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332:578 Deep Submicron VLSI Design Lecture 3 Deep Sub-micron MOS Transistor Theory

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## 332:578 Deep Submicron VLSI Design Lecture 3 Deep Sub-micron MOS Transistor Theory

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**332:578 Deep SubmicronVLSI DesignLecture 3Deep Sub-micron**MOS Transistor Theory Michael L. Bushnell -- CAIP Center and WINLAB ECE Dept., Rutgers U., Piscataway, NJ Material from: Low-Power CMOS VLSI Circuit Design By Kaushik Roy and Sharat C. Prasad Deep Submicron VLSI Des. Lec. 3**Outline**• Deep Sub-micron Transistor Models • Subthreshold current and subthreshold swing • Drain Induced Barrier Lowering (DIBL) • Punchthrough • Gate Induced Drain Leakage (GIDL) • Summary Deep Submicron VLSI Des. Lec. 3**Deep Sub-Micron Threshold Equations**Deep Submicron VLSI Des. Lec. 3**Motivation for Transistor Review**• Reformulate MOSFET models and equations to: • Obtain better VT computation • Obtain critical subthreshold current • Obtain critical subthreshold swing • Calculate drain induced barrier lowering (DIBL) • Allows correct estimation and understanding of low-power currents Deep Submicron VLSI Des. Lec. 3**Definitions**• Egis Band gap energy of semiconductor in eV (1.1 eV for Si) • Eiis intrinsic energy level in undoped semiconductor (halfway through band gap) • Ecis energy at bottom of conduction band • Evis energy at top of valence band • EF = - q Fis the average energy (Fermi level) in conductor • VT is transistor threshold • d is insulator thickness • B is potential difference between Eiand EF Deep Submicron VLSI Des. Lec. 3**Ideal MIS Diode**• Type p semiconductor • At V = 0, • fms = energy difference between metal & semiconductor • c = semiconductor electron affinity • fms = fm – (c + + B ) = 0 • Flat-band condition – usually have to apply VFB (flat-band voltage) to cause this to happen Eg 2q Deep Submicron VLSI Des. Lec. 3**Definitions**• pois hole concentration in semiconductor in equilibrium • ppis hole concentration in semiconductor p side of junction • npis e- concentration in semiconductor in equilibrium • niis intrinsic carrier concentration in undoped semiconductor of both holes and e- • k is Boltzmann’s constant • T is absolute temperature in degrees Kelvin • NA is acceptor concentration • ND is donor concentration • es is dielectric constant of Si • b = q / kT (reciprocal of thermal voltage) • E is the electric field • d is depletion region depth Deep Submicron VLSI Des. Lec. 3**Accumulation**(Ei – EF) / kT • p0 = ni e • Energy bands when a negative voltage is applied: Deep Submicron VLSI Des. Lec. 3**Weak Inversion**• Energy bands when small positive bias voltage is applied: Deep Submicron VLSI Des. Lec. 3**Strong Inversion**• Ei at surface now below EF by 2 B =fS • B or B = bulk potential difference between EF and Ei • VT = voltage necessary to cause strong inversion Deep Submicron VLSI Des. Lec. 3**Surface Space Charge and VT**• Charge sheet model • Poisson equation: D = r (x, y, z) • D = es E (disp. Vector) • r (x, y, z) = total electric charge density • Neglect fringing fields at edge of transistor, so E isnormal to SiO2 insulator D Deep Submicron VLSI Des. Lec. 3**Derivation of Bulk Charge**Deep Submicron VLSI Des. Lec. 3**Problem**• Next slides introduce the conventional VT derivation and model • Problem: Simply does not work any more for l < 0.35 mm due to: • Much greater sub-threshold current, which is due to carriers diffusing in the channel before VGS exceeds VT • VT no longer behaves the way the conventional model predicts • Less susceptible to body effect • Much more susceptible to VD (drain voltage) due to drain-induced barrier lowering (DIBL) • Much more susceptible to gate-induced drain leakage (GIDL) • Forced the adoption of a radically different transistor model • Will give a new, corrected model later • Models DIBL, GIDL, VT correctly using curve-fitting to measurements Deep Submicron VLSI Des. Lec. 3**Conventional VT Derivation**• From Gauss’s Law, total charge in semiconductor is: • Note:fs = surface potential = 2 fBat strong inv. • b = q / kT, d = SiO2 insulator thickness • Ci = insulator capacitance, i = insulator permittivity Deep Submicron VLSI Des. Lec. 3**Depletion Region Depth**• Depletion assumption – regard depletion layer as totally devoid of mobile charges • One-sided abrupt-junction assumption – carrier concentrations abruptly change to their intrinsic values at distance W (= depletion region depth) beneath surface • QT = total trapped charge at semiconductor-insulator boundary Deep Submicron VLSI Des. Lec. 3**Flat-Band Voltage and Depletion Layer Depth**• Poisson equation (used to compute depletion layer depth): Deep Submicron VLSI Des. Lec. 3**Depletion Layer Depth Wm at Strong Inversion**Deep Submicron VLSI Des. Lec. 3**Inversion Layer Charge**• Qi = inversion layer charge • Qd = depletion layer charge • Qs = surface charge Deep Submicron VLSI Des. Lec. 3**Inversion Layer Charge**Deep Submicron VLSI Des. Lec. 3**Inversion Layer Thickness ti**Deep Submicron VLSI Des. Lec. 3**Long-Channel MOSFETBody Effect**• VGS = VGB – VBS • Surface potential was fs, becomes fS + VBS relative to source • VT now becomes (relative to source): Deep Submicron VLSI Des. Lec. 3**Subthreshold Current – New Problem**• Weak inversion – variation of minority carrier concentration along channel Deep Submicron VLSI Des. Lec. 3**Subthreshold Current (cont’d)**• Consider grounded nFET source, VGS < VT, |V DS| 0.1 V • Weak inversion – VDS drop almost entirely across reverse-biased substrate-drain p-n junction • Small variation of fs along semiconductor surface • y component Ey = f / y is small • Due to few mobile carriers and small Ey, drift component of subthreshold ID,st negligible Deep Submicron VLSI Des. Lec. 3**Subthreshold Current (cont’d)**• Long channel allows the gradual channel approximation to be used • np = e • np depends exponentially on fs, np (y)/ y can be large • Diffusion current proportional to carrier concentration gradient – varies along y (distance along channel) bfs ni2 NA Deep Submicron VLSI Des. Lec. 3**Terminology**• A = channel cross-sectional area • Dn = electron diffusion coefficient • Z = channel width • ti = inversion layer thickness • Qi = ti q n (y) (per-unit inversion layer area charge) • Equilibrium electron concentration: • Charge in inversion layer (weak inversion): Deep Submicron VLSI Des. Lec. 3**Derivation (Continued)**Source: Drain: Deep Submicron VLSI Des. Lec. 3**Observation**• Different situation from MIS diode – potential gradient along y axis, must consider effect of VDS • ID,st is the subthreshold component of drain current Deep Submicron VLSI Des. Lec. 3**Subthreshold Current**• For long-channel MOSFET, subthreshold drain-source current remains independent of drain-source voltage • fs (y = 0) varies exponentially with applied gate voltage, so the drain-source current also does • Independence of ID,st from VDS ceases when L is as large as 2 mm when VDS is large enough to merge source and drain depletion regions (punchthrough) • Must prevent punchthrough, as it makes ID,st independent of gate control voltage • Must keep punchthrough current smaller than ID,st using implants Deep Submicron VLSI Des. Lec. 3**Subthreshold Swing**• Subthreshold swing is inverse of slope of logID,st vs. VGS • Cd = gate depletion layer capacitance • Ci = insulator layer capacitance • es = permittivity of semiconductor • ei = permittivity of insulator • d = insulator thickness • W = depletion layer thickness • Sst shows how effectively we can stop device drain current flow when VGS goes below VT (units of milliV/decade) Deep Submicron VLSI Des. Lec. 3**Subthreshold Swing (cont’d)**• Subthreshold swing (mV/decade) limits how small a power supply we can use • For d 0, Sst = 60 mV/decade (100 in practice) • Due to non-zero oxide thickness and other factors • Sst = 100 reduces ID,st from 1 mA/mm at VGS = VT = 0.6 V to 1 pA/mm at VGS = 0 V • Ways to make Sst smaller: • Thinner oxide layer to reduce d • Lower substrate doping (larger W) • Lower temperature • Lower substrate bias Deep Submicron VLSI Des. Lec. 3**Submicron MOSFET**• Number of circuits on chip and their speed grow exponentially • Make faster devices – Increase ID,st (now drain current in saturation) to charge/discharge parasitic C’s faster • Was predicted that: • L 2 mm, VT would be independent of L, Z, VDS • Instead, decreases with L, varies with Z (width), decreases as VDSincreases • Instead, VTincreases less rapidly with VBS than with longer channels • Need to understand these effects with small dimension MOSFETs – need to use curve-fitting to model SPICE parameters Deep Submicron VLSI Des. Lec. 3**Submicron Effects on VT**• Short-channel-length effect: • VT decreases with decreasing L and increasing VDS • Causes excessive leakage currents • Can only achieve VT in 0.6 to 0.8 V range with lightly doped substrate by using VTadjust implants to increase surface doping • Lowers carrier mobility, subthreshold current, etc. • When L same order of magnitude as width of drain-substrate or substrate-source depletion region: • Ionic charge in these depletion regions reduces charge needed by gate bias (added to total space charge) to cause inversion • Smaller VGS turns on device • Drain depletion area goes deeper into substrate, making turn-on VT even smaller when drain–substrate reverse bias increases Deep Submicron VLSI Des. Lec. 3**Modeling Problems**• To understand this, must numerically solve 2-dimensional Poisson equation • Charge-sharing model: considers channel charge to be shared among source, gate, and drain, didn’t work • Drain-induced barrier lowering (DIBL) – VT decreases due to depletion region charges in potential energy barrier between source and semiconductor surface. • Reduces 2-dimensional Poisson equation to 1-D by approximating 2f / x2 as a constant. Works for L = 0.8 mm and VDS as large as 3 V Deep Submicron VLSI Des. Lec. 3**Liu Model for DIBL**• Predicts short-channel threshold voltage shift DVT,sc for deep submicron devices • Quasi-2D solution of 2D Poisson equation • E has a horizontal component Ey (drain field) and vertical component Ex (due to gate charge) • Ex maximal at source and decreases with y to a minimum value at drain • Ex (x, y) value at insulator-semiconductor surface is Ex (0,y) and goes to 0 at bottom edge of depletion region (Ex (W, y) = 0) Deep Submicron VLSI Des. Lec. 3**DIBL Model**• Replace Ex/ x at each point (x,y) with its average of values at (0, y) and (W, y) • Use depletion approximation, so depletion region charge is simply the ionic charge (r (x, y) = qNA) Deep Submicron VLSI Des. Lec. 3**DIBL (cont’d)**Deep Submicron VLSI Des. Lec. 3**DIBL (cont’d)**• h is empirical fudge factor and W = Wm at onset of strong inversion • VsL = VGS – VT Effective gate voltage • Vbi is built-in potential at drain-substrate and substrate-source p-n junctions • Characteristic length: • Find DVT,sc by subtracting long-channel fs value at VT from minimum of fs(y), using plotting and curve fitting • Note that surface potential is never constant for L = 0.35 mm Deep Submicron VLSI Des. Lec. 3**Surface Potential Along Channel**Deep Submicron VLSI Des. Lec. 3**Finding DVT**• Subtract minimum value of fs(y) from RHS of Eq. (2.39) to get DVT,sc • If l > 5L, • Simplification: • Problem: h makes it hard to find l (the characteristic length) Deep Submicron VLSI Des. Lec. 3**Relating l to Lmin**• l can be related to minimum channel length Lmin needed in a MOSFET to make it have long-channel characteristics • If Lmin = 4 l, then • Leads to VT: Deep Submicron VLSI Des. Lec. 3**Relating l to Lmin**• Note that Wjis the junction depth Deep Submicron VLSI Des. Lec. 3**Significant Changes in VT**• Need: • Then, for nFET with n+ poly gate: • For nFET with p+ poly gate: • Old VTequation – becomes independent of VBS when L< 0.7mm: Deep Submicron VLSI Des. Lec. 3**DIBL Concluded**• Dropped e term as being negligibly small • For shorter channel lengths and higher drain biases, • VT less sensitive to VBS than Eq. (2.49) indicates • Instead, VT becomes completely independent of VBS when • L = 0.7 mm and for large values of VBS in all cases -2bfs-VBS Deep Submicron VLSI Des. Lec. 3**Narrow-Gate-Width Effects**• Have less effect on VT than short-channel effects • View channel as rectangle in horizontal cross section • First two effects caused by MOSFETs with raised field-oxide isolation or semi-recessed local oxidation (LOCOS) • 1st effect: • Parallel edges border drain and source, and therefore are on depletion regions • Other two edges have no depletion region under them • Charges under first 2 edges decrease charge needed from gate voltage, so absence of depletion region under other 2 edges increases VGS needed to invert channel (increased VT) Deep Submicron VLSI Des. Lec. 3**Narrow-Gate-Width Effects**• 2nd Effect: • Higher channel doping along edges along width dimension (due to channel stop dopants (nFET) or oxidation of piled-up phosphorous (pFET) under gate) • Need a higher VT to invert channel • 3rd Effect: • Reverse short-channel effect: As channel length reduces from L = 3 mm, VT initially increases until L = 0.7 mm. Below that, VT decreases faster than predicted by theory • Caused by trench or fully-recessed isolation – when gate biased, field lines from gate region overlapping channel are focused by edge geometry, and make it easier to invert the channel Deep Submicron VLSI Des. Lec. 3**Overlapping Depletion Regions (or Punchthrough)**• As L decreases, separation between source and drain depletion regions decreases • Increased reverse bias pushes boundaries further from junction and closer to each other • Deep submicron MOSFET has a VT adjust implant only at the surface. Causes greater expansion in depletion regions below the surface, so punchthrough first happens below the surface Deep Submicron VLSI Des. Lec. 3**Punchthrough**• Any drain voltage increase after punchthrough happens lowers potential energy barrier for majority carriers in the source • More of these enter the substrate, but some collected by drain • Increases subthreshold current ID,st • Slope of Sstcurve flatter if subsurface punchthrough occurred • Use VPT (punchthrough voltage) defined as value of VDS where ID,st reaches some specific value with VGS = 0 Deep Submicron VLSI Des. Lec. 3**Punchthrough (concluded)**• VPTis approximate value whereS(source and drain depletion widths) = L • NB = bulk doping • Very bad for low-power devices: • Fix with extra implants (cannot fix by changing dopings alone) Deep Submicron VLSI Des. Lec. 3**Gate-Induced Drain Leakage**• Large field exists in oxide where n+ drain of MOSFET lies under the gate and the drain is at VDD, and the gate is at VSS • Causes a charge Qs = eox Eox (Gauss’s Law) to be induced in drain, sweeps any minority carriers that are under the drain laterally to the substrate • Enables tunneling in drain via a near-surface trap, completes a path for a gate-induced drain leakage (GIDL) current • Contributes to standby power, so must control this by increasing oxide thickness, increasing drain doping, or eliminating traps Deep Submicron VLSI Des. Lec. 3**Gate-Induced Drain Leakage**Deep Submicron VLSI Des. Lec. 3