June 26, 2004 oal of this chapter Chapter 2 MO Transistor Theory oonchuay upmonchai Integrated esign Application Research (IAR) Laboratory June 16th, 2004; Revised June 16th, 2005 q Present intuitive understanding of device operation q Introduction of device basic equations q Introduction of models for manual analysis First-Order Model q Analysis of secondary and deep-sub-micron effects q Future trends 2102-545 igital ICs MO Transistor Theory 2 The iode iode - epletion Region Al A io 2 hole diffusion electron diffusion p p n (a) Current flow. Cross-section of pn-junction in an IC process A diode symbol 2102-545 igital ICs MO Transistor Theory 3 A p n One-dimensional representation Mostly occurring as parasitic element in igital ICs n Al Charge ensity Electrical Field Potential -W 1 hole drift electron drift - r x V + W 2 x istance 2102-545 igital ICs MO Transistor Theory 4 y 0 x x (b) Charge density. (c) Electric field. (d) Electrostatic potential. 2102-545 igital ICs 1
June 26, 2004 iode - Zero ias iode - Forward ias q uild-in (Electrostatic) Potential: current Ê f 0 = f T ln N AN ˆ Á 2 Ë n i f T = Thermal Voltage = kt/q = 26 mv at 300 K (i) n i = Intrinsic carrier concentration ~ 1.5 x 10 10 cm -3 N A = Acceptor concentration (atoms/cm 3 ) N = onor concentration (atoms/cm 3 ) 2102-545 igital ICs MO Transistor Theory 5 Excess Carriers Excess Carriers iffusion iffusion Typically avoided in igital ICs 2102-545 igital ICs MO Transistor Theory 6 iode - Reverse ias iode Types current iffusion iffusion 0.37p n0 Linear Approximation Exponentially istributed The ominant Operation Mode 2102-545 igital ICs MO Transistor Theory 7 hort-ase iode is the standard in semiconductor devices 2102-545 igital ICs MO Transistor Theory 8 2102-545 igital ICs 2
June 26, 2004 iode Current Models for iode Manual Analysis V + I V + I + V on (typ. 0.7 V) V = iode ias Voltage, I = iode Current 2102-545 igital ICs MO Transistor Theory 9 Ideal iode Model I = I e V f ( T -1) First-order iode Model I s = aturation Current ~ 10-17 A/mm 2 2102-545 igital ICs MO Transistor Theory 10 Example: A iode Circuit iode - Junction Capacitance 1: I = I [exp(v /f T ) - 1] 2: I = (V - V )/R Using V (ON) = 0.7 V I = 0.23 ma V = 0.7 V raphic olution I = 0.224 ma V = 0.757 V C j = C j 0 ( ) m 1-V f 0 C j0 = Zero-iased Junction Capacitance = f(physical parameters) m = rading Coefficient (0.5 - Abrupt, 0.33 - linear ) 2102-545 igital ICs MO Transistor Theory 11 2102-545 igital ICs MO Transistor Theory 12 2102-545 igital ICs 3
June 26, 2004 iode - iffusion Capacitance iode witching Time V 1 R src V V 2 t = 0 t = T V src I Excess charge pace charge C d = dq di = t T ª t T I dv dv f T t = mean transit time V ON OFF ON witching Time is strongly determined by how fast the charge can be moved around = average time for a carrier to be transported from the junction to the metallic contact Time 2102-545 igital ICs MO Transistor Theory 13 2102-545 igital ICs MO Transistor Theory 14 iode - econdary Effects I iode - econdary Effects II Avalanche reakdown Temperature Effects E crit = 2x10 5 V/cm f T µ T I = f(t) Theory: 2X every 5ºC Experiment: 2X every 8ºC -20 reakdown Voltage At Critical Field E crit, carriers crossing the depletion region is accelerated to high velocity such that when they collide with immobile silicon atoms, electron-hole pairs are created 2102-545 igital ICs MO Transistor Theory 15 I increases 6% per ºC (2X every 12 º C) (For fixed I ) V decreases 2mV per ºC 2102-545 igital ICs MO Transistor Theory 16 2102-545 igital ICs 4
June 26, 2004 iode PICE Model PICE iode Model Parameters + I R Neutral Regions + V V I C - - I = I e V nf ( T -1) C j = C j 0 ( ) m + t T I 1-V f 0 n = emission coefficient ( 1) f T e V nf T 2102-545 igital ICs MO Transistor Theory 17 2102-545 igital ICs MO Transistor Theory 18 What is a MO(FET) Transistor? q Metal-Oxide-emiconductor Field-Effect Transistor (MOFET, or MO, for short) q A Four-terminal device ate controls how much current can flow from the ource to the rain. ody modulates device characteristics and parameters - secondary effect. q A switch! 2102-545 igital ICs MO Transistor Theory 19 MO Transistors - Types and ymbols NMO with ulk Contact NMO epletion 2102-545 igital ICs MO Transistor Theory 20 NMO Enhancement PMO Enhancement The ody terminal, if not shown, is assumed to be connected to the appropriate supply. 2102-545 igital ICs 5
June 26, 2004 witch Model of NMO Transistor witch Model of PMO Transistor V ate V ate ource (of carriers) rain (of carriers) ource (of carriers) rain (of carriers) Open (off) (ate = 0 ) Closed (on) (ate = 1 ) R on Open (off) (ate = 0 ) Closed (on) (ate = 1 ) R on V < V T V > V T V > V V T V < V V T 2102-545 igital ICs MO Transistor Theory 21 2102-545 igital ICs MO Transistor Theory 22 Why MO Transistor? q MO performs well as a switch with very few parasitic effects. q Relatively imple manufacturing process (compared to other types of transistor) q High Integration ensity Large and Complex circuits can be created economically. The NMO Transistor Polysilicon Aluminum 2102-545 igital ICs MO Transistor Theory 23 2102-545 igital ICs MO Transistor Theory 24 2102-545 igital ICs 6
June 26, 2004 The NMO Transistor Cross ection ource n+ W Polysilicon ate L p substrate ulk (ody) ate oxide rain n+ Field-Oxide (io 2 ) p+ stopper n areas have been doped with donor ions (arsenic) of concentration N - electrons are the majority carriers p areas have been doped with acceptor ions (boron) of concentration N A - holes are the majority carriers MO Transistors - ehaviors q tatic ehavior: Threshold Voltage Channel-Length Modulation Velocity aturation ub-threshold Conduction q ynamic (Transient) ehavior: MO tructure Capacitances Channel Capacitances Junction Capacitances ources-rain Parasitic Resistance 2102-545 igital ICs MO Transistor Theory 25 2102-545 igital ICs MO Transistor Theory 26 Threshold Voltage Concept n channel V + n+ n+ p substrate The value of V where strong inversion occurs is called the threshold voltage, V T 2102-545 igital ICs MO Transistor Theory 27 depletion region Threshold Voltage Components I q Work function difference between the gate and the channel, f C f C = f F (substrate) - f M for metal gate f C = f F (substrate) - f F (gate) for polysilicon gate q ate voltage component to change (invert) the surface potential, 2f F Fermi Potential, f F = f T ln(n A / n i ) f F ~ -0.3 V for p-type silicon substrate 2102-545 igital ICs MO Transistor Theory 28 2102-545 igital ICs 7
V T (V) June 26, 2004 Threshold Voltage Components II q ate voltage component to offset the depletion region charge, Q / C ox ate Oxide Capacitance per unit area, C ox = e ox / t ox epletion region charge, Q = 2qN A e si -2f F -V q Voltage component to offset fixed charges in the gate oxide and in the silicon-oxide surface, Q / C ox q Threshold adjustment by applying the ion implantation into the channel, Q I / C ox 2102-545 igital ICs MO Transistor Theory 29 The Threshold Voltage V T = f C - 2f F - Q C ox - Q C ox - Q I C ox V T = V T 0 + g ( -2f F + V - -2f F ) V T 0 = V T V = 0 g = 2q N Ae si C ox ody-effect coefficient 2102-545 igital ICs MO Transistor Theory 30 The ody Effect - Empirically 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4-2.5-2 -1.5-1 -0.5 0 V (V) V normally positive for n-channel devices with the body tied to ground A negative bias causes V T to increase from 0.45V to 0.85V 2102-545 igital ICs MO Transistor Theory 31 V Transistor in Resistive (Linear) Mode Assume V > V T n+ - V(x) + n+ x The current is a linear function of both V and V 2102-545 igital ICs MO Transistor Theory 32 V I 2102-545 igital ICs 8
June 26, 2004 Transistor in aturation I-V Relations: Long-Channel evice Assume V > V T V V > V - V T Quadratic Relationship n+ - V -V T + n+ x Pinch-off The current remains constant (saturates). 2102-545 igital ICs MO Transistor Theory 33 Linear Relationship Effective Length of the conductive channel is inversely proportional to V 2102-545 igital ICs MO Transistor Theory 34 Long-Channel I-V Plot (NMO) cut-off I (A) X 10 6-4 5 4 3 2 1 V = V - V T Linear V = 2.5V V = 2.0V aturation V = 1.5V V = 1.0V 0 0 0.5 1 1.5 2 2.5 V (V) NMO transistor, 0.25um, L d = 10um, W/L = 1.5, V = 2.5V, V T = 0.4V 2102-545 igital ICs MO Transistor Theory 35 Quadratic dependence Velocity aturation u n (m /s ) Constant velocity Constant mobility (slope = µ) Ï m n x Ô for x x u = Ì c 1+ x x c Ó Ô u sat for x > x c u sat = 10 5 x c = 1.5 x (V/µm) 2102-545 igital ICs MO Transistor Theory 36 2102-545 igital ICs 9
June 26, 2004 hort-channel evices I-V Relation: hort-channel evices I V = V Long-channel device hort-channel device q Linear Region: V V V T I = k(v ) k n W/L [(V V T )V V 2 /2] where k(v) = 1/(1 + (V/x c L)) is a measure of the degree of velocity saturation V AT Extended saturation V - V T V For an NMO device with L of.25mm, only a couple of volts between and are needed to reach velocity saturation 2102-545 igital ICs MO Transistor Theory 37 q aturation Mode: V = V AT V V T I AT = k(v AT ) k n W/L [(V V T )V AT V AT2 /2] where V AT = (V V T )k(v V T ) 2102-545 igital ICs MO Transistor Theory 38 hort-channel IV Plots (NMO) I (A) X 10 2.5-4 2 1.5 1 0.5 Linear Early Velocity aturation aturation V = 2.5V V = 2.0V V = 1.5V V = 1.0V 0 0 0.5 1 1.5 2 2.5 V (V) NMO transistor, 0.25um, L d = 0.25um, W/L = 1.5, V = 2.5V, V T = 0.4V 2102-545 igital ICs MO Transistor Theory 39 Linear dependence I (A) Velocity aturation Effects 6 5 4 3 2 1 0 X 10-4 I -V Characteristics long-channel quadratic (for V = 2.5V, W/L = 1.5) short-channel linear 0 0.5 1 1.5 2 2.5 V (V) q hort-channel evices tend to operate in saturation conditions more often than the longchannel devices. q Velocity-saturation causes the short-channel device to saturate at substantially smaller values of V resulting in a substantial drop in current drive 2102-545 igital ICs MO Transistor Theory 40 2102-545 igital ICs 10
June 26, 2004 A PMO Transistor ub-threshold Conduction I (A) -0.2-0.4-0.6-0.8 0 x 10-4 V = -1.0V V = -1.5V V = -2.0V V = -2.5V Assume all voltage Variables negative! -1-2.5-2 -1.5-1 -0.5 0 V (V) PMO transistor, 0.25um, L d = 0.25um, W/L = 1.5, V = -2.5V, V T = -0.4V 2102-545 igital ICs MO Transistor Theory 41 ) (A ) (I ln I (A) 10-2 10-4 10-6 10-8 10-10 Quadratic region 90 mv/decade Linear region ubthreshold exponential region 10-12 0.0 V 1.0 2.0 3.0 T V (V) Ê = n kt ˆ Á ln 10 Ë q ( ) Charges are leaking through the devices, of which the rate is determined by the slope factor in the subthreshold region 2102-545 igital ICs MO Transistor Theory 42 A Unified Model for Manual analysis imple Model versus PICE For NMO, all five parameters (V TO, g, V AT, k, l) are positive. For PMO, they are negative. I (A) -4 x 10 2.5 2 1.5 Linear V =V AT PICE Velocity aturated Model 1 0.5 V =V T aturated V AT =V T 0 0 0.5 1 1.5 2 2.5 V (V) 2102-545 igital ICs MO Transistor Theory 43 2102-545 igital ICs MO Transistor Theory 44 2102-545 igital ICs 11
June 26, 2004 Transistor Model for Manual analysis The Transistor Modeled as a witch Parameters for manual model of generic 0.25 um CMO process (Minimum length device) q q NMO PMO V T0 (V) 0.43-0.4 g(v 0.5 ) 0.4-0.4 V AT (V) 0.63-1 k (A/V 2 ) 115 x 10-6 -30 x 10-6 l(v -1 ) 0.06-0.1 Caution! Try to extrapolate the behavior of the device other than W and L given in the table can lead to sizable errors. igital Circuits usually use Minimum Length devices R eq (Ohm) x10 5 7 6 5 4 3 2 1 0 V V T R o n 0.5 1 1.5 2 2.5 V (V) (for V = V, V = V ÆV /2) V (V) NMO(kW) PMO (kw) 1 35 115 1.5 19 55 Modeled as a switch with infinite off resistance and a finite on resistance, R on l Resistance inversely proportional to W/L (doubling W halves R on ) 2 15 38 l For V >>V T +V AT /2, R on independent of V l Once V approaches V T, R on increases dramatically 2.5 13 31 R on (for W/L = 1) For larger devices divide R eq by W/L 2102-545 igital ICs MO Transistor Theory 45 2102-545 igital ICs MO Transistor Theory 46 ynamic ehavior of MO Transistor MO Transistor Capacitances C C C C C 2102-545 igital ICs MO Transistor Theory 47 2102-545 igital ICs MO Transistor Theory 48 2102-545 igital ICs 12
June 26, 2004 Overlap Capacitances ate-channel Capacitances Polysilicon gate ource n + x d x d rain W n + C ox = e ox t ox (F/m 2 ) Cut-off Resistive aturation L d Top view ate-bulk overlap C ol = C ox x d W = C o W ate oxide C gso = C gdo = C ol t ox n + L n + Cross section *C fringe = (2e ox /p) ln (1+T poly /t ox ) Most important regions in digital design: saturation and cut-off 2102-545 igital ICs MO Transistor Theory 49 2102-545 igital ICs MO Transistor Theory 50 Variation of ate-channel Capacitances iffusion Capacitances WLC ox WLC ox 2 C C V T C C C C = C C V WLC ox WLC ox 2 C C C C C C 0 V /(V -V T ) 1 2WLC ox 3 io 2 p ate 4 3 L 5 1 2 W n+ x j ubstrate Capacitance as a function of V (with V = 0) Capacitance as a function of the degree of saturation C diff = C ottom + C idewall = C 1 + (C 2 + C 3 + C 4 + C 5 ) C diff = C j L W + C jsw (2L + W ) 2102-545 igital ICs MO Transistor Theory 51 2102-545 igital ICs MO Transistor Theory 52 2102-545 igital ICs 13
June 26, 2004 Junction Capacitance: Recap Linearizing the Junction Capacitance Replace non-linear capacitance by large-signal equivalent linear capacitance which displaces equal charge over voltage swing of interest 2102-545 igital ICs MO Transistor Theory 53 2102-545 igital ICs MO Transistor Theory 54 MO Transistor Capacitance: ummary ate Capacitances in 0.25 mm CMO process Capacitance parameters of NMO and PMO transistors in 0.25 mm CMO process. C = C gs + C gso C = C gd + C gdo ource C = C gb C = C diff rain C = C diff q For an NMO transistor with t ox = 6 nm, L = 0.24 mm, W = 0.36 mm, L = L = 0.625 mm Total ate Capacitance C = C g + 2C ol = 0.7 ff C = C = 0.89 ff ody 2102-545 igital ICs MO Transistor Theory 55 2102-545 igital ICs MO Transistor Theory 56 2102-545 igital ICs 14
June 26, 2004 Parasitic Resistance The M MO Transistor V,eff R R Polysilicon gate L rain contact q econdary Effects become more pronounce in the deep-submicron transistor. Threshold Variations Hot Carrier Effects W CMO Latchup R, = L, W R sq + R C R sq = heet Resistance per square (20-100 ohms/sq.) R C = Contact Resistance rain Careless Layout may lead to resistances that severely degrade device performance. 2102-545 igital ICs MO Transistor Theory 57 q esigning the circuits with all secondary effects taken into account is intractable and results can be obscure. q Analyze with first-order model, then readjust the model with the help of CA simulation tools. 2102-545 igital ICs MO Transistor Theory 58 Threshold Variations Hot Carrier Effects V T Long-channel threshold V T Low V threshold q Electrons become hot, i.e. reaching a critical high level of energy, under intense electric field which occurs when the channel is short. E crit 10 4 V/m hort-channel threshold q Hot electrons can leave the silicon and tunnel into the gate oxide. Threshold as a function of the length (for low V ) L V rain-induced barrier lowering or IL (for low L) q Electrons trap in the gate oxide increase NMO threshold and decrease PMO threshold. q Hot electron phenomenon leads to a long-term reliability problem. 2102-545 igital ICs MO Transistor Theory 59 2102-545 igital ICs MO Transistor Theory 60 2102-545 igital ICs 15
June 26, 2004 CMO Latch-up Future Perspectives V V p + n + n + p + p + n + R nwell p-source n-well R nwell R psubs p-substrate n-source R psubs (a) Origin of latchup (b) Equivalent circuit q q q Latchup causes positive feedback of the current until the circuit fails or burns out. To avoid Latchup, R nwell and R psubs should be minimized. evices carrying a lot of current need uard Rings. 2102-545 igital ICs MO Transistor Theory 61 25 nm FINFET MO transistor 2102-545 igital ICs MO Transistor Theory 62 2102-545 igital ICs 16