1. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Chiara Guazzoni Politecnico di Milano and INFN Sezione di Milano e-mail: Chiara.Guazzoni@mi.infn.it www: http://home.dei.polimi.it/guazzoni

2. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Table of contents  Noise definitions, noise analysis and theorems  Noise physical sources  Noise modeling in electronic devices  Equivalent Noise Charge Definition and Calculation

3. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Noise analysis – definitions – I interference noise it results from unwanted interaction between the detection system and the outside world or between different parts of the system itself; it may or may not appear as random signals (power supply noise on ground wires – 50 or 60 Hz, electromagnetic interference between wires, …). inherent noise  We will deal with inherent noise only. all noise signals have a mean value of zero  We will assume all noise signals have a mean value of zero. inherentnoise inherent noise it refers to random noise signals due to fundamental properties of the detector and/or circuit elements; therefore it can be never eliminated; it can be reduced through proper choice of the preamplifier/shaper design.

4. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Noise analysis – definitions – II For those more rigorously inclined, we assume also that random signals are ergodic therefore their ensemble averages can be approximated by their time averages. from S. Cova

5. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Time-domain noise analysis - I noise rms (root mean square) value noise rms (root mean square) value where T is a suitable averaging time interval. A longer T usually gives a more accurate rms measurement. It indicates the normalized noise power of the signal. amplitude Probability distribution is normalised Mean value is zero Noise derives from superposition of a very high number of elementar process, under good approximation mutually uncorrelated.  v n,rms time “central limit”, i.e. Gaussian distribution stationary noise stationary noise non stationary noise non stationary noise probability density constant with time probability density varies with time stationary noise: p m does not depend on time stationary noise p j depends only on time interval  full noise description: full noise description: marginal probability p m (v n1,t 1 ) for every instant t 1 joint probability p j (v n1, v n2,t 1,t 2 )=p j (v n1, v n2,t 1,t 1 +  )

6. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Time-domain noise analysis - II autocorrelation function of the noise R xx autocorrelation function of the noise R xx function of the interval  between two instants and for non stationary noise also function of t 1 noise variance is the autocorrelation function value in 0 signal-to-noise ratio (SNR) signal-to-noise ratio (SNR) (in dB) noise summation noise summation noise sums “quadratically” (in power)

7. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Frequency-domain noise analysis I noise spectral density noise spectral density: average normalized noise power over 1-Hz bandwidth, measured in V 2 /Hz or A 2 /Hz. The rms value of a noise signal can be obtained also in the frequency domain: Wiener-Khintchine theorem is the Fourier transform of the autocorrelation function of the time- domain signal v n (t) (Wiener-Khintchine theorem). One-side spectral density One-side spectral density: noise is integrated only over positive frequencies. Bilateral spectral density Bilateral spectral density: noise is integrated over both positive and negative frequencies. The bilateral definition results in the spectral density being divided by two since, for real-valued signals, the spectral density is the same for positive and negative frequencies. frequency

8. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Frequency-domain noise analysis II f V n (f) white noise white noise A noise signal is said to be white if its spectral density is constant over a given frequency, i.e. if it has a flat spectral density. 1/f (or flicker) noise 1/f (or flicker) noise f V n (f) -10dB/dec 1/f noise corner The noise power of the 1/f noise is constant in every decade of frequency: where A f is a constant. V nw where V nw is constant In the time domain white noise shows no correlation at any finite time interval τ, no matter how small. t R nn (  )

9. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Noise analysis – useful theorems noise source with bilateral power spectrum N (  ) superposition (in the time domain) of randomly distributed events with Fourier transform  (  ) occurring at an average rate Carson’s theorem Carson’s theorem the r.m.s. value of a noise process resulting from the superposition of pulses of a fixed shape  (t), randomly occurring in time with an average rate is: Campbell’s theorem Campbell’s theorem Parseval’s theorem Parseval’s theorem

10. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Noise physical sources – Thermal noise Thermal noise Johnson Nyquist Thermal noise (also known as Johnson or Nyquist noise - 1928): present in all dissipative systems, as a consequence of the fundamental mechanisms ruling their energy state; due to thermal excitation of charge carriers in a conductor; from fundamental thermodynamics laws (first and second) and from Planck's law, can be seen as the black body radiation in a single propagation mode. from thermodynamics, the power spectral density of the thermal noise is where k = 1,38 10 -23 J/K (Boltzmann’s constant) h = 6,624 10 -34 Js (Planck’s constant) 011

11. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Noise physical sources – Shot noise Shot noise Shot noise (first studied by Schottky in 1918 in vacuum tubes): due to the granularity of charge carriers forming the current flow; number of emitted (or collected) electrons shows statistical fluctuation; white spectral density and dependent on the DC bias current, easily derived from statistical considerations (or Campbell’s theorem) t random sequence of independent pulses f(t) = q h(t), with h(t) normalized pulse shape pdt probability that a pulse starts in (t, t+dt) p=const, independent of other pulses f(t)=qh(t) mean current mean square current noise mean square value if we neglect correlation on time scales shorter than the transit time, h(t)  (t)

12. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Noise physical sources – Flicker noise Flicker noise Flicker noise (commonly referred to as 1/f noise or pink noise): it is a “fundamental” noise, present in different processes; least understood of the noise phenomena; usually arises due to traps in the semiconductor, where carriers constituting the DC current flow are held for some time period and then released; power spectral density: from M. Bertolaccini Time domain from M. Bertolaccini Frequency domain with 0.8<  <1.3; K process dependent and 1<  <2.

13. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Noise physical sources – G-R noise Generation-Recombination noise Generation-Recombination noise in semiconductors due to fluctuations in the carriers number due to thermal generation and recombination, due to trapping/detrapping or due to direct transition from valence to conduction band non-white noise with components of the power spectral density if only one carrier type is involved and only one process dominates (as it occurs in practical cases) the power spectral density is where  is the transition time constant; where  is a constant depending on the technology and on the physical properties of the semiconductor AlGaN/Gan HFET

14. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Noise physical sources – Burst noise Burst noise Pop-Corn noise Random Telegraph Noise Burst noise (also known as Pop-Corn noise or Random Telegraph Noise) in semiconductor is due to fluctuations of carriers number due to trapping/detrapping of a large number of carriers, not of single particles. the power spectral density is similar to the one of Genration- Recombination noise from M. Bertolaccini where   e  are constants depending on the physical characteristics of the semiconductor and on the fabrication process

15. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Noise in Electronic Devices: Resistors I  The power spectral density of such voltage fluctuations was originally derived by Nyquist in 1928, assuming the law of equipartition of energy states that the energy on average associated with each degree of freedom is the thermal energy. R (noiseless)  Resistors exhibit thermal noise. R (noisy) R (noiseless) 1 k  resistor exhibits a root spectral density of 4nV/  Hz (4pA/  Hz) of thermal noise at room temperature (300 K). k: Boltzmann’s constant (1.38  10 -23 J/K) T: absolute temperature in Kelvin Only physical resistors (and not resistors used for modeling) contribute thermal noise.

16. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Noise in Electronic Devices: Resistors II  At frequencies and temperatures where quantum mechanical effects are significant (hf~kT) each degree of freedom should on average be assigned the energy: at “practical” frequencies and temperatures resistors thermal noise is independent of frequency  white noise R=1k 

17. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Noise in Electronic Devices: MOSFET (Van der Ziel - 1986) 1/f noise (due to random capture and release of carriers by a large number of traps with different time constants): Thermal noise (the channel can be treated as a resistor whose increment resistance is a function of the position coordinate): saturation region The thermal noise current in the channel is equal to Johnson noise in a conductance equal to  g m where  =2/3 for long channel and  =  (V GS -V T ) for short channel MOSFETs. G D S ohmic region P-channel MOSFETs feature lower 1/f noise than N-channel MOSFETs. G D S G D S W drain gate source p-sub L oxide Metal Oxide Semiconductor F E T

18. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Noise in Electronic Devices: JFET (Van der Ziel - 1962) Shot noise (due to leakage current I G across the gate-channel junction): 1/f noise (due to random capture and release of carriers by traps in the device): G D S G D S G D S G S D t Thermal noise (the channel may be treated as a resistor whose increment resistance is a function of the position coordinate): saturation region The thermal noise current in the channel is equal to Johnson noise in a conductance equal to  g m where  =2/3. However, much lower than in MOSFET

19. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Noise in El. Dev.: lossy capacitor (Van der Ziel - 1975) Re Im  As far as the loss angle (  ) is independent of frequency, the output voltage noise shows a 1/f spectrum. C (lossy) inin R Power spectral density of the thermal noise current generator C (loss-less) At low frequency the loss resistance is merely a measure of the conductivity (  ) of the dielectric vnvn S v (  ) shows a frequency dependence of the form

20. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model kTC noise R C Q  (t) noise power spectral density voltage noise r.m.s. charge fluctuation: C=10fF  40 electrons r.m.s. C=100fF  125 electrons r.m.s. C=1pF  400 electrons r.m.s. C=10pF  1250 electrons r.m.s. …kTC noise sets ultimate limit of dynamic range f S v (f) filter transfer function high R low R In the case of switched capacitors (reset switch, analog memories, …)… independent of R!! 1/2RC

21. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model ADC: quantization noise Quantization intrinsically introduces an error (an input voltage range is represented by a single output code): Typical input-output characteristics of a 3-bit ADC with the indication of the quantization error quantization error is less for higher resolution ADCs, lowering the quantization noise and leading to a higher maximum theoretical SNR

22. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Equivalent Noise Charge - I o Identification of the detector and preamplifier noise sources shaping amplifier preamp. C det CiCi (leakage current feedback resistor) (capacitor dielectric losses) (1/f voltage noise) (white voltage noise) (gate current shot noise) Detector Preamplifier Shaping Amplifier Radiation

23. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Equivalent Noise Charge - II o Equivalent circuit for ENC calculation shaping amplifier noiseless preamp. C det +C par CiCi (leakage current feedback resistor gate current) (capacitor dielectric losses) (1/f voltage noise) (white voltage noise) Equivalent Noise Charge Equivalent Noise Charge is the value of charge that injected across the detector capacitance by a  -like pulse produces at the output of the shaping amplifier a signal whose amplitude equals the output r.m.s. noise, i.e. is the amount of charge that makes the S/N ratio equal to 1.

24. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Equivalent Noise Charge - III o Time domain representation of signal and noise Charge Current step  pulse random walk  pulses signalwhite parallel  pulses  ‘ pulses doublets white series

25. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Equivalent Noise Charge - IV shaping amplifier noiseless transamp CTCT Parseval’s theorem o ENC calculation in presence of white parallel noise independent of C T  pulses h(t) 1 T 0 gated integrator RC-CR shaping 0 t 1 h(t)

26. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Equivalent Noise Charge - V o ENC calculation in presence of white series noise shaping amplifier noiseless transamp shaping amplifier noiseless transamp CTCT CTCT Parseval’s theorem h(t) T 1 2T 0 triangular shaping  ‘ pulses doublets RC-CR shaping 0 t 1 h(t)

27. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Equivalent Noise Charge - VI o ENC calculation in presence of 1/f noise and/or dielectric losses shaping amplifier noiseless transamp shaping amplifier noiseless transamp CTCT triangular shaping independent of shaping time T 2T 0 h(t) 1 RC-CR shaping CTCT  0 h(t) 1

28. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Equivalent Noise Charge - VII o ENC calculation in presence of white and 1/f + dielectric noises Introducing, where  is a typical width of h(t) as the peaking time or the FWHM: are shape factors depending only on the shape of the filter:

29. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Equivalent Noise Charge - VIII o ENC vs. shaping time (  ) 5mm 2 SDD (on-chip JFET)

30. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model Equivalent Noise Charge - VIII 5mm 2 SDD (on-chip JFET) o ENC vs. shaping time (  ) 5mm 2 pn-diode (NJ14 JFET)

31. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model

32. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model MOSFET operating principle – I L Metal Oxide Semiconductor F E T W drain gate source p-sub Basic structure The conducting channel is formed … Metal Oxide Semiconductor F E T V D =0 V S =0 p-sub V G >0 p-sub V S =0 V D >0 V G >0 … current can flow between D and S! The threshold voltage: INVERSION V S =0 V G =V T p-sub with N A holes/cm -3 oxide Free electrons with density equal to N A depleted region The gate contact oxide

33. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model MOSFET operating principle – II MOS capacitor oxide V G >V T Channel resistance MOS as variable resistor: OHMIC region V GS >V T V DS IDID p-sub L W Z V G -0 V G -V(x)V G -V D V D >0 V G >V T V S =0 as V DS increases … V GS >V T V DS IDID V D >0 V G >V T V S =0 V G -0V G -V(x)V G -V D

34. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model MOSFET operating principle – III Channel pinch-off: saturation V G >V T V S =0 V D =V Dsat V Dsat = V GS -V T V DS MOS as transistor: SATURATION region p-sub L W Z V G -0 VTVT V G >V T V G -0 V G -V D =V T V D >V Dsat V G -0 V G -V D =V T V S =0 V G >V T IDID Current at pinch-off voltage

35. C. Guazzoni – Advanced School and Workshop on Nuclear Physics Signal Processing - November 21, 2011 Noise mechanisms in electronic devices: physical origin and circuit model MOSFET operating principle – IV Small signal operation Transcharacteristic curve Transconductance G D S I V V GS T D Small signal condition: Basic amplifier configuration (Common source) Voltage gain: