Noise and electronics for semiconductor detectors A big

Noise and electronics for semiconductor detectors A big subject but restrict to very essential information only Some slides will be skipped and are there only to provide supplementary details for those wishing to seek further information. Key point: Semiconductors need amplifiers since they usually do not have any built-in amplification hence some understanding of amplifiers is required when considering how to build detector systems if you are prepared to accept the noise is what it is, then it may be enough for working with data from such systems just to be aware that noise is present and it probably cannot be improved, although it might be worsened! Geoff Hall 1 Jan 2014

Noise • What is NOISE? A definition: Any unwanted signal obscuring signal to be observed two main origins • EXTRINSIC NOISE examples. . . pickup from external sources unwanted feedback RF interference from system or elsewhere, power supply fluctuations ground currents small voltage differences => currents can couple into system may be hard to distinguish from genuine signals but AVOIDABLE Assembly & connections, especially to ground, are important • INTRINSIC NOISE Fundamental property of detector or amplifying electronics Can’t be eliminated but can be MINIMISED Geoff Hall 2 Jan 2014

Noise in amplifier systems n VFE systems comprise n n preamplifier - with noise sources n shaping amplifier or other filter Preamplifier usually designed with noise as an important consideration n n preamplifier pulse shape is long duration with short, sharp peak so modify it with shaper to n optimise signal to noise n generate a more practical pulse shape, avoiding pile-up the first (pre-) amplifier is the most important part of the system for noise The system noise can be calculated once sources are understood n relies on Campbell’s theorem and summation over bandwidth Jan 2014 3 Geoff Hall

Preamplifier types Omit most – just be aware that different amplifier types have different noise properties and are not interchangeable • Current sensitive - common for photodiode signals vout ≈ -iin. Rf • signals follow input current, ie fast response but not lowest noise • Charge sensitive amplifier Ideally, simple integrator with Cf but need means to discharge capacitor - large Rf • Simple integrator vout ≈ -Q/Cf • with feedback resistor Rf vout(t) ≈ -(Q/Cf)exp(-t/ ) = Rf Cf Geoff Hall 4 Jan 2014

Signal processing n If noise sources are defined, their impact can be calculated n pulse shaping is most common series (Rs) sampling an amplifier signal can produce equivalent behaviour n parallel (I) numerical result for many cases n Useful point of comparison: CR-RC filter Jan 2014 5 Geoff Hall

Some numerical values • An approximate numerical value • using CR-RC filter, ignoring 1/f noise ie I = 1 n. A = 1µs ENCp ≈ 100 e Rs = 10Ω C = 10 p. F = 1µs ENCs ≈ 24 e Geoff Hall 6 Jan 2014

Noise vs technology after V. Radeka peaking time Jan 2014 7 Geoff Hall

Noise calculations n Summary of principles integrate signal spectrum over bandwidth n integrate noise in quadrature over bandwidth n computation can be done in time or frequency domain but simplifications are often possible n n System noise can be computed with knowledge of impulse response and noise sources n s 2 ~ en 2 C 2 ∫ [h' (t)]2 dt + in 2 ∫ [h (t)]2 dt n provided noise sources en & in are white n Impulse response = output of system following fast -like input signal h(t) properly normalise to signal of unit amplitude Jan 2014 8 Geoff Hall

Omit Campbell’s theorem • Most amplifying systems designed to be linear S(t) = S 1(t) + S 2(t) +S 3(t) + … • Impulse response h(t) = response to • Transfer function H(w) = vout(w)/vin(w) = ∫-∞∞ h(t). e-jw t dt ie impulse response h(t) and transfer function H(w) are Fourier pair • In a linear system, if random impulses occur at rate n average response <v> = n ∫-∞tobs h(t)dt variance s 2 = n ∫-∞tobs [h 2(t)]dt i. e. sum all pulses preceding time, tobs, of observation so s 2 = n ∫-∞∞ h 2(t) dt = n ∫-∞∞|H(w)|2 df Geoff Hall 9 Jan 2014

Omit "Rules" of low noise amplifier systems • Combine uncorrelated noise sources in quadrature e 2 tot = e 12 + e 22 + e 32 + … + in 2 R 2 +. . . follows from Campbell's theorem consider as combinations of gaussian distributions • First stage of amplifier dominates noise originates at input transistor is most important - defines noise in most cases • Noise is independent of amplifier gain or input impedance so noise can be referred to input • In real systems both are approximations - but normally good ones so often sufficient to focus on input device Geoff Hall 10 Jan 2014

Equivalent Noise Charge n n Systems need to be calibrated: ENC is the signal magnitude which produces an output amplitude equal to the r. m. s. noise n n ideally measure in some absolute units - e, coul, ke. V(Si), … rather than ADC channels to calibrate n n inject charge and look at result n eg x-ray signal of known size n or electronic test pulse n preferably in-situ measure Vout for known Qin Qtest = Ctest. Vtest = Ne Jan 2014 11 Geoff Hall

Noise sources n Thermal noise n Quantum-statistical phenomenon; carriers in constant thermal motion n Typically associated with input transistor or resistive components Shot noise n n n macroscopic fluctuations in electrical state of system Random fluctuations in DC current flow Typically associated with sensor 1/f noise n n commonly associated with interface states in MOS electronics Luckily, less important for high speed electronics Jan 2014 12 Geoff Hall

Shot noise • Poisson fluctuations of charge carrier number eg arrival of charges at electrode in system - induce charges on electrode quantised in amplitude and time • Examples electrons/holes crossing potential barrier in diode or transistor electron flow in vacuum tube < in 2> = 2 q. I. ∆f I = DC current WHITE (NB notation e = q) gaussian distribution of fluctuations in i Geoff Hall 13 Jan 2014

Thermal noise Just note that this is needed to do calculations • Einstein (1906) , Johnson, Nyquist (1928) Mean voltage <v> = 0 gaussian distribution of fluctuations in v Variance <v 2> = 4 k. T. R. ∆f = observing bandwidth s(v) = √<v 2> = 1. 3 10 -10 (R. ∆f)1/2 volts at 300 K e. g. R = 1 MΩ ∆f = 1 Hz s(v) = 0. 13µV Noise power = 4 k. T. ∆f independent of R & q independent of f - WHITE • Circuit representations Noise generator + noiseless resistance R • Spectral densities mean square noise voltage or current per unit frequency interval w. V(f) = 4 k. TR (voltage) w. I(f) = 4 k. T/R (current) Geoff Hall 14 Jan 2014

CMOS transistor n Reminder of basic FET physics n n Inversion layer n n n bias “metal” gate to deplete substrate beyond a certain threshold voltage, substrate does not deplete deeper instead “inversion layer” created L extremely shallow, at oxide-silicon interface carriers mobile in applied field Transistor operation n Modulation of source-drain current via Vgate Jan 2014 15 Geoff Hall

Omit Noise in MOS circuits n Gate shot noise is negligible n Thermal noise voltage from channel n n insulating gate and no current g = excess noise factor ~ 1 Transconductance n n Cox = eox /tox W/L = transistor width/length n 1/f noise usually unimportant (for LHC) n Implications C = capacitance T = temperature ∆f = bandwidth µ = mobility (v/E) n To achieve low noise, aim for large W/L and large (tolerable) IDS n but Camp = Cox. WL and require capacitance matching: Camp ≈ Cdet/3 n Mobility is also T dependent, influencing noise and speed µ(T) ~ T-3/2 Jan 2014 16 Geoff Hall

Noise spectra n p. MOS preferred for lower 1/f noise n 3 d. B bandwidth n eg LHC ∆f 3 db = 2. 6 - 15. 4 MHz n n n CR-RC pulse shaping = 25 ns or 1/f noise might be an issue Jan 2014 17 Geoff Hall

Bipolar transistor noise n n Omit Basic sources are n Shot noise in IC ic 2 = 2 e. IC∆ƒ n Shot noise in IB ib 2 = 2 e. IB∆ƒ n Thermal noise in base & contacts 2 n eb = 4 k. T. rbb'. ∆ƒ Reconfigure so that noise sources are external which then shows that i 2 n and e 2 n are correlated, ie can’t reduce both simultaneously so achievable range of noise is limited and happens to provide best performance for high speed applications n n however bipolar noise determined mainly by currents n so easy to estimate Jan 2014 18 Geoff Hall

Time variant filters - sampling n Alternative to pulse shaping n filters based on summation n easy to implement in several technologies n eg. typically switched capacitor filters n but also delay-line or digital possible n n beware of extra noise issues based on sample & hold n n delay line DCS e. g. double correlated sampling Switched capacitor design convenient for CMOS n accurate capacitances (ratios) n MOSFET switches Jan 2014 19 MX ASIC DCS Geoff Hall

Weighting function n Omit How to calculate noise of time variant systems? n n What output is produced at Tm by impulse at time t? consider all t - defines weighting function n Time invariant filter w(t) is mirror image of h(t) n Noise calculation ENC 2 = en 2 C 2 ∫ [w' (t)]2 dt + in 2 ∫ [w (t)]2 dt Jan 2014 20 Geoff Hall

Double correlated sampling • Sample & hold method initially switches S 0 B 1 B 2 open, S 1 S 2 closed switch S 0 is Reset Vout = output from charge sensitive preamplifier open S 1 : preserves Vout on C 1 after time ∆t open S 2 : preserves Vout on C 2 then, close B 1 and B 2: output A = V 1 - V 2 reset preamp later • need to know when signal will arrive! Geoff Hall 21 Jan 2014

CR-RC pulse + integrating ADC n Example of time-variant filter. . n Convolution of pulse shape with gate n n n w(t) = h(t) * ggate(t) (ignoring t reflection) examples Tgate = 5 t Tgate << Tgate >> similar to peak sensing ADC gated at peak! new, wider weighting function recompute noise integrals ADC may change filtering and increase or decrease noise Jan 2014 22 Geoff Hall

Digitisation noise • Eventually need to convert signal to a number quantisation (rounding) of number = noise source the more precise the digitisation, the smaller the noise • After digitisation all that is known is that signal was between -∆/2 and ∆/2 <x> = ∫x. p(x). dx/∫p(x). dx s 2 = <x 2> = ∫x 2. p(x). dx /∫p(x). dx = ∫-∆/2∆/2 dx = [x] -∆/2∆/2 = ∆ ∫x 2. p(x). dx = ∫-∆/2∆/2 x 2. dx = [x 3/3] -∆/2∆/2 = 2∆3/24 so s 2 = ∆2/12 • ie statistical noise which is proportional to digitisation unit Geoff Hall 23 Jan 2014

Time measurements and noise • When did signal cross threshold ? noise causes “jitter” Dt = snoise/(d. V/dt) • compromise between bandwidth (increased d. V/dt) noise (decreased bandwidth) • limits systems where preamplifier pulse used to generate trigger eg x-ray detection • typical preamp response V = Vmax(1 -e-t/ rise) so ∆t ≈ snoise rise/ Vmax t << Geoff Hall 24 Jan 2014