Chapter 9: Short channel effects and ECE 4211 L12 FETs, Gate Sizing, FET Scaling 04112017 F. Jain 8.7 MOSFETs 571 8.7.1 Voltage-Current Equation of a n-channel Al-SiO2-pSi Device 572 8.7.2 Various Regions of ID - VD Characteristics 575   8.7.3 MOSFET Summary 579 8.7.4 Solved Problem Set 582 Chapter 9: Short channel effects and FET Scaling Laws p. 606-612: Slide 25+ Chapter 10: FET Scaling p. 606-612: Slides FET SIZING for NMOS Inverters and Logic Gates Inverters using driver and load transistors Inverter threshold VINV(not FET threshold VTH) Propagation delay in NMOS CMOS Operation CMOS Inverter sizing: W/L ratio of NMOS and PMOS Propagation Delay in CMOS inverters 1

2011 ITRS equivalent scaling process technologies, including high mobility channel materials, high-k gate dielectrics, and novel device structures . 2

Fig. 1b Fig. 1c N-channel n-FETs and p-channel p-FETs Fig. 1b, 1c p-channel comprise of mobile holes. It is induced on p-Si surface when gate voltage of negative polarity in magnitude Vg>VTH N-channel comprise of mobile electrons. It is induced on p-Si surface when gate voltage Vg>VTH 3

The work function difference increases as ND is increased. 8.5.1 Voltage-Current Equation of a n-channel Al-SiO2-pSi N-channel FET, Fig. 1(A) page 572 The work function difference increases as ND is increased. 4

Fig. 4, p 576 Finite slope in saturation part due to channel length modulation -‘L’ shrinks -Id increases - (Z/L increases )

Fig. 5 Sub-threshold conduction Sub threshold figure of merit expresses the required reduction in gate voltage VGS to decrease the leakage drain current ID by an order of magnitude. Page 597 Fig. 5. ID-VG or transfer characteristics of an n-channel FET(Al-SiO2-pSi).

Fig. 1a. Channel pinch off, p 587 Background (Sections 9.1-9.6) 9.1 Short-Channel Effects 587 9.2 Mobility Degradation 590 9.3 Subthreshold Conduction 595 9.4 Subthreshold Figure of Merit  597 9.5 High-field Effects 599 9.6 Punch-through 601 Fig.4, page 600 High Field Effects Fig. 1a. Channel pinch off, p 587

FETs Device Type (volt) nMOS - Enhancement type 0.6 to 1.1 volts nMOS - Depletion type -2.5 to -4.0 volts nMOS - zero threshold device ~ 0.2 volt pMOS - Enhancement type -0.6 to -1.1 volts pMOS - Depletion type 2.5 to 4.0 volts Chapter10.1(page 637) FETs Symbols for enhancement type and depletion type

FET Characteristics N-FET enhancement N-FET Depletion p-FET enhancement p-FET depletion

FET Scaling Laws (p.606) Constant electric field (CE): The central point is to maintain electric field constant in the gate oxide and in the depletion region, after scaling down the dimensions. Thus, L, W, tox, are reduced by a factor k, voltages are reduced by the same factor k, and substrate doping is increased by k. 1. Linear dimensions are reduced by a factor k: L, W, TOX are divided by k (k>l) to obtain scaled-down values. e.g. L' = L/k, W' = W/k, T'OX = TOX/k (1) 2. Voltages are reduced by k. e.g. V'DS = VDS/k, V'GS = VGS/k (2)   3. Substrate doping is increased by k. e.g. N'A = NA* k (3) The applied voltages are reduced to maintain electric field strengths as in the case of long-channel or un-scaled devices. In case of substrate doping, the rationale is to keep the depletion width x'p = xp/k

CE Scaling and Power-delay product Parameter Unscaled Scaled Value Capacitance (total; F) cOXwL wLcOX = cOXwL/k Charge (Total, coulomb) QwL QwL = QwL/k2 Capacitance per unit area cOX cOX = cOX*k Charge per unit area Q Q = Q Power Dissipation (VI) P p = p/k2 Power Density (VI/wL) (p/wL) (p/wL) = (p/wL) Delay Time (wLQ/I)   = /k Resistance R R = Rk

Constant Voltage (CV) and Quasi Constant Voltage QCV: p.609 Parameter (unscaled) Constant Voltage Quasi Constant Voltage Channel length (L) L = L/k Channel width (w) w = w/k Gate oxide thickness (TOX) TOX = TOX/ TOX = TOX/k Substrate Doping (NA) NA = NAk Voltages (V) V = V V = V/ k >  > 1

Generalized scaling (GS) p.610 1) The scaled-down potentials/voltages ϕ' = ϕ/k here, k >1 2) The scaled-down dimensions (x',y',z') = (x,y,z)/λ here, λ >1 3)The scaled-down concentrations (n',p',N'D,N'A) = (n,p,ND,NA)/δ It will be shown, following Baccarani et al that δ = k/λ2, if potential distribution shapes are to be preserved in scaled- down devices. Design steps using Generalized Scaling, p613 1. Find dimensional scaling l from existing channel dimensions and desired scaled- down 2. Using processing parameters, determine threshold variation DVTH Determine VTH (=~4 DVTH) and VDD (VDD ~4*VTH) 3. Find the voltage scaling factor k 4. Compute the scaling factor d for doping.

Finding DVTH Dopant density variation (due to implant or in substrrate) Oxide or gate insulator thickness variation Oxide dielectric constant variation in thin films of 1-2nm Channel width and length variation, Oxide charge density variation

Verification of scaled-down design 1. Is the oxide thickness realistic in terms of gate leakage current? 2. Is supply voltage and threshold realistic in terms of source to drain tunneling? 3. Is the device to device fluctuation in a die and in dies in a wafer acceptable? 4. Is the drive current acceptable? Is the ID-VG and ID-VD characteristics ok in terms of fan-in and fan-out and logic noise margins?

Scaling Parameters LATV 1.3micron 0.25 micron QMDT* (IBM) 25nm SiGe (Home work) Scaling factor Comments Channel Length L(m) 1.3 0.25 0.025 =10 Gate Insulator Oxide tox (nm) 25 5.0 (SiO2) 0.5 (SiO2) 10 0.5(eHfO2 /eSiO2) = 1.7nm Junction Depth xj(nm) 350 70-140 7-14 Gives high Rs and Rd VTH (V) VTH =4x DVTH 0.6 V’TH =4x DV’TH DV’TH =0.06 0.06 V’TH =4x DV’TH DV’TH =0.015 =4 DVTH=0.015V VDS = VDD (V) VDD = 4 x VTH 2.5 1.0 Band Bending (V) 1.8 0.8 0.3 ? Doping NA (cm-3) 3x1015 NA =31016 N’A=7.51017 NA x 2/=25 (Rs + Rd)ID IR Drop (mV) NA < 10mV < 1mV ?? How to solve this RC Delay t (ps) Not appl. (NA) 100ps 2-5 ps?? How to solver this

Chapter 10 NMOS Inverter Fig. 1, p. 638

NMOS Inverter (load and driver resistance ratios) p.639

NMOS Inverter Configurations

10.2.2 Device sizing in static (or ratioed) gates/networks Eq. (8) p. 642

Inverter Gain VDD VOUT VINV Wpd increasing VIN Fig. 6. Output-Input voltage characteristics a a function of Wpd The slope of the voltage transfer characteristics

Fig. 7. A dynamic or two-phase ratio-less inverter 10.2.3 Dynamic logic gates/networks Fig. 7. A dynamic or two-phase ratio-less inverter

Fig. 13, p.649 Layout of NMOS Inverter Fig. 10. (b) Schematic and (b) layout an NMOS inverter.

Fig. 11. NMOS gate with W/L ratios of various FETs. Sizing of FETs in a logic gate (p.647) Fig. 11. NMOS gate with W/L ratios of various FETs.

Fig. 14(b) Intrinsic model showing capacitances. Circuit Model Fig. 14(b) Intrinsic model showing capacitances. Fig. 14a. Capacitances Page 650

Capacitances are computed to find propagation delay(p. 651-660)

p.660 CMOS Inverter p.661 Fig. 21 Voltage transfer characteristic

Fig. 26. Sizing of CMOS transistors (p 668) Fig. 33. Latch up in CMOS inverter (p672) Fig. 26. Sizing of CMOS transistors (p 668)

Fig. 27 Sizing of 2-input NOR 2-input NAND CMOS inverter (p668)