Compact Modeling of Noise in the MOS Transistor

Transcription

1 Compact Modelig of Noise i the MOS Trasistor Aada Roy, Christia Ez, ) Swiss Federal Istitute of Techology, ausae (EPF), Switzerlad ) Swiss Ceter for Electroics ad Microtechology (CSEM) Neuchâtel, Swtzerlad Outlie Itroductio (defiitios) Effect of elocity saturatio (VS) Effect of carrier heatig (CH) Effect of mobility reductio due to ertical field (MRV) Effect of chael-legth reductio (CM) Coclusio Slide No.

2 Itroductio Noise sets the lower limit for sigal amplificatio ad detectio, whereas upper limit is set by deice o liearity Reductio of supply oltage i deep submicro CMOS techologies reduces upper limit ad forces oise to become smaller at the cost of a higher power cosumptio Flicker oise largely domiates at low frequecy (below the corer frequecy), particularly for deep submicro CMOS Thermal oise domiates at HF ad is hece importat for RF IC desig Thermal oise domiated by the itrisic chael oise (~9%) It is therefore crucial to properly model thermal ad flicker oise for aalog ad RF IC desig Slide Chael Thermal Noise ad Termial Noise Currets oisy piece of chael δi iduced gate oise S D source oise δi S δv δi D drai oise At low-frequecy: δi S δi D B δi B iduced substrate oise The thermal oise geerated by oltage fluctuatios i the chael appears at the drai, source, gate ad bulk as termial curret fluctuatios The chael oltage fluctuatios are trasferred to the drai ad source through the (tras)coductaces ad to the gate ad bulk by capacitie couplig Slide No.

3 Two-Trasistor Approach oisy piece of chael Equialet small-sigal circuit Noiseless M M M =x = x dr δv B M δi D Noiseless md (x) δi ch D δv dr(x) = = ch md ms (x) δi D δv where ch is the chael coductace from poit x + ms Slide og-chael Model PSD of drai curret fluctuatios δi D due to δv S = S with S = kt dr( x) δ ID ch δv where T C is the carrier temperature og-chael mobility µ idepedet of lateral field E x ad o carrier heatig (T C =T ) where T is the lattice temperature dr = W dx ( Q i ) µ ch Q i δ V W W = ( ) µ Sδ I kt Qi dx D = ( ) µ Total oise PSD at the drai is the gie by W I kt = µ µ ( Qi ) dx = Q I S D C Slide 6 No.

4 Short-Chael Model Mobility µ depeds o positio ad hece o the lateral field E x Carrier get heated (T C T ) ad T C depeds also o positio ad hece o the lateral field E x Has to be accouted for whe ealuatig dr ad ch dx dr = W ( Q i ) ( µ + µ Ex ) W ( Qi ) µ ch = VD µ dv + V µ + S µ Ex The PSD of the drai curret fluctuatios is ow gie by dµ µ W µ ( Qi ) T = E V x µ D µ dv + T µ + + V Ex µ µ S Slide 7 C dex dx Thermal Noise Parameter Seeral thermal oise excess factor ca be defied The thermal oise parameter δ related to the drai is defied as δ dso where dso is the chael coductace at V DS = og-chael alues δ = for V DS = ad δ sat = / i saturatio δ tells how much the thermal oise deiates from the alue it takes whe it operates like a resistor haig a coductace dso δ compares oise at a gie operatig poit to the oise at V DS = Maily useful for deice modelig but useless for circuit desigers Slide 8 No.

5 Thermal Noise Excess Factor The thermal oise excess factor γ is defied as γ where m is the gate trascoductace m γ shows how much oise is geerated at the drai for a gie m Cotrary to δ, the oise coductace ad the trascoductace m are ealuated at the same operatig poit γ is becomig large for small V DS dso γ is related to δ by γ = = δ dso m dso m ms md Where is the slope factor with.k.6 I saturatio md = ad ms = dso γ sat = δ sat. = Slide 9 Values of δ Published i the iterature Very differet alues of δ for short chael deices hae bee published i the literature (old topic but still cotroersial today) Abidi (TED 86) preseted measured alues of δ as large as 7 Scholte (IEDM 99) preseted alues of δ measured o seeral CMOS processes that are always smaller tha Some authors preted that elocity saturatio is the oly ect that should be accouted for ad there is o eed for carrier heatig Che (TED ) attributes the icrease of δ to the ect of chael legth modulatio Why bother? Noise factor strogly impacts oise performace of RF circuits (NA) Slide No.

6 6 Mai Effects Affectig Chael Thermal Noise Better uderstad the differet mechaisms affectig the MOST chael thermal oise The followig ects will be cosidered:. Velocity saturatio (VS). Carrier heatig (CH). Mobility reductio due to the ertical field (MRV). Chael legth modulatio (CM) Ealuate the impact of each of these ects o δ ad γ Each ect will be aalyzed separately Slide ν = drift / sat VS ad Velocity-Field Models e = E x / E c.. ν ν ν U λ T c. for =. µ m Ec drift sat drift sat drift sat E e E x c e = e = + e e = + e U T E c for e <. for e. for e < for e µ k T q sat Slide No.

7 7 Effect of VS o δ δ..8.6 λ c = λ c =. δ dso... λ c =. U λ T c E c d = V D / U T dso ot affected by elocity because defied at V DS = δ becomes smaller tha the log-chael alue / Slide st -Order Approximatio of From full expressio W µ ( Qi ) TC = E V x µ D µ dv + T µ + + V Ex µ µ S Neglectig carrier heatig (T C =T ) ad the µ term, leads to W µ ( x) ( Q ( x)) dx Thermal oise coductace is the itegral of the product of the mobility ad the iersio charge alog the chael i dx Slide No.

8 8 Effect of VS o Charge ad Mobility Profiles p =, q s =, q d = q i ad u q i 8 6. λ c =. λ c =. q i ad u q i for λ c = q i λ c =. u q i. Iersio charge icreases due to elocity saturatio The µ Q i product ad hece decreases due to VS source ξ = x / drai λ c =. λ c =. λ c =. Slide Effect of VS o Trascoductaces λ c = V P pich-off oltage g mssat λ c =. λ c =. /λ c = V P V V T 6 8 /λ c = p = V P / U T Trascoductace is limited by elocity saturatio This will affect the γ oise excess factor Slide 6 No.

9 9 Effect of VS o δ ad γ (i saturatio) δ sat λ c =. δ sat ad γ sat γ sat λ c =. λ c = λ c = γ m λ c =. λ c =. p = V P / U T Because of m degradatio due to elocity saturatio, the γ oise excess icreases to alues much larger tha the log-chael alue Slide 7 Carrier Heatig (CH) Effect of elocity saturatio is closely liked to carrier heatig Carrier temperature T C correspodig to mobility model gie by TC E x ( e) E = x + = + where e T Ec E c Itroducig temperature depedace ito the oise coductace, ca the be split ito δ δ + = + = where accouts for VS oly ad h for additioal CH Same splittig ca be applied to the δ ad γ oise factors δ h h γ γ + = γ h Slide 8 No.

10 Combied Effects of VS ad CH o δ (saturatio). λ c =. δ sat, δ hsat, δ sat δ sat δ hsat δ sat δ + δ sat = δ sat hsat. p = V P / U T Carrier heatig icreases δ sat which gets back to a alue slightly larger tha the log-chael alue / Slide 9 Combied Effects of VS ad CH o γ (saturatio) λ c =. γ sat, γ hsat, γ sat 8 6 γ sat γ hsat γ + γ sat = γ sat hsat γ sat p = V P / U T Carrier heatig ee further icreases γ sat to alues much larger tha the log-chael alue ( / ) Slide No.

11 MRV ad CM Effects o δ g = V / U T = 7 =.8 µ m E c = V/ µ m ( λ c =.) θ =. χ = m o MRV, with CM δ with MRV, with CM o MRV, o CM with MRV, o CM 6 7 d = V D / U T MRV teds to decrease δ, whereas CM icreases δ, resultig i a alue close to that obtaied with VS ad CH oly Slide MRV ad CM Effects o δ (i saturatio) d = V D / U T = 7 =.8 µ m E c = V/ µ m ( λ c =.) θ =., χ = m Scholte (IEDM99) =.7 µ m Che (TED) =.8 µ m o MRV, with CM δ sat with MRV, with CM with MRV, o CM o MRV, o CM p = V P / U T Slide No.

12 MRV ad CM Effects o γ (i saturatio) sat γ g = V / U T = 7, =.8 µ m E c = V/ µ m ( λ c =.) θ =., χ = m with MRV, with CM (left axis) o MRV, o CM (right axis) CM teds to icrease γ further, whereas MRV reduces it back to alues close to about o MRV, with CM (right axis) with MRV, o CM (left axis) p = V P / U T γ sat Slide Coclusio VS, CH, MRV ad CM ects hae bee accouted for whe ealuatig the chael thermal oise ad the oise factors Two differet oise factors δ ad γ to be cosidered that are differetly affected by short chael ects δ is usefull for deice modelig but useless for circuit desig, whereas γ is more dedicated to circuit desig VS ad CH hae opposite ects o δ but lead to a icrease of γ MRV ad CH hae compesatig ects o both δ ad γ Accoutig for all ects leads to alues of δ (~ ) close to those measured by Scholte ad Che o seeral CMOS processes Slide No.