DIFFUSION Part 2

1. Chapter 7 DIFFUSION Part 2 Dr. Wanda Wosik ECE 6466, F2012

2. Models and Simulations Numerical Solutions of the Diffusion Equations. No predetermined boundary conditions - no analytical solutions Planar density of atoms Hopping to a vacancy or exchange places with frequency vb vd - Debye frequency ~1013sec-1 in Si Atoms jump between planes They have to surmount the energy barrier Eb For stable numerical solution: Average volume concentration Ci=Nix[cm-3] Max. numerical interval (Imax) means that we cannot have more than available number of atoms to jump in t F=-vb/2(N2-N1)=-DDC/Dx Result: Adjacent concentrations calculated  SUPREM etc. solve for any dopant profile http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_3/backbone/r3_2_1.html

3. Modifications Of Fick's Laws A. Electric Field Effects • When the doping is higher than ni, E field effects become important. • E field induced by higher mobility of electrons and holes compared with dopant ions. • E field enhances the diffusion of dopants causing the field (see derivation in text).

4. Modification to Fick’s Loss to Account for Electric Field Effects. Built-in E-field enhances diffusion Very strong effect of  at low concentrations Set up by the dopants @ increased concentrations As The potential Donors will drift B Flux due to E-field F.-II Law The enhancement of diffusion by the electric field is by a factor of two @ high concentrations. This equation is solved in simulators such as SUPREM under equilibrium conditions Useful when E is due to multiple dopants

5. E-field Effect - SLVACO simulation NMOS transistor with B implanted channel region Diffusion of As doped N+ S/D affect B diffusion in the channel Simulations: with w/o field induced enhancement • SUPREM simulation at 1000˚C. Note the boron profile (h ≤ 2 for the As but  field effects dominate the B diffusion). • Field effects can dominate the doping distribution near the source/drain of a MOS device.

6. B. Concentration Dependent Diffusivity Boron diffusion ideal theoretical and with diffusion enhancement (match experiments). • At high doping concentrations, the diffusivity appears to increase. Fick's equation must then be solved numerically since D ≠ constant. erfc Boxlike 5x1020cm-3 • Isoconcentration experiments indicate the dependence of D on concentration; e.g. B10 in a B11 background. erfc 1018cm-3 • The n and n2 (p and p2 for P type dopants) terms are due to charged defect diffusion mechanisms.

7. Modifications to Fick’s Laws to Account for Concentration Dependent Diffusion ISO Concentration experiments: B11 (substrate) B10 diffusant give DAeff Original Fick’s Law depended on gradient not on C, now D=f(C) Deff(C) Often, D is well described by • The n and n2 (p and p2 for P type dopants) terms are due to charged defect diffusion mechanisms. Neutral and charged point defects For intrinsic conditions Different Activation Energies Ex: As at 1000°C For 1*1018cm-3DAs = 1.43*10-15 cm2 sec-1 For 1*1020cm-3DAs = 1.65*10-14 cm2 sec-1

8. SUPREM Simulation 1000°C/30min CED Boxlike BJT As Emitter Base Due to E-field Boron Collector Phosphorus • SUPREM simulation including E field and concentration dependent D effects. Note: • E field effects around junctions (As determines the field). • Steep As profile - concentration dependent effects. • Boron in the base region does not show concentration dependent effects. Boron inside As is slowed down by concentration dependent effects. • Phosphorus diffusing up inside As profile is affected by concentration effects.

9. Segregation of Dopants at Interfaces • Dopants segregate at interfaces. N-type dopants tend to pile-up while boron depletes (SUPREM simulation).

10. Segregation; Interfacial Dopant Pileup. DAS << Dp steeper profile close to the interface. Dopants may also segregate to an interface layer, perhaps only a monolayer thick. Interfacial dopant dose loss or pile-up may consume up to 50% of the dose in a shallow layer As • In the experiment (right) ~40% of the dose was lost in a 30 sec anneal Q=integrated profile Kasnavi et. al. Dopant Loss at the surface - SIMS does not detect that (see the interface). Important problem in small devices (dominant). Entrapped dopants can diffuse later. SUPREM includes a trapping flux. Very thin  monolayer acts a sink for dopants (inactive there); Stripping of the oxide removes dopants.

11. Segregation of Dopants at Interfaces • This gives an interface flux of interstitials Oxidation of a uniformly doped boron substrate depletes the boron into the growing SiO2 (SUPREM simulation). Ex : Oxide Silicon Flux: B segregates into the oxide P piles up at the Si Surface  Snowplow during oxidation. Segregation h is the interface transfer coefficient. SIMS - for thick oxides can give ko (difficult measurements). - for thin oxides SIMS is inadequate (no steady state reached). So use VT or C-V areas.

12. The Physical Basis for Atomic Scale Diffusion • Fick's first law macroscopically describes dopant diffusion at low concentrations. • "Fixes" to this law to account for experimental observations (concentration dependent diffusion and  field effects), are useful, but at this point the complexity of the "fixes" begins to outweigh their usefulness. • Many effects (OED, TED etc) that are very important experimentally, cannot be explained by the macroscopic models discussed so far. We turn to an atomistic view of diffusion for a deeper understanding. Vacancy Assisted or Exchange Mechanism: Kick-out and Interstitial(cy) Assisted Mechanisms (Identical from a mathematical viewpoint.) Typical diffusion in metals  use XRD to measure changes in lattice constant with T  extract vacancy concentration. For Si it is below the detection limit of XRD. V models were used earlier for diffusion in Si especially CED; Nv = f(EF) Dopant and Si-I diffuse as bound pairs  split Dopant stays in the substitusional position, I is released. Both are “Interstitial –” assisted diffusion http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_3/backbone/r3_2_1.html

13. A. Modeling I And V Components Of Diffusion • Oxidation provides an I injection source. • Nitridation provides a V injection source. • Stacking faults serve as "detectors" as do dopant which diffuse. • Experiments like these have "proven" that both point defects are important in silicon. Therefore, (22) • Thus dopant diffusion can be enhanced or retarded by changes in the point defect concentrations.

14. OED and ORD • Measurements of enhanced or retarded diffusion under oxidizing or nitriding conditions allow an estimate of the I or V component of diffusion to be made. • Oxidation injects interstitials, raises and reduces through I-V recombination in the bulk silicon. Nitridation does exactly the opposite. • TSUPREM IV simulations of oxidation enhanced diffusion of boron (OED) and oxidation retarded diffusion of antimony (ORD) during the growth of a thermal oxide on the surface of silicon. The two shallow profiles are Sb, the two deeper profiles are B. • Note that the and profiles are relatively flat indicating the “stiff source” characteristic of the oxidation process. Sb B

15. Oxidation – Enhanced or Retarded Diffusion also OISF  OISF . B, P – enhanced by oxidation Sb – retarded by oxidation. Two different mechanisms of diffusion: by interstitials and by vacancies. Oxidation injects I (relieve of larger volume) OEDB,P( I ) ORDSb (V ) B, P Larger atoms by vacancy mechanism OISF Concentration (supersaturation) of interstitials increases with oxidation rate.

16. Dopant Diffusion Occurs by Both I and V Recent consensus confirmed by computer simulations fI a fraction via interstitial type mechanism. fV =1 – fI a fraction via vacancy type mechanism CI*, CV*  CI,CV * Means equilibrium Affected by point defects Inert conditions Surface oxidized fI+fv=1 Sb retarded even deep in the Si substrate Oxidation Retardation condition: point defects: equilibrium Oxidation: As enhanced Sb retarded Because point defects (I in oxidation) affect D constants CI/CI*=1 For excess of I: Cv/Cv*=0 Inert Ambient: Dopants, whose diffusivity decreases in oxidation to 1/10 must diffuse at least 9/10 by a vacancy mechanism Nitridation: B, P, As retarded diffusion Sb enhanced diffusion Injection of vacancies

17. For Dopants which Show Oxidation Enhanced Diffusion @ low concentrations Interstitials and vacancies assisted diffusion have different. D0 and EA in respective diffusion constants Conservative Assumptions: Enhancement won’t exceed I super saturation. CI vs. CI* Diffusivities of mobile species In steady state I&V recombine Estimations of CI and CV from OISF growth or annihilation less accurate than from diffusion of dopants. computed I I Dual V Activation Energy for Self-Diffusion (Si) and Dopant Diffusion. EAdopant (3-4 eV) < EASi (4-5 eV) Lowering of the activation barrier: Coulombic interaction, Dopant interaction, ex. relaxation of Si lattice (atom size), electronic interaction (charge transfer)

18. B. Modeling Atomic Scale Reactions • Consider the simple chemical reaction • This contains a surprising amount of physics. • For example OED is explained because oxidation injects I driving the equation to the right, creating more AI pairs and enhancing the dopant D. A + V  AV A+IAI mobile bound pair or a substitutional Dopant “kicked out” by I Not mobile in a substitutional position I: Increased diffusion of a Dopant A (P, B) I: decreased diffusion of Dopant A P, B); increased diffusion of Sb I +V SiS Oxidation: Nitridation: Pumping of point defects AI A+I I supersaturation CED P concentration high B CED due to I Phosphorus diffuses with I, and releases them in the bulk. This enhances the tail region D. "Emitter push" is also explained by this mechanism.

19. (23) • If we assume “chemical equilibrium” between dopants and defects in Eqn. (23), then from the law of mass action, (24) (25) • Applying Fick’s law to the mobile species •Applying the chain rule from calculus, •Thus, gradients in defects as well as gradients in dopant concentrations can drive diffusion fluxes. • The overall flux equation solved by simulators like SUPREM (see text) is (26) (27) (written for boron diffusing with neutral and positive interstitials as an example).

20. (27) • Thus there are several distinct effects that drive the dopant diffusion: • inert, low concentration diffusion, driven by the dopant gradient • the interstitial supersaturation •high concentration effects on the dopant diffusivity • the electric field effect • Compare the above expression with Fick’s Law, which is where we started. (4)

21. Coupling Between Dopant and Defects Continuity equation Interstitials’ flux 1100°C 800°C EASi = 4.8 eV, EAdopant=3-4 eV The effect of I supersaturation is larger at T  and increases for dopants of large DA( ex. P compared to As) Interstitial component of the self diffusion flux • TSUPREM IV simulations of the interstitial supersaturations generated by a phosphorus versus an arsenic diffusion to the same depth. The fast diffusing phosphorus profile has a larger effect on than the slow diffusing arsenic profile. Dp>DAs P tail

22. Boron: Coupling Between Dopant and Defects • TSUPREM IV simulations of boron diffused from a polysilicon source for 8 hours at 850˚C, with experimental data (diamonds) from [7.29]. The simulations use identical coefficients, but with and without full coupling between dopants and defects. The curve (right axis) is for the fully coupled case. Without full coupling, = 1. • No coupling produces a “boxier” profile because of concentration dependent diffusion. experimental

23. As • 2D SUPREM simulation of small MOS transistor. • Ion implantation in the S/D regions generates excess I. These diffuse into the channel region pushing boron (channel dopant) up towards the surface. • Effect is more pronounced in smaller devices. • Result is that VTH depends on channel length (the "reverse short channel effect" only recently understood). (See text for more details on these examples.)

24. Charge State Effects Simplified Expressions for Modeling. Continuity Equation Solved in simulators Fully Kinetic Description Potential included Effective diffusivity Chemical equilibrium not reached in Ion Implantation & RTP Effects of Electric Field Concentrations of V&I depend on EF Total flux of mobile dopant Simulations will include more physico-chemical parameters to accurately model dopant diffusions. Enhancements due to Fermi level

25. Future Projections - Shallow Junctions • Assuming ND or NA ≤ 2 x 1020 cm-3 and µ ≤ 52 cm2volt-1 sec-1 an ideal box-shaped profile limits the xJrS product to values outside the red area. • The ITRS goals for S/D extension regions are not physically achievable towards the end of the roadmap without metastable doping concentrations > 2 x 1020 cm-3.

26. Future Projections - Shallow Junctions • Flash annealing - ramp to intermediate T (≈ 800 ˚C) then msec flash to high T (≈ 1300 ˚C). • Recent flash annealing results with boron are much better than RTA. = flash data points • We’ll see why this works in the next set of notes on ion implantation and damage annealing. msec Flash Overall, the shallow junction problem seems manageable through process innovation. Spike Anneal RTA Furnace

27. Summary of Key Ideas • Selective doping is a key process in fabricating semiconductor devices. • Doping atoms generally must sit on substitutional sites to be electrically active. • Both doping concentration and profile shape are critical in device electrical characteristics. • Ion implantation is the dominant process used to introduce dopant atoms. This creates damage and thermal annealing is required to repair this damage. • During this anneal dopants diffuse much faster than normal (Chapter 8 - TED). • Atomistic diffusion processes occur by pairing between dopant atoms and point defects. • In general diffusivities are proportional to the local point defect concentration. • Point defect concentrations depend exponentially on temperature, and on Fermi level, ion implant damage, and surface processes like oxidation. • As a result dopant diffusivities depend on time and spatial position during a high temperature step. • Powerful simulation tools exist today which model these processes and which can predict complex doping profiles.