Process simulation. MNT 2015; Lecture Ion Implantation. Analytic distribution functions

Transcription

1 Process simulation 1. Ion Implantation. Impurity diffusion 3. Oxidation 4. Thin-film deposition 5. Etching 6. References 1. Ion Implantation Analytic distribution functions Gaussian distribution Pearson Type IV distribution Double Pearson Type IV distribution Particle (Monte Carlo) methods 1

2 Gaussian distribution C( x ) D T x R exp R: Range : Standard deviation C( f ( x ) x ) D K b T f ( Pearson Type IV x ) x R b x R 4 3 b b 1 b 0 where K is a normalization factor such exp b1 b b1 4b b b 0 3 b f 1 b x R b1 arctan 4bb0 b1 ( x )dx 1 R=Range, =Standard deviation, =skewness,=kurtosis 0 and 3: Gaussian distribution 3 6 b Double Pearson, 9 fitting parameters C( x ) D1 f1( x ) D f( x )

3 Monte-Carlo calculated moments for B and Ph implanted in Si S. M. Sze, VLSI Technology, McGraw-Hill Int. S. M. Sze, VLSI Technology, McGraw-Hill Int. 3

4 G. F. Carey et al., Circuit, device and process simulation, J. Wiley & Sons Monte Carlo Implantation Accurate simulation of channelling in crystalline material. Provides insight into defect generation due to ion impact. Computationally expensive. Two basic energy loss mechanisms Nuclear scattering: alter energy and direction Electron energy loss: alter energy, analogous to frictional drag 4

5 MC in amorphous material G. F. Carey et al., Circuit, device and process simulation, J. Wiley & Sons G. F. Carey et al., Circuit, device and process simulation, J. Wiley & Sons 5

6 G. F. Carey et al., Circuit, device and process simulation, J. Wiley & Sons MC in crystalline material An ion may travel a fairly long distance along a primary axis of the crystal without scattering against lattice atoms. This phenomenon is called channelling. Can be suppressed by 7º tilt, or/and an implantation oxide. The implanted ions may damage the crystal lattice during the implantation process. 6

7 Damage to the crystal lattice G. F. Carey et al., Circuit, device and process simulation, J. Wiley & Sons Damage buildup during implantation G. F. Carey et al., Circuit, device and process simulation, J. Wiley & Sons 7

8 . Impurity diffusion Single species diffusion C < n i (T): intrinsic diffusion, the diffusivity D is almost constant (n i cm -3 at 1000 C in Si) C > n i (T): extrinsic diffusion, D depends on C Multiple species diffusion Impurities occupying substitutional sites in Si cannot move without the presence of point defects (vacancies and interstitials). The generation, annihilation, and movement of point defects and their interaction with the impurity atoms affect the diffusion results. Single Species Diffusion Fick s first law of diffusion F DC Fick s second law of diffusion C t DC Cv G R 8

9 Intrinsic (low concentration) diffusion t C D C D(T ) 0 D e E a / kt Exact solution for some cases: predeposition drive-in. C( x,t ) C( x,t ) x Cserfc Dt Q x exp Dt 4Dt Intrisic diffusivity for some dopants in Si S. M. Sze, VLSI Technology, McGraw-Hill Int. 9

10 Extrinsic (high concentration) diffusion Diffusivity depends on concentration Vacancies and interstitials Compound diffusion coefficient D( n ) n 1 C t D N D 0 i D N A DC ( ) C i ni n D i n n i Di N N 4n D A i n n i (Charge neutrality) G. F. Carey et al., Circuit, device and process simulation, J. Wiley & Sons 10

11 Additional effects Transport and segregation across interface. At concentrations near solid solubility, impurities combine to form immobile clusters. The distribution of ionised impurities adds a drift term. Ionised impurities adds a drift term G. F. Carey et al., Circuit, device and process simulation, J. Wiley & Sons 11

12 Multiple Species diffusion Point defects Vacancies and interstitials are formed during ion implantation. Oxidation generates interstitials at the silicon surface. Both play a critical role in diffusion. Very difficult to measure point defects. Large tightly coupled system of reaction-diffusion PDE. Models the emitter push-effect and Oxidation Enhanced Diffusion (OED) and Oxidation Retarded Diffusion (ORD). Example from an eight-species model G. F. Carey et al., Circuit, device and process simulation, J. Wiley & Sons 1

13 Emitter push effect Diffusion in III-V compounds The multiple-species models extend to GaAs and are complicated only by the presence of two sublattices and the large number of possible species. 13

14 3. Oxidation Silicon oxidation is one of the most complex modelling challenges in TCAD since it involves coupled viscous oxide flow, species transport, a moving boundary and deformable free surface. The moving boundary increases the degree of difficulty significantly. Flow of oxide At low temperatures local forces are so strong that the time scale for flow is much higher and the oxide should be treated as an elastic material, and the effect of stress is more pronounced. The diffusivity of the oxidant, the reaction rate, the solubility of the oxidant, and the viscosity of the oxide may all be significantly effected by mechanical stress. For high temperatures Stokes flow for fluids can be used. 14

15 4. Thin-film deposition Apart from a film with desirable physical and chemical properties, we want to achieve proper coverage and filling of the underlying topography. Simulators SPEEDIE: D simulator from Stanford University based on physical models for deposition and etching. SAMPLE from University of California SHADE from IBM ELITE topography tool in Silvaco s ATHENA: More empirical models and user-friendly than SPEEDIE. Deposition rate, time and step coverage are the input parameters. Partly based on SAMPLE Sentaurus Structure Editor: a geometrical set of models including isotropic and anistropic deposition. Sentaurus Topography: Physical models, but not included in academic programme 15

16 Direct and indirect fluxes J. D. Plummer et al., Silicon VLSI Technology, Prentice Hall Incoming flux distribution 1 J. D. Plummer et al., Silicon VLSI Technology, Prentice Hall From 1 and, the direct flux On every point MNT on 1015; can Lecture be calculated 3 16

17 Isotropic and nonisotropic distributions J. D. Plummer et al., Silicon VLSI Technology, Prentice Hall Influence on deposited topography Local surface topography affect the deposition, e.g. shadowing. Atoms can diffuse along the surface to areas in less direct view of the source, resulting in better step coverage. However, emission and redeposition can model the same effects, and may be more physical correct. The sticking coefficient S c is the ratio of the flux of species that react and stay on the surface to the flux of incident species. The lower S c, the better step coverage. 17

18 Angle distribution and sticking coefficient for PVD and CVD J. D. Plummer et al., Silicon VLSI Technology, Prentice Hall Trench filling for different n and S c Sc=0.1, n=1 Sc=0.01, n=1 Sc=1, n=1 Sc=1, n=10 J. D. Plummer et al., Silicon VLSI Technology, Prentice Hall 18

19 5. Etching J. D. Plummer et al., Silicon VLSI Technology, Prentice Hall Linear vs. Saturation etch model Linear etch model: The two components are assumed to be independent of each other. The etch profile is a linear combination of isotropic chemical etching and vertical ion sputtering. Saturation etch model: Without any ion sputtering an etch byproduct layer may not be removed, and the chemical etching can not proceed. Without any chemical process, the ion sputtering alone may be negligible. The two components are acting in series rather than in parallel. The process is limited by the slower of the two component processes. 19

20 Saturated etch rate J. D. Plummer et al., Silicon VLSI Technology, Prentice Hall Fc=E18 cm - s -1 Fi=0,...,1E16 cm - s References 1. J. P Biersack, Basic physical aspects of high energy implantation, Nuclear Instruments in Physics Research, B35, pp , G. F. Carey et al., Circuit, device and process simulation, Wiley, S. M. Sze, VLSI Technology nd edt., McGraw-Hill, J. D. Plummer et al., Silicon VLSI Technology, fundamentals, practice and modeling, Prentice Hall, M. E. Law, Process modeling for future technologies, IBM Res. & Dev., 46, p. 339, A. M. Mazzone, Monte Carlo and molecular dynamics simulations applied to ion implantation, in Process and Device Modeling for Microelectronics edt. By G. Baccarani, Elsevier Science, T. Troffer et al., Doping of SiC by implantation of boron and aluminum,, Phys. Stat. Sol., 16, p. 7,