Transistor Noise Lecture 14, High Speed Devices
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1 Transistor Noise Lecture 14, High Speed Devices 016 1
2 Transistor Noise A very brief introduction Lecture 13, High Speed Devices 016
3 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 Lecture 14, High Speed Devices 016 3
4 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 Lecture 14, High Speed Devices 016 4
5 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 Lecture 14, High Speed Devices 016 5
6 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 Lecture 14, High Speed Devices 016 6
7 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 Lecture 14, High Speed Devices 016 7
8 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 Lecture 14, High Speed Devices 016 8
9 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! Lecture 13, High Speed Devices 016 9
10 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 Lecture 13, High Speed Devices
11 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 Lecture 13, High Speed Devices
12 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 Lecture 13, High Speed Devices 016 1
13 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 Lecture 13, High Speed Devices
14 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 Lecture 13, High Speed Devices
15 Lecture 13, High Speed Devices
16 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 Lecture 13, High Speed Devices
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