Transistor Noise 016-03-03 Lecture 14, High Speed Devices 016 1
Transistor Noise A very brief introduction 016-03-0 Lecture 13, High Speed Devices 016
Summary hybrid p Noise is a randomly varying voltage/current Causes small fluctuations around a mean value v v(t) V 0 t The instantaneous value v(t) can not be predicted The mean square value can usually be calculated for physical mechanism: T v = v t V 0 = 1 T v t V 0 dt 0 T i = i t I 0 = 1 T i t I 0 dt 0 016-03-0 Lecture 14, High Speed Devices 016 3
Noise Spectral Density Each process that causes noise is associated with a noise spectral density S I (f) S V (f) (A /Hz) (V /Hz) i = S I f Δf In a small bandwidth Df around f: i = S I f Δf RMS value of i Equivalent to a sinusoidal current generator with amplitude i! Noise problems can thus be treated using ordinary, linear circuit analysis! Several noise sources : we calculate the total root mean square value from each noise generator and add. Square to the the mean square value. Easy if the sources are uncorrelated. 016-03-0 Lecture 14, High Speed Devices 016 4
Correlation Several noise sources : we calculate the total root mean square value from each noise generator and add. v 1 (t) + v (t) = v 1 t + v t + v 1 t v t If v 1 and v are independent (uncorrelated) : v 1 t v t = 0 Most physical noise sources can be considered independent v 1 (t) + v (t) = v 1 t + v t 016-03-0 Lecture 14, High Speed Devices 016 5
Thermal Noise All resistive materials show Thermal Noise Random fluctuations in the kinetic energy of the carriers Essentially independent of current through the resistor Constant spectral density : white noise v = 4kTRΔf i = 4kT R Δf R v i R Increases linear with temperature Thevenin Norton Total noise power: P = v R = 4kTΔf Antennas also show thermal noise black body radiation 016-03-0 Lecture 14, High Speed Devices 016 6
Shot Noise (Hagelbrus) Discrete nature of electron charge Only associated with a DC current flow Non-degenerate electron gas (pn-junction, i C for HBTs) Low transmission (MOS oxide leakage i g ) Generation/recombination (i B for a HBT) Constant spectral density : white noise i = qi D Δf Antennas also show thermal noise black body radiation 016-03-0 Lecture 14, High Speed Devices 016 7
1/f Noise (flicker noise) Semiconductor defects can cause trapping or electrons: Mobility fluctuations Variation in resistivity r(t) Carrier concentration fluctuations A DC current must be present for this r(t) variation to be transformed into noise FETs : drain current noise HBTs: base current noise Can also be present in ordinary resistors Shows a 1/f spectral density (Pink Noise) i = K 1 I a f Δf a 0.5 K 1 is a measure of the quality of the device 016-03-0 Lecture 14, High Speed Devices 016 8
Noise Models - Diodes v s = 4kTR s Δf R S R S R S r D = kt qi D r D = kt qi D i = qi D Δf + KI D a f Δf A diode shows thermal noise due to contacts and semiconductor access regions modeled as R S The current shows shot noise and 1/f noise Note that r d is an fictitious resistance does not cause thermal noise! 016-03-0 Lecture 13, High Speed Devices 016 9
Noise Models HBT R B r p C p C m R E R C g m e jωτ mv 1 Real resistances cause thermal noise Collector current shot noise Base Current shot noise and 1/f noise No thermal noise from r p! v B = 4kTR B Δf R B C m R C v c = 4kTR C Δf r p C p i c = qi C Δf i b = qi B Δf + K 1I B a R E f Δf i c, i b are correlated. Should be v E = 4kTR E Δf taken into account for exact analysis 016-03-0 Lecture 13, High Speed Devices 016 10
Noise Models FET R G C gd,t R D Small Signal FET model C gs,t g 0 C sd,t (g m +jωc m )v 1 R S v G = 4kTR B Δf R G C gd,t R D v D = 4kTR B Δf C gs,t g 0 C sd,t i g i d R S Physical resistances cause thermal noise v S = 4kTR B Δf 016-03-0 Lecture 13, High Speed Devices 016 11
Noise Models FET R G C gd,t R D C gs,t g 0 C sd,t i g i d R S Resistive Channel: Thermal Noise i d = 4kTγg m Δf + KI D a Interface Defects: Flicker Noise f Δf γ = /3 γ = 3.5 γ 3 Long Channel Velocity saturation Ballistic Increases due to higher mean electron kinetic energy 016-03-0 Lecture 13, High Speed Devices 016 1
Noise Models FET R G C gd,t R D C gs,t g 0 C sd,t i g i d R S Oxide Leakage shot noise i g = qi G Δf + 4kTω C GS g m Δf Channel induced gate noise. (Rough expression) Thermal noise in the channel couples capacitively through the gate oxide capacitance. This is correlated to the drain thermal noise current. 016-03-0 Lecture 13, High Speed Devices 016 13
Noise Models FET v G = 4kTR G Δf Medium frequencies R G C gs,t g 0 i d = 4kT 3 g mδf v in If g m =0mS, g 0 =5mS and R g =10W what is the smallest detectable input voltage for a 1 MHz bandwidth? Reefer all noise voltages to the input calculate v in, equivalent input voltage. Superposition of uncorrelated sources: v in = v G + 4kT 3 v in = 840 nv rms 1 = 4kTΔf(R g G + 1 ) m 3 g m 016-03-0 Lecture 13, High Speed Devices 016 14
016-03-0 Lecture 13, High Speed Devices 016 15
Master Thesis in nanoelectronics The nanoelectronics group at EIT Nanotechnology - process development in the nanolab. Measurements : DC/RF measurements. Noise Measurements. CV characterization. Theory/Modeling : 3D COMSOL Modeling. Ballistic FET modeling. TFET modeling. Circuit Design: Large Signal Model development. Circuit Implementation. 016-03-0 Lecture 13, High Speed Devices 016 16