 or τc / τe << 1 ( or τe / τc =1) after bias switch

2.Unified 1/f noise model BSIM3 ∆N + ∆µ(∆N) predicts the noise by applying non-physical model and using non-physical parameters

• ∆µ(∆N) induced Coulomb scattering at (1/f ) trap charges• µCit assumed to be constant ↔ experimental results and theory

( )

++= 2

221

Co

eff

inCo

eff

invFnt NN

ENkTµµ

µµ

γαinvCit N/1/1 ∝µ


80

1/f noise parameter

α

*GV

Increase in α at high Vgs is due to 1/f noise in the series resistance

2nd correction term is negligibly small

⇒ ∆µ - ∆N models cannot explain the Vgs-dependence of a for p-type MOSFETs


81Conclusions

1.1/f noise in MOSFETs is predictable with α values often observed in bulk Si between 10-6 and 3 × 10-4 ( SOS, SOI). Data collected over 35 years.Higher substrate dopes in scaling down processes → lower µ → lower α

Epi-layers lower α than CZ substrates with high O contentNon uniform channel higher 1/f noise

Lattice damage by implantation in the inversion layer region: α↑2.p-channel MOSFETs: VG

* independent α -value (about 10-6 on quality wafers, 3x10-5 on CZ wafers and 3x10-4 on old small diameter wafers. straightforward ∆µ interpretation.

3.n-channel MOSFETs in a CMOS technology with n+ poly gate often have α ∝ 1/VG

* dependence for 0.1 V < VG* < 1 V (straightforward ∆N- or ∆µ –

interpretation possible). α -values at VG* = 1 V 3 × 10-5

4.noise parameters in SPICE, BSIM are often geometry, oxide thickness and VG

* dependent poor predictions, different technologies are better compared in α-values obtained for the same N.


82

5. The observed dependence (2004 and 1971) Sveq ∝ tox points to the ∆µorigin. This holds for technologies with 3 nm < tox < 600 nm(∆N-noise holds Sveq ∝ t2

ox )6. Apart from serious 1/f noise in the series resistance of premature

technologies, the geometry dependence is well understood: SI @ VG* ∝

W/L3 for L > 0.15 mm ; SI @ VG* ∝ W/L for L < 0.15 mm but always

holds SVeq @ VG* ∝ 1 / Wl

7. In sub threshold: SI / I2 = α / N0 f with N0 = (kT / q2) Cox W l ⇒ same α-values. a is a perfect figure of merit to describe the 1/f noise in MOSTs (the contribution of one charge carrier to the relative noise in the conduction at f = 1 Hz) [lowest value ever observed in a bulk p-channel MOSFET is 4 × 10-7]

9. Some problems: (1/f noise = sum of RTS); 1/f due to trapping; traps calculated from 1/f noise; ∆N+ ∆µ(∆N) is a non-physical model; Sveq∝ tox or Sveq ∝ t2

ox a-values constant or ∝ 1/ VG* ?


83

V. Low frequency noise as a diagnostic tool for quality evaluation of electronic devices [20,57-69]

1. Types of noise1.1 Thermal noise : is fundamental and independent of technology,SV = 4.k.T.R (Brownian motion)

A) Calibration of noise measuring set up. For I = 0 the noise SV is proportional to Ta R0. If power dissipation P= I.V ≠ 0, SV is still proportional to T.R

B) Static heat resistance: Rtherm = T-Ta / IV → too high, problems in e.g.,SOA (104 K/ Watt) → higher harmonics, delaminating and temperature induced failures.


84

C) Transport mechanism / Ballistic transport? Hot carriers? Impact ionization? Thermal noise to investigate transport properties.

Deviations from SI = (2/3)4kTgm in MOST are indications for either or: avalanche phenomena, hot carrier effects, non uniformmobility along the channel.

Multi quantum well devices show a white noise comparable to the thermal noise in injection diodes, SI ~ Im .

MOSFETs biased in sub threshold also SI~ I


85

1.2 Shot noise : deviations from SI = 2qI for diode type structures:

A) calibration purposes B) junction quality, forward biased → series resistance problems, in reverse biased junctions e.g. gate of Schottkybarrier in MES- or MODFETs , : at low I, leakage current problems. Rsh in prototype structures: IV-IV, III-V and II-IV and at higher I, onset of micro plasmas or the quality of multiplication ( noise in the gain by multiplication, Mc Intyre) can be observed from the deviations from 2qI.

Beyond a critical local field [65] an onset of unintentional avalanche multiplication can occur that gives a weak increase in current and a strong increase in white (shot) noise


86

1.3 Conductance noise (∆σ) due to trapping A, Generation recombination noiseB, Burst-, popcorn- or RTS- noise

FEonstronglydependsNandN 4/11 2 ≤⟩∆⟨≡∆

Generation recombination noise is often observed in III-V devices.RTS noise is often an inevitable problem of submicron devices with traps and a low number of carriers like in MOSFETs, also a problem in diode type devices with dislocations in sensitive areas and quantum dot devices. In general strongly dependent on temperature and on bias conditions (EF position dependent) and therefore a poor device indicator, because traps can be avoided.


87

1.4 Conductance noise due to mobility fluctuations (1/f noise: current-, excess-, flicker- or low-frequency noise)

Pitfalls in interpretation ( traps, interface roughness and poor crystal quality due to lattice damage by implantation often go hand in hand)

Phenomenological approach with Hooge’s empirical relation

fNRSR α

=2

The 1/f noise parameter α (Hooge parameter αH) cannot be predicted but calculated from experimental results. Most values are in resistors, MOSFETs, MODFETs and BJTs between 10-6 and 10-4 .


88

2. The omnipresent 1/f noise is a favorite diagnostic tool2.1 Without RTS or GR-noise, there is still 1/f noise

Implantation and lattice damage due to proton bombardment and anneal temperature play a role. Interface (roughness) and implantation damage, make 1/f noise position dependent.

If a poor oxide with a high number of traps goes hand in hand with interface charges and roughness as a result of fast oxide growth on damaged poor crystal material, then the controversy about the bulk or surface origin of the 1/f noise is solved (reconciled)


89

The α-value represents the contribution to the relative 1/f noise at 1 Hz from one carrier ( electron or hole), assuming that the N carriers have uncorrelated contributions to the total noise. Thevalue is in principle dimensionless and independent of sample size, applied current and frequency at least for pure 1/f.

α-values can be used as a figure of merit without suggesting a ∆µ or ∆N origin for the fluctuations.

Its value depends on crystal quality in the current path and mobility. Current crowding always increases the effects of conductance noise on voltage or current noise. Overlooking this problem in 1/f noise always results in high apparent α-values [20, 60].


90

2.2 Contact noise as a diagnostic tool [16, 17, 17a, 20,21, 34, 57]

Current crowding goes hand in hand with increased power density ρJ2, heat dissipation, local temperature (hot spots), higher 1/f noisethan in homogeneous samples and higher risk of failures due to ∆T-based degrading mechanisms.

fndJnf

dJ

VS

eff2

2

4

2v

Ωα

≡

Ω

Ωα=

∫

∫

Ω

Ω⇒Ω= ∫Ω

dn

JfI

Sv

42

2

1 αρ


91

2x2/I)x(J π=

dxx2d 2π=Ω

adxx

xI

IR

a πρπ

πρ

22

22

2

22 =

= ∫

∞

Ω<<π=π

π

π

π=Ω

∫

∫∞

∞

3

24

2a

2

22

2a

eff a10dxx2

x2I

dxx2x2I

Constriction dominated contacts, equipotentials, approximationsand calculations

3

32

2/13

322

3

2

202020 ραπ

ρπα

πα

nR

VfSC

fnRV

fanVS V

fV =≡⇒==


92

Contacts with complications [17a]

l. interface :

2. multi-spot contacts (region- III) :

3. region-II multi-spot contacts:

In all cases strong deviations from the simple constriction dominated contact which results in:

taand a

t R 2

eff2 ππρ

=Ω≅ film

32

eff2

R R toalproportion of instead Ra11

RS

∝∝Ω

∝

3eff akand

akR ⋅∝Ω∝

ρ

constant is a if Rak

11RS

3eff

2R ∝

⋅∝

Ω∝

)20(5, ≈>>∝ mmwithRS mR

5RSR ∝


93

Experimental results on metal-semiconductor contacts [69] and movable contact on thick film tracks in potentiometers [59]

Full squarres: a film-dominated metal semiconductor contact with SR proportional to R3

Open symbols: three different constriction dominated movable contacts on a thick film track of a potentiometer with a contact resistance noise proportional to:

35 RSandRS RR ∝∝


94

Alloying of metal-semiconductor contacts under forming gas or pure hydrogen reduces the noise, this is no arguments for ∆N [20]


95

Calculated and experimental results of noise versus resistance of voids [64]induced by degradation. The noise is more sensitive than resistance only.

dAJ1 22 ⋅= ∫ ρ

IR

∫ ⋅= dAJ

fnI1S 4

2

4Rαρ

l

w 2a


96

Multi spot contact model on a cylinder [57, 60, 63,]

klb

=2

2

ππ

eAA

al

=2

2

ππ

2/1

=

eAAk

ab

L

A=π b2 Ae = π a2 k

LRh ∝


97

No contact problems

−+= 11

eh A

AkL

bRR 2bLRh π

ρ=

−

+= 1

201

2/5

eRR A

AkL

bSSh

No contact problems

hR

RR S

SS =*

hRRR =*

63

2

bnfLS

hR πρα

=


98

Noise model for BGA contacts

• Constriction resistance RC Degradation dependent• Access resistance fixed during degradation

cca

c

c

RRRRR

aca

ca

aa

SSSSSRRRRR

RRRRRRRR

≈⇒+=∆∆+∆+∆=∆

∆+∆=∆≈⇒+=

2222


99

Calculated Degradation (a-reduction) and m-values [74]

Degradation results in a reduction of the real electrical contact area Ae , by a reduction in the number of spots k and spot diameter 2a. This is provoked by aging tests like thermo-cycling, temperature-humidity tests or by mechanical bending

25≈∝ mwithRS mR

2

*

*

41

=

eR AA

SRm

We assumed in the following diagrams: k = 50, l = 120nm,

L = 5µm, 12nm < a < 60nm and 1% < Ae/A < 25%


100

100

101

102

103

104

105

10-3 10-2 10-1 100

R* and SR* versus A

e/A with k = 30

R* b/L = 0.1

SR* b/L = 0.1

R* b/L = 1

SR* b/L = 1R*

SR*

Ae/A

SR* (Ae / A)

R*(Ae / A)


101

100

101

102

103

104

105

100 101

SR

* more sensitive for current crowding than R*

k = 30 b/L = 0.1 m = 29.9 k = 30 b/L = 1 m = 7.7

SR*

R*

SR ∝ Rm

5 < m < 30


102

10-17

10-16

10-15

0.3 0.4 0.5

RP ( Ω )

C

0.6

CDM, 450, p=3

CDM, 250, p=3

CPoly, 100, p=3

CPoly, 250, p=3

10-17

10-16

10-15

10-14

0.3 0.4 0.5 0.6 0.7 0.8

C

R ( Ω)

10-13

Polysolder

Ablebond

DM4030 SR

C vs R after aging by thermo-cycling and bending of fresh samples [58]

6 < m < 25 and D = 6.3 m≈15


103

Conclusions on conductive adhesives [58, 63]

With noise measurements: you see more, C∝ Rm with m>> 3 points to a region II multi-spot contact with 0,4 % < Ae/A < 25%

in a shorter time (thermo-cycling and temperature-humidity tests last for weeks, while bending and noise measurements takes only minutes) and in an non destructive way (bending) a quantitative result.

5/2

≅=

unst

stress

e

eC

CAA

Dstess

unst


104

Investigation of new materials: polymer transistor [62]

Samples

• Channel material by spin coating:– pentacene– polythienylene vinylene (PTV)

• p-type accumulation FET• Au drain and source at the

bottom, poly-Si gate contact below

• glass substrate

Drain electrode (Au)Source electrode (Au)

metal gate

polysilicon gate materialSiO2 - gate oxide

spin coated organic semiconductor


105

Conclusion

• 1/f noise in organic FETs satisfies the empirical relation (geometry, illumination dependence)

• 1/f noise is (too) high, α ≈ 0.01 – 1.0

• High noise is due to current crowding between grains of organic material (leads also to apparent low mobility)

• No Au-polymer contact noise contribution in these samples


106

Investigation of new materials: WO3 nano particle films [61]

Sample description• WO3 samples• Made by advanced gas

deposition with reactive ambient gas: synthetic air

• Thickness: 0.1 - 4µm• Nano particles with lognormal

distribution with average size≈5 nm

• C12 = C13 = 2 C23 ⇒ no electrode interface problems

1 2 3


107

Discussion

Two kinds of noise were detectedThermal noise: explained by: SV = 4 kT Re[Z]1/f noise: explained by “shunted capacitor” model. Shunts are formed by Al spikes from the contacts on top of the WO3 dielectrics.

Al

WO3

ITO


108

Conclusions

Quality dielectrics do not show 1/f noise: (Ec;1/f > Ebreakdown)

Empirical relation is valid for nano particle sized Al wires αAl ≈2.5×10-3 assuming homogeneity

The thinnest WO3 layers deposited at the highest speed are porous and suffer from Al shunts which generate 1/f noise

Therefore 1/f noise can be used as quality assessment tool of WO3nanostructures.


109

3. Diode type devices (solar cells,) [66]

For long diodes holds

2

2 1fqIS

NfIS qNI II ττ

αατ

∝∝⇒⋅

==

For diode with series resistance contact problems 2ISI ∝

Traps can reduce carrier lifetime τ, increase I and 1/f-noise. This is not a proof for ∆N

too high α-values are an indication of non uniform current density at weak spots with very small τ-valuesexperimental results of solar cells


110

4. FET type devices and series resistance [67]

Modern short channel devices have series resistance problems

Four possible situations forsRSS = S and R + R = R

chRRsch +

3 *G

2ch

R*G

ch V1

NRSand

V1R

ch∝∝∝

0 *G

0 *Gs VandV R ∝∝

SRS

Four possible dependencies of SI / I2 on VG


111

All trends are observed [67, 68]

1*G

2RRRsch VRSSS and RR

Sch

−∝⇒>>

3*G

2RRRchs VRSSS and RR

Sch

−∝⇒>>

0 *G

2RRRchs VRSSS and RR

chS∝⇒>>

2 *G

2RRRsch VRSSS and RR

chS∝⇒>>

←poor technology


112

Conclusions on noise spectroscopy [20]

Different types of noise play a different role in reliability analysis

•1/f noise successful for lifetime characterization of metallization

•g-r noise traps (AlGaAs)

•RTS noise test submicron MOS technology

•thermal noise for heat contact diagnosis

•1/f noise general purpose diagnosis tool

crystal and device quality sensitive

always present especially in H.F. devices (small)


113

• crystal defects : α at low Tlow a value is not necessarily good crystal quality

• current crowding gives more 1/f noise, also a higher local temperature

• contacts : lowest limit no constriction, constriction, interface or multi-spot ( region I (Ae/A> 0.16), region II (0.01<Ae /A< 0.16), and region III (k and a estimation). The different dependence on contact resistance can be used as diagnostic tool for conductive adhesives

• diode type devices: traps can reduce minority carrier life time and increase 1/f noise. This is not a proof for number fluctuations

• series resistance in MES, MOD and MOS transistors


114

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117

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[47] L. K. J. Vandamme and L. S. H. Dik.” Bias-temperature treatment, surface state density, and 1/f noise in MOSTs”. Eds. Meijer, P. H. E., Mountain, R. D., and Soulen, R. J. , pp.244-247. 1981.Washington, NBS. Sixth International Conference on Noise in Physical Systems, Gaithersburg, MD April 6-10,1981 Proceedings of a conference held at the National Bureau of Standards NBS.

[48] L. K. J. Vandamme and R. G. M. Penning de Vries, "Correlation between MOST 1/f noise and CCD transfer inefficiency," Solid-State Electronics, vol. 28, no. 10, pp. 1049-1056,1985.

[49] L. K. J. Vandamme. “1/f noise in CMOS transistors”.Ed. Ambrozy, A.; pp. 491-494. 1990. Budapest, Akadémiai Kiadó. 10th International Conference on Noise in Physical Systems - ICNF 1989,August 21 - 25 1989, Budapest, Hungary.

[50] L. K. J. Vandamme, X. Li, and D. Rigaud, "1/f noise in MOS devices, mobility or number fluctuations? ," IEEE Transactions on Electron Devices, vol. 41, no. 11, pp.1936-1945, Nov.1994.

[51] X. Li, C. Barros, E. P. Vandamme, and L. K. J. Vandamme, "Parameter extraction and 1/f noise in a surface and a bulk-type, p-channel LDD MOSFET," Solid-State Electronics, vol. 37, no. 11, pp. 1853-1862, 1994.

[52] E. P. Vandamme and L. K. J. Vandamme. “ Unsolved Problems on 1/f Noise in MOSFETs and Possible Solutions”.2nd Int. Conference on Unsolved Problems on Noise and Fluctuations (UPoN) 481-486. 1999.


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[53] E. P. Vandamme and L. K. J. Vandamme, "Critical discussion on unified 1/f noise models for MOSFETs," IEEE Transactions on Electron Devices, vol. 47, no. 11, pp. 2146-2152, Nov.2000.

[54] L. K. J. Vandamme and G. Trefan. 1/f Noise in MOSFETs (ISBN 90-73461-29-4). pp. 195-208. 2001. "4th Annual Workshop on Semiconductor Advances for Future Electronics" -SAFE 2001 .

[55] L. K. J. Vandamme and G. Trefan. Low frequency noise (1/f and RTS) in submicron MOSFETs(28-11-2001) http://www.stw.nl/programmas/safe/proc-2001/Vandamme.pdf

[56] L. K. J. Vandamme. 1/f Noise in MOSTs: Faster is Noisier, Kluwer, 2004 Proceedings from ARW NATO, held in Brno August 2003,

[57] L. K. J. Vandamme. Opportunities and limitations to use low-frequency noise as a diagnostic tool for device quality. ICNF 2003, 17th Conference on Noise and Fluctuations. J. Sikula. Czech Republic:CNRL s.r.o. 735-748, 2003. ISBN 80-239-1005-1. August-2003.

[58] L. K. J. Vandamme, M. G. Perichaud, E. Noguera, Y. Danto, and U. Behner. 1/f noise as a diagnostic-tool to investigate the quality of isotropic conductive adhesive bonds. IEEE Transactions on Components and packaging Technology 22 (3):446-454, 1999.

[59] E. P. Vandamme and L. K. J. Vandamme. 1/f Noise and its Coherence as a Diagnostic Tool for Quality Assessment of Potentiometers. IEEE Transactions on components, packaging, and manufacturing technology - part A 17 (3):436-445, 1994.

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[60] E. P. Vandamme and L. K. J. Vandamme. Current crowding and its effect on 1/f noise and 3rd-harmonic distortion - a case-study for quality assessment of resistors. MICROELECTRONICS RELIABILITY 40 (11):1847-1853, 2000.

[61] A. Hoel, L. K. J. Vandamme, L. B. Kish, and E. Olsson. Current and voltage noise in WO3 nanoparticle films. JOURNAL OF APPLIED PHYSICS 91 (8):5221-5226, 2002.

[62] L. K. J. Vandamme, R. Feyaerts, G. Trefan, and C. Detcheverry. 1/f noise in pentacene and poly-thienylene-vinylene thin-film transistors. J. App. Phys. 91 (2):719-723, 2002.

[63] R. J. J. M. Jongen, L. K. J. Vandamme, H. H. Bonne, and J. W. C. de Vries. 1/f noise as a diagnostic tool to investigate the quality of anisotropic conductive adhesive (ACA) bonds for ball grid arrays (BGA's). Fluctuation and Noise Letters 3 (1):L31-L51, 2003.

[64] L. K. J. Vandamme and A. J. van Kemenade. Resistance noise measurement: a better diagnostic tool to detect stress and current induced degradation. MICROELECTRONICS RELIABILITY 37 (1):87-93, 1997.

[65] L. Benoit, N. Malbert, F. Verdier, N. Labat, A. Touboul, and L. K. J. Vandamme. Low frequency gate noise in a diode-connected MESFET: measurements and modeling. J. App. Phys. 48 (4):628-633, 2001.

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[67] J. M. Peransin, P. Vignaud, D. Rigaud, and L. K. J. Vandamme. 1/f Noise in MODFET'sat Low Drain Bias. IEEE TRANS. ELECT. DEV. 37 (10):2250-2253, 1990.

[68] X Li and L. K. J. Vandamme. 1/f noise in MOSFET as a diagnostic tool. SOLID-STATE ELECTRONICS 35 (10):1477-1481, 1992.

[69] L. K. J. Vandamme and A. Douib. Specific contact resistance and noise in contacts on thin layers. SOLID-STATE ELECTRONICS 25 (11):1125-1127, 1982.

[70] L. K. J. Vandamme. 1/f noise of point contacts affected by uniform films. JOURNAL OF APPLIED PHYSICS 45 (10):4563-4565, 1974.

[71] T. G. M. Kleinpenning and A. H. de Kuijper. Relation between variance and sample duration of 1/f noise signals. JOURNAL OF APPLIED PHYSICS 63 (1):43-45, 1988.

[72] H. J. Butterweck. Noise voltages of bulk resistors due to random fluctuations ofconductivity. Philips Res.Repts 30 (Issue in honour of C.J. Bouwkamp):316*-321*, 1975.

[73] T. G. M. Kleinpenning and A. J. Holden. 1/f noise in n-p-n GaAs/AlGaAs heterojunctionbipolar transistors: impact of intrinsic transistor and parasitic series resistances. IEEE TRANSACTIONS ON ELECTRON DEVICES 40 (6):1148-1153, 1993.

[74] L.K.J. Vandamme. To be published

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