Presentation on theme: "MSE, The Ohio State University, Columbus, OH, USA"— Presentation transcript:
1MSE, The Ohio State University, Columbus, OH, USA Ab-initio Assisted Process and Device Simulation for Nanoelectronic Devices800 oC20 minAs impl.SIMSModelIVWolfgang WindlMSE, The Ohio State University, Columbus, OH, USA
2Semiconductor Devices – MOSFET Metal Oxide Semiconductor Field Effect Transistor0VG– VG– VD– VDInsulator(SiO2)Gate(Me)SpacerGateIDSourcePChannelDrainP+++SourcePDrainP+-++++++-++++++-++++++++++++-N-++++++-+++++++++--N++++-Si-----Si---------Doping:N: e-, e.g. As(Donor)P: holes, e.g. B(Acceptor)Analog: AmplificationDigital: Logic gates
31. Semiconductor Technology Scaling – Improving Traditional TCAD Feature size shrinks on average by 12% p.a.; speed sizeChip size increases on average by 2.3% p.a.Overall performance: by ~55% p.a. or~ doubling every 18 months (“Moore’s Law”)The switching speed increase comes from the decrease in gate delay. The gate delay time is ~ RC. The resistivity stays roughly constant, but the capacitance scales as w*l/s, where the capacitor plates have an area of w * l, and are separated by distance s. All the lengths scale down with the feature size, so C scales down with it. The clock frequency ~ 1/ delay time.
5Role of Ab-Initio Methods on Nanoscale Improving traditional (continuum) process modeling to include nanoscale effectsIdentify relevant equations & parameters (“physics”)Basis for atomistic process modeling (Monte Carlo, MD)Nanoscale characterization= Combination of experiment & ab-initio calculationsAtomic-level process + transport modeling= structure-property relationship (“ultimate goal”)
61. “Nanoscale” Problems – Traditional MOS What you expect:Intrinsic diffusion800 °C20 min800 °C1 month800 °C20 minWhat you get:fast diffusion (TED)immobile peaksegregationActive B¯
7Bridging the Length Scales: Ab-Initio to Continuum Need to calculate: ● Diffusion prefactors (Uberuaga et al., phys. stat. sol. 02)● Migration barriers (Windl et al., PRL 99)● Capture radii (Beardmore et al., Proc. ICCN 02)● Binding energies (Liu et al., APL 00)
82. The Nanoscale Characterization Problem Traditional characterization techniques, e.g.:SIMS (average dopant distribution)TEM (interface quality; atomic-column information)Missing: “Single-atom” informationExact interface (contact) structure (previous; next)Atom-by-atom dopant distribution (strong VT shifts)New approach: atomic-scale characterization (TEM) plus modeling
9Abrupt vs. Diffuse Interface Si0GradedSi0Si2+Si1,2,3+Si4+Si4+How do we know? What does it mean?Buczko et al.
10Atomic Resolution Z-Contrast Imaging < 0.1 nmScanningProbeZ=31Z=33GaAsA n n u l a r D e t e c t o rGaAs1.4ÅEELSSpectrometerComputational Materials Science and Engineering
12Theoretical Methods ab initio Density Functional Theory plus LDA or GGAimplemented withinpseudopotentialandfull-potential (all electron) methods
13Si-L2,3 Ionization Edge in EELS ground state of Si atomwith total energy E0excited Si atomwith total energy E1energyconduction band minimumEF~ 90eV~ 115eVsite andmomentumresolvedDOS2p3/22p62p1/22p52s1/2Transition energy ET = E1 - E0ET = ~100 eV1s1/2
14Calculated Si-L2,3 Edges at Si/SiO2 0.80.4Si3+0.6Si1+0.21.2Si2+0.4Si4+10.5100104108Energy-loss, eV
15Combining Theory and Experiment Calculation of EELS Spectra from Band StructureSiIntensitySi - L2,30.5 nm100105110Energy-loss (eV)
16Combining Theory and Experiment Calculation of EELS Spectra from Band StructureSi0 Si1+ Si2+ Si3+ Si4+4321.74FractionsSiIntensitySi - L2,30.5 nm100105110Energy-loss (eV) “Measure” atomic structure of amorphous materials.
17Band Line-Up Si/SiO2 Real-space band structure: Calculate electron DOS projected on atomsAverage layersAbrupt would be better!Is there an abrupt interface?Lopatin et al., submitted to PRL
18Interfaces with Different Abruptness: Si/SiO2 vs. Si:Ge/SiO2 Yes!Ge-implanted sample from ORNL (1989).Sample history:Ge implanted into Si (1016 cm-2, 100 keV)~ 800 oC oxidationInitial Ge distribution~4%~120 nm
19Z-Contrast Ge/SiO2 Interface Ge after oxidation packed into compact layer, ~ 4-5 nm wide123456nmIntensitySiSiO2Gepeak ~100% Ge
20Kinetic Monte Carlo Ox. Modeling Simulation Algorithm for oxidation of Si:Ge:Si lattice with O added between Si atomsAddition of O atoms and hopping of Ge positions by KMC*First-principles calculation of simplified energy expression as function of bonds:*Hopping rate Ge: McVay, PRB 9 (74); ox rate SiGe: Paine, JAP 70 (91).Windl et al., J. Comput. Theor. Nanosci.
21Monte Carlo Results - Animation Ge conc.O conc.Concentration (cm-3)OGeSi not shown2422 nm3Depth (cm)
22Monte Carlo Results - Profiles Initial Ge distribution25 min, 1000 oCoxide
23Atomic Resolution EELS Si/SiO2 vs. Ge/SiO2Atomic Resolution EELSIntensitySi - L2,3SiIntensitySi - L2,3Ge0.5 nm0.5 nm100105110100105110Energy-loss (eV)Energy-loss (eV)oxideSiGeS. Lopatin et al., Microscopy and Microanalysis, San Antonio, 2003.
24Band Line-Up Si/SiO2 & Ge/SiO2 Lopatin et al., submitted to PRL
25Conclusions 2Atomic-scale characterization is possible: Ab-initio methods in conjunction with Z-contrast & EELS can resolve interface structure.Atomically sharp Ge/SiO2 interface observedReliable structure-property relationship for well characterized structure (band line-up)Abrupt is goodSharp interface from Ge-O repulsion (“snowplowing”)
263. Process and Device Simulation of Molecular Devices Possibilities:Carbon nanotubes (CNTs) as channels in field effect transistorsSingle molecules to function as devicesMolecular wires to connect device moleculesSingle-molecule circuits where devices and interconnects are integrated into one large molecule300 nmWind et al., JVST B, 2002.
27Concept of Ab-Initio Device Simulation UsingLandauer formula for Ip(V)Lippmann-Schwinger equation, Tlr(E) = lV + VGV r Rigid-band approximation T(E,V) = T(E + V) with = 0.5Zhang, Fonseca, Demkov, Phys Stat Sol (b), 233, 70 (2002)
28Tlr from Local-Orbital Hamiltonian device(Hd)right elec.(Hr)TlTdlTdrTrleft elec.(Hl)...Tlr(E) can be constructed from matrix elements of DFT tight-binding Hamiltonian H. Pseudo atomic orbitals: (r > rc)=0.We use matrix-element output from SIESTA.Zhang, Fonseca, Demkov, Phys Stat Sol (b), 233, 70 (2002)
29The Molecular Transport Problem IExpt.Strong discrepancy expt.-theory!Suspected Problems:Contact formation molecule/lead not understoodInfluence of contact structure on electronic propertiesTheor.
30What is “Process Modeling” for Molecular Devices? Contact formation: need to follow influence of temperature etc. on evolution of contact.Molecular level: atom by atom Molecular DynamicsProblem: MD may never get to relevant time scalessmsnsYear199020002010Moore’s lawAccessible simulated time** 1-week simulation of 1000-atom metal system, EAM potential
31Accelerated Molecular Dynamics Methods Possible solution: accelerated dynamics methods.Principle: run for trun. Simulated time: tsim = n trun, n >> 1Possible methods:Hyperdynamics (1997)Parallel Replica Dynamics (1998)Temperature Accelerated Dynamics (2000)Voter et al., Annu. Rev. Mater. Res. 32, 321 (2002).
32Temperature Accelerated Dynamics (TAD) Concept:Raise temperature of system to make events occur more frequently. Run several (many) times.Pick randomly event that should have occurred first at the lower temperature.Basic assumption (among others):Harmonic transition state theory (Arrhenius behavior) w/ E from Nudged Elastic Band Method (see above).Voter et al., Annu. Rev. Mater. Res. 32, 321 (2002).
33Carbon Nanotube on Pt From work function, Pt possible lead candidate. Structure relaxed with VASP.Very small relaxations of Pt suggest little wetting between CNT and Pt ( bad contact!?).
34Movie: Carbon Nanotube on Pt Temperature-Accelerated MD at 300 K tsim = 200 sNordlund empirical potentialNot much interaction observed study different system.
35Carbon Nanotube on TiLarge relaxations of Ti suggest strong reaction (wetting) between CNT and Ti.Run ab-initio TAD for CNT on Ti (no empirical potential available).Very strong reconstruction of contacts observed.
36TAD MD for CNT/Ti 600 K, 0.8 ps tsim (300 K) = 0.25 s CNT bonds break on top of Ti, very different contact structure.New structure 10 eV lower in energy.
37Contact Dependence of I-V Curve for CNT on Ti Difference 15-20%
38Relaxed CNT on Ti “Inline Structure” In real devices, CNT embedded into contact. Maybe major conduction through ends of CNT?
39Contact Dependence of I-V Curve for CNT on Ti Inline structure has 10x conductivity of on-top structure
40Conclusions Currently major challenge for molecular devices: contacts Contact formation: “Process” modeling on MD basis.Accelerated MDEmpirical potentials instead of ab initio when possibleMajor pathways of current flow through ends of CNT
41Funding Semiconductor Research Corporation NSF-Europe Ohio Supercomputer Center
42Acknowledgments (order of appearance) Dr. Roland Stumpf (SNL; B diffusion)Dr. Marius Bunea and Prof. Scott Dunham (B diffusion)Dr. Xiang-Yang Liu (Motorola/RPI; BICs)Dr. Leonardo Fonseca (Freescale; CNT transport)Karthik Ravichandran (OSU; CNT/Ti)Dr. Blas Uberuaga (LANL; CNT/Pt-TAD)Prof. Gerd Duscher (NCSU; TEM)Tao Liang (OSU; Ge/SiO2)Sergei Lopatin (NCSU; TEM)
43Left:Ti below 25 a.u. and above 55 a.u.CNT (armchair (3,3), 12 C planes) in the middleRight:Ti below 10 a.u. and above 60 a.u.CNT (3,3), 19 C planes, in contact with Ti between 15 a.u. and 30 a.u. and between 45 a.u. and 60 a.u.CNT on vacuum between 30 a.u. and 45 a.u.
44Minimal basis set used (SZ); I did a separate calculation for an isolated CNT(3,3) and obtained a band gap of 1.76 eV (SZ) and 1.49 eV (DZP). Armchair CNTs are metallic; to close the gap we need kpts in the z-direction.
45Notice the difference in the y-axis Notice the difference in the y-axis. The X structure (below) carries a current which is about one order of magnitude smaller than the CNT inline with the contacts (left)The main peak in the X structure is located at ~5 V, which is close to the value from the inline structure (~5.5 V). This indicates that the qualitative features in the conductance derive from the CNT while the magnitude of the conductance is set by the contacts. The extra peaks seen on the right may be due to incomplete relaxation.
46Notice the difference in the y-axis Notice the difference in the y-axis. The X structure (below) carries a current which is about one order of magnitude smaller than the CNT inline with the contacts (left)The main peak in the X structure is located at ~5 V, which is close to the value from the inline structure (~5.5 V). This indicates that the qualitative features in the conductance derive from the CNT while the magnitude of the conductance is set by the contacts. The extra peaks seen on the right may be due to incomplete relaxation.
48PDOS for the relaxed CNT in line with contacts PDOS for the relaxed CNT in line with contacts. The two curves correspond to projections on atoms far away from the two interfaces. A (3,3) CNT is metallic, still there is a gap of about 4 eV. Does the gap above result from interactions with the slabs or from lack of kpts along z? This question is not so important since the Fermi level is deep into the CNT valence band.
49Previous calculations and new ones Previous calculations and new ones. Black is unrelaxed but converged with Siesta while blue is relaxed with Vasp and converged with Siesta. From your results it looks like you started from an unrelaxed structure and is trying to converge it.
50Current (A)Bias (V)Previous calculations and new ones. Black is relaxed with Vasp and converged with Siesta.
51MD smoothes out most of the conductance peaks calculated without MD MD smoothes out most of the conductance peaks calculated without MD. However, the overall effect of MD does not seem to be very important. That is an important result because it tells us that the Schottky barrier is extremely important for the device characteristics but interface defects are not. Transport seems to average out the defects generated with MD. Notice in the lower plot that there is no exponential regime, indicating ohmic behavior. Slide 7 shows that for the aligned structure the tunneling regime is very clear up to ~6 V.
53MOSFET Scaling: Ultrashallow Junctions Shallower ImplantHigher DopingTo get enough current with shallow source & drainBetter insulation (off)*P. Packan, MRS Bulletin
54Implantation & Diffusion Dopants inserted by ion implantation damageDamage healed by annealingDuring annealing, dopants diffuse fast (assisted by defects) important to optimize anneal*GateGeneral bla-bla (first 3 bullets well known, last one straightforward enough to not reveal anything new)SourceDrainChannel*Hoechbauer, Nastasi, Windl
55Ab-Initio Calculations – Standard Codes Input:Coordinates and types of group of atoms(molecule, crystal, crystal + defect, etc.)OHHOutput:Solve quantum mechanical Schrödinger equation, Hy = Ey total energy of systemCalculate forces on atoms, update positions equilibrium configuration thermal motion (MD), vibrational propertiesOHH
56Ab-Initio Calculations “real”effective potentialDFTError from effective potential corrected by (exchange-)correlation termLocal Density Approximation (LDA)Generalized-Gradient Approximations (GGAs)Others (“Exact exchange”, “hybrid functionals” etc.)“Correct one!?”“Everybody’s” choice: Ab-initio code VASP (Technische Universität Wien), LDA and GGA
57How To Find Migration Barriers I “Easy”: Can guess final state & diffusion path (e.g. vacancy diffusion) “By hand”, “drag” method. Extensive use in the past.DE ~ 0.4 eVDEEnergyFails even for exchange N-V in Si (“detour” lowers barrier by ~2 eV)dragrealUnreliable!
58How To Find Migration Barriers II New reliable search methods for diffusion paths exist like:Nudged elastic band method” (Jónsson et al.). Used in this work.Dimer method (Henkelman et al.)MD (usually too slow); but can do “accelerated” MD (Voter)All in VASP, easy to use.Elastic band method:Minimize energy of all snapshots plus spring terms, Echain:a b cInitial Saddle Final
59Calculation of Diffusion Prefactors Vineyard theoryFrom vibrational frequenciesDEEnergyA S BASBPhonon calculation in VASPDownload our scripts from Johnsson group website (UW)
60Reason for TED: Implant Damage NEBM-DFT: Interstitial assisted two-step mechanism:Intrinsic diffusion:Create interstitial, B captures interstitial, diffuse together Diffusion barrier: Eform(I) – Ebind(BI) + Emig(BI)4 eV eV eV ~ 3.6 eVAfter implant:Interstitials for “free” transient enhanced diffusionW. Windl, M.M. Bunea, R. Stumpf, S.T. Dunham, and M.P. Masquelier,Proc. MSM99 (Cambridge, MA, 1999), p. 369; MRS Proc. 568, 91 (1999); Phys. Rev. Lett. 83, 4345 (1999).
61Reason for Deactivation – Si-B Phase Diagram 2200209220202000BL185018001600T(oC)1414140013851270Si12001000SiB14Si10B60Si1.8B5.2800102030405060708090100BSi
62Deactivation – Sub-Microscopic Clusters Experimental findings:Structures too small to be seen in EM only “few” atomsNew phase nucleates, but decays quicklyClustering dependent on B concentration and interstitial concentration formation of BmIn clusters postulated;experimental estimate: m / n ~ 1.5* Approach:Calculate clustering energies from first principles up to “max.” m, nBuild continuum or atomistic kinetic-Monte Carlo model*S. Solmi et al., JAP 88, 4547 (2000).
63Cluster Formation – Reaction Barriers Dimer study of the breakup of B3I2 into B2I and BI showed:*BIC reactions diffusion limitedReaction barrier can be well approximated by difference in formation energies plus migration energy of mobile species.*Uberuaga, Windl et al.
64B-I Cluster Structures from Ab Initio Calculations BxIBI+B2I0B3I-B4I2-LDA 0.5GGA 0.42.01.23.02.25.54.3BxI2BI20B2I20B3I20B4I202.52.33.02.220.127.116.11.3BxI3BI3+B2I30B3I3-B4I3-4.84.56.05.36.65.67.05.9I>3B4I4-B12I72-9.27.824.4N/AX.-Y. Liu, W. Windl, and M. P. Masquelier,APL 77, 2018 (2000).
65Activation and Clusters 30 min anneal, different T (equiv. constant T, varying times)GGAB3I3-B3I-
66Calibration with SIMS Measurements Sum of small errors in ab-initio exponents has big effect on continuum model refining of ab-initio numbers necessaryUse Genetic Algorithm for recalibration800 oC20 minDepth (mm)As impl.SIMSModel1019650 oC20 min1025 oC20 s1018Conc. (cm-3)101730 min1016
67Statistical Effects in Nanoelectronics: Why KMC?SIMSNeed to think about exact distribution atomic scale!*A. Asenov
68Conclusion 1Atomistic, especially ab-initio, calculations very useful to determine equation set and parameters for physical process modeling.First applications of this “virtual fab” in semiconductor field.In future, atomistic modeling needed (example: oxidation model later).
69CNT-FET as Schottky Junction VoMetal leadCNTLeadCNTEoVacuum levelCBCBCNTLEFB = L – CNTVBEFEFVBBefore contactAfter contactDesirable: B = 0 to minimize contact resistance.Metals with “right” B: Pt, Ti, Pd.
71Notice the difference in the y-axis Notice the difference in the y-axis. The X structure (below) carries a current which is about one order of magnitude smaller than the CNT inline with the contacts (left)The main peak in the X structure is located at ~5 V, which is close to the value from the inline structure (~5.5 V). This indicates that the qualitative features in the conductance derive from the CNT while the magnitude of the conductance is set by the contacts. The extra peaks seen on the right may be due to incomplete relaxation.
73PDOS for the relaxed CNT in line with contacts PDOS for the relaxed CNT in line with contacts. The two curves correspond to projections on atoms far away from the two interfaces. A (3,3) CNT is metallic, still there is a gap of about 4 eV. Does the gap above result from interactions with the slabs or from lack of kpts along z? This question is not so important since the Fermi level is deep into the CNT valence band.