Low frequency noise \(1/f and RTS\) in submicron MOSFETs - Free

3From the analysis of RTS-, 1/f- and thermal-noise in MOSTs weexplain 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 shotnoise, 1/f noise and generation-recombination (RTS-) noise areimportant for quality assessment in e.g., diode type devices like:solar cells, laser diodes, LEDs, avalanche photo diodes and bipolartransistorsApplications are e.g.,: contacts, conductive adhesive joints, thickand thin film resistors, parasitic series resistance or parallelconduction paths in devices like in: submicron MOS-, MES-,andMODFET and poly silicon emitter BJT and HBT.L.K.J. Vandamme / Noise / 26-02-2004

4Why knowledge of the physical origin of noise isimportant?a. Stochastic fluctuations set a detection limit to measuring systemsand telecommunication systemsb. 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 microplasmadue to non uniform fields in reverse biased (FET) junctions)Generation recombination-, and RTS noise (∆N→∆σ→∆R: avoidtraps)1/f noise (∆µ→ ∆σ →∆R: N or N eff not too low)L.K.J. Vandamme / Noise / 26-02-2004

52. Some definitions and remarks [1-4]Electrical noise is a real stochastic signal often described in terms ofvariance (σ 2 ), rms values or standard deviation (σ), average absoluteamplitudes (∆I ) or relative absolute amplitudes, e.g., ∆I / I, correlationfunction, C (τ), amplitude distribution function (pdf) or spectral noisedensity (S x (f)). There is a difference between: amplitude spectrum [x]and power spectrum [x 2 ], both are line spectra for periodic functions.The power density spectrum [x 2 / Hz] of the noise is continuous .Power often means x 2 , not Watt.”x” can be a fluctuation in time of voltage V, current I, resistance R,optical power P [Watt], magnetization (Ni / Fe), extinction coefficientof an optical fiber, or height along a line (surface roughness) [x 2 /(1/x)].Spectral density, S x (f) and correlation functions C(τ) of physicalquantities are real and we use positive frequencies.L.K.J. Vandamme / Noise / 26-02-2004

6Correlation functions: C 2 (τ) is a two-point correlation function [x 2 ]C 2 (τ) = ,C(τ) = C 2 (τ) and S (f) are two differentrepresentations of x (t). The cosine transform or the Wiener-Khintchine theorem or the so- called Fourier transform of C(τ)gives S(f):S(f )=4∞∫0C( τ)cos2πfτ.dτSpectral density Sx (f) is also defined as the variance of a bandpass filtered x (t), that becomes per bandwidth ∆f atfrequency fVariance 2 2∫ ∞0Sx( f ) df = ( ∆ x ) =σL.K.J. Vandamme / Noise / 26-02-2004

73. Analogue noise measurement set-up [5, 5a, 5b]AAC amplifier and sample in a cage of Faraday and output at A ismonitored with oscilloscope for 50Hz, 150Hz parasitic, do we have“normal Gaussian noise”, clipping or oscillations? At B, the signallooks like amplitude modulated carrier at frequency f with randomenvelope if ∆f is small enough, ∆V f (t). Variance of band pass filterednoise divided by ∆f gives the power spectral density: ∆V 2 f(t)S V≡L.K.J. Vandamme / Noise / 26-02-2004∆fB

8FFTFast Fourier Transform (FFT) systems (Spectrum analyzer) are basedon:“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., V 2 /Hz or V 2 sT 2 2S(fa) ≈ ( an+ bn) with fa=2" harmonics"On the next slide some FFT artefacts with rectangular windowingnTL.K.J. Vandamme / Noise / 26-02-2004

FFT of a sine wave of 1Hz, T = 1s; 1.25s; 1,5s → f 1 =1, 0.8, 0.66 Hz9L.K.J. Vandamme / Noise / 26-02-2004

Thermal- and 1/f noise, in time- and frequency domain, decomposition10V=I.(R+∆R)Top: thermal noise,bottom left and below:the 1/f noise in time andfrequency domain, at highfrequencies the thermalnoise always becomesvisible and can be usedfor calibrationS V(V 2 /Hz)S2∆Vf(t)∆f10 -11 figuur 2V≡10 -12 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 f (Hz)10 -13V = V + ∆V+V th10 -1410 -1510 -16L.K.J. Vandamme / Noise / 26-02-2004

111. Thermal noiseII. Noise Sources [6-11]Sv = 4 kTR and SI= 4kT/Johnson or Nyquist-noise: Phys Rev, 32 (1928)no 1, pp 97-113.R→ R eal [Z] and 1/R→ R eal [Y] white noise for 0 < f < 3x10 12 HzPhysicists avoid problems at f → ∞by replacing “kT ” withEngineers and material scientists multiply S V by 1/(1 + (fwith f 0 = 1/2πRC; τ = RC is a circuit time constant or the dielectrictime constant τ diel : τ with 0.1s > τ diel >10 -12 s fordiel= εoεr/ qµnmost dielectrics and for metals.We observe in a bandwidth ∆f a variance of the voltage or currentfluctuations given by = 4kTR ∆f or = (4kT/R) ∆fL.K.J. Vandamme / Noise / 26-02-2004R/ fo)2e)hfhf / kT−1

12Equivalent circuit for network analysis ( SPICE ) with test sourcesA noise free resistor with a noise voltage inseries or a noise current in parallel. The opencircuit resistance is not heated by the currentnoise source. The short circuited resistor isnot heated by the noise voltage! Equivalent,means equal to a certain level !eeeen1n1n2n=.e≠=n2eeen2= 0n12n1++= 0een22n2L.K.J. Vandamme / Noise / 26-02-2004Independent noisesources are added insquarred values, not innV/√Hz

13Origin of thermal noiseBrownian motion (1827) of free charge carriers (electrons 1897)Random motion of particles in a fluid (1827-1900) in plants, organicand inorganic material; due to light?; due to evaporation?; persistafter a year!; smaller particles move faster; motion increases withtemperature; molecular impact;In analogy: electrons within a conductor’s lattice make a randomwalk at T > 0K. Average kinetic energy of an electron:E 1 m*v2 th(3/ 2)kT2=kT= v 3 2th= ≈ 107 cm / s at T = 300Km*17nm < λ = v th τ < 300 nm for 50 < µ ( cm2 /Vs ) < 16000L.K.J. Vandamme / Noise / 26-02-2004

14For f < f c holds: for the short circuit current fluctuations S I = 4kT/Rand for the open circuit voltage fluctuations S V = S I R 2 = 4kTRThermal noise is independent of dc or ac current passed throughthe resistor. A temperature raise due to power dissipation can be takeninto account by adapting T in the above equations. Ohms law, and thesimple S V = 4kTR holds if collision time τ is not influenced by the field(v drift < v th ).We can expect deviations, if there are no collisions, (e.g. at 0 K at f >f c (THz) in very short time intervals and for resistors with a length L

15Remarks on thermal noise:Thermal noise is reduced by lowering the temperature, e.g., cryogenicapplications in satellites. In MOSFET design, very often wide and shortchannels are chosen to reduce equivalent input thermal noise voltage.Thermal noise and resistance measurements are used to measure thetemperature in hostile environments (neutron flux and other ionizingradiation).Equivalent voltage noise at the input of amplifier (S Vin = S Vout / G 2 ) areoften expressed in an equivalent noise resistance(@ 289K) or equivalentnoise temperature (has nothing to do with the real device temperature).R eq and T eq are equivalent noise parameters defined bySv in= 4kTReq( f )andSvsystem+ 4kTRTeq ( f ) = T + ∆T=>4kRL.K.J. Vandamme / Noise / 26-02-2004T

162. Shot noise [8]Stochastic emission of electrons is often like a Poisson process. Ifthe average transit time is t 0 = τ and G is the generation rate (s -1 ) ofelectrons at the cathode, then we have at the average = G. t 0crossing electrons underway. The noise is in the emission-time andalso in the transit-time due to initial velocity fluctuations.Nqτ2∆Nq22 qI = ∆I=( ∆I ) = ( ∆N )2ττ222 q qPoisson ⇒ ( ∆N) = N ( ∆I ) = N = I2τ τC(t) = 0 for t > t 0 (no overlap in populations) and for 0 < t < τC(t)=( ∆I)2(1−t/τ)L.K.J. Vandamme / Noise / 26-02-2004

S IS∞= 4∫C(t)cosω t.dt ⇒ C(τ ) = for t > τI0=o4qIτ(1 −)cos∫ ω tτ τ0( f ) = 2qIfor f

183. Generation Recombination Noise [10]∆N( t)=∆N(0) e− t /τN is number of free electrons, notconcentration, τ is lifetime of ∆N2 4τS n( f ) = ( ∆N)21 + (2πfτ)electenerand∞∫01 +GRConductionbandbandgaptrapsGeneration-recombination fromtraps4τdf = 12(2πfτ)2( ∆N ) =N?Is the smallest value of N, the number of full trapsand the number of empty traps. It depends on E F .L.K.J. Vandamme / Noise / 26-02-2004

19One single trap (∆N=1) and low N ==> RTS-noise; ∆I/I = ∆G/G =∆N/N = 1/N10Lorentzian-spectrum2S N / (4τ ∆ N )τ can be read from the spectrum10−6< τ [ s] f c = 1/2πτ [Hz] >1610 -210 -22πfτ10 -1 1 10L.K.J. Vandamme / Noise / 26-02-2004

204. Burst noise, popcorn noise, RTS noise [9,11-14]RTS-noise is a special case of generation recombination noise withone single trap, ∆N = 1, if τ e = τ c then = ¼ , has its highestvalueTwo level noise and superimposed 1/f noise in time domainand its amplitude propability density function (pdf)L.K.J. Vandamme / Noise / 26-02-2004

21Pure RTS without 1/f noise component has a Lorentzian spectrum.SISS4τI v Np= = = K⇒1/τp= 1/ τe+2 2 22V N 1+(2πfτp)RTS is a problem of submicron devices with traps, e.g., in diode typedevices with dislocations in sensitive areas and submicronMOSFETs with a low number of carriers. RTS is a poor (traps)device indicator. For strong asymmetric noise holds 2 → 0.Symmetric traps can become asymmetric in a MOSFET, by applyingswitching bias, but asymmetric ones can become symmetric21< ∆N> =2 + τ / τ + τ / τL.K.J. Vandamme / Noise / 26-02-20041/ τ2∆N1 τp τeτcK ≡ ⇒ or K = . =2222NN τ + τ N ( τ + τ )eeccceecc

22Analysis of RTS in time and frequency domain [13,14]V(t)8⋅10 4pdfLED#4kpdf examplesa6⋅10 4ϑi4⋅10 4Solid line: I d =2.15⋅10 -6 ADoted line: I d =1.53⋅10 -4 AV 00t-bτi2⋅10 40U, Volt-10 -4 -5⋅10 -5 0 5⋅10 -5 10 -4 2⋅10 -4The waveform of the measured noisedisplayed by the oscilloscopeThe probability densityfunction of the raw noiseL.K.J. Vandamme / Noise / 26-02-2004

Detection of noise in noiseV(t)a23ϑiTotal noise: V(t) = V 1/f(t) + V RTS(t)V 00-bτitState “1” (V(t) > V 0 ):State “0” (V(t) < V 0 ):V 1/f(t) = V (1) (t) – a ; V RTS(t) = +aV 1/f(t) = V (0) (t) + b ; V RTS(t) = −bV 0 threshold voltage to be found using the standardsignal detection theory in the noise backgroundL.K.J. Vandamme / Noise / 26-02-2004

8⋅10 46⋅10 4The pdf of the raw noise:pdfLED#4kpdf examplesNoise reconstructionW V( V )=q2πσ⎛⎜( V + b)exp−2⎝ 2σ2⎞⎟+⎠2 2 2p2πσ⎛⎜( V − a)exp−2⎝ σ2⎞⎟⎠244⋅10 42⋅10 4Solid line: I d=2.15⋅10 -6 ADoted line: I d=1.53⋅10 -4 AU, Volt0-10 -4 -5⋅10 -5 0 5⋅10 -5 10 -4 2⋅10 -4p = /( +)q = /( +)Probabilities forstates “1” and “0”Likelihood relation:Λ(V )=⎛p exp⎜−⎝( V− a)2σ22⎞⎟⎠⎛⎜( V + b)q exp−2⎝ 2σV(t)2⎞⎟⎠Λ =1V0=a−2b+2σa + blnabV 00aϑitL.K.J. Vandamme / Noise / 26-02-2004-bτi

25Obtained results after detection reconstructionaV 00-bVV 1/ft10 -12 S V, V 2 /Hz10 -1310 -14RTS1/fRAWIf 1/f and RTShave a differentdependence onbias, then thereis a differentphysical origin0t10 -15a0-bV RTS10 -16t10 10 2 10 3 10 4L.K.J. Vandamme / Noise / 26-02-2004f, HzRaw noise spectrum and its decomposition in a1/f and RTS

265. 1/f Noise [15-19]For metal-, semiconductor-, organic- samples with perfect contacts, holdsan empirical relation for the 1/f conductance fluctuations. Spectra are 1/f γwith 0.8< γ

27a) Experimental facts on 1/f noise1. For I = 0 → S R ∝ 1/f already exists as a conductance fluctuation inequilibrium.2. For I (dc) → S V = I 2 S R ∝ 1/ f (Ohm, ∆V = I∆R).3. I (ac)→ S V ∝ 1/( f c ±f ) ∝ 1/∆fnoise(up conversion of 1/f noise→phase noise in RF) (best values dependon f o ,-100 dB < dB c @ 10 kHz < -90 dBfor 10 -14 < C < 10 -13 ).4. Observable in homogeneous sampleswith a number of carrier N between 10 7and 10 14 . For N < 10 7 often homogeneityproblems, RTS-noise on top of 1/f, for N>10 14 detection problems, always 4kTR.L.K.J. Vandamme / Noise / 26-02-2004dB = 10Logc∆f = 10kHzSPP2c

285. ∆ρ is not due to ∆T: because samples with a negligible smalltemperature coefficient have the same 1/f noise as samples with anormal ∆R/R∆T=∆ρ/ρ∆T=-∆µ/µ∆T∆ρδ.∆Tµ ∝ T −δ ⇒ log µ = −δlogT + A ⇒ = ⇒ δ → 0 ⇒ ∆ρρ T6. omnipresent as a bulk phenomenon (S V /V 2 ∝ 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 magnetoresistivesensors (NiFe) and in devices like: (photo) diodes, laserdiodes, BJT, HBT, JFET, MESFET, MODFET and MOSFET.Exist also in non electronic systems: loudness in music; heartbeatfluctuations; electro encephalic-graphs during sleep or in the state ofattention→0L.K.J. Vandamme / Noise / 26-02-2004

30About the 1/N dependence, N in the empirical relation does notsuggest number fluctuations → noise source is distributed uniformlyin the volumeN∆σ∆N∆µ= + ⇒ ∆Nor ∆µor both? ⇒ G ∝ ∑ µσ N µii=1Mobility fluctuationsG ∝ N µ∆22G ∝ N ∆µiNumber fluctuations2⎛ ∆G⎞ ⎛ ∆N⎞G ∝ N µ ⇒ ⎜ ⎟ = ⎜ ⎟⎝ G ⎠ ⎝ N ⎠Poisson, or sub-Poissonian in bulk2∆N = pN with p = 1 or∆N 2 = pN [p < 1]⎛ ∆G ⎞2⎜ ⎟ =⎝ G ⎠pN⎛ ∆G⎞⎜ ⎟⎝ G ⎠L.K.J. Vandamme / Noise / 26-02-200422=N∆µN2µ2i2=1N⎛⎜⎝∆µµi⎞⎟⎠Or traps at interface, Fermiwith1∆N2=⎛ ∆G⎞⎜ ⎟⎝ G ⎠1N2+1N+21tP t=∆N2N2

31About N eff [17, 20,21]1/f noise is only detectable above thermal noise for N < 10 14 [71] (MOST;t ox = 2nm, L = 0.2µm, W = 2 µm, V G*= 46mV N = 2x10 3 )Inhomogeneous current density (current crowding) in homogeneousmaterial: N must be replaced by N eff

32Experimental facts in favor of a bulk origin for the 1/f noise [19,22-24]The relative 1/f noise at 1 Hznormalised versus N for Pt (dots), Au(full line) and GaSb (solid triangles).The dotted line is calculated withα=10 -4 and the full line [19, 22,23](Au and GaSb) with α=10 -3← metals, Au, Pt, GaSb; Si ↑ holds over morethan 5 orders of magnitude in volumeα-values for silicon samples with different volume.α is not a strong function of temperature and isvolume 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]L.K.J. Vandamme / Noise / 26-02-2004

338. ∆µ→∆ρ, 1/f-fluctuations are in the lattice scattering →∆µ andα-value is a parameter [25-27]Experimental values of α versus µ/µ lattat 300K. Circles denote p-type Ge withresistivities in the range of 4.5x10 -4Ωcm < 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 concentrationbetween 2.5x10 14 cm -3 < n < 10 17 cm -3 .Solid line: α proportional to µ 2L.K.J. Vandamme / Noise / 26-02-2004

34Physical origin for ∆µ due to 1/f fluctuations in lattice scattering [25]1 1 1= +Hypothesis: ∆µ latt ≠ 0 and ∆µ Coul = 0 ⇒µ µ latt µ Coul⇒dµ 2 =µdµµlatt2lattand⎛ ∆µ⎞⎜ ⎟⎝ µ ⎠2=⎛⎜⎝µµlatt⎞⎟⎠2⎛ ∆µ⎜⎝ µlattlatt⎞⎟⎠2⇒⇒SSR α meas µ ⎛ µ2 2R Nf µ µ ⎟ ⎞= = =⎜⎝ latt ⎠2αNflattαmeas=2( µ / µ ) latt αlattand⎛⎜⎝D=µkT⎞⎟⇒q ⎠∆µ=µ∆DDL.K.J. Vandamme / Noise / 26-02-2004

359. 1/f noise is in the lattice scattering [25]α⎛ µ ⎞= ⎜ ⋅αµ⎟⎝ latt ⎠2lattA 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 qualityeven if µ ≈ µ latt.On top of the ubiquitous lattice scattering there may be numberfluctuations of the McWhorter-type or several generationrecombination contributions. This often leads to 1/f-like spectra~1/f γ with a frequency exponent 1.15 < γ

36α is not a constant, and not predictable with a high precision [23, 60]α versus thickness ton bismuth samples1/λ = 1/λ b + 1/t [28]α vs V G [29], inn-type Si layer.α is high ifcarriers are atthe surface inaccumulation.In depletion(carriers awayfrom surface)low α-valuesare observedL.K.J. Vandamme / Noise / 26-02-2004

37-3log10. α depends oncrystal quality-4-5-1T an (K -1 )-68 x10 -4 1.5x10 -3α vs reciprocal anneal temperaturein boron implanted S i. The dots areobtained at T = 300K, the squaresindicate results at T = 77K. The dottedline through the results at 300K showthe proportionality with activationenergy of 1.1eV. [30, 31]α versus versus proton flux in irradiated n-GaAs. α-values at T = 78 K (•) and at T = 295K (0) versus irradiation doses Φ. The solidline shows proportionality between the lowtemperature α-values and proton irradiationdose Φ. The dose-independent α-values@300K (broken line)[32]L.K.J. Vandamme / Noise / 26-02-2004

38Remedies to reduce 1/f noise1/f noise is inherent in the conduction and cannot be avoided. Devicescan be designed in such a way that 1/f noise is reduced at the cost ofdevice area and speed. Avoid that the current is carried by a smallnumber 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, thickfilm resistors consisting of touching grains, too thin film resistors), hightech conductive adhesives, N eff

39b) Some 1/f Noise problemsfh2CVS V is divergent for f → 0 and the variance∫2 fhdf = CV lnfffllis logarithmic divergent for f l → 0 and f h →∞ . This can be solvedby introducing two corner frequencies: one where S V levels off for f< f lc and a second cut off frequency f hc where holds that S V becomesproportional to 1/f 2 for f > f hc . However, f lc and f hc have never beenobserved. The 1/f noise component disappears in the thermal or shotnoiseat high frequencies. A finite measuring time (10 periods of 10 -7Hz in 3 years) and thermal stability problems set a limit at the lowestfrequencies. The variance of 1/f noise increases logarithmically withmeasuring time. A plot of the measured variance (linear) over a timet meas versus the logarithm of t meas is an other way to measure 1/f noisewith a drift free and sensitive dc voltmeter [71]σ2tmeas=< ∆V2>tmeas=CV2lnfhtmeasL.K.J. Vandamme / Noise / 26-02-2004

40Controversy 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 < 10 7 s ; McWhorter model → 1/τ distributionexplained 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, hotcarrier mobility, diffusion coefficient in diodes, and α~µ 2 by changingthe ratio of lattice scattering and Coulomb scattering changes µ, but alsoα. It can only be explained by ∆µ latt ≠ 0 and ∆µ Coul = 0.L.K.J. Vandamme / Noise / 26-02-2004

41SummaryFluctuation in Spectrum RemedyThermalShotV,I: resistance-typedevices, MOS-FETS,MOD-, MES-,J-FETSI: diode type devices,BJT, HBTS v =4kTRS I =2qINo, low Rand T, high µsensorsNo, FanofactorG-RN, conductance:semiconductorsFermi level positiondependent2< ∆N> 4τNo trapsS N=21+(2πfτ) No noiseLorentzian1/f R: in metals, liquidspolymers andsemiconductors∝ 1/fL.K.J. Vandamme / Noise / 26-02-2004? Avoid submicron. It isnot dependenton Fermi level

42III. Sensitivity coefficient for current crowding [17, 17a,33, 34, 72]Important for conductance fluctuations with inhomogeneous currentdensities. A distributed system is considered as a limit case of a network.A local change in the resistivity will provoke a voltage fluctuation if aconstant current is applied. In a arbitrarily-shaped sample holds forresistance R and conductance G between two contacts1∫21∫22 2R = ρJdΩ⇒ G = σE. dΩ⇒ I R = V G =∑(Pdensity)∆Ω2 2IΩVΩThe total dissipated power is the sum over the whole sample volume Ωof the power density multiplied by sub volumes dΩ. For a homogeneoussample submitted to uniform electric field E (J is constant) the well knowequation is obtained, R = ρL/ A = 1/ GL.K.J. Vandamme / Noise / 26-02-2004

43The sensitivity coefficientthe sub area where the resistivity increase occurs, Ω lδ V /δρis taken from the derivative inVδ1 21= ∫2 Vρ J d Ω ⇒ = ∫ J dΩwith dimension [ A/cm]Iδρ I Ω lFor a homogeneous increase in resistivity over the complete volume,the integral must be taken over Ω . The voltage or current fluctuationis given by the product of the sensitivity coefficient and ∆ρ or ∆σ1∆ = ∫2V ∆ρJdΩI Ω l1∆ = ∫2I ∆σEdΩV Ω lIf the 1/f noise source is spatial uncorrelated and distributedhomogeneously over the sample the empirical relation can be appliedon a sub volume which results inL.K.J. Vandamme / Noise / 26-02-2004

44Sv1= ∫ 2I fΩ2αρ Jn4dΩandV222 1 ⎡ ⎤2 ρ ⎡= =2 ⎢∫ρ J dΩ⎥2 ⎢∫IΩIΩL.K.J. Vandamme / Noise / 26-02-2004⎣⎦⎣J2⎤dΩ⎥⎦In homogeneous samples: α, ρ and the concentration of free carriers ncan be in front of the integral. The relative voltage fluctuation becomesSVΩv2eff=α⎡nf ⎢⎣=⎡⎢⎣∫Ω∫Ω∫Ω∫ΩJJ42dΩ⎤dΩ⎥⎦22⎤J dΩ⎥⎦4J dΩ2≡αnΩ< Ωefffthe effective number of carriersN eff = nΩ eff is given by theeffective volume Ω eff that seemsto be concentrated at the spots ofthe highest current density.Only for uniform current density(J constant) holds Ω = Ω eff2

45Some applications, contacts and sensors [17, 17a, 33, 35, 36]L.K.J. Vandamme / Noise / 26-02-2004

Contact noise (constriction dominated, no interface or multispot)46Top: Qualitative shape of current and equipotentiallines of a circular contact on a thick homogeneoussample.Bottom:Simplified model of a point contact on. Thesemi circles represent hemispherical equipotentialsurfacesR ∝ ρ / aNSReffR2=∝Ca31/ff=Nαeff∝R3C 1/fvs R at T=300 K for two alloyswith negligible temperaturecoefficient [34]• Manganin; o Constantan. Thelines are drawn using a bulk 1/fnoise origin. The full line is formanganin with α = 6 × 10 -4 , thedotted line is for constantan withα = 1.2 × 10 -4 . ∆ρ/ρ∆T→0, 1/f notcaused by temperature fluctuationsL.K.J. Vandamme / Noise / 26-02-2004

47Point 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 77and 300K, with and without H 2 O 2 treatment, (native oxide thickness). p-typeInSb, @ 300K, intrinsic ”n-type”, dope 10 15 cm -3 and ρ 77K / ρ 300K = 10 3L.K.J. Vandamme / Noise / 26-02-2004

48Remarks on current crowding and interfacesDeviations from homogeneity in electric field and current density insamples with homogeneous properties in ρ,n, and noise result in anincrease 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 ofJ is much higher at weak spots. Due to a poor local crystal quality,2 γdepletion at crystal boundaries or a native oxide, α and the 1/fiρi/ nifnoise is higher.L.K.J. Vandamme / Noise / 26-02-2004

49For samples with 4 contacts: [33,35] a pair of current contacts, D 1 , D 3(drivers) and 2 voltage contacts, Q 4 , Q 2 ,(sensors) holds for the 1/f noise21 αρ ~~=J • J represents the dot product of the∫2SVQ( J • J ) dΩ2 ~I nftwo current densities with J thecurrent density in the ad joint situationby interchange of the current source Ifrom the driver contacts to the sensorcontacts. Areas with conductivityfluctuations where the J and J ~ areperpendicular do not contribute to theobserved voltage noise at the sensorcontacts. For a given current I at thedriver contacts, we always find highervoltage fluctuations at the currentcontacts, than at the sensors [36]Hall sensorL.K.J. Vandamme / Noise / 26-02-2004

50IV. Noise in devices: resistors, diodes, BJT, MOST1. Resistors [5b]1/f Noise only exceeds thermal and amplifier noise above a certainminimum power dissipated in the sample:αVfN2>4kT(R2⎛ L4kT⎜⎝ qµNIf R eq 4kTf / αqµ⇒ E [ 4 kTf / αqµ] 21crit=Req)=+Req⎞⎟⎠Dielectrics, low (hopping) µ, E crit >> E break down → ”no” 1/f noise, it is notdetectable. Dielectrics with soft or hard breakdow show high 1/f and RTSnoiseL.K.J. Vandamme / Noise / 26-02-2004

51Power density criterion for metals and semiconductors⇒2αρJf crit=4kTnρ J 2 > 4kTfn / α6 2In thin metal layers (ρ ≈3.10 -6 Ωcm ):J < J =maxx10A /2 cmPd 2x10 6 A/cm 2 . Electromigration damage, drift andcurrent induced non stationary 1/f γ –noise (with γ>2) will occur forJ>3x10 6 A/cm 2.L.K.J. Vandamme / Noise / 26-02-2004

52f max for homogeneous semiconduc. resistors at highest current densityJ max≅qnvth⇒P dmax= ρ J2 = kTn / τ ⇒maxf cmax =τ = 10 -12 s, collision timeα4τN < 10 14 criterion: from the choice f crit =100 Hz (to be able to judge a 1/fspectrum from 1Hz on) and a maximum power dissipated in a samplevolume Ω at T=300K, P d Ω < 0.1 Watt, and an α = 1.6x10 -3 follows⇒fcrit=α ρ J4kTn2 2α ρ J Ω α PdΩ⇒nΩ =4kTfcrit=N=max4kTfcritA sample resistance R larger than R eq and with N < 10 14 is always a safestart to be able to detect 1/f conductance fluctuations above the thermalnoise under reasonable bias conditions.L.K.J. Vandamme / Noise / 26-02-2004

531/f noise of m resistors in series or in parallelFor m resistors in series holds:mm 2SRiαS= ⇒ = ∑Rα R⇒ = ∑jR Ri≠22 2mRiNifi=1 R f R j=1 Nj∑i=1For m conductors in parallel holds:≠ ⇒ = only for R = R or G = G and N =ijijiNjα /mm 2SGiαS= ⇒ = ∑Gα G⇒ = ∑jG Gi≠222mGiNifi=1 G f G j=1 Nj∑= 1fNiiα /fNiProof is based on the empirical relation and uncorrelated noisesources: = 0 for i≠jL.K.J. Vandamme / Noise / 26-02-2004

54The 1/f noise can be quite different for resistors with the samethermal noiseThin film resistors all having the same thickness and width, lengthratio: W/L, will show the same thermal noise but a different 1/f noise:S R ~ 1/WL.Resistors with the same ratio of length over cross section : L/Wt with tthe thickness, will show the same thermal noise but a different 1/fnoise: S R ~ 1/WLtA noisy but small series resistance in series or a small but noisyleakage conductance in parallel can be very annoying.This makes 1/f noise a very useful diagnostic toolL.K.J. Vandamme / Noise / 26-02-2004

55Overlooking a small, but noisy series resistance or small leakageconductance in parallel can result in apparently high α-values. Thatis one of the reasons of a wide spread in 1/f noise and α-values.m resistors in series and n lines in parallelFor a resistance with value R consisting of a network of n branches inparallel, with each branch consisting of m resistances in series; all withthe same average value r and 1/f noise value S r results a resistance and ina relative 1/f noise given by:R=m rn⇒SRR=21m nSrr2For m=n, R=r, and the thermal noise remains 4kTR, but the 1/f noiseof the network is the 1/f-noise of one resistance r reduced by n 2.L.K.J. Vandamme / Noise / 26-02-2004

56Decomposition of a spectrum for frequency index analysis inthree independent componentslog S V (V 2 /Hz)The precision in the calculated frequencyindex of 1/f γ noise is reduced by a lack offor a poor decomposition of spectra.1/fG-RAt low bias, a competition of thermalnoise, white background noise gives toolow γ-values and at strong bias often anadditional non-stationary current inducednoise and drift with a 1/f 2 dependenceresults in too high γ-values4kTR1/2πτlog f(Hz)L.K.J. Vandamme / Noise / 26-02-2004

572. 1/f noise in long and short diffusion dominated diodes [37-39]If V > kT/q then I ∝ I 0 exp(qV/kT) and I ∝ I 0∝ D/L and with D/µ= kT/q holds I ∝ (µ/τ) 1/2 with I 0the saturation current, D thediffusion coefficient of the dominant carriers, L the diffusionrecombination length defined by (Dτ) 1/2 , τ the minority carrierlifetime, and µ the mobility. Hence holds: ln I = 1/2 ln µ + constant,thus: ∆I/I = ½ ∆µ / µ and S I/ I 2 = ¼ S / µ µ2 and I=qN/τ (chargecontrol) [37-39]S1/IIfSµα1 1/= = ⇒ SI==2S4µ2shotI(f)4Nf(q4αIτfL.K.J. Vandamme / Noise / 26-02-2004)1/ f= SIf ⇒ fc=α8τfqαI4τfAt the corner frequency f c holds S Ishot = 2qI = S 1/f (f c )

Corner frequency f c in long diodes, is current independent onlywhen the 1/f noise only stems from one type of current (withe.g,, ideality factor =1) and α is homogeneousf c=α8ττ is large, slow device ; low 1/f noiseτ is small, fast device; high 1/f noisef c independent of current and device area10 -2110 -2210 -2310 -2410 -25S I[A 2 /Hz]f cf [Hz]5810 -20 10 0 10 2 10 4 10 6 10 8f c is a real figure of merit, if there is 1/f and shot noise onlyτ in III-V direct band gap semiconductors

No edge effects in diodes ifSI∝IAkxifk=x+159A ≡ A AA = A 1 +A 2SI∝fJγk( A( A11++AA22))xk≡⇒SI∝( JAA1x1)k+( JAA2x2)kSI∝Jk( A1+fγA2)( k −x)≡SI∝Jfkγ( A( k −x)1+A( k −x)2)Holds only for any A 1 and A 2 if: k-x=1L.K.J. Vandamme / Noise / 26-02-2004

60If there is no perimeter effect (in mature technology) then⇒SIAkI∝ =γ k −1fJfkγAComparing noise at the same current leads to S I ∝ 1/A k-1 or at the samecurrent density (junction voltage) leads to S I ∝ A.shot noise: γ = 0, k = 1 (no perimeter effect)1/f noise: γ =1, and 1 ≤ k < 2 ( for η 1 and η 2 contributions, or seriesresistance noise gives k = 2)k = 1 then holds for S 1/f = αqI/4τf often observed in SiL.K.J. Vandamme / Noise / 26-02-2004

61k > 1 often observed in poly-emitter BJTs, HBTs (III-V) and SiGe BJTscan be explained by either an α-profile increasing towards the junction,or by different contributions of the current components with idealityfactor η 1 , η 2 to I and S I ;I=I 1 (η=1) +I 2 (η=2) and S I = S I1 + S I2If, I ≅ I 1 ∝ I 2 2 ; and if S I ≅ S I2 ∝ I 1/2 or I ≅ I 2 ∝ I 11/2;and S I ≅ S I1 ∝I 2IkS k −1 k −1I∝I J1/f τ k −1⇒ fc∝ ∝fAk −1τ τand f c becomesAfor the same A, current dependentfor the same current, f c ∝ 1/A k-1for the same J, independent of Afigure of merit, f c without mentioning I or J becomes doubtful.L.K.J. Vandamme / Noise / 26-02-2004

623. Noise in BJTs and HBTs [40-44]pnI3pIIIII~IWW4 1 25• r e ,r b, r c: 3x3 (thermal, 1/f-, and g-r noise) = 94 3 5• e-b, b-c junctions (short diode) 2x3 (shot, 1/f, g-r) =61 2In total: 15 possible independent noise sources (15 = 9+6)L.K.J. Vandamme / Noise / 26-02-2004

631/f noise in series resistances (high dope, low noise)α r2e,br=e ,f Ne , b effectiveSbkI I BS b∝SVre , b=I2e,bfα rAbout (1/2 ≤ k ≤ 2)N2e,be,b effectiveqV qVkT 2kTI B = I e I e10 +20SIb∝ID1 +2WeIτ2jI B= I 1+ I2⇒I B dominated byS Ib⇒dominated by I 1 or I 2I 1→2IB∝ I 1 ; I B ∝ I 2I 2→IB∝ I 2 ; I B ∝ I 11/ 2S ∝IIbS ∝IIbB2BDW2eDW2eL.K.J. Vandamme / Noise / 26-02-2004SSIbIb∝∝I1/ 2BτIτjjB

64f c / f T a new figure of merit [42]Highest f T , highest f cUnit current gain approximatedf T11= ≈2πτ 2π( τ + τ + τ + τ + τ )f Tec≤jejc12π ( τ + τBloadA new empirical relation if f cand f T ∝ 1/(τ B +τ c )c)T≅Bα8If 1/f noise is dominated byfcαnative oxide than >>fffTc8cf T(GHz)302225305446403010f c(Hz)500≈ 4x10 4≈ 4x10 43x10 5> 10 5> 10 63003x10 37005000L.K.J. Vandamme / Noise / 26-02-2004α1.3x10 -71.5x10 -51.3x10 -58x10 -5>1.4x10 -5>1.7x10 -46x10 -86x10 -71.9x10 -71.9x10 -7CommentSiGe (IBM)AlGaAs/GaAs (TI)GaInP/GaAs (Thompson)AlGaAs/GaAs (NEC)InGaAs (NEC)SiGe epitaxial polysiliconemitterSiGe MotorolaSiGe MBE (Daimler-Benz)

Experimental results: poly-emitter Si BJTs [42]65Author, publication year, affiliationk inS Ib ∝ I bkComments onfS Ib /I b [A], f c , α, area APong-Fei Lu (1987) IBMk ≈ 1.52x10 -17 -5x10 -16 , 2kHzKleinpenning & Holden (1992) Eindhovenk = 13x10 -16 -5x10 -15 , 2x10 -6 < α < 2x10 -5Mounib et.al. (1993) Grenoblek = 110 -16 , 330 Hz (A E = 10x10 3 µm 2 )Quon et. al. (1994) CaliforniaMarkus & Kleinpenning (1995) EindhovenMounib et.al. (1996) GrenobleSimoen et. al. (1996) IMECMarkus et. al. (1997) Eindhovenk = 11.2 < k < 1.8k = 2k = 2k = 1.3k = 1k = 1.8k = 2L.K.J. Vandamme / Noise / 26-02-2004no oxidethin oxidethick oxide7.5 Å oxide, S Ib ∝ I B2 /A (no perimetereffect)A E = 10x10 3 µm 2 , 2x10 -17 < fS Ib /I B

66Experimental results III-V HBTs npn – GaAs/GaAlAs10 -1510 -16S Ib[A 2 /Hz]S Ib ∝I B3/210 -14S IC[A 2/Hz]10 -17→∆µ10 -1610 -1810 -1910 0 10 1 10 2 10 3I B[µA]•, , • Kleinpenning – Holden (1993) [73], • Tutt et al. (1990, 1992) Jue et. al. (1989)• Costa et. al. (1992,1994) Plana et. al. (1992);10 -1810 -20SL.K.J. Vandamme / Noise / 26-02-2004I [µA] C10 0 10 2 10 4IkCI c∝ 1.3 < k < 1.4f∆µ – model with 2x10 -5 < α < 3x10 -3

67Discussion and conclusions [40, 42]•1/f noise is unavoidable / RTS- or g-r noise on top of the 1/f noise with1/(1+(2πfτ) 2 ) can be avoided by avoiding traps. Some III-V HBT havean “inherent” g-r noise, e.g., GaAlAs with Al > 20%, often shows τ ≤ 10 -4s and a f g-r ≥ 1.6 kHz.A new figure of merit is proposed: f c / f T ≈ α /8 useful to comparetechnologies. The lowest values of f c /f T are from SiGe devices.Native oxide at the poly-emitter results in more 1/f noise (S V ∝ α iJ 4 /n i3 dΩ ). 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 candominate the 1/f noise of the junction.L.K.J. Vandamme / Noise / 26-02-2004

68•Contact noise, S IBE ∝ I B2 , I E2 visible at higher currents contributions of∆r e , ∆r b and on top of the 1/f noise, often GR noise with τ ≤ 10 -4 s•S Ib ∝ I bk 1 ≤ k < 2 can be understood as ∆µ noise either by a nonuniformα-profile increasing towards the junction or noise and currentdominated by different areas (depletion layer or outside space chargelayer) 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 aremobility fluctuations: D/µ = kT/q ⇒ ∆µ/µ= ∆D/D.•For long diodes τ is the minority carrier lifetime at the low dopedside of the junction. For a short diode it is the transition time W 2 /D(W = emitter or base width, D diffusion coefficient.)L.K.J. Vandamme / Noise / 26-02-2004

694. MOSFET [45-55]• Substrate dope: 10 14 < N A (cm -3 )

1/f noise in MOSFETs (Geometry and bias dependence) [48-50]70Equations in terms of αOhmic region V d

SSIsVeq=2αINf=SgEquations in terms of α2sIs2m==2αg4CαV2Cox*Gox2mVWlVqWlf*2G*Gqfαg=2Ct∝ox∝Wl2mox1Cg*GV qWlfSKKIsaaCircuit-oriented parameters, bias….dependentK≡Ca2oxor[2 2Coulomb /m ]= αqV2gmWlf*GCox/ 2SVeqKa≡C Wlf2ox71Sub threshold [52]gSINmI2S0= Iq / ηkT==veq( N + N )Coxα0f≈I∝αN fWl(kT / q)/q2αη kTC Wlfox0kTe qV G /η( N>= kT [ Coulomb V]qox

72Experimental Results vs Wl, V G and I sat [50, 51, 54,55]10 -910 -10f S Veq(V 2 )"5"Sveq ∝toxWl10 -4αSurface channel10 -11"3""2""1"10 -510 -12"4"10 -6Bulk channel10 -1310 -7V G * (V)10 -8 10 -12 10 -11 10 -10 10 -9 10 -8 10 -7 10 -610 -14The equivalent 1/f noise S Veqat 1 Hz (fS Veq) versus the area W × L. Theextrapolated values at 1 Hz (f S Veq) of the1/f noise measured for “1” t ox = 600 nmand “2” t ox = 150 nm, at f = 1 kHz, 25µm technology; α p = 1.7 × 10 -4 ; S Veq ∝ t oxfor “3” and “4” t ox = 100 nm, at f = 10 Hz,α n = 10 -4 @ V G = 1V; α p = 10 -6 ;for “5” t ox = 12 nm, 0.6 µm technology,at f = 100 Hz, α n = 10 -4 [54]W x L (m 2 )10 -2010 -2110 -2210 -2310 -24f S Isat(A 2 )slope = 3/2I sat(A)10 -3 10 -1 10 0 10 1The 1/f noise parameter α versus V G*for a surface(p+poly) and bulk(n+poly) p-MOST. The α–values are calculated with eq. (2) fromexperimental results obtained in the ohmic region [50,51] : ∆ surfacechannel with L = 5 µm, surface channel with L = 0.8 µm,ο bulk channel with L = 5 µm, bulk channel with L = 0.8 µmThe quantity fS Isatversus the saturation current I sat.The results obtained on n-type MOSFETs show apower low with exponent 3/2 [54]10 -19 10 -7 10 -6 10 -5 10 -4L.K.J. Vandamme / Noise / 26-02-2004

73n-MOSTs often show a surface origin, tunneling (∆N), Experimental factsin favor and at variance with ∆N, 1/f ∝ N ss ? [47, 48]The equivalent input noise at1 Hz and V G* = 1V versusx 0 D 0 [cm 2 eV -1 ]. The dottedline follows the McWhortermodel. [48]The equivalent input noise at 1 Hz and 1carrier(α values) versus x 0 D 0 [cm 2 eV -1 ]. [47] Thedotted line follows the McWhorter model.1…6are n- channels, b,c,d,e,f are p- channelsL.K.J. Vandamme / Noise / 26-02-2004

74Independent verification of traps with there characteristic low valuesof time constants responsible for the 1/f noise at f < 10 Hz and at agiven value V G* , corresponding to MOST bias condition is oftenlacking.n-MOSTs : a ∝ 1/V G* ⇒ in favor of a ∆N interpretation, but a ∆µinterpretation is also possiblep-MOSTs : a = const. ⇒ in favor of a ∆µ interpretationSI/ I22 2 2 22= S ∆ N/ N ∝∆N/ N ∝1/N if ∆N∝NtUnsolved problem: α-values are not predictable with a highprecision, only trend can be given. There is no theory for theshape of the 1/f spectrumL.K.J. Vandamme / Noise / 26-02-2004

75Faster MOSFETs are noisier [54], [56]• Resistance:SVth=4kTR=2V α=NfSV 1/f⇒fcαqµV=4kTl22• MOSFETs: S I th = S I 1/f ⇒fc=3αqµV16kTl* 2G2∝1/l2• “Highest” frequency f T• New figure of merit for MOSFETskT = 1/40 eV, V G* = 1V f c = 47 × α f T , ; α= 2x10 -5 f c = f T /10 3gL.K.J. Vandamme / Noise / 26-02-2004fT=m*µ VG/ 2πCg= ∝1/l22πlffcT=3παqV8kT*G2

76Some a values (10 -6 < a < 3×10 -4 )Supplier/GroupYeart oxnmW × lµm 2α fromS I / I 2 = α / N fLeti /Grenoble20011.5 nm < t ox< 3.5 nm10 × 10α n = 1 × 10 -4Philips Research20011.8multiple gate oxide process10 × 4α n = 5.7 × 10 -5without F implantUniv. of Singapore200117.50.8 < L < 5 µm1.5 < W < 10 µmα n= 9 × 10 -5α p= 4.4 × 10 -6STMicroelectronics20013 < t ox< 16comparing different t ox0.18 < L < 0.5 µmα p,n≈ 1.9 × 10 -6S Veq ∝ t ox ⇒ ∆µIMEC /EindhovenUniv. 19984.510 × 0.50.2 < L < 2 µmα p= 9.6 × 10 -5Alcatel /EindhovenUniv. 1989252 < L < 100 µm3 < W < 300 µmα n= 1 × 10 -4α p= 6 × 10 -6L.K.J. Vandamme / Noise / 26-02-2004

α-values from sub threshold bias77SupplierYeart oxnmW × lµm 2Experimentalplateau valuef S Is/ I2sα fromS I/I 2 = α/N 0fN 0Hitachi19772001040 × 101 × 10 -92.7 × 10 -42.9 × 10 5Thomson1984120200 × 151.3 × 10 -9 (T=300K)2 × 10 -10 (T=77K)1.8 × 10 -47 × 10 -61.4 × 10 53.6 × 10 4Grenoble19912620 × 2.41.5 × 10 -81.5 × 10 -41 × 10 4IMEC19984.510 × 22 × 10 -9α p= 5 × 10 -52.5 × 10 4N= CWl(kTq20 ox/ )inSII2L.K.J. Vandamme / Noise / 26-02-2004=αN f0

78RTS noise is not 1/f noise [9, 11, 12, 13,14]SII2∆Nτ=2/ τ=S I = α ∝12I Nf NecSN=N2=12( 2 + τ / τ + τ / τ )K>Ne1or11c4τ∆N+K(2πfτ)

79Misunderstandings [53]1.1/f noise is different from RTS noise (uniformly distributed and local)•uniformly distributed 1/f noise source in device S I / I 2 = α/Nf•RTS noise is due to one trap (local) close to Fermi level very bias andtemperature sensitive (in contrast to 1/f )•RTS noise can be reduced (or increase) by switching bias techniquesmaking τ e / τ c

801/f noise parameterα*V GIncrease in α at high V gs is due to1/f noise in the series resistance2 nd correction term is negligiblysmall⇒ ∆µ - ∆N models cannotexplain the V gs -dependence of afor p-type MOSFETsL.K.J. Vandamme / Noise / 26-02-2004

Conclusions1. 1/f noise in MOSFETs is predictable with α values often observed in bulkSi between 10 -6 and 3 × 10 -4 ( SOS, SOI). Data collected over 35 years.Higher substrate dopes in scaling down processes → lower µ → lower αEpi-layers lower α than CZ substrates with high O contentNon uniform channel higher 1/f noiseLattice damage by implantation in the inversion layer region: α↑2. p-channel MOSFETs: V G*independent α -value (about 10 -6 on qualitywafers, 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 haveα ∝ 1/V G*dependence for 0.1 V < V G*< 1 V (straightforward ∆N- or ∆µ –interpretation possible). α -values at V G*= 1 V 3 × 10 -54. noise parameters in SPICE, BSIM are often geometry, oxide thicknessand V G*dependent poor predictions, different technologies are bettercompared in α-values obtained for the same N.L.K.J. Vandamme / Noise / 26-02-200481

825. The observed dependence (2004 and 1971) S veq∝ t oxpoints to the ∆µorigin. This holds for technologies with 3 nm < t ox< 600 nm(∆N-noise holds S veq∝ t 2 ox )6. Apart from serious 1/f noise in the series resistance of prematuretechnologies, the geometry dependence is well understood: S I@ V G*∝W/L 3 for L > 0.15 mm ; S I@ V G*∝ W/L for L < 0.15 mm but alwaysholds S Veq@ V G*∝ 1 / Wl7. In sub threshold: S I/ I 2 = α / N 0 f with N 0= (kT / q 2 ) C oxW l ⇒ sameα-values. a is a perfect figure of merit to describe the 1/f noise inMOSTs (the contribution of one charge carrier to the relative noise inthe 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; trapscalculated from 1/f noise; ∆N+ ∆µ(∆N) is a non-physical model; S veq∝ t oxor S veq∝ t 2 ox a-values constant or ∝ 1/ V G * ?L.K.J. Vandamme / Noise / 26-02-2004

83V. Low frequency noise as a diagnostic tool forquality evaluation of electronic devices [20,57-69]1. Types of noise1.1 Thermal noise : is fundamental and independent of technology,S V = 4.k.T.R (Brownian motion)A) Calibration of noise measuring set up. For I = 0 the noise S V isproportional to T a R 0 . If power dissipation P= I.V ≠ 0, S V is stillproportional to T.RB) Static heat resistance: R therm = T-T a / IV → too high, problems ine.g.,SOA (10 4 K/ Watt) → higher harmonics, delaminating andtemperature induced failures.L.K.J. Vandamme / Noise / 26-02-2004

84C) Transport mechanism / Ballistic transport? Hot carriers? Impactionization? Thermal noise to investigate transport properties.Deviations from S I = (2/3)4kTg m in MOST are indications foreither or: avalanche phenomena, hot carrier effects, non uniformmobility along the channel.Multi quantum well devices show a white noise comparable to thethermal noise in injection diodes, S I ~ I m .MOSFETs biased in sub threshold also S I ~ IL.K.J. Vandamme / Noise / 26-02-2004

851.2 Shot noise : deviations from S I = 2qI for diode type structures:A) calibration purposes B) junction quality, forward biased → seriesresistance problems, in reverse biased junctions e.g. gate of Schottkybarrier in MES- or MODFETs , : at low I, leakage current problems.R sh in prototype structures: IV-IV, III-V and II-IV and at higher I, onsetof micro plasmas or the quality of multiplication ( noise in the gain bymultiplication, Mc Intyre) can be observed from the deviations from 2qI.Beyond a critical local field[65] an onset of unintentionalavalanche multiplication canoccur that gives a weakincrease in current and a strongincrease in white (shot) noiseL.K.J. Vandamme / Noise / 26-02-2004

861.3 Conductance noise (∆σ) due to trappingA, Generation recombination noiseB, Burst-, popcorn- or RTS- noise2∆N ≡ 1 and 〈∆N〉 ≤1/4depends strongly on E FGeneration recombination noise is often observed in III-V devices.RTS noise is often an inevitable problem of submicron devices withtraps and a low number of carriers like in MOSFETs, also a problemin diode type devices with dislocations in sensitive areas and quantumdot devices. In general strongly dependent on temperature and on biasconditions (E F position dependent) and therefore a poor deviceindicator, because traps can be avoided.L.K.J. Vandamme / Noise / 26-02-2004

871.4 Conductance noise due to mobility fluctuations (1/f noise:current-, excess-, flicker- or low-frequency noise)Pitfalls in interpretation ( traps, interface roughness and poor crystalquality due to lattice damage by implantation often go hand in hand)Phenomenological approach with Hooge’s empirical relationS R2R=αfNThe 1/f noise parameter α (Hooge parameter α H ) cannot bepredicted but calculated from experimental results. Most values arein resistors, MOSFETs, MODFETs and BJTs between 10 -6 and 10 -4 .L.K.J. Vandamme / Noise / 26-02-2004

882. The omnipresent 1/f noise is a favorite diagnostic tool2.1 Without RTS or GR-noise, there is still 1/f noiseImplantation and lattice damage due to proton bombardment andanneal temperature play a role. Interface (roughness) andimplantation damage, make 1/f noise position dependent.If a poor oxide with a high number of traps goes hand in hand withinterface charges and roughness as a result of fast oxide growth ondamaged poor crystal material, then the controversy about the bulkor surface origin of the 1/f noise is solved (reconciled)L.K.J. Vandamme / Noise / 26-02-2004

89The α-value represents the contribution to the relative 1/f noise at 1Hz from one carrier ( electron or hole), assuming that the Ncarriers 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 ∆µor∆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 onvoltage or current noise. Overlooking this problem in 1/f noise alwaysresults in high apparent α-values [20, 60].L.K.J. Vandamme / Noise / 26-02-2004

902.2 Contact noise as a diagnostic tool [16, 17, 17a, 20,21, 34, 57]Current crowding goes hand in hand with increased power densityρJ 2 , heat dissipation, local temperature (hot spots), higher 1/f noisethan in homogeneous samples and higher risk of failures due to ∆Tbaseddegrading mechanisms.21 αρ J= ∫ 2I f nS v 4ΩdΩ ⇒SVv2=α⎡nf ⎢⎣∫Ω∫ΩJJ42dΩ⎤dΩ⎥⎦2≡αnΩefffL.K.J. Vandamme / Noise / 26-02-2004

Constriction dominated contacts, equipotentials, approximationsand calculationsJ(x)=I / 2πx291dΩ =2πx2dxR∞ρ ⎛ I ⎞ 2= ∫ 2πxdx2⎜=2⎟I ⎝ 2πx⎠a2ρ2πaΩeff=⎡⎢⎣∞∫a∞∫a⎛⎜⎝⎛⎜⎝I2πx2I2πx⎞⎟⎠22⎞⎟⎠2πx422πx⎤dx⎥⎦2dx2= 10πa3

92Contacts with complications [17a]ρ t2l. interface : R and Ωeff= π a t2π aSR1 1∝ ∝ ∝ R instead of proportion al to R22R Ωeffa2. multi-spot contacts (region- III) : R ∝ ρ and Ωk aSR1 1∝ ∝ ∝ R if a is constant23R Ω k ⋅aeff3. region-II multi-spot contacts:≅ film 3In all cases strong deviations from the simple constrictiondominated contact which results in:SR∝Rm5S R∝ Reff∝ k ⋅awith, m >> 5 ( m ≈320)L.K.J. Vandamme / Noise / 26-02-2004

93Experimental results on metal-semiconductor contacts [69] andmovable contact on thick film tracks in potentiometers [59]Full squarres: a film-dominatedmetal semiconductor contactwith S R proportional to R 3Open symbols: three differentconstriction dominated movablecontacts on a thick film track ofa potentiometer with a contactresistance noise proportional to:SR∝ R5andSR∝R3L.K.J. Vandamme / Noise / 26-02-2004

94Alloying of metal-semiconductor contacts under forming gas or purehydrogen reduces the noise, this is no arguments for ∆N [20]L.K.J. Vandamme / Noise / 26-02-2004

95Calculated and experimental results of noise versus resistance of voids [64]induced by degradation. The noise is more sensitive than resistance only.RSR1 2⋅ J2= ∫IρdA1 αρ= ∫ J4dAI4n ⋅f2w2aL.K.J. Vandamme / Noise / 26-02-2004l

96Multi spot contact model on a cylinder [57, 60, 63,]A=π b 2A e = π a 2 kπ b2=π2lkππbala22⎛=⎜⎝k=A eAA eA ⎞⎟⎠1/ 2LR h∝ LL.K.J. Vandamme / Noise / 26-02-2004

97R⎡ b ⎛ ⎞⎤⎢ ⎜A= R⎟h1+−1⎥⎢⎣L k ⎝ Ae⎠⎥⎦No contact problemsR h=ρπL2bSR5/ 2⎡⎤b ⎛ ⎞⎢ ⎜⎛A ⎞= S 1+⎜ ⎟ −1⎟⎥R⎢ ⎜h20Lk⎟⎥⎣ ⎝⎝Ae⎠ ⎠⎦No contact problemsSRh=α ρ2L3f nπb6*R =RR hL.K.J. Vandamme / Noise / 26-02-2004*RS =SSRR h

98Noise model for BGA contacts• Constriction resistance R C Degradation dependent• Access resistance fixed during degradationR =∆RRa+= ∆RaRc⇒ R ≈+ ∆RcRa∆RSR2== ∆RSRa+2aS+ ∆RRc⇒2cS+ 2∆RR≈SRca∆RcL.K.J. Vandamme / Noise / 26-02-2004

99Calculated Degradation (a-reduction) and m-values [74]SRm∝ R with m≈ 25m=14RS*⎡⎢⎣A*RA e⎤⎥⎦2Degradation results in a reductionof the real electrical contact areaA e , by a reduction in the numberof spots k and spot diameter 2a.This is provoked by aging testslike thermo-cycling, temperaturehumiditytests or by mechanicalbendingWe assumed in the following diagrams: k = 50, l = 120nm,L = 5µm, 12nm < a < 60nm and 1% < A e /A < 25%L.K.J. Vandamme / Noise / 26-02-2004

100R* and S R* versus A e/A with k = 3010 4R*S R*10 5 10 -3 10 -2 10 -1 10 0S R* b/L = 1S R* b/L = 0.1R* b/L = 1R* b/L = 0.1S R* (A e / A)10 310 2R * (A e / A)10 1Ae/A10 0L.K.J. Vandamme / Noise / 26-02-2004

101SR * more sensitive for current crowding than R*10 5 10 0 10 110 4S R*S R ∝ R m5 < m < 3010 310 2k = 30 b/L = 0.1 m = 29.9k = 30 b/L = 1 m = 7.710 110 0R*L.K.J. Vandamme / Noise / 26-02-2004

102C vs R after aging by thermo-cycling and bending of fresh samples [58]10 -1610 -15 0.3 0.4 0.5C10 -1510 -1610 -13 PolysolderC10 -14 0.3 0.4 0.5 0.6 0.7 0.8DM4030 SRAblebondC DM, 450, p=3C DM, 250, p=3C Poly, 100, p=3C Poly, 250, p=310 -17R Ω) (6 < m < 25 and D = 6.3 L.K.J. Vandamme / Noise / 26-02-2004 m≈1510 -17R P( Ω )0.6

103Conclusions on conductive adhesives [58, 63]With noise measurements: you see more, C∝ R m with m>> 3points to a region II multi-spot contact with 0,4 % < Ae/A < 25%in a shorter time (thermo-cycling and temperature-humidity testslast for weeks, while bending and noise measurements takes onlyminutes) and in an non destructive way (bending) a quantitativeresult.D=AAeeunststess≅⎛⎜⎝CCstressunst⎞⎟⎠2 /5L.K.J. Vandamme / Noise / 26-02-2004

104Investigation of new materials: polymer transistor [62]SamplesDrain electrode (Au)spin coatedorganic semiconductorSiO 2 - gate oxidepolysilicon gate materialmetal gateSource electrode (Au)• Channel material by spincoating:– pentacene– polythienylene vinylene (PTV)• p-type accumulation FET• Au drain and source at thebottom, poly-Si gate contactbelow• glass substrateL.K.J. Vandamme / Noise / 26-02-2004

105Conclusion• 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 organicmaterial (leads also to apparent low mobility)• No Au-polymer contact noise contribution in these samplesL.K.J. Vandamme / Noise / 26-02-2004

106Investigation of new materials: WO3 nano particle films [61]Sample description• WO 3 samples• Made by advanced gasdeposition with reactive ambientgas: synthetic air• Thickness: 0.1 - 4µm• Nano particles with lognormaldistribution with average size≈5nm• C 12 = C 13 = 2 C 23 ⇒ no electrodeinterface problems12 3L.K.J. Vandamme / Noise / 26-02-2004

107DiscussionTwo kinds of noise were detectedThermal noise: explained by: S V = 4 kT Re[Z]1/f noise: explained by “shunted capacitor” model. Shunts are formed byAl spikes from the contacts on top of the WO 3 dielectrics.AlWO 3ITOL.K.J. Vandamme / Noise / 26-02-2004

108ConclusionsQuality dielectrics do not show 1/f noise: (E c;1/f > E breakdown )Empirical relation is valid for nano particle sized Al wires α Al ≈2.5×10 -3 assuming homogeneityThe thinnest WO 3 layers deposited at the highest speed are porousand suffer from Al shunts which generate 1/f noiseTherefore 1/f noise can be used as quality assessment tool of WO 3nanostructures.L.K.J. Vandamme / Noise / 26-02-2004

1093. Diode type devices (solar cells,) [66]qNI =τFor long diodes holdsSI2I α= ⇒f ⋅ NSIαqI∝τf1∝2τFor diode with series resistance2contact problems S I∝ ITraps can reduce carrier lifetimeτ, increase I and 1/f-noise. This isnot a proof for ∆Nexperimental results of solar cellstoo high α-values are anindication of non uniformcurrent density at weak spotswith very small τ-valuesL.K.J. Vandamme / Noise / 26-02-2004

1104. FET type devices and series resistance [67]Modern short channel devices have series resistance problemsFour possible situations for R= Rch+ Rsand SR= SR+chS Rs21RchRch∝ and SR∝ ∝chVN*G1V* 3GRs∝V* 0GandS R S∝V* 0GFour possible dependencies of S I / I 2 on V GL.K.J. Vandamme / Noise / 26-02-2004

111All trends are observed [67, 68]Rch> R andSsRch> SRS⇒SRR2∝V* −1G←poor technologyRch> Rsand SRS> SRch⇒SRR2∝V*2GRs>RchandSRch> SRS⇒SRR2∝ V* −3GRs>RchandSRS> SRch⇒SRR2∝ V*0GL.K.J. Vandamme / Noise / 26-02-2004

112Conclusions 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 toolcrystal and device quality sensitivealways present especially in H.F. devices (small)L.K.J. Vandamme / Noise / 26-02-2004

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 localtemperature• contacts : lowest limit no constriction, constriction, interface ormulti-spot ( region I (A e /A> 0.16), region II (0.01

114References[1] D. K. C. MacDonald, Noise and fluctuations: an introduction, John Wiley & Sons New York,1962.[2] A. Ambrozy, Electronic Noise McGraw-Hill New York, 1982. ISBN 0-07-001124-9[3] R. Muller, Rauschen, 2nd ed. Springer - Verlag, Berlin, 1990. ISBN 0-387-51145-8[4] M. J. Buckingham, Noise in electronic devices and systems. Ellis Horwood limited publishers,Chichester (John Wiley & Sons) New York, 1983. ISBN 0-85312-218-0[5] L. K. J. Vandamme, "Low frequency noise measurement techniques," in M. A. Py, M-O.Hongler, J-P. Laedermann, J-F. Loude, and M.Droz (eds.) Fluctuations et bruit, Vercorin (Suisse):Frontier Group, 2001, pp. 97-112.[5a] R. J. W. Jonker, J. Briaire, and L. K. J. Vandamme, "Automated-system for noisemeasurementson low-ohmic samples and magnetic sensors," IEEE Transactions onInstrumentation and Measurement, vol. 48, no. 3, pp. 730-735, June1999.[5b] L. K. J. Vandamme and G. Trefan, "1/f noise in homogeneous and inhomogeneous media,"IEE Proceedings-Circuits Devices and Systems, vol. 149, no. 1, pp. 3-12, Feb.2002.L.K.J. Vandamme / Noise / 26-02-2004

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116[13] L. K. J. Vandamme, A. V. Belyakov, M. Y. Perov, and A. V. Yakimov. Difference independence of 1/f and RTS noise on current in quantum dots light emitting diodes. In: NOISE INDEVICES AND CIRCUITS, edited by M. J. Deen, Z. CelikButler, and M. E. Levinshtein,BELLINGHAM:SPIE-INT SOCIETY OPTICAL ENGINEERING, 2003, p. 368-378.[14] A. V. Belyakov, L.K.J.Vandamme, M. Y. Perov, and A. V. Yakimov, “The different physicalorigins of 1/f noise and superimposed RTS noise in light-emitting quantum dot diodes”, Fluctuationand noise letters (FNL) vol. 3, no. 3, L325-L339, 2003[15] F. N. Hooge, "1/f-noise is no surface effect," Physics Letters A, vol. 29A, no. 3, pp. 139-140,1969.[16] F. N. Hooge, T. G. M. Kleinpenning, and L. K. J. Vandamme, "Experimental studies on 1/fnoise," Reports on Progress in Physics, vol. 44, no. 5, pp. 479-532, May1981.[17] L. K. J. Vandamme, "On the Calculation of 1/f Noise of Contacts," Applied Physics, vol.11 pp.89-96, 1976.[17a] L. K. J. Vandamme. On 1/f noise in Ohmic contacts. Technische Universiteit Eindhoven. 1976.2000. Ph. D. Dissertation accessible at URL http://alexandria.tue.nl/extra1/PRF2B/7607686.pdf[18] F. N. Hooge, "1/f noise sources “, IEEE Transactions on Electron Devices, vol. 41, no. 11, pp.1926-1935, Nov.1994.L.K.J. Vandamme / Noise / 26-02-2004

117[19] F. N. Hooge, "1/f-noise is no surface effect," Physics Lett. A, vol. 29A, no. 3, pp. 139-140, 1969.[20] L. K. J. Vandamme, "Noise as a Diagnostic Tool for Quality and Reliability of ElectronicDevices," IEEE Transactions on Electron Devices, vol. 41, no.11, pp.2176-2187, Nov.1994.[21] L. K. J. Vandamme and J. C. F. Groot, "1/f noise and resistance between circular electrodes,"Electronics Letters, vol. 14, no. 2, pp. 30-32, Jan.1978.[22] D. M. Fleetwood, J. T. Masden, and N. Giordano, "1/f Noise in Platinum Films and UltrathinPlatinum Wires: Evidence for a Common, Bulk Origin," Physical Review Letters, vol.50,no.6, pp.450-453, 1983.[23] L. K. J. Vandamme. Is the 1/f noise parameter α a constant? (Invited paper). Savelli, M., Lecoy,G., and Nougier, J. P. 183-192. 1983. Elsevier Science Publ. 7 th International Conference on Noisein Physical Systems and the 3rd International Conference on 1/f Noise May 17-20, 1983 Montpellier.[24] R. H. M. Clevers, "Volume and temperature dependence of the 1/f noise parameter α in Si,"Physica B, vol. 154 pp. 214-224, 1989.[25] F. N. Hooge and L. K. J. Vandamme, "Lattice scattering causes 1/f-noise," Physics Letters A, vol.66, no. 4, pp. 315-316, May1978.[26] L. Ren and F. N. Hooge. Temperature dependence of 1/f noise in epitaxial n-type GaAs. PhysicaB 176:209-212, 1992.L.K.J. Vandamme / Noise / 26-02-2004

118[27] J. Berntgen, A. Behres, J. Kluth, K. Heime, W. Daumann, U. Auer, and F. J. Tegude. Hoogeparameter of InGaAs bulk material and InGaAs 2deg quantum-well structures based on InPsubstrates. MICROELECTRONICS RELIABILITY 40 (11):1911-1914, 2000.[28] F. N. Hooge, J. Kedzia, and L. K. J. Vandamme, "Boundary scattering and 1/f noise," Journal ofApplied Physics, vol. 50, no. 12, pp. 8087-8089, Dec.1979.[29] L. K. J. Vandamme. Bulk and Surface 1/f Noise. IEEE TRANSACTIONS ON ELECTRONDEVICES 36 (5):987-992, 1989.[30] L. K. J. Vandamme and S. Oosterhoff, "Annealing of ion-implanted resistors reduces the 1/fnoise," Journal of Applied Physics, vol. 59, no. 9, pp. 3169-3174, May1986.[31] L. K. J. Vandamme. ION IMPLANTATION IN SEMICONDUCTORS Application totechnology Annealing of implants reduces lattice defects and 1/f noise. In: Solid State PhenomenaVol. 1&2, edited by D. Stievenard and J. C. Bourgoin, Lille;Paris:Trans Tech Publications Ltd.Switzerland, 1988, p. 153-158.[32] L. Ren, "Intrinsic and extrinsic 1/f noise sources in proton-irradiated n-GaAs epitaxial layers,"Journal of Applied Physics, vol. 74, no. 7, pp. 4534-4539, Oct.1993.[33] L. K. J. Vandamme and W. M. G. van Bokhoven. Conductance Noise Investigations with FourArbitrarily Shaped and Placed Electrodes. Applied Physics 14:205-215, 1977.L.K.J. Vandamme / Noise / 26-02-2004

119[34] L. K. J. Vandamme, "Comments on "1/f Noise in Metal Contacts and Granular Resistors","IEEE Transactions on components, hybrids, and manufacturing technology, vol. CHMT-10, no. 2,pp. 290-291, June1987.[35] L. K. J. Vandamme and A. H. de Kuijper. Conductance noise investigations on symmetricalplanar resistors with finite contacts. SOLID-STATE ELECTRONICS 22 (11):981-986, 1979.[36] A. H. de Kuijper and L. K. J. Vandamme. Charts of spatial noise distribution in planar resistorswith finite contacts. TH-Report 79-E-94, ISBN 90-6144-094-7:1-60, 1979. 01-1979.[37] T.G.M. Kleinpenning; Charge-control model applied to 1/f noise in long p + -n diodes, Physicavol. 145B pp. 190-194 (1987).[38] T.G.M. Kleinpenning; 1/f noise in p-n junction diodes, Journal of Vacuum Science &Technology A vol. 3 (no 1) pp. 176-182 (1985).[39] L. K. J. Vandamme, E. P. Vandamme, and J. J. Dobbelsteen. Impact of silicon substrate, ironcontamination and perimeter on saturation current and noise in n+p diodes. SOLID-STATEELECTRONICS 41 (6):901-908, 1997.[40] T.G.M. Kleinpenning; Low-frequency noise in modern bipolar transistors: impact of intrinsictransistor and parasitic series resistances , IEEE Transactions on Electron Devices vol. 41 (no 11)pp. 1981-1991 (1994)..L.K.J. Vandamme / Noise / 26-02-2004

120[41] L. K. J. Vandamme and G. Trefan. Review of low-frequency noise in bipolars over the lastdecades. Zampardi, P. pp. 68-73. 2001. Piscathaway, N.J. "IEEE Proceedings of the BCTM";(Bipolar/BiCMOS Circuits and Technology Meeting), September 30 – October 2, 2001. J.Shott andJ.Burghartz[42] L. K. J. Vandamme and G. Trefan, "A review of 1/f noise in terms of mobility fluctuations andwhite noise in modern submicron bipolar transistors - BJTs and HBTs ,“ Fluctuation and NoiseLetters, vol. 1, no. 4, pp. R175-R199, 2001[43] S.P.O. Bruce, L.K.J Vandamme and A. Rydberg; Measurement of Low-Frequency Base andCollector Current Noise and Coherence in SiGe Heterojunction Bipolar Transistors UsingTransimpedance Amplifiers, IEEE Transactions on Electron Devices vol. 46 (no 5) pp. 993-1000(1999).[44] S. Bruce, L.K.J Vandamme and A. Rydberg; Improved Correlation Measurements UsingVoltage and Transimpedance Amplifiers in Low-Frequency Noise Characterization of BipolarTransistors, IEEE Transactions on Electron Devices vol. 47 (no 9) pp. 1772-1773 (2000).[45] T. G. M. Kleinpenning. On 1/f trapping noise in MOST's. IEEE TRANSACTIONS ONELECTRON DEVICES 37 (9):2084-2089, 1990.[46] L. K. J. Vandamme. Model for 1/f noise in MOS transistors biased in the linear region.SOLID-STATE ELECTRONICS 23 (4):317-323, 1980.L.K.J. Vandamme / Noise / 26-02-2004

121[47] L. K. J. Vandamme and L. S. H. Dik.” Bias-temperature treatment, surface state density, and 1/fnoise 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, MDApril 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 andCCD 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 - ICNF1989,August 21 - 25 1989, Budapest, Hungary.[50] L. K. J. Vandamme, X. Li, and D. Rigaud, "1/f noise in MOS devices, mobility or numberfluctuations? ," 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 ina 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 andPossible Solutions”.2 nd Int. Conference on Unsolved Problems on Noise and Fluctuations (UPoN)481-486. 1999.L.K.J. Vandamme / Noise / 26-02-2004

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