IN3170/4170, Spring 2020 Philipp Hfliger hafliger@ifi.uio.no - PowerPoint PPT Presentation

IN3170/4170, Spring 2020 Philipp Häfliger hafliger@ifi.uio.no Excerpt of Sedra/Smith Chapter 5: CMOS Field Effect Transistors (FETs)

Content CMOS FET Large Signal Models (book 5.1-5.2) MOSFET circuits at DC (book 5.3) Further Model Refinements (book 5.4, will be discussed later)

Content CMOS FET Large Signal Models (book 5.1-5.2) MOSFET circuits at DC (book 5.3) Further Model Refinements (book 5.4, will be discussed later)

Device Concept

Device Cross Section

Short Sidetrack: PN-junction (from book: Carusone, Johns, Martin) C j 0 C j = ( 1 . 17 ) � 1 + V R Φ 0 � qK S ε 0 N A N D C j 0 = ( 1 . 18 ) 2 Φ 0 N A + N D � N A N D � Φ 0 = U T ln ( 1 . 6 ) n 2 i

nFET/NMOS and pFET/PMOS cross section

nMOSFET Device Symbols

pMOSFET Device Symbols

The EKV model (Check hand out paper by Vittoz, equations (1)-(12).) i D = i F − i R � 2 vG − Vtn − nvS ( D ) � i F ( R ) = I S ln 1 + e ( 1 + λ v DS ) nVT (Note that parameter λ is also expressed as the Early Voltage V A = 1 λ and V A is proportional to the transistor length L and thus sometimes expressed as V A = V ′ A L , where V ′ A is a process parameter.) This complete formula is usually simplified for 4 specific regions of operation as follows. (The book only consider those region dependent simpler equations.

Regions of operation: strong- vs weak inversion This two regions of operation are dependent on v GS !!! INDEPENDENT of the active- and triode region of operation (see next slide) the transistor can operate in either: weak inversion = subthreshold vs. strong inversion = above threshold These are dependent on v GS ≥ V tn for strong inversion and v GS < V tn for weak inversion. The transition between the two is not really aprupt and refered to as moderate inversion.

Regions of operation: triode- vs active region This two regions of operation are dependent on v DS !!! INDEPENDENT of weak- and strong inversion the transistor can operate in either: Triode region = ’linear’ region vs. saturation = active region These are dependent on v DS ≥ V sat for active region and v DS < V sat for triode region, where the definition of V sat is different dependent on if the transistor is in weak ( V sat ≈ 4 V T )or strong inversion ( V sat = V OV ).

Regions of operation summary So there are 4 differnt combinations possible: 1) weak inversion, triode region OR 2) weak inversion, active region OR 3) strong inversion, triode region OR 4) strong inversion, active region!

strong inversion, active region i D = 1 2 nk n ( v G − V tn − nv S ) 2 ( 1 + λ v DS ) Different name in the EKV model: β := k n and 1 ≤ n ≤ 2 and often n ≈ 1 and is neglected

weak inversion, active region vG − Vtn − nvS i D = I S e ( 1 + λ v DS ) ( 16 . 13 ) nVT Where I S = 2 nk n V 2 T

strong inversion, triode region (Note: term ∗ ( 1 + λ v DS ) neglected here ... not so influential for small v DS ) EKV: v G − V tn − n � � i D = k n v DS 2 ( v D + v S ) Sedra & Smith: � � v OV − 1 i D = k n v DS 2 v DS Which is the same for v S = 0 and n = 1 For v DS << V OV (1st order Taylor expansion around v DS = 0): i D = k n v OV v DS ⇒ g DS = k n v OV

weak inversion, triode region EKV: � � vG − Vtn − vS − vD VT − e i D = e nVT e VT For v S = 0: � � vOV − vD i D = e nVT 1 − e VT For v DS << V OV (1st order Taylor expansion around v DS = 0): vOV nVT V D vOV nVT 1 i D = e ⇒ g DS = e V T V T

Illustration I D vs V GS

Illustration I D vs V GS ’old school’ without considering weak inversion. (fig. 5.14)

Illustration I D vs V DS , channel length modulation Here in saturation, but this works in subthreshold too. (fig. 5.17)

Chapter 5 NFET Note! Chapter 5 only treats Above Threshold Regions of Operation ’Above Threshold’ is also called ’Strong Inversion’

Chapter 5 PFET ’Above Threshold’ is also called ’Strong Inversion’

Subthreshold in book? Mentioned in passing in chapter 5 and equation in chapter 16.1.4

Effects of Parameter Tweaking: λ λ can be tweaked at design time by changing L : note that λ = V A = L ∗ V ′ A where V ′ A is a process parameter.

Effects of Parameter Tweaking: k n k n can be tweaked at design time by chaging W / L . Note that k n = W L µ C ox where µ C ox is a process parameter.

Effects of Parameter Tweaking: v tn , v tp v tn , v tp cannot be tweaked at design time. They are process parameters.

Content CMOS FET Large Signal Models (book 5.1-5.2) MOSFET circuits at DC (book 5.3) Further Model Refinements (book 5.4, will be discussed later)

Diode Connected Transistor In strong inversion: I = 1 2 k n ( V − V tn ) 2

Simple Current Mirror When will I out = I in , I out � = I in , I out ≈ I in , I out ≈ xI in ?

Content CMOS FET Large Signal Models (book 5.1-5.2) MOSFET circuits at DC (book 5.3) Further Model Refinements (book 5.4, will be discussed later)