Noise models for diodes and transistors Noise models for diodes and transistors V.Vasudevan, Department of Electrical Engineering, Indian Institute of Technology Madras Noise models for diodes and transistors I pn junctions and BJTs - shot noise, flicker noise, burst noise I MOSFETs - flicker noise, thermal noise in strong inversion, shot noise in weak inversion, burst noise I Shot noise occurs due to various reasons - random emission of carriers across a barrier, random tunneling of carriers, generation/recombination processes in bulk and depletion region, thermal fluctuations triggering a relaxation current through diffusion. The PSD of shot noise is proportional to the current I Some controversy on origin of flicker noise - whether it occurs due to number (of carriers) or mobility fluctuations. Models are empirical models. I Burst noise (or random telegraph signal) is seen as random “bursts” of noise in the time domain - occurs due to charging/discharging of a single defect Noise models for diodes and transistors Diodes I Shot noise occurs because the minority carrier density in the bulk fluctuates due to thermal motion and generation/recombination of carriers. This triggers a relaxation current - the current flow is by diffusion I The noise spectral density is given as SI (f ) = 2q(I + 2Is ) I A more accurate expression includes a frequency dependent term Noise models for diodes and transistors Bipolar Junction transistor B 2qIB ∆ f C rBE CBE gm vBE 2qIC ∆ f E I Shot noise - mechanism is similar to diodes (narrow diodes) I The spectral densities are given by SIE = 2qIE , SIB = 2qIB , SIC = 2qIC Noise models for diodes and transistors I The three noise current sources are correlated √ SCE = −2qIC ⇒ cCE = − α r α SBE = −2qIB ⇒ cBE = − β I The collector base correlation occurs due to charging and discharging of the diffusion capacitance SCB = −2qIC p jωτt jωτt ⇒ cCB = − β 3 3 where τt is the base transit time Noise models for diodes and transistors MOSFET - strong inversion I I I I Random thermal motion of carriers in the inversion layer Modelled as a voltage dependent nonlinear resistor The noise in the drain current is µ id2 = 4kT 2 |Qinv |∆f L where Qinv is the total inversion charge in the MOSFET In a simple model, ignoring channel length modulation, Qinv = 2 1 + α + α2 WLCox (VGS − VT ) 3 1+α where VDS VGS − VT More complex models take into account velocity saturation α=1− I Noise models for diodes and transistors Induced gate noise I Voltage fluctuations in the channel coupled to the gate through Cg I Induced gate noise correlated to the drain noise I A potential fluctuation at v (x) causes a gate current ig given by Z L Cg (x)v (x)dx ig = −jωW o Noise models for diodes and transistors Long channel transistor in saturation G ig2 D Cgs gm vgs id2 S I For long channel devices in saturation (VDsat = VGS − VT ), the PSDs of the drain current and induced gate current are 2 Sid = 4kT gm , 3 Sig = 4kT 16 ω 2 (WLCox )2 135 gm Noise models for diodes and transistors I I The drain and gate noise are correlated and the cross spectral density is 1 Sig id ∗ = 4kT jωCox WL 9 The correlation coefficient (coherence function) is therefore Si i ∗ c= pgd ≈ 0.395j Sid Sig Noise models for diodes and transistors 1/f Noise I Fluctuations in the curent due to trapping/detrapping by interfacial defects I A simple model is 2 idf = I 2 1 Kgm ∆f 2 f WLCox Often just modelled as 2 idf = K0 a IDS f where a is left as a parameter I K depends on device type and processing Noise models for diodes and transistors Other noise sources I Thermal noise due to the distributed gate resistance (Rg ) I Thermal noise due to source and drain resistances Rs and Rd I Shot noise due to gate tunneling current and junction diodes I Noise due to hot electrons (in submicron devices) I Substrate noise I RTS noise Noise models for diodes and transistors References 1. A.van der ziel “Noise in solid state devices and circuits” 2. A good introduction to noise in MOSFETs is contained in the book “Analysis and modelling of MOS transistors” by Y.Tsividis 3. A.J.Scholten et al, “Noise modelling for RF CMOS circuit simulation”, IEEE trans. Elec. Devices, vol.50, no.3, pp 618-632, Mar. 2003 4. A.Van der ziel, “Unified presentation of 1/f noise in electronic devices: Fundamental 1/f noise sources”, Proc. IEEE, vol.76, no.3, Mar 1988