MOS Field Effect Transistors A gate contact gate interconnect n polysilicon gate source contacts W active area (thin oxide area) polysilicon gate contact metal interconnect drain contacts A bulk contact source interconnect deposited oxide source interconnect (a) n polysilicon gate edge of active area bulk drain interconnect interconnect field oxide n source diffusion [ p-type ] L gate oxide drain interconnect n drain diffusion L diff p (b)
MOSFET Circuit Symbols Two complementary devices (each with two symbols): both are very useful p-substrate (n-type channel under gate oxide) n-substrate (p-type channel under gate oxide) G n _ D V DS > 0 B _ V BS S G n D S B _ G V SG p S V _ SB B V SD > 0 D G p S D B (a) n-channel MOSFET (b) p-channel MOSFET Drain n Source p Gate p Bulk or Body Gate n Bulk or Body Source n Drain p Four electrical terminals: source (lowest potential for n-channel highest for p- channel) drain gate and bulk. Basic concept: inversion layer (called the channel) formed under gate between source and drain enables drift current
n-channel MOSFET Drain Characteristics Set-up: I G = 0 V DB = V DS > 0 to reverse-bias pn junctions to bulk. Measurement scheme: short bulk to source to make it a three terminal device vary gate voltage drain voltage and see effect on drain current. D n ( V DS ) G S B V DS (a) = 3.5 V 600 n (µa) 500 400 300 200 100 (triode region) V DS = V Tn = 1 V constant current (saturation) region = 3 V = 2.5 = 0 0.5 1 V (cutoff region) = 2 V = 1.5 V 1 2 3 4 (b) 5 V DS (V)
p-channel MOSFET Drain Characteristics Set-up: I G = 0 V BD = V SD > 0 to reverse-bias pn junctions to bulk. Measurement scheme: short bulk to source to make it a three terminal device vary gate voltage drain voltage and see effect on drain current - S V SG _ V SD G B V G p _ D V D 5 V (V SG V SD ) (a) V SG = 3.5 V 300 p (µa) 250 200 150 100 50 (triode region) V SD = V SG V Tp = V SG 1 V V SG = 3 V (saturation region) V SG = 25 V SG = 0 0.5 1 V (cutoff region) V SG = 2 V V SG = 1.5 V 1 2 3 4 (b) 5 V SD (V)
Quantitative MOSFET Step 1. Connect the MOS capacitor results for the electron charge in the inversion layer Q N to the drain current. V DS _ n source polysilicon gate y = y * 0 x metal interconnect to gate n polysilicon gate y p-type metal interconnect to bulk (a) W y* t ox E y (y * ) n drain gate oxide x channel electrons at position y = y * drifting with velocity v y (y * ) from source to drain x (b)
Drift Current Equation Drift current for electrons in the channel: J y ( x y) = qnx ( y)v y () y The drain current at position y is the integral of the drift current density across the cross section. Since the conventional direction of is opposite to the direction of the y axis we insert a minus sign: x x = W J y ( x y)dx = Wv y () y qn( x y)dx 0 0 The integral is the negative of the electron charge in the channel per unit area at point y. The symbol for this quantity is - Q N (y): = Wv y ()Q y N () y Note that isn t a function of the position in the channel
MOSFET DC Model: a First Pass metal interconnect to gate V GS _ n polysilicon gate Start simple -- small V DS makes the channel uniform V DS (< 0.1 V) n source 0 x y Q N p-type metal interconnect to bulk y = L n drain Channel charge: MOS capacitor in inversion with V GB =. Q N = C ox ( V GB V Tn ) = C ox ( V Tn ) Drift velocity: electric field is just E y = - V DS / L so v y = - µ n (-V DS / L) Drain current equation for V DS small... say less than 0.1 V. W = µ n C ox ---- ( VGS V L Tn )V DS Note that is proportional to V DS with channel resistance under gate control. This voltage controlled resistor region is sometimes useful.
Triode Region metal interconnect to gate n polysilicon gate Increase V DS -- channel charge becomes a function of position y. V DS _ n source 0 y x Q N (y) p-type metal interconnect to bulk n drain y = L First pass: approximate the drain current equation by taking averages of the channel charge and the drift velocity (Second pass: Section 4.4 (not assigned)) WQ N v y Average drift velocity: still use µ n (V DS / L) -- which is a very rough approximation.
Triode Region (Cont.) Next approximate the average channel charge by averaging Q N (y=0) at the source end and Q N (y=l) at the drain end of the channel: Q N ( y=0) = C ox ( V Tn ) At the drain end the positive drain voltage reduces the magnitude of the channel charge... why? The effect can be approximated by using V GD (the drop from drain to channel at y = L) -- Q N ( y=l) = C ox ( V GD V Tn ) = C ox ( V DS V Tn ) Note that V GD = - V DS > V Tn in order for there to be a channel left at the drain end. Substituting we derive the equation for the triode region which is defined by - V DS > V Tn and > V Tn. = µ n C W ox ---- ( VGS V L Tn V DS 2)V DS
Drain Characteristics Example: µ n C ox (W/L) = 50 µa/v 2 V Tn = 1 V and (W/L) = 4. (µa) 1000 800 = 4 V SAT 600 400 = 3 V 200 = 2 V < V Tn 0 1 2 3 4 V DS (V) What happens when V DS > - V Tn = V DS(sat)? Q N (y = L) = 0! Initial thought is that the lack of a channel at the drain end means that must drop to zero... WRONG! Drain terminal loses control over channel --> drain current saturates and remains constant (to first approximation) at the value given by V DS = V DS(sat).
Saturation Region When > V Tn and V DS > V DS(sat) = - V Tn the drain current is: W = ( sat ) = µ n C ox ------ ( VGS V 2L Tn ) 2 V DSSAT metal interconnect to gate I V DSAT GS _ n polysilicon gate n source 0 y n drain x Q N (y = L) = 0 p-type metal interconnect to bulk Full model: (µa) 1000 800 600 400 triode region Eq. (4.17) SAT = 4 V vs. V DSSAT constant current (saturation) region Eq. (4.21) = 3 V 200 = 2 V 0 1 2 3 4 V DS (V) < 1 V
MOSFET Circuit Models n-channel MOSFET drain current in cutoff triode and saturation: = 0 A ( V Tn ) = µ n C ox ( W L) [ V Tn ( V DS 2) ]( 1 λ n V DS )V DS ( VGS V Tn V DS V Tn ) = µ n C ox ( W ( 2L) )( V Tn ) 2 ( 1 λ n V DS ) ( VGS V Tn V DS V Tn ) Numerical values: µ n is a function of along the channel and is much less than the mobility in the bulk (typical value 215 cm 2 /(Vs) ) -- therefore we consider that µ n C ox is a measured parameter. Typical value: µ n C ox = 50 µav -2 λ n sometimes called the channel length modulation parameter increases as the channel length L is reduced: 0.1µmV 1 λ n ------------------------- L The triode region equation has (1 λ n V DS ) added in order to avoid a jump at the boundary with the saturation region. For hand calculation of DC voltages and currents this term is usually omitted from. V Tn = threshold voltage = 0.7-1.0 V typically for an n-channel MOSFET.
Backgate Effect The threshold voltage is a function of the bulk-to-source voltage V BS through the backgate effect. V Tn = V TOn γ n ( V BS 2φ p 2φ p ) where V TO is the threshold voltage with V BS = 0 and γ is the backgate effect parameter γ n = ( 2qε s N a ) C ox Physical origin: V BS (a negative voltage to avoid forward biasing the bulk-tosource pn junction) increases the depletion width which increases the bulk charge and thus the threshold voltage. = ( V DS V BS ) since V Tn = V Tn (V BS ) Common situation is that V BS = 0 by electrically shorting the source to the bulk (either the substrate or a deep diffused region called a well) source and bulk terminals are shorted together --> no backgate effect p n source p well n substrate n drain For this case V Tn = V TOn.
p-channel MOSFETs Structure is complementary to the n-channel MOSFET In a CMOS technology one or the other type of MOSFET is built into a well -- a deep diffused region -- so that there are electrically isolated bulk regions in the same substrate n-channel p-channel MOSFET MOSFET (a) A A common bulk contact for all n-channel MOSFETs (to ground or to the supply) isolated bulk contact with p-channel MOSFET shorted to source (b) p n source n drain p drain p source n p-type substrate n well