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S. Saha and B. Gadepally Technology CAD: Technology Modeling, Device Design and Simulation S. Saha and B. Gadepally 2004 VLSI Design Tutorial, January 5, 2004 Mumbai, India

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S. Saha and B. Gadepally Coordinator: Prof. Bhaskar Gadepally Adjunct Prof., Electrical Engineering, IIT Bombay Chairman, Reliance Software Consulting, Inc. 155 E. Campbell Ave., Campbell, CA (USA) 2004 VLSI Design Tutorial, January 5, 2004 Mumbai, India Technology CAD: Technology Modeling, Device Design and Simulation

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S. Saha and B. Gadepally Instructor: Dr. Samar Saha Silicon Storage Technology, Inc Sonora Court Sunnyvale, CA (USA) 2004 VLSI Design Tutorial, January 5, 2004 Mumbai, India Technology CAD: Technology Modeling, Device Design and Simulation

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Mumbai, IndiaS. Saha and B. Gadepally4 Tutorial Outline Prof. B. Gadepally: –Introduction and Tutorial Overview. Dr. S. Saha: –Front-end Process Technology CAD (TCAD) Models and Process Simulations –Device TCAD Models and Device Simulations –Industrial Application of TCAD Calibration of Process and Device Models –Industrial Application of TCAD in Device Research Compact / SPICE Modeling.

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Bhaskar Gadepally Technology CAD: Technology Modeling, Device Design and Simulation Introduction and Tutorial Overview 2004 VLSI Design Tutorial, January 5, 2004 Mumbai, India

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Bhaskar Gadepally6 Overview of IC Technology In the past three decades: –device densities have grown exponentially –device and technology complexities have increased significantly –design constraints are many-fold: ultra thin oxide interconnect power supply –technology development cost has increased enormously.

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Mumbai, IndiaBhaskar Gadepally7 Overview of IC Technology Channel Engineering - non-uniform channel doping - Quantum Mechanical effects - low-diffusivity impurities - threshold voltage control Source-Drain Engineering - ultra-shallow extensions - low-energy implants - RTA/LTA techniques - halo optimization p-substrate p-welln-well n+ PMOS n+p+ STI Halo P+ poly Spacer NMOS STI (Shallow Trench Isolation) Gate Engineering: Dielectric - ultra-thin gate oxide - direct tunneling - high-k dielectrics Gate Engineering: Stack - dual-poly / poly depletion - work function engineering - interface properties N+ poly

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Mumbai, IndiaBhaskar Gadepally8 Overview of IC Devices New device and device physics are continuously evolving: –nano-scale devices –microscopic diffusion –quantum mechanical carrier transport –molecular dynamics –quantum chemistry –high-frequency interconnect behavior.

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Mumbai, IndiaBhaskar Gadepally9 Technology CAD With the increased complexities in IC process and device physics: –intuitive analysis is no longer possible to design advanced IC processes and devices –TCAD tools are crucial for efficient technology and device design to quantify potential roadblocks to indicate new solutions for continuos scaling of devices.

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Mumbai, IndiaBhaskar Gadepally10 Technology CAD Scope of TCAD: –front-end process modeling and simulation implant, diffusion, oxidation etc. –numerical device modeling and simulation I - V, C - V etc. simulation –topography modeling and simulation deposition, lithography, etching etc. –device modeling for circuit simulation compact / SPICE modeling –interconnect simulation capacitance, inductance etc.

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Mumbai, IndiaBhaskar Gadepally11 Tutorial Objective Offer insight into the physical basis of TCAD, especially, bulk-process and device TCAD. Describe systematic methodologies for an effective application of TCAD tools. Describe systematic calibration methodology for predictive usage of TCAD tools: –process models –device models. Offer users sufficient insight to leverage new tools.

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Mumbai, IndiaBhaskar Gadepally12 Session 1: Bulk-Process Simulation Front-end process models implemented in process TCAD tools: –ion implantation models analytical Monte Carlo –microscopic diffusion models point defects –oxidation transient enhanced diffusion.

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Mumbai, IndiaBhaskar Gadepally13 Session 2: Device Simulation Device models implemented in device TCAD tools: –fundamentals of carrier transport drift-diffusion solution hydrodynamic solution carrier mobility models –device physics of nanoscale technology inversion layer quantization –fundamental limits of MOSFETs.

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Mumbai, IndiaBhaskar Gadepally14 Session 3: Industry Application Introduction to process and device simulation tools. Mesh generation. Model selection. Predictive usage of TCAD: –process model calibration –device model calibration. Predictive simulation of CMOS technology.

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Mumbai, IndiaBhaskar Gadepally15 Session 3: Industry Application - Calibration Calibration Effort TD Effectiveness LowModerateHigh Low Moderate High No or a limited calibration only provides some physical trends and is useful for a first-order process and device analysis. Global calibration provides higher accuracy and predictability of simulation data. Local calibration with the previous generation of technology will provide physical trends. Absolute values may not match real data.

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Mumbai, IndiaBhaskar Gadepally16 Session 4: TCAD in Research & Modeling Simulation tools in device research: –simulation structure –model selection –examples sub-100 nm MOSFETs DG-MOSFETs - FinFETs. TCAD in device (compact) modeling: –examples substrate current model flash memory cell macro-model.

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Samar Saha Technology CAD: Technology Modeling, Device Design and Simulation Bulk-Process Simulation 2004 VLSI Design Tutorial, January 5, 2004 Mumbai, India

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Samar Saha18 Outline Introduction. Bulk-process Models: –Ion Implantation –Diffusion –Oxidation. Summary.

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Mumbai, IndiaSamar Saha19 Introduction Front-end IC fabrication processes include: –implant: S/D and halo (low energy); well (high energy) etc. –diffusion: Rapid thermal annealing (RTA) Transient Enhanced Diffusion (TED) and other anomalous effects –oxidation: gate oxide, STI liner oxide etc. p-substrate p-welln-well n+ PMOS n+p+ STI Gate oxide Halo P+ poly Spacer N+ poly NMOS STI (Shallow Trench Isolation) Source Drain

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Mumbai, IndiaSamar Saha20 Introduction Objective of this session: –understanding of physical models implemented in a process TCAD tool model hierarchy model limitations building new models –basic understanding of general purpose simulator internals –TCAD models in general without considering any particular tools.

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Mumbai, IndiaSamar Saha21 Ion Implantation Ion Implantation Mechanisms. Ion Implant Models: –Analytical –Monte Carlo (MC). Implant-induced Damage Modeling. Plus-one Approximation. Summary.

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Mumbai, IndiaSamar Saha22 Ion Implantation Bombard wafers with energetic ions energy, E 0.5 KeV - 1 MeV > E binding. Ions collide elastically with target atoms creating: –ion deflections, energy loss –displaced target atoms (recoils). Ions suffer inelastic drag force from target electrons –ion energy loss –lattice heating. Ion Target Recoil channeling

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Mumbai, IndiaSamar Saha23 Ion Implantation Channeling is caused by ions traveling with few collisions and little drag along certain crystal directions. Ions come to rest after losing all the energy on: –elastic collisions (nuclear stopping) –inelastic drag (electronic stopping). Ion Target Recoil channeling

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Mumbai, IndiaSamar Saha24 Ion Energy Loss Mechanisms Nuclear stopping (S n (E)): –ion energy loss to target atom by interaction with the electric field of the target atoms nucleus –classical relationship of two colliding particles –the scattering potential with the exponential screening function is given by where Z 1 = atomic number of incoming ion Z 2 = atomic number of target atom. Deflected Ion Target Recoil Ion

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Mumbai, IndiaSamar Saha25 Ion Energy Loss Mechanisms Electronic stopping (S e (E)) is due to the viscous drag force on moving ion in a dielectric medium. –k e is a model parameter. Accurate model must account for the variation of S e in space. Stopping power S of an ion is given by:

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Mumbai, IndiaSamar Saha26 Ion Range Distribution Ions come to rest over a distribution of locations. Peak, depth, and lateral spread of distribution are determined by: –ion mass, energy, dose, and incident angle –target atom, composition, geometry, structure, and temperature. Implanted profile can be represented by: –particles –distribution functions.

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Mumbai, IndiaSamar Saha27 Ion Range Distribution

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Mumbai, IndiaSamar Saha28 Ion Range Distribution The as-implanted 1D distribution function is described by a series of coefficients called moments. 2D distribution of the implanted profile is constructed from 1D distribution function taking lateral spread vertical spread.

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Mumbai, IndiaSamar Saha29 1D Analytical Ion Implantation Models Gaussian distribution: –amorphous targets –two coefficients where Q = implant dose (#/cm -2 ) R p = projected range normalized first moment p = straggle/standard deviation second moment. x RpRp N

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Mumbai, IndiaSamar Saha30 1D Analytical Ion Implantation Models Pearson-IV: –crystalline targets without channeling four coefficients (R p, p, skewness, kurtosis) –crystalline targets with channeling, tilt, and rotation. six coefficients. Dual Pearson-IV: –crystalline targets with channeling, tilt, and rotation –second profile to model the channeling –nine coefficients. Legendre Polynomials - 19 coefficients.

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Mumbai, IndiaSamar Saha31 1D Analytical Ion Implantation Models Coefficients are fit to the measured doping profiles. Coefficient-set for each distribution is tabulated for different: –ion mass (As, B, In, P, Sb) –dose, energy, tilt, and rotation –target type. Multi-layer targets: –each material is treated separately and scaled by its R p. –dose absorbed on the top layer is calculated and is used as the dose matching thickness for the layer below.

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Mumbai, IndiaSamar Saha32 2D/3D Analytical Ion Implantation Models Each 1D profile along a vertical line is converted to 2D or 3D distribution by multiplying it by a function of lateral coordinates: here lateral straggle, l p Multi-layer targets and sloped surfaces are converted to 2D/3D by dose matching approach. More complex models have l (x). Low energy profiles need non-separable point- response functions.

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Mumbai, IndiaSamar Saha33 Monte Carlo Modeling of Ion Implantation The collision energy loss is modeled by binary collision approximation (BCA), that is, each ion collides with one target atom at a time. The energy loss ( E) is modeled in terms of: –incident energy, E 0 and scattering angle, 0 of ion –separation between two particles –coulomb potential between two particles –impact parameter. BCA requires special formulation for: –ion channeling –low energies when lattice movements come into play.

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Mumbai, IndiaSamar Saha34 Monte Carlo Modeling of Ion Implantation Ongoing development in MC modeling is to improve: –speed of calculations –electronic stopping power, S e model detailed local model for S e local and non-local split in energy loss due to S e where f nl = fraction of non-local energy split a = universal screening length p = impact parameter. Overall accuracy of MC implant model is excellent.

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Mumbai, IndiaSamar Saha35 Ion Channeling in Crystalline Silicon Along certain angles in crystal, ion may encounter no target atoms. Ion Repeated small-angle collisions steer the ion back into the channel. Channeling was first discovered by MC simulation. Channeling is: –important at any energy –critical at low energy where channels steer Boron ions under MOS gate. Analytic channeling model is complex.

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Mumbai, IndiaSamar Saha36 Ion Channeling in Crystalline Silicon

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Mumbai, IndiaSamar Saha37 Damage Creation Models Each incoming ions generates damage seen by subsequent ions: –recoils target atoms knocked out of lattice sites –amorphous pockets. The effect of damage is significant on as-implanted profile as well as during subsequent diffusion. Models based on Kinchin-Pease formulation is used to estimate damage density: n = E r /2E d where E r = recoil energy E d = target displacement energy (~ 15 eV for Silicon).

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Mumbai, IndiaSamar Saha38 Plus-one Damage Model Most recoiled interstitials (I) find a vacancy (V) and recombine rapidly either during the implantation or the first instants of annealing. Distribution of remaining recoils shows: –net excess of V near the surface –net excess of I toward bulk. At low ion mass and/or moderate energy: –population of net I and net V is less than the population of I due to dopant atoms taking substitutional sites –one extra-ion is created for each dopant atom taking a substitutional site.

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Mumbai, IndiaSamar Saha39 Deviation from Plus-one Model Plus-one approximation often fails for: –heavy ions as the population of recoils can become quite large relative to extra ion population –low energy –low dose. An effective plus-n factor as a function of ion species, energy, and dose is used. Typical values: As:n E 5 KeV; n E 500 KeV B: n E 5 KeV; n 1.0 for E > 20 KeV P: n E 5 KeV; n E 500 KeV.

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Mumbai, IndiaSamar Saha40 Ion Implantation: Summary Ion implantation with ion energy > E binding of target atoms is used to implant impurity atoms into target. Analytical ion implantation model: –the impurity profile is represented by moments for different species, dose, energy, tilt, and rotation –the moments are extracted from the experimental profile to create look-up table –simulation is performed using this look-up table. MC ion implantation model is more accurate, particularly for low energy. The implant damage is modeled by plus-n model.

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Mumbai, IndiaSamar Saha41 Diffusion Fundamentals of Dopant Diffusion –Ficks Laws –Oxidation Enhanced Diffusion (OED) –Oxidation Retarded Diffusion (ORD) –Transient Enhanced Diffusion (TED). Point Defect Model. Clusters and Precipitates. Polysilicon Diffusion. Impurity Profiling. Summary.

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Mumbai, IndiaSamar Saha42 Ficks Laws of Diffusion Ficks first law: –describes flux (F) through any surface –diffusion is downhill - high low concentration, - sign Ficks second law law of conservation of particles Low concentration diffusion in silicon is Fickian - each dopant A satisfies: F in F out x C (D diffusivity = constant)

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Mumbai, IndiaSamar Saha43 Concentration-Dependent Diffusion Typically, intrinsic carrier concentrations (n i ) at processing temperatures are high cm -3. For high doping concentrations, C n i, dopant diffusion shows enhancements of the form: Diffusion enhancement is due to the variation of point defect population with Fermi level. The effective extrinsic diffusivity is given by:

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Mumbai, IndiaSamar Saha44 Surface Effects on Bulk Diffusion: O ED/ O RD Experimental data show that processes which modify the surface can affect diffusion in the bulk. Enhancement of diffusivity in one species while retardation in another is the evidence of two different diffusion mechanisms I and V.

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Mumbai, IndiaSamar Saha45 Transient Enhanced Diffusion (TED) Anomalous displacement of implanted dopants during low temperature anneals. Reverse temperature effect: displacement larger at lower temperatures - up to m. Displacement increases with implant dose and energy. Corresponds to temporary increase in diffusivity ~ 10,000X. Implant of one species can drive diffusion of another. Enhancement is transient. Spatially non-uniform diffusion enhancements. Reduced activation.

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Mumbai, IndiaSamar Saha46 Transient Enhanced Diffusion (TED) As implanted over a buried B layer. As implant creates damage deep into the substrate. The implant damage causes a significant enhancement in B diffusion deep into the substrate during 20 sec. anneal at 850 °C. Simulation results

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Mumbai, IndiaSamar Saha47 Point Defect Model for Dopant Diffusion Point defects (I and V) model explains: –most of the observed trends in dopant diffusion by relating them to the properties of I and V –action-at-a-distance effect of the surface on bulk diffusion. Vacancy mechanism As, Sb Kick-out mechanism B, P, In, As, Au, Zn, P above 900 °C Frank-Turnbull mechanism Zn, below 900 °C

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Mumbai, IndiaSamar Saha48 Defect Charge States Defects which have states in the gap will have a distribution of charge states. The concentration of charged point defects depends on Fermi level. Dopants can diffuse with any of the defect charge states, some combinations have higher probability. In principle, must solve a set of: PDE s one for each combination. Five-stream diffusion model solves equations: Three-stream model solves equations.

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Mumbai, IndiaSamar Saha49 Electric-field Effects For high doping concentration > n i at the processing temperature, the electric field set up by ionized dopants affects diffusivity. Example: As + B co-diffusion at 900 °C, 15 min. B- pulled towards the N+ region due to e-field effects.

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Mumbai, IndiaSamar Saha50 Generation/Recombination of Defects General flux model: where = fraction of silicon atom injected –V m = silicon atom/cm 3 –assumed generation growth rate, G. –recombination rate surface excess I - I* and increases under a growing surface. Lateral diffusion of defects during OED is governed by the ratio of D I /K inert 10 m.

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Mumbai, IndiaSamar Saha51 Surface Generation/Recombination During OED, recombination/generation fluxes are large and must balance: Fixed interstitial super-saturations, also, occur under nitride, silicide surfaces. During TED, recombination appears to be fast, even at inert surfaces, recombination rate: Several models are available. Optimize K inert for TED and adjust to fit OED at the expense of lateral OED decay length.

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Mumbai, IndiaSamar Saha52 Gradient Effects in Transient Diffusion Dopant flux arises from diffusion of defects-dopant pairs: boron flux = D BI [BI]. Number of pairs is proportional to the boron and interstitial concentrations: boron flux = D BI k pair (I B + B I) where I B = interstitials enhance boron diffusion I = boron diffusion due to defect gradient During TED, I is large near the surface causing: –extra dopant flux to the surface –surface pile-up (and possible interface loss) of dopant.

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Mumbai, IndiaSamar Saha53 Interstitial Clustering Model The growth and dissolution is given by: where k d is the decay constant k c is the growth constant C = concentration of clustered interstitials I = concentration of unclustered interstitials. After implantation I is large, C/ t = C(k c I) clusters grow exponentially until I = k d /k c. When I is small, clusters decay exponentially with time constant 1/k d.

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Mumbai, IndiaSamar Saha54 {311} Cluster Dissolution {311} defects: –rod-shaped defect clusters condensed from +1 amount of damaged silicon-I at annealing T > 400 °C –precipitate on {311} planes and extend in the directions to form planar defects. Time scale for {311} evaporation is similar to the time scale for TED. Simple reaction-based model offers first-order account of evaporation curve. Steady super saturation of dopant diffusion is observed during TED.

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Mumbai, IndiaSamar Saha55 Dopant Clustering/Precipitation Dopants are only soluble up to a limit at any temperature (solid solubility limit). Dopants also show deactivation below the solid solubility limit. Due to the clusters of size m dopant atoms such as As with m = 4, –clustering reaction emits interstitials to generate required V. Can generate enhanced diffusion at the same level as TED. As V

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Mumbai, IndiaSamar Saha56 Chemical Pump Effects Dopant atom A interacting with I form A + I AI interstitial-assisted mobile species. When AI pairs diffuse out of a region of high I* to a region of low I*, pairs are out of equilibrium and must dissociate, AI A + I. A is deposited while I diffuses (pumped) away from the surface enhancing diffusion in bulk. Surface dopant layer may cause enhanced diffusion in bulk - e.g. D/D* = 70 at 900 °C. Causes cooperative diffusion, e.g. emitter push effect in bipolar junction transistors.

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Mumbai, IndiaSamar Saha57 Diffusion in Polysilicon Point defects usually pinned near equilibrium in poly due to grain boundaries. Dopants diffuse in two streams via grain and in boundary. An effective model includes: –two streams –dopant transfer from grain to grain boundary –grain growth with time –dopant transfer to grain boundary. Segregation coefficient, growth rate, and re-growth rate = f( temperature, grain size, Fermi level ).

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Mumbai, IndiaSamar Saha58 Metrology for Developing Diffusion Models Spreading resistance profile (SRP) –1D carrier profiles –good sensitivity –modest depth resolution –carrier spilling –difficult to use for shallow junctions. n p

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Mumbai, IndiaSamar Saha59 Metrology for Developing Diffusion Models Secondary Ion Mass Spectroscopy (SIMS) –1D chemical profiles –good sensitivity to all dopants –excellent depth resolution –surface region troublesome. 2D carrier profiling with excellent space resolution: –scanning capacitance microscopy (SCM) measurement affects sample –transmission electron holography (TEH) measures electrostatic potential difficult sample preparation.

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Mumbai, IndiaSamar Saha60 Monte Carlo Diffusion Methods: Algorithm Monte Carlo diffusion program (MARLOWE, UT-Austin) offers accurate diffusion modeling. MARLOWE Generates initial I, V positions THEORETICAL CALCULATIONS Energy of interactions and diffusion barriers EXPERIMENTS MONTE CARLO DIFFUSION CODE - Diffusion - Clustering - I - V recombination - Surface annihilation - I, V trapping - Boron kick-out, kick-in

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Mumbai, IndiaSamar Saha61 Diffusion is critical to activate the implanted dopants in the semiconductor devices. Dopants diffuse in silicon by interacting with point defects through a number of possible atomic-scale mechanisms. For short times, the diffusion is dominated by TED because of high concentration of point defects. Point defect concentrations depend on temperature, Fermi level, implant damage, and surface processes like oxidation. 1D/2D metrology is used to calibrate diffusion model. Diffusion: Summary

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Mumbai, IndiaSamar Saha62 Oxidation Fundamentals of Thermal Oxidation. Oxide Growth Model: –Deal-Grove Model –Thin Oxide Model. Oxidation Chemistry. Oxide Flow: –Oxidation-induced Stress –Visco-elastic Model. Summary.

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Mumbai, IndiaSamar Saha63 Oxidation: Diffusion, Reaction, Flow Oxidation proceeds by three sequential processes: –oxidant diffuses through existing oxide –oxidant reacts at silicon surface to create new oxide –overlying oxide flows to accommodate new volume. Process is at first limited by reaction but diffusion through growing oxide becomes limiting. O 2 or H 2 O ambient Oxidant Reaction zone Nitride Silicon

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Mumbai, IndiaSamar Saha64 Oxidation: Deal-Grove Model C0C0 CLCL SiliconSiO 2 F reac = kC L D = diffusivity of oxidant C L = concentration at Si-SiO 2 interface C 0 = concentration at the SiO 2 surface L = oxide thickness k = interface reaction rate constant

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Mumbai, IndiaSamar Saha65 Oxidation: Deal-Grove Model C0C0 CLCL SiliconSiO 2 F reac = kC L At equilibrium: F diff = F reac, C L = C 0 / [1 + kL/D] Oxidation growth rate is given by: where C* = equil. oxidant conc.; N s = # oxidant/cm 3 in oxide

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Mumbai, IndiaSamar Saha66 Thin Oxide Models Deal-Grove model does not fit the early part of oxidation curve. The data in thin regime can be fitted with an addition to Deal-Grove model given by: where and C 0 3.6x10 8 m/hr, E A 2.35 eV, and 7 nm in or oriented silicon substrates. This model can be found in TCAD tools like SUPREM4.

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Mumbai, IndiaSamar Saha67 Oxidation - Planar Growth Two-step oxidation shows a significant difference in oxide density. Planar growth generates an intrinsic stress in oxide during growth process: –modest stress (3x10 9 dynes/cm 2 ) –density increases (< 3%) –refractive index increases (1%) relative to fully relaxed oxides. First oxidation Second oxidation 1100 C800 C 900 C L grown in the second step varies depending on the thermal history of oxide (not just on L).

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Mumbai, IndiaSamar Saha68 Oxidation - Planar Growth Intrinsic stress is an atomistic process. Relaxes gradually with annealing at a rate which steadily decreases. Recent measurements show that relaxation rate is independent of stress level. History effects are not accounted for in most process simulators. Measured linear/parabolic coefficients describe oxidation in a state of intrinsic stress. 1D stress already accounted for in one-step oxidation.

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Mumbai, IndiaSamar Saha69 Oxidation Chemistry Oxidation rate coefficients are sensitive to ambient additives: –steam times faster than O 2 –3% Cl 2 increases growth rate by % –100 ppm NF 2 increases growth rate by –heavy substrate doping increases rate by according to the relation –all easily accounted for by building table of B, B/A vs. additive or dopant concentration. –NO, NO 2 are not supported in most process TCAD tools.

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Mumbai, IndiaSamar Saha70 Oxide Flow Oxide growing on a curved surface must flow. Resulting deformations (and stresses) can be large! L OCOS top surface must stretch by %. Elastic limit of glass << 1% Si 3 N 4 Silicon Oxide Silicon Old Oxide New Oxide

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Mumbai, IndiaSamar Saha71 Oxide Flow Large deformations on a curved surface during oxidation mean viscous flow must occur. Viscous flow model used to model stress during oxide growth includes: –incompressible viscous flow –linear elasticity. Visco-elastic flow model: –allows oxide to be slightly compressible –eliminates pressure equation –offers a significant numerical benefit.

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Mumbai, IndiaSamar Saha72 Visco-elastic Model: Stress Simulation Oxide stress after local oxidation. Length of stress vector amount of stress. Compression Tension SiO 2 Si 3 N 4

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Mumbai, IndiaSamar Saha73 Oxidation: Summary Basic growth mechanism of thermal oxide: –oxidant transport through the SiO 2 layer to Si/SiO 2 interface –chemical reaction at the interface to produce the new layer of oxide. The growth is linear parabolic law. The basic Deal-Grove model is extended to explain: –thin oxide growth –mixed ambient oxidation. Important effects of thermal oxidation include OED, ORD, and impurity redistribution and segregation.

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Mumbai, IndiaSamar Saha74 Bulk-Process Simulation: Summary Accurate process models and TCAD tools are extremely critical for continuous scaling of ICs. Workstation performance is continuously improving for cost-effective computer experiments. Existing models and TCAD tools treat different aspects of process simulation quite well. As new understanding develops, new models are incorporated in TCAD tools to improve predictability. Successful process TCAD will require a firm grasp of the controlling process physics.

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Samar Saha Technology CAD: Technology Modeling, Device Design and Simulation Device Simulation 2004 VLSI Design Tutorial, January 5, 2004 Mumbai, India

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Samar Saha76 Outline Introduction. Carrier Transport Models. Inversion Layer Mobility. Quantum Mechanical Confinement. Discrete Dopant Effects. Numerical Methods. Summary.

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Mumbai, IndiaSamar Saha77 Introduction p-substrate p-well n+ STI Poly STI hot carriers Non-local transport (velocity overshoot) QM tunneling Electrostatics: - 2D/3D effects - discrete charges Atomic scale effects QM confinement Surface scattering Quasi-ballistic transport A device TCAD tool solves a set of equations to deal with various physical phenomena in semiconductor devices:

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Mumbai, IndiaSamar Saha78 Introduction Objectives of this session is to: –focus on the underlying physics and models for practical application of device TCAD such as identify device physics issues for simulation discuss and compare simulation approaches identify limitations uncertainties challenges.

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Mumbai, IndiaSamar Saha79 Carrier Transport Models A device TCAD tool generates device characteristics by solving: –Poissons [.D = (r)] + carrier transport equations self- consistently. Carrier transport models include: –drift-diffusion (DD) - standard –Monte Carlo (MC) –molecular dynamics –hydrodynamic (HD) –Boltzmann equation –quantum balance equations.

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Mumbai, IndiaSamar Saha80 Carrier Transport Models The basic concept in transport theory is the carrier distribution function = f(r,p x,t). f(r,p x,t) = probability of a carrier at the position r with momentum p x at any instant t. f(r,p x,t) is a Maxwellian distribution function with: –area = carrier density, n(r,t) –the spread depends on carrier temperature –first moment is velocity –second moment is kinetic energy. f(r,p x,t) pxpx Equilibrium

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Mumbai, IndiaSamar Saha81 Carrier Transport Models At equilibrium, f(r,p x,t) is symmetric around p x = 0. If an e-field is applied along the negative p x direction: –electron distribution is distorted and displaced from the origin –causes electron scattering. Device TCAD challenge is to solve f(r,p x,t). f(r,p x,t) pxpx Equilibrium f(r,p x,t) pxpx Non-equilibrium x

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Mumbai, IndiaSamar Saha82 Carrier Transport Models To solve for f(r,p,t) - Boltzmann Transport Equation (BTE): –six dimensions three in position space three in momentum space –solution techniques: MC simulation spherical harmonics scattering matrix and so on.

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Mumbai, IndiaSamar Saha83 Carrier Transport Models Solving f(r,p,t), we can find the quantities that device engineers deal with directly such as: –carrier density, n(r,t) –current density, J n (r,t) –energy current, J E (r,t) –average kinetic energy, u n (r,t) –electron temperature, T n (r,t) –heat flux, Q n (r,t). Six-dimensional equation is difficult to solve and computationally demanding. In TCAD, we directly solve for the quantities of interest.

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Mumbai, IndiaSamar Saha84 Carrier Transport: Balance Equations Basic idea to solve for a quantity (n ) of interest is to formulate a balance equation such as: –rate of increase in n = rate n flows into the volume + net generation rate. Examples: –n = n(x,t): continuity equation. –n = J nx (x,t): current equation.

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Mumbai, IndiaSamar Saha85 Carrier Transport Models Assuming slowly varying time, we can write the current equation: where = average time between collisions m* = effective mass of electrons. We need a balance equation for kinetic energy, u xx. For simplicity of computation: –approximate the effects of scattering in n –close the balance equations by approximating u xx.

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Mumbai, IndiaSamar Saha86 Carrier Transport Models: Drift-Diffusion The simplest solution of carrier transport equation is local field or DD approach. In DD, is determined by scattering, scattering is determined by u xx, and u xx is determined by. For high fields in bulk silicon, (x) and u xx are constants or slowly varying: here n = 0 [N,T L, (x)];D n = (k B T L /q) n Then the current equation is given by: Local field transport model: [ n = f(local field)]

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Mumbai, IndiaSamar Saha87 Carrier Transport Models: Drift-Diffusion DD solution fails to predict device characteristics for small geometry ( 0.1 m) MOSFETs. We know: here is related to the average carrier energy, u n (T n ) and T n = local electron temperature. Thus, the DD-transport model can be improved by assuming, n as a function of local energy. Local energy transport model: n = f(local energy) Alternatively, n = 0 [N,T L,T n ]

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Mumbai, IndiaSamar Saha88 Carrier Transport Models: Local Energy Solve for energy density, n = W(x,t) = nu: where E = relaxation time. n = J E (x,t): Unknowns: (x), n(x), p(x), u n (x), and u p (x) increase in energy flux input e-fieldrate of energy dissipation

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Mumbai, IndiaSamar Saha89 Carrier Transport Models: DD vs. HD DD vs. HD model data deviate significantly for 40 nm devices.

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Mumbai, IndiaSamar Saha90 Macroscopic Transport Models: Summary Models are derived directly from BTE. Require numerous simplifying assumptions: closure, scattering. Difficult to assess the validity of assumptions. Many flavors: HD, energy transport (ET). Beyond DD, adds significant numerical complexity. HD/ET generally provide good estimates of: –average carrier energy –current density. Significant differences between various models.

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Mumbai, IndiaSamar Saha91 Carrier Transport Models: MC Simulation MC is a rigorous transport model. The essence of the model is: electron r1r1 r2r2 r 3, r 4 r1r1 r2r2 r1r1 r 1 : free flight duration r 2 : scattering event r 3 : direction after scattering r 4

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Mumbai, IndiaSamar Saha92 MC Simulation: Summary Advantages: –numerical method for solving the BTE with e-e correlation –advanced physics is readily treated (e.g. scattering and complete band structures) –most reliable transport method for treating hot electron distributions and for assessing novel devices. Disadvantage: –computationally demanding: under near-equilibrium conditions for examining rare events.

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Mumbai, IndiaSamar Saha93 Carrier Transport Models: Quantum Different techniques available include: (1) equilibrium or ballistic transport simplest form is used for MOS capacitor simulation (2) wave propagation with phase randomizing scattering non equilibrium Greens function approach (Wigner functions, density matrix) (3) density gradient/QM potential approach

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Mumbai, IndiaSamar Saha94 Carrier Transport Models: Summary Drift-diffusion (local field model): = f(local field) Balance equations (mostly local energy): = f(local energy) Examples: HD, ET, etc. Boltzmann solvers: –MC Quantum transport: –Schrodinger-Poisson –density gradient / quantum potential.

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Mumbai, IndiaSamar Saha95 Inversion Layer Mobility Choice of mobility model can significantly alter the simulation results. Inversion layer mobility versus effective normal electric field show well- known characteristics: –high fields: universal behavior independent of doping density. –low fields: dependent on 1) doping density and 2) interface charge. universal behavior

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Mumbai, IndiaSamar Saha96 Inversion Layer Mobility Mobility versus effective normal electric field curve is modeled using three components: –coulomb scattering ( due to ionized impurity ) –phonon scattering - almost constant –surface roughness scattering ( at Si/SiO 2 interface ). At low normal fields: –less inversion charge density –ionized impurity scattering dominates and eff = f(N A ). At high normal fields: –higher inversion charge density close to the interface –surface roughness scattering dominates.

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Mumbai, IndiaSamar Saha97 Inversion Layer Mobility For higher normal fields, universal behavior as a function of effective normal field: The effective field is a non-local quantity. Local field mobility models preferred for device TCAD should produce universal behavior in terms of the computed effective field. –Example: Lombardi Surface Mobility Model.

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Mumbai, IndiaSamar Saha98 Inversion Layer Mobility For ultra-thin gate oxide thickness the inversion layer carrier wave function can extend through Si/SiO 2 interface to SiO 2 /polysilicon interface. Mobility may depend on the surface roughness of SiO 2 /polysilicon interface remote interface roughness scattering. p-substrate p-well n+ STI NMOS STI Poly Gate Oxide Electron wave function

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Mumbai, IndiaSamar Saha99 Choice of Surface Mobility Models

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Mumbai, IndiaSamar Saha100 Inversion Layer Mobility: Summary Mobility is extremely critical for advanced MOSFET device simulation. Choice of mobility model can effect simulation data. Local field mobility models are being extended for high normal fields and high doping densities. New effects may begin to be felt in ultra-thin oxide devices –Example: remote interface scattering.

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Mumbai, IndiaSamar Saha101 Quantum Mechanical Confinement The charges near the silicon surface are confined to a potential well formed by: –oxide barrier –bend Si-conduction band due to applied gate potential. Due to QM confinement of charges near the surface: –energy levels are grouped in discrete energy sub-bands –each sub-band corresponds to a quantized level for carrier motion in the normal direction. E C (y) Depth into Si (y) EFEF Energy

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Mumbai, IndiaSamar Saha102 Due to QM confinement, the inversion layer concentration: –peaks below the SiO 2 / Si interface 0 at the interface and is determined by the boundary condition for the electron wave function. Quantum Mechanical Confinement Depth into Si (y) n(y) Classical Quantum z z = shift in the centroid of charge in silicon away from the interface. Equivalent oxide thickness for z is:

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Mumbai, IndiaSamar Saha103 Classical: –C Si >> C OX (accumulation / inversion) –C total ~ C OX (accumulation / inversion) Quantum: –C Si ~ Si / z –C total < C OX (accumulation / inversion) Impact of QM confinement: –V th since more band bending is required to populate the lowest sub-band –T OX eff since a higher V G over-drive is required to produce a given level of inversion charge density –C total since T OX eff = T OX + ( OX / Si ) z. Quantum Mechanical Confinement C ox C Si V gate

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Mumbai, IndiaSamar Saha104 QM Confinement: Modeling Approach van Dorts model: amount of band-gap widening due to splitting of energy levels is given by: where B = constant y = distance from Si/SiO 2 interface y ref = reference distance for the material E n = normal electrical field and,

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Mumbai, IndiaSamar Saha105 QM Confinement: Modeling Approach Modified local density approximation (MLDA): –robust and efficient formulation to compute quantization of carrier concentration near Si/SiO 2 interface –offers a good compromise between the accuracy and simulation time –the confined carrier density is given by FD statistics

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Mumbai, IndiaSamar Saha106 QM Confinement: C OX Reduction Simulation data obtained by simulation program TSUPREM4

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Mumbai, IndiaSamar Saha107 QM Confinement: T OX Measurement T OX T OX eff - T OX

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Mumbai, IndiaSamar Saha108 QM Confinement: Effect on V th V th increase due to QM effect depends on channel doping, N ch. Maximum increase in V th ~ 100 mV for N ch ~ 1x10 18 cm -3. 1e18 uniform 1e17 GR AR ST N ch (cm -3 ) Transition depth 1E18 1E17 GR -Graded Retrograde 1E18 1E17 AR -Abrupt Retrograde 1E18 1E17 Depth Conventional Step, ST

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Mumbai, IndiaSamar Saha109 QM Confinement: Effect on I ON GR AR ST 1e18 uniform 1e17 I on decrease due to QM confinement depends on N ch. Maximum drop in I on ~ 20% for N ch ~ 1x10 18 cm -3.

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Mumbai, IndiaSamar Saha110 QM Confinement: Summary Impact of QM confinement becomes significant for T OX < 4 nm. QM confinement affects: –T OX measurement –drive current –scaling limits. Modeling approaches: –semi-physical (e.g. van Dort) –quantum potentials - MLDA –1D self-consistent Schrodinger-Poisson.

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Mumbai, IndiaSamar Saha111 Discrete Dopant Effects The volume of active channel region for an advanced MOSFET: V = (W) x (L) x (X j ) Typically: length, L = 40 nm width, W = 100 nm; junction depth, X j = 25 nm; N channel = 1x10 18 cm -3 N tot = 100 impurity atoms. The number of dopants in V is a statistical quantity. V P (N A cm -3 ) Source Drain XjXj

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Mumbai, IndiaSamar Saha112 Discrete Dopant Effects Effects of discrete dopants: –significant threshold (V th ) variation, V th (10s of mV) –lower average V th (10s of mV) –asymmetry in drive current, I DS. 3D transport leads to inhomogeneous conduction in sub-100 nm devices. Continuum diffusion models are inadequate to model discrete dopant effects in sub-100 nm MOSFETs. Source Drain

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Mumbai, IndiaSamar Saha113 Discrete Dopant Effects: Summary 2D continuum models can predict spread in V th. Full 3D simulation is necessary to predict mean. The role of continuum versus granular models will become increasingly important as devices continue to shrink.

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Mumbai, IndiaSamar Saha114 Hot Electron Effects Effect: –hot electron injection. Outcome: –substrate current. Trends: –power supplies are decreasing –electric fields are increasing.

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Mumbai, IndiaSamar Saha115 Hot-Carrier Effects Channel electron traveling through high electric field near the drain end can: –become highly energetic, i.e. hot –cause impact ionization and generate e and holes holes go into the substrate creating substrate current, I sub. Some channel e have enough energy to overcome the SiO 2 -Si energy barrier generating gate current, I g. The maximum e-field, E m near the drain has the greatest control of hot carrier effects. Gate IgIg n+ Drainn+ Source I sub m hole hot e l llllll

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Mumbai, IndiaSamar Saha116 Hot Electron Effects: Substrate Current Local field model (DD) c = critical electrical field 1.2 MV/cm = impact ionization coefficient. –calibration of impact ionization model parameters are required to match silicon data –tuned parameter values can be non-physical and non- predictive for a new technology.

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Mumbai, IndiaSamar Saha117 Hot Electron Effects: I sub using DD Model DD simulation results with default I sub model parameters do not match the measurement data.

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Mumbai, IndiaSamar Saha118 Hot Electron Effects: Substrate Current Local energy model (HD / ET model) surface impact ionization –better predictive capability than DD approach, but still uses tuned parameters. Non-local energy model. Full band MC.

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Mumbai, IndiaSamar Saha119 Hot Electron Effects: Summary Local field models are highly unphysical that result in unphysical calibrated parameters. Local energy models are more physical, but still require calibration of model parameters. Physically sound models that provide accurate results without calibration of model parameters are: –full band MC –non-local energy transport models.

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Mumbai, IndiaSamar Saha120 Device TCAD: Summary As devices scale down to 0.1 m and below, new physical effects are coming into play. Existing tools treat different aspects of device simulation fairly well. No single tool treats all of the important physics. Successful device TCAD will require a firm grasp of the controlling device physics.

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Samar Saha Technology CAD: Technology Modeling, Device Design and Simulation Industry Application: Calibration of Process and Device Models 2004 VLSI Design Tutorial, January 5, 2004 Mumbai, India

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Samar Saha122 Outline Objectives. Technology and Industry Trends affecting TCAD. TCAD Challenges. TCAD Tool Set. Calibration: –Process Models –Device Models. Mesh Generation. TCAD in Technology Development. Summary.

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Mumbai, IndiaSamar Saha123 Objectives Present issues and solutions for industrial TCAD: –process simulation calibration –device simulation key physical models –mesh generation optimal approach –calibration examples submicron process submicron device.

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Mumbai, IndiaSamar Saha124 Industry Trends affecting TCAD CMOS logic as technology driver: –CMOS logic technology design-space much larger than that of DRAM or BJT technologies –CMOS logic generation life-span is extremely short –CMOS simulation is essentially 2D. Logic technology offerings becoming broader: –high-V th devices –thick-oxide devices –low-V th devices.

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Mumbai, IndiaSamar Saha125 Industry Trends affecting TCAD System-on-a-chip (SOC) and logic derivatives: –integration issues driving increasing share of TCAD cycles integrating memory and logic (NVRAM, DRAM) BiCMOS CMOS imaging SiGe BJT and PFET. Net result: Rapidly expanding opportunities for TCAD to contribute.

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Mumbai, IndiaSamar Saha126 Industry Trends affecting TCAD Rapid thermal processing (RTP): –easy process addition increases design space –many subtle electrical effects. Larger wafer sizes: –interaction of process variations on circuit performance becoming increasingly important new TCAD arena. New impurity species increase design options: –In –Ge –N.

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Mumbai, IndiaSamar Saha127 Industry Trends affecting TCAD New materials and methods: –nitrided gate oxide –high-K gate dielectric –junction pre-amorphization –SOI –selective epitaxial growth –laser thermal annealing (LTA). Net result: –rapidly expanding design space for TCAD to cover –process TCAD challenges predominate.

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Mumbai, IndiaSamar Saha128 Industrial TCAD Challenges Challenge is to transform TCAD potential into valuable results for process and device engineers. Key tasks: –system perspective connect process recipes to device parametric/circuit performance (virtual fab) organize TCAD process to make non-experts productive TCAD users and maximize productivity of experts –process and device simulations process simulation reflect actual process results accurate electrical results for compact model extraction.

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Mumbai, IndiaSamar Saha129 Industrial TCAD Challenges Critical assumptions for success: –calibrate/characterize complex physical models for the present range of operation - global calibration –timely development/implementation of required physical models –timely calibration (local calibration) of process and device models to contribute significantly for the next generation technology development technology transfer. TCAD usage can be significantly broadened.

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Mumbai, IndiaSamar Saha130 TCAD Tool Set Process simulation: –2D capability with extensive detailed physical model set for implantation, diffusion, oxidation, deposition, and etching detailed knowledge of model formulation and modification. –examples based on vendor supported SUPREM4-process platform generalized calibration procedure.

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Mumbai, IndiaSamar Saha131 TCAD Tool Set Device Simulation: –general 2D capability based on moments of Boltzmann equation –control-volume discretization of DD/HD equations –examples based on vendor supported MEDICI-device platform generalized calibration procedure –user environment vendor supported TWB-framework platform.

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Mumbai, IndiaSamar Saha132 Calibration - Role of TCAD TCAD in research: –evaluate advanced device options –understand device physics. TCAD in technology development (TD): –perform tradeoffs for design options to reduce experimental wafer starts –assess manufacturability and design options –diagnose device/layout problems. TCAD in manufacturing: –process simplification for production technologies –problem diagnosis and fix. Accuracy is crucial, especially, for TD and manufacturing.

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Mumbai, IndiaSamar Saha133 Need for Calibration Deviation of simulation and measured data: –technology dependent: different focus area and application different physical models involved. –site/fab dependent: equipment material environment measurement techniques human interface.

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Mumbai, IndiaSamar Saha134 Need for Calibration Limitation of physical models: –secondary mechanisms become important –model dependency on implementation details –model short-fall in describing the target generation of process technology and devices. Limitation of model characterization/range: –may not cover all possible process conditions –may not cover all technologies –may not be able to measure directly.

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Mumbai, IndiaSamar Saha135 Calibration Challenges Experimental data: –expensive to obtain, especially, SIMS profiles –insufficient processing information –statistical fluctuations. Model complexity: –some parameters can not be directly measured –more parameters than data points. Simulation accuracy: –grid dependency –practical limitation on CPU and memory.

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Mumbai, IndiaSamar Saha136 Objective of Tool Calibration Device specific calibration: –operation region (optimization) –technology development –items of importance. DOE and characterization. Calibration of model parameters. Supporting software utilities.

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Mumbai, IndiaSamar Saha137 General Calibration Methodology Use short flows to characterize process profiles: –design process splits to cover design space. Use full flows to characterize devices with different dimensions (L and W dependencies). Tool calibration: –match SIMS profiles –use device data to correlate 2D effects –match device characteristics. Two-phase process.

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Mumbai, IndiaSamar Saha138 Process Simulation Overview Model calibration for process simulation: –overview of calibration process –Phase 1: 1D impurity calibration methodology example - nMOSFET channel profile –Phase 2: 2D calibration (process + device) methodology example - reverse short channel effect (RSCE). Summary.

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Mumbai, IndiaSamar Saha139 Process Modeling Approach Predictive capability for a wide range of logic and memory technologies necessitates: –new implant tables with new species like In, Ge etc. –3-stream TED model for dopant, interstitials, and vacancies –plus-n damage model with accumulated damage from multiple implants –amorphization due to implant damage –transient activation/deactivation of dopants –dislocation loops as source/sink for interstitials –3-phase segregation model.

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Mumbai, IndiaSamar Saha140 Process Simulation Calibration: Overview Model calibration (Phase 1) –implant models –diffusion models –oxidation models –etch/deposition models. TEM/SEM cross-sections, SIMS profiles, key (1D) electrical parameters. Technology/2D calibration (Phase 2) –key process model parameters –selected set of 2D electrical parameters.

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Mumbai, IndiaSamar Saha141 MOSFETs Process Model Calibration Flow Match SIMS profiles Adjust for dose loss Match V th RSCE Two-dimensional Calibration DIBL Surface recombination Damage by S/D implant One-dimensional Calibration Implant moments/table OED Segregation (set by channel profile) Diffusivity (in oxide for dose loss) T ox (QM,Poly-depletion corrections) One-dimensional Calibration Diffusivity of dopant-defect pair Diffusivity of defects

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Mumbai, IndiaSamar Saha142 MOSFETs 1D Process Model Calibration p-substrate p-welln-well n+ PMOS n+p+ STI NMOS A B CF E D Cross-section for short loop experiments: A / D NMOS / PMOS channel B / E NMOS / PMOS SDE C / F NMOS / PMOS S/D.

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Mumbai, IndiaSamar Saha143 A Typical Short Loop Experiment for P-Well

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Mumbai, IndiaSamar Saha144 Calibration Example: Channel Profile Use of detailed physical models to achieve 1D SIMS profile fit: –typical Phase-1 calibration activity –model updated over several technology generations. Channel profile after complete technology thermal cycle. Initial approach for implant and diffusion –MC implant significant CPU burden –scaled solid solubility –physics-based implant moments / implant table update.

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Mumbai, IndiaSamar Saha145 Example: NMOS Channel Profile P-Well B, 200 KeV after spacer deposition/etch Depth ( m) log10 (Boron) SIMS Simulation

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Mumbai, IndiaSamar Saha146 Technology Calibration - Phase 2 Coupled process and device simulations using Phase 1 calibration data. Target output (electrical) parameters: –C - V curves –V th –RSCE. Input variables (5 - 8 process model parameters): –point-defect distributions from implants plus-n model –key impurity segregation coefficients –parabolic oxidation rate.

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Mumbai, IndiaSamar Saha147 2D Calibration Example: RSCE

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Mumbai, IndiaSamar Saha148 Process Modeling: Summary Systematic process model calibration methodology is critical. Observed success within a (CMOS) technology: –process re-optimization offered a significant improvement in device performance –process centering achieved at manufacturing co-location with minimum development effort. Observation: –each successive technology generation requires a significant calibration effort (model update).

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Mumbai, IndiaSamar Saha149 Device TCAD Role of device simulation in TCAD Key physical models and examples: –mobility models for deep sub-micron CMOS –quantum effects in scaled CMOS devices –DD model. Device model calibration: –impact ionization with DD model. Summary.

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Mumbai, IndiaSamar Saha150 Device Simulation Role in TCAD Simulate device electrical behavior with sufficient accuracy to calibrate process simulation models: –primarily 2D electrostatic simulation V th, DIBL, I off, body effect, capacitances –expect DD model is sufficient for most requirements for MOSFETs with L eff 0.1 m. Provide capability for the physical simulation of wide range of device parameters: –substrate current, latch-up, ESD, and so on. Support exploratory device simulation for research.

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Mumbai, IndiaSamar Saha151 Device Simulation: CPU Burden Numerical issues associated with device simulation are well established: –core issue is repeated solution of large, sparse, ill- conditioned, non-symmetric sets of linear equations –typical industrial CMOS problem: ~ 10,000 mesh nodes simultaneous solution for (, n, p) –iterative solution methods often exhibit lack of convergence on problems of industrial interest. Optimized direct solution methods along with optimal mesh generation techniques can reduce CPU burden significantly without sacrificing accuracy.

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Mumbai, IndiaSamar Saha152 Critical TCAD Models: Carrier Mobility Device-design trends arising from CMOS scaling require consideration of: –coulombic scattering in the inversion layer high substrate/channel doping levels channel doping can vary significantly across the device –inversion- and accumulation-layer mobility. Industrial use of a mobility model requires: –strictly local calculation of mobility minor increase in program complexity no restrictions on device geometries or device designs.

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Mumbai, IndiaSamar Saha153 Critical Device TCADModels: QM Effects CMOS scaling requires inclusion of inversion-layer QM effects in device simulation for: –thinner gate oxides –higher substrate doping. Inversion-layer QM correction model must be: –strictly local calculation of required physical quantities minor increase in program complexity no restrictions on device geometries or device designs –acceptable CPU burden –no significant degradation in robustness. Models: van Dort / MLDA.

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Mumbai, IndiaSamar Saha154 MOSFETs: Device Model Calibration Flow Work function QM model Low field mobility High field mobility Band to band tunneling Impact Ionization I DS vs. V GS (V th V BS = 0,V DS = 50 mV I sub vs. V V BS = 0,V GS = 0 I DS vs. V GS (I DS vs. V DS V BS = 0,V DS = V DD I DS vs. V V BS = 0,V GS = 0

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Mumbai, IndiaSamar Saha155 Example: Impact Ionization Model DD-simulation over estimates I sub by more than an order.

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Mumbai, IndiaSamar Saha156 Example: Impact Ionization Model Impact Ionization model calibration: –used calibrated process model (technology calibration) –used calibrated device models (device calibration) –calibrate impact ionization coefficients. The electron impact ionization rate: where A i and B i are empirical constants E eff = effective electric field due to non-local effect.

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Mumbai, IndiaSamar Saha157 Example: Impact Ionization Model For DD, transform the model in terms of local electric field, E. Assume, E eff E, E eff = k * where k and are constants depending on the spatial variation of E near the drain-end of the channel. Substituting for E eff and defining B i k * i, the modified impact ionization coefficient is: Optimize i and to fit the measurement data.

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Mumbai, IndiaSamar Saha158 Example: Impact Ionization Model Calibrate device TCAD models: comparison of I - V data.

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Mumbai, IndiaSamar Saha159 Example: Impact Ionization Model Simulation with calibrated impact ionization coefficients.

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Mumbai, IndiaSamar Saha160 Example: Impact Ionization Model Simulation with calibrated impact ionization coefficients.

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Mumbai, IndiaSamar Saha161 Device TCAD: Summary Vendor supported device TCAD tools work very well with the present applications such as: –MOSFET I - V and C - V characteristics for technology development logic DRAM. Model selection and calibration show good results for sub-0.25 m technology development. Device TCAD effectiveness depends on: –mobility model suitable for the target technology –inversion-layer QM effects.

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Mumbai, IndiaSamar Saha162 Mesh Generation for Simulation Role and Requirements. Methods: –structured –quadtree –unstructured –hybrid. Example: –typical MOSFET mesh and gridding considerations. Summary.

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Mumbai, IndiaSamar Saha163 Mesh Generation: Role and Requirements Requirement is to support complete automation of process-to-device simulation transition: –highest barriers to expanded TCAD usage are mesh generation process simulation accuracy. Consistent and specialized grid distribution is an important key to simulation of high-performance MOSET devices: –resolution of inversion layers and depletion regions –resolution of mobility-model physical effects.

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Mumbai, IndiaSamar Saha164 Mesh Generation: Role and Requirements Requirements: –must accept device structures from detailed process simulation –no restrictions on device structures –mesh generation approach must minimize computational burden without compromising solution robustness and accuracy key: anisotropic grid-point distributions (the capability of supporting extreme differences in grid-point spacing in x- and y-directions).

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Mumbai, IndiaSamar Saha165 Mesh Generation Methods

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Mumbai, IndiaSamar Saha166 Hybrid Mesh Generation: Half-MOSFET x y Gate S/D Channel Source/Drain

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Mumbai, IndiaSamar Saha167 Mesh Generation Dependence of device performance on vertical grid-spacing.

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Mumbai, IndiaSamar Saha168 Mesh Generation Dependence of device performance on horizontal grid-spacing.

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Mumbai, IndiaSamar Saha169 Mesh Generation: Summary Mesh generation is the critical component of an effective TCAD system. Simulation results vary significantly on mesh and may result in: –unphysical calibration parameters –unpredictable/inconsistent results. Robust mesh: –allows process simulators to be consistently and robustly linked to device simulators by non-experts –significantly reduces CPU burden for device simulation.

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Mumbai, IndiaSamar Saha170 Industry Application: Summary Vendor supported TCAD tools offer most simulation capabilities for industrial usage. Systematic calibration procedure is required to support efficient: –process technology optimization –future technology development. Mesh generation is crucial for predictive technology simulation. Well calibrated physical models provide efficient predictive TCAD capability.

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Samar Saha Technology CAD: Technology Modeling, Device Design and Simulation Industry Application: TCAD in Device Research and Compact Modeling 2004 VLSI Design Tutorial, January 5, 2004 Mumbai, India

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Samar Saha172 Research Application: Overview Role of TCAD in device research: –how it differs from development/manufacturing. –examples sub-100 nm MOSFET device design design optimization of FinFETs. TCAD for compact modeling: –TCAD-based compact model parameter extraction for substrate current modeling –flash memory cell macro model. Summary.

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Mumbai, IndiaSamar Saha173 Role of TCAD in Research Performance analysis of future device design options to guide development effort. Understand device physics for new device concepts. Typically, research TCAD is not the virtual fab paradigm: –process simulation is not used, since device cannot be made with current process technologies. Circuit performance is directly evaluated from the output of device simulation using two different ways: 1d evice simulation m odel extraction circuit simulation 2mixed-mode device/circuit simulation.

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Mumbai, IndiaSamar Saha174 Example: Sub-100 nm MOSFET Design Design issues in achieving MOSFET devices near the lower limit of channel length: –scaling requirements –material limitations of scaling –feasibility of continuous scaling. Methodology to generate sub-100 nm MOSFET device characteristics vs. scaling parameters. Results and discussions. Summary.

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Mumbai, IndiaSamar Saha175 Scaling Requirements vs. Limitations

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Mumbai, IndiaSamar Saha176 Feasibility of Continuous T OX and X j Scaling Scaling T ox (eff) 2 nm is feasible with a high K dielectric gate material to maintain: –a thicker value of T OX (physical) for a tolerable value of Lg –a target value of gate capacitance (C OX ) equivalent to that of an ultra-thin SiO 2 gate material. Scaling X j 30 nm is essential to: –scale down Lg, gate area, and C OX –improve ac device performance.

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Mumbai, IndiaSamar Saha177 Idealized Device Simulation Structure Channel doping profile : vertically and laterally non-uniform. SDE : heavily-doped source-drain extension regions with junction depth X j. DSD : heavily-doped deep source-drain of junction depth X jd. Halo : channel-type doping around SDE regions. L eff Halo X jd XjXj Halo DSD SDE L ext T OX Lg Body (B) Poly-Si gate Spacer

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Mumbai, IndiaSamar Saha178 Design Simulation Experiment Designed CMOS technologies for L eff = 25 nm with: –{Lg = 40 nm, X j 14 nm, T ox (eff) = {1,1.5, 2} nm} –{Lg = 50 nm, X j 20 nm, T ox (eff) = {1,1.5, 2} nm} –{Lg = 60 nm, X j 26 nm, T ox (eff) = {1,1.5, 2} nm}. For each technology: –non-uniform vertical channel doping profile was optimized for the target long channel |V th | 0.23 V –two halo profiles (double halo architecture) were used to reduce DIBL from both SDE and DSD regions achieve non-uniform lateral channel doping profile with the target |I off | 10 nA |V DD | = 1 V.

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Mumbai, IndiaSamar Saha179 Simulation Strategy Optimized technology parameters: –SDE peak concentration 2.5x10 20 cm -3 –DSD peak concentration 3.7x10 20 cm -3 –peak halo concentration 5x x10 19 cm -3. Channel concentration dependent on Lg. Device characteristics were generated using MEDICI with: –hydrodynamic model for semiconductors –van Dorts Quantum Mechanical model –calibrated device models ( global calibration!! ).

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Mumbai, IndiaSamar Saha180 Simulated Channel Doping Contours Lg

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Mumbai, IndiaSamar Saha181 |V th | increases with the increase in T OX (eff) for all devices. Devices with L eff = 25 nm and T OX (eff) = 2 nm, |V th | > 0.4 V is too high for high-performance |V DD | 1 V. T OX (eff) < 2 nm offers lower |V th | for low power operation. Simulated V th vs. L eff for different T OX (eff)

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Mumbai, IndiaSamar Saha182 Simulated I DSAT vs. I off for different T OX (eff) Devices with |I off | nA m represents L eff = 25 nm. At a constant |I off | 2 nA/ m: –|I DSAT | increases as T OX (eff) decreases –T OX (eff) < 2 nm is essential to improve I DSAT for L eff = 25 nm devices.

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Mumbai, IndiaSamar Saha183 For a typical 50 nm technology with L eff = 25 nm and T ox (eff) = 1 nm: –S 80 mV/decade –|DIBL| 60 mV –I DSAT (n) 680 A/ m, |I DSAT (p)| 275 A/ |V GS | = 1 V = |V DS |. Simulated I - V Data for T OX (eff) = 1 nm

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Mumbai, IndiaSamar Saha184 For 25 nm devices of a 50 nm CMOS technology, as T ox (eff) increases from 1 nm 1.5 nm: –S increases [ S 8 mV/decade] –DIBL increases [ (DIBL) 30 mV] –|I DSAT | decreases [ I DSAT (n) 102 A/ m; I DSAT (p) 42 A/ m]. Simulated I - V Data for T OX (eff) = 1.5 nm

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Mumbai, IndiaSamar Saha185 For 25 nm devices of a 50 nm CMOS technology, as T ox (eff) increases from 1 nm 2 nm: –S increases [ S 16 mV/decade] –DIBL increases [ (DIBL) 60 mV] –|I DSAT | decreases [ I DSAT (n) 214 A/ m; I DSAT (p) 72 A/ m]. Simulated I - V Data for T OX (eff) = 2 nm

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Mumbai, IndiaSamar Saha186 Simulated V th vs. X j for Different T OX (eff)

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Mumbai, IndiaSamar Saha187 Simulated I DSAT vs. X j for Different T OX (eff)

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Mumbai, IndiaSamar Saha188 Simulated DIBL vs. X j for Different T OX (eff)

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Mumbai, IndiaSamar Saha189 Simulated S vs. X j for Different T OX (eff)

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Mumbai, IndiaSamar Saha190 Simulated Delay for Different X j and Lg

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Mumbai, IndiaSamar Saha191 Sub-100 nm MOSFET Design: Summary The simulation results show the feasibility of 25 nm MOSFETs with: –T OX (eff) 2 nm to maintain lower |V th | for |V DD | 1 V operation achieve higher |I DSAT | for a target value of |I off | lower value of DIBL lower value of S 80 mV/decade –X j 30 nm to scale Lg 60 nm improve device speed. 25 nm devices with X j 14 nm and Lg 40 nm show a significant improvement in speed.

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Mumbai, IndiaSamar Saha192 Design FinFET (double-gate MOSFET) Simulation Structure. Optimize Different Fin-dimensions. Feasibility of 20 nm FinFET Device. Comparison of 20 nm Device Performance using FinFET vs. Conventional MOSFET Architecture. Summary. Example: Double Gate MOSFET Design

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Mumbai, IndiaSamar Saha193 Idealized Double Gate MOSFET Structure T ox T Si SourceDrain Top Gate Bottom Gate LgLg T ox = Top/bottom gate oxide thickness. T Si = Un-doped/lightly-doped channel width. L g = Channel length.

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Mumbai, IndiaSamar Saha194 Simulated DG-MOSFET FinFET Structure T fin H fin LgLg

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Mumbai, IndiaSamar Saha195 Major Process Steps to Generate FinFETs 1. Define Si-Fin2. Gate oxidation 3. Poly-Si gate 4. Nitride spacer S/D implant 5. Half-structure 6. Full-structure Oxide Si-Fin BOX Nitride Poly Nitride

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Mumbai, IndiaSamar Saha196 Critical Parameters for FinFET Simulation Parameters used for simulation structure design: –T fin = 10 to 30 nm –H fin = 50 nm –L g = 10 to 50 nm –T ox = 1.5 nm. For device simulation, channel doping was optimized to obtain V th 0.1 V for L g = 20 nm nFinFETs. Device structures and the characteristics were generated using 3D-simulation tool Taurus ( from Synopsys ).

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Mumbai, IndiaSamar Saha197 V th vs. L g for Different T fin ; H fin = 50 nm

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Mumbai, IndiaSamar Saha198 I DSAT vs. L g for Different T fin ; H fin = 50 nm

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Mumbai, IndiaSamar Saha199 S vs. L g for Different T fin ; H fin = 50 nm

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Mumbai, IndiaSamar Saha200 I V Characteristics of 20 nm FinFETs

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Mumbai, IndiaSamar Saha201 FinFETs vs. Conventional MOSFETs 20 nm FinFETs show superior device performance compared to 20 nm conventional MOSFETs.

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Mumbai, IndiaSamar Saha202 TCAD is used to design and study FinFET device characteristics. The simulation data for nFinFETs with 10 nm < L g < 50 nm and H fin = 50 nm show: –higher V th roll-off as L g decreases for thicker T fin devices –lower I DSAT in thinner T fin devices due to higher s/d resistance –increase in S with decrease in L g for T fin < 50-nm –S 60 mV/decade for all T fin with L g >>40-nm. 20 nm FinFETs show superior device performance than 20 nm conventional bulk-MOSFETs. FinFET Design: Summary

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Mumbai, IndiaSamar Saha203 Example: Compact Model Extraction for I sub Procedure for TCAD-based Compact Model Parameter Extraction. Simplification of I sub Model for TCAD-based Compact Modeling. Model Extraction. Model Verification. Summary.

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Mumbai, IndiaSamar Saha204 Substrate Current, I sub Model I sub generated due to impact ionization is given by: where A i and B i are impact ionization parameters l c = characteristic length of saturation region E m = maximum lateral electric field near the drain E c = critical electric field for velocity saturation.

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Mumbai, IndiaSamar Saha205 Substrate Current, I sub Model At strong inversion ( V DS >> V DSAT ) E m is given by: where L eff = effective channel length of device V th = threshold voltage of device.

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Mumbai, IndiaSamar Saha206 Substrate Current, I sub Model The bias dependence of E c is given by: E c = E c0 + E cg V GS + E cb V BS where E c0, E cg, and E cb are model parameters given by: E c0 = E V GS = V BS = 0 E cg = slope of E c vs. V GS V BS = constant E cb = slope of E c vs. V BS V GS = constant The bias dependence of l c is given by: l c = (l c0 + l c1 V DS ) T OX here l c0 and l c1 are model parameters.

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Mumbai, IndiaSamar Saha207 I sub Model Parameters Empirical constants: –A i = 1.65x10 6 (1/cm) –B i = 1.66x10 6 (V/cm) Technology dependent parameters: –E c0 = bias independent constant (V/cm) –E cg = gate bias dependent parameter (1/cm) –E cb = back-gate bias dependent parameter (1/cm) –l c0 = bias independent constant ( cm) –l c1 = bias dependent constant ( cm/V). We assume, l c = l c0 is a technology dependent constant for TCAD-based parameter extraction (i.e. ignore l c1 ).

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Mumbai, IndiaSamar Saha208 TCAD-based I sub Model Extraction V DSAT extraction E c extraction l c extraction SPICE simulation Format I - V data Compute I sub /I DS Device Simulation Device Model Calibration At each V GS, generate: I DS - V DS and I sub - V DS Process Simulation Process Model Calibration Generate: Device Structure Extraction of {E c0, E cg, E cb }

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Mumbai, IndiaSamar Saha209 Parameter Extraction: V DSAT V DSAT is extracted by mapping constant I sub /I DS contours on I DS vs. V DS family of simulated curves.

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Mumbai, IndiaSamar Saha210 Parameter Extraction: E c0, E cg, and E cb E c0 and E cg extraction: –extract V DSAT for different values of V GS at V BS = 0. –compute E c from: –plot E c vs. V GS to extract: E c0 = V GS = 0 E cg = slope. Same procedure to extract E cb with V BS 0.

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Mumbai, IndiaSamar Saha211 Parameter Extraction: l c and Components The simplified from of the expression: log(Y) = mX + C, where X = 1/(V DS - V DSAT ) Y = I sub /[I DS (V DS - V DSAT )] Parameters are extracted from log(Y) vs. X plots: slope, m = - B i l c intercept, C = ln(A i /B i ).

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Mumbai, IndiaSamar Saha212 Parameter Extraction: l c and Components

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Mumbai, IndiaSamar Saha213 TCAD-based I sub Models For nMOSFET devices of the target technology: +E c0 = 5.50E+04 (V/cm) +E cg = 3.50E+03 (1/cm) +l c = 1.38E-05 (cm) +A i = 1.65E+06 (1/cm) +B i = 1.66E+06 (V/cm)

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Mumbai, IndiaSamar Saha214 Model Verification Measurement and simulation data using the extracted models.

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Mumbai, IndiaSamar Saha215 Model Verification Measurement and simulation data using the extracted models.

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Mumbai, IndiaSamar Saha216 Model Extraction for I sub : Summary The example shows the basic idea to use TCAD for compact model parameter extraction using: –calibrated process models for process TCAD –calibrated device models for device TCAD –simplified equations and extraction routines, as needed. Process and device models were calibrated for the target technology. I sub model is simplified to extract model parameters. The simulation data using TCAD-based model agree very well with the measurement data.

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Mumbai, IndiaSamar Saha217 Example: Flash Memory Cell - Macro Model Flash Memory Cell Compact Modeling –split gate cell –two-transistor macro model –necessity for TCAD-based macro model. Model extraction. –procedure.

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Mumbai, IndiaSamar Saha218 Flash Memory Cell - Split Gate Structure Cell consists of: –WL transistor –FG transistor. FG may not have contact pad for measurement. Typically, 1T-cell model is used. 2T-model provides more accurate cell characteristics. TCAD-based.

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Mumbai, IndiaSamar Saha219 Flash Memory Cell: TCAD-based Model Calibrated Device Model Calibrated Process Model Extract SPICE Model for T1 Extract SPICE Model for T2 Model Verification Simulate I - V for T1 Simulate Test Structures SPICE/Circuit Simulation Generate Macro Model Calibrated Device Model Simulate I - V for T2

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Mumbai, IndiaSamar Saha220 TCAD in Research & Modeling: Summary Device TCAD can be successfully used in device research to: –study different device options –examine new device ideas –optimize device design range for technology development guideline. Calibrated TCAD models can be used accurately to: –predict device performance –extract compact model –predict circuit performance.

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Mumbai, IndiaSamar Saha221 References [1] J.D. Plummer et al., Silicon VLSI Technology - Fundamentals, Practice and Modeling. Prentice Hall, New Jersey, [2] S. Tian, Predictive Monte Carlo ion implantation simulator from sub-keV to above 10 MeV, J. Appl. Phys., vol. 93, No. 10, p 5893, [3] S. Furukawa et al., Theoretical considerations on lateral spread of implanted ions, Jap. J. Appl. Phys., vol. 11, p 134, [4] S. Hobler and S. Selberherr, Two-dimensional modeling of ion implantation induced point defects, IEEE Trans. Computer-Aided Design, vol. 7, p 174, [5]L. Pelaz et al., Modeling of the ion mass effect on transient enhanced diffusion: deviation from +1 model, Appl. Physics. Lett., vol. 73, p 1421, [6] S. Chakravarthi and S.T. Dunham, Influence of extended defect models on prediction of boron transient enhanced diffusion, in Silicon Front End Technology - Materials Processing and Modeling, N. Cowern, P. Griffin, D. Jacobsen, P. Packan, and R. Webb, eds. (Mat. Res. Soc. Proc. vol. 532, Pittsburgh, PA, 1998).

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Mumbai, IndiaSamar Saha222 References [7]P.M. Fahey et al., Point Defects and Dopant Diffusion in Silicon, Rev. Modern Physics, vol. 61, p. 289, [8]A. S. Grove, Physics and Technology of Semiconductor Devices. John Wiley & Sons, New York, [9]H.Z. Massoud et al., Thermal Oxidation of Silicon in Dry Oxygen: Growth- Rate Enhancement in the Thin Regime I. Experimental Results, II Physical Mechanisms, J. Electrochem. Soc., vol. 132, p and 2693, [10]F. Nouri et al., Optimized shallow trench isolation for sub-0.18 m technology, Proc. SPIE Conf. on Microelectronic Device Technology, vol. 3506, p. 156, [11]TSUPREM4, Synopsys Corp., Mountain View, CA. [12]H. Kosina et al., Device modeling for the 1990s, Microelectron. J., vol. 26, p. 217, [13]S.E. Laux and M.V. Fischetti, Transport models for advanced device simulation-truth or consequences?, BCTM Tech. Dig., 1995.

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Mumbai, IndiaSamar Saha223 References [14]M.K. Ieong and T.W. Tang, Influence of hydrodynamic models on the prediction of semiconductor device characteristics, IEEE-TED, vol. 44, p. 2242, [15]M.S. Lundstrom, Fundamentals of carrier transport, 2nd edition Cambridge University Press, [16]M.N. Darwish et al., An improved electron and hole mobility model for general purpose device simulation, IEEE-TED, vol. 44, p. 1529, [17]D. Vasileska et al., Scaled silicon MOSFETs: Degradation of the total gate capacitance, IEEE-TED, vol. 44, p. 584, [18]C. Rafferty et al., Multi-dimensional quantum effect simulation using a density-gradient model and script-level programming techniques, Simulation of Semiconductor Process and Devices, K.De Meyer and S Biesemans (eds.), p. 137, 1998, Springer-Verlag. [19]M.J. van Dort et al., A simple model for quantization effects in heavily-doped silicon MOSFETs at inversion conditions, Solid-St. Electron., vol. 37, p. 411, 1994.

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Mumbai, IndiaSamar Saha224 References [20]P. Vande Voorde et al., Accurate doping profile determination using TED/QM models extendible to sub-quarter micron nMOSFETs, IEDM Tech. Dig., p. 811, [21]S. Selberherr, MOS device modeling at 77K, IEEE-TED, vol. 36, p.1464, [22]S. Saha, Effects of inversion layer quantization on channel profile engineering for nMOSFETs with 0.1 m channel lengths, Solid-State Electron., vol. 42, p. 1985, [23]S. Saha et al., Effects of inversion layer quantization and polysilicon gate depletion on tunneling current of ultra-thin SiO 2 gate material, Mater. Res. Soc. Symp. Proc., vol. 567, p. 275, [24]P. Wong and Y. Taur, Three-dimensional atomistic simulation of discrete random dopant distribution effects in sub-0.1 m MOSFETs, IEDM Tech. Dig., p. 705, [25]P.A. Stolk et al., Modeling statistical dopant fluctuations in MOS Transistors, IEEE-TED, vol. 45, p. 1960, 1998.

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Mumbai, IndiaSamar Saha225 References [26]S.E. Laux and M.V. Fischetti, The physics of hot-electron degradation of Si MOSFETs: can we understand it?, App. Surf. Sci., vol. 39, p. 578, [27]C. Jungemann et al., Is physically sound and predictive modeling of NMOS substrate currents possible?, Solid-St. Electron., vol. 42, p. 647, [28]S. Saha et al., Impact ionization rate of electrons for accurate simulation of substrate current in submicron devices, Solid-State Electron., vol. 36, p. 1429, [29]R.W. Dutton and Z. Yu, Technology CAD: Computer simulation of IC processes and devices. Kluwer, [30]S. Selberherr, Analysis and simulation of semiconductor devices. Springer- Verlag, [31]N. Arora, MOSFET models for VLSI circuit simulation – theory and practice. Springer-Verlag, [32]S. Saha, Managing technology CAD for competitive advantage: An efficient approach for integrated circuit fabrication technology development, IEEE Trans. Eng. Manage., vol. 46, p. 221, 1999.

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Mumbai, IndiaSamar Saha226 References [33] S. Saha, Improving the efficiency and effectiveness of IC manufacturing technology development, in Technology and Innovation Management, D.F. Kocaoglu, T.R. Anderson, D.Z. Milosevic, K. Niwa, and H. Tschirky (eds.), Portland, OR: PICMET 1999, p. 540, [34]S. Saha, Technology CAD for integrated circuit fabrication technology development and technology transfer, in Proc. SPIE Conf. on Design and Process Integration for Microelectronic Manufacturing II, vol. 5042, p. 63, [35]C.V. Mouli, Models and methods: Effective use of technology-computer aided design in the industry, J. Vac. Sci. Tech. B., vol. 18, p. 354, [36]C. Lombardi et al., A physically based mobility model for numerical simulation of non-planar devices, IEEE Trans. Computer-Aided Design., vol. 17, p. 1164, [37]S. Saha, MOSFET test structures for two-dimensional device simulation, Solid-State Electron., vol. 38, p. 69, [38]O.C. Zienkiewcz, The Finite Element Method, McGraw-Hill, 1977.

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Mumbai, IndiaSamar Saha227 References [39]S. Saha, Scaling considerations for high performance 25 nm metal-oxide- semiconductor field-effect transistors, J. Vac. Sci. Tech.. B, vol. 19, p. 2240, [40]S. Saha, Design considerations for 25 nm MOSFET devices, Solid-State Electron., vol. 45, p. 1851, [41]C.C. Hu, FinFET – a device for nanoscale IC (NSI), in IEEE Silicon Nanoelectronics Workshop Digest, p. 1, [42]S. Saha, Device characteristics of sub-20 nm silicon nanotransistors, in Proc. SPIE Conf. on Design and Process Integration for Microelectronic Manufacturing II, vol. 5042, p. 172, [43]G. Pei et al., FinFET design consideration based on 3-d simulation and analytical modeling, IEEE Trans. Electron. Dev., vol. 49, p.1411, [44]TAURUS, Synopsys Corp., Mountain View, CA. [45]MEDICI, Synopsys Corp., Mountain View, CA. [46]S. Saha, Extraction of substrate current model parameters from device simulation, Solid-State Electron., vol. 37, p. 1786, 1994.

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