Dopant and Self-Diffusion in Semiconductors: A Tutorial

Transcription

1 Dopant and Self-Diffusion in Semiconductors: A Tutorial Eugene Haller and Hughes Silvestri MS&E, UCB and LBNL FLCC Tutorial 1/26/04 1 FLCC

2 Outline Motivation Background Fick s Laws Diffusion Mechanisms Experimental Techniques for Solid State Diffusion Diffusion with Stable Isotope Structures Conclusions 2

3 Motivation Why diffusion is important for feature level control of device processing Nanometer size feature control: - any extraneous diffusion of dopant atoms may result in device performance degradation Source/drain extensions Accurate models of diffusion are required for dimensional control on the nanometer scale 3

4 Semiconductor Technology Roadmap (International Technology Roadmap for Semiconductors, 2001) Thermal & Thin-film, Doping and Etching Technology Requirements, Near-Term

5 Fick s Laws (1855) Fick s 1st Law: Flux of atoms J = D C S x J in J out dx 2nd Law Diffusion equation does not take into account interactions with defects! C S = t x D C S S x only valid for pure interstitial diffusion J in +G S -R S J out Example: Vacancy Mechanism G AV = k f C AV t [ ][] V A S = x D AV C AV x A s + V AV R AV = k r [ AV] k r [ AV]+ k f [ A S ]V [] 5

6 Analytical Solutions to Fick s Equations D = constant C S t = x D C S 2 C S x = D S S x Finite source of diffusing species: 0.4 Solution: x S 4 Dt Gaussian - Cx,t ( )= 0 πdt e Normalized Concentration Depth 1 - Infinite source of diffusing species: Solution: Complementary error function - Cx,t ( )= C o 1 2 π y e z 2 0 dz, y = 6 Normalized Concentration x 0 2 Dt Depth

7 Solutions to Fick s Equations (cont.) D = f (C) Diffusion coefficient as a function of concentration Concentration dependence can generate various profile shapes and penetration depths 7

8 Solid-State Diffusion Profiles Experimentally determined profiles can be much more complicated - no analytical solution B implant and anneal in Si with and without Ge implant 8 Kennel, H.W.; Cea, S.M.; Lilak, A.D.; Keys, P.H.; Giles, M.D.; Hwang, J.; Sandford, J.S.; Corcoran, S.; Electron Devices Meeting, IEDM '02, 8-11 Dec. 2002

9 Direct Diffusion Mechanisms in Crystalline Solids Pure interstitial (no native defects required) Elements in Si: Li, H, 3d transition metals Direct exchange No experimental evidence High activation energy 9

10 Vacancy-assisted Diffusion Mechanisms (native defects required) Vacancy mechanism A s + V AV (Sb in Si) Dissociative mechanism A s A i + V 10 (Cu in Ge)

11 Interstitial-assisted Diffusion Mechanisms (native defects required) Interstitialcy mechanism A s + I AI (P in Si) Kick-out mechanism A + I A s 11 i (B in Si)

12 Why are Diffusion Mechanisms Important? Device processing can create nonequilibrium native defect concentrations Implantation: excess interstitials Oxidation: excess interstitials Nitridation: excess vacancies High doping: Fermi level shift 12

13 Oxidation Effects on Diffusion Oxidation during device processing can lead to non-equilibrium diffusion Oxidation of Si surface causes injection of interstitials into Si bulk Increase in interstitial concentration causes enhanced diffusion of B, As, but retarded Sb diffusion Nitridation (vacancy injection) causes retarded B, P diffusion, enhanced Sb diffusion (Fahey, et al., Rev. Mod. Phys (1989).) 13

14 Implantation Effects on Diffusion Transient Enhanced Diffusion (TED) - Eaglesham, et al. Implantation damage generates excess interstitials Enhance the diffusion of dopants diffusing via interstitially-assisted mechanisms Transient effect - defect concentrations return to equilibrium values TED can be reduced by implantation into an amorphous layer or by carbon incorporation into Si surface layer Substitutional carbon acts as an interstitial sink (Stolk, et al., Appl. Phys. Lett (1995).) Eaglesham, et al., Appl. Phys. Lett. 65(18) 2305 (1994). 14

15 Doping Effects on Diffusion Heavily doped semiconductors - extrinsic at diffusion temperatures Fermi level moves from mid-gap to near conduction (n-type) or valence (p-type) band. Dopant charge state extrinsic n-type + A s extrinsic p-type - A s Fermi level shift changes the formation enthalpy, H F, of the charged native defect C eq V,I = C o Si exp S F V,I k B exp H F V,I, H F k B T V = H F V o ( E F E V ) Increase of C I,V affects Si self-diffusion and dopant diffusion V states (review by Watkins, 1986) 0.05 ev V o/ ev 0.57 ev V +/ ev V -/o V --/- Native defect charge state I -, V - I +, V ev Io/+ E c E v

16 Doping Effects on Diffusion Fermi level shift lowers the formation enthalpy, H F, of the charged native defect Increase of C I,V affects Si self-diffusion and dopant diffusion C eq V,I = C o Si exp S F V,I exp H F V,I, H F k B T V = H F V o k B ( E F E V ) Numerical example: If E F moves up by 100 mev at 1000 C, the change in the native defect concentration is: eq C ext eq C int H int = e F F H ext k B T ~3 Native defect concentration is 3 times larger for a Fermi level shift of only 100 mev 0.05 ev 0.11 ev 0.57 ev V -/o 0.13 ev V +/++ V o/+ 16 V --/ ev E c 100 mev Io/+ E v E F (ext) E F (int)

17 Doping Effects on Diffusion D (cm 2 s -1 ) D As (ext) D As (n i ) Dn ( i )= D ext ( ) n i eq C As D Si (n i ) D Si (ext) /T (1000/K) The change in native defect concentration with Fermi level position causes an increase in the self- and dopant diffusion coefficients 17

18 Experimental Techniques for Diffusion Creation of the Source - Diffusion from surface - Ion implantation - Sputter deposition - Buried layer (grown by MBE) Annealing Analysis of the Profile - Radioactivity (sectioning) - SIMS - Neutron Activation Analysis - Spreading resistance - Electro-Chemical C/Voltage 18 Modeling of the Profile - Analytical fit - Coupled differential eq.

19 Primary Experimental Approaches Radiotracer Diffusion Implantation or diffusion from surface Mechanical sectioning Radioactivity analysis Stable Isotope Multilayers Diffusion from buried enriched isotope layer Secondary Ion Mass Spectrometry (SIMS) Dopant and self-diffusion 19

20 Radiotracer diffusion Diffusion using radiotracers was first technique available to measure self-diffusion Limited by existence of radioactive isotope Limited by isotope half-life (e.g Si: t 1/2 = 2.6 h) Limited by sensitivity Radioactivity measurement Width of sections Application of radioisotopes to surface annealing Mechanical/Chemical sectioning 20 Measure radioactivity of each section Generate depth profile Concentration (cm -3 ) Depth (µm)

21 Diffusion Prior to Stable Isotopes What was known about Si, B, P, and As diffusion in Si Si: self-diffusion: interstitials + vacancies known: interstitialcy + vacancy mechanism, Q SD ~ 4.7 ev unknown: contributions of native defect charge states B: interstitial mediated: from oxidation experiments known: diffusion coefficient unknown: interstitialcy or kick-out mechanism P: interstitial mediated: from oxidation experiments known: diffusion coefficient unknown: mechanism for vacancy contribution As: interstitial + vacancy mediated: from oxidation + nitridation experiments known: diffusion coefficient unknown: native defect charge states and mechanisms 21

22 Stable Isotope Multilayers Diffusion using stable isotope structures allows for simultaneous measurements of self- and dopant diffusion No half-life issues Ion beam sputtering rather than mechanical sectioning Mass spectrometry rather than radioactivity measurement a-si cap nat. Si 28 Si enriched concentration (cm -3 ) FZ Si substrate Depth (nm)

23 Stable Isotope Multilayers Simultaneous dopant and self-diffusion analysis allows for determination of native defect contributions to diffusion Multilayers of enriched and natural Si enable measurement of dopant diffusion from cap and self-diffusion between layers simultaneously concentration (cm -3 ) a-si cap nat. Si 28 Si enriched Depth (nm) FZ Si substrate 23 Secondary Ion Mass Spectrometry (SIMS) yields concentration profiles of Si and dopant

24 Secondary Ion Mass Spectrometry Incident ion beam sputters sample surface - Cs +, O + Beam energy: ~1 kv Secondary ions ejected from surface (~10 ev) are mass analyzed using mass spectrometer Detection limit: ~ cm -3 Depth profile - ion detector counts vs. time Depth resolution: 2-30 nm Ion gun Mass spectrometer Ion detector 24

25 Diffusion Parameters found via Stable Isotope Heterostructures Charge states of dopant and native defects involved in diffusion Contributions of native defects to self-diffusion Enhancement of dopant and self-diffusion under extrinsic conditions Mechanisms of diffusion which mediate self- and dopant diffusion 25

26 Si Self-Diffusion Enriched layer of 28 Si epitaxially grown on natural Si Diffusion of 30 Si monitored via SIMS from the natural substrate into the enriched cap (depleted of 30 Si) 855 ºC < T < 1388 ºC Previous work limited to short times and high T due to radiotracers Accurate value of self-diffusion coefficient over wide temperature range: D Si = ( + ( ) ) 4.76± exp 170 k B T ev +240 D Si = ( )exp 1153 ºC, 19.5 hrs ( 4.76 ± 0.04)eV k B T 1095 ºC, 54.5 hrs 26 (Bracht, et al., PRL )

27 Si and Dopant Diffusion Arsenic doped sample annealed 950 C for 122 hrs extrinsic intrinsic concentration (cm -3 ) n i V o -V - - V Vacancy mechanism ( AsV) o As + s + V Depth (nm) Interstitialcy mechanism ( AsI) o As + s + I o + e 27

28 Si and Dopant Diffusion Arsenic doped sample annealed 950 C for 122 hrs concentration (cm -3 ) n i V o -V - - V Vacancy mechanism ( AsV) o As + s + V Depth (nm) Interstitialcy mechanism ( AsI) o As + s + I o + e 28

29 Si and Dopant Diffusion Arsenic doped sample annealed 950 C for 122 hrs concentration (cm -3 ) n i V o -V - - V Vacancy mechanism ( AsV) o As + s + V Depth (nm) Interstitialcy mechanism ( AsI) o As + s + I o + e 29

30 Native Defect Contributions to Si Diffusion D Si (n i ) D Si (I o ) D (cm 2 s -1 ) D Si (I o +I + +V - ) D Si (V - ) (Bracht, et al., 1998) D Si (I + ) Diffusion coefficients of individual components add up accurately: D Si (n i ) tot = f I oc I od I o + f I +C I + D I + + f V C V D V = D Si (n i ) (As diffusion) 1000/T (1000/K) (B diffusion) 30 (As diffusion)

31 GaSb Self-Diffusion using Stable Isotopes as-grown structure 31

32 GaSb Self-Diffusion using Stable Isotopes Annealed 650 C for 7 hours Isotope Concentrations (cm -3 ) nat GaSb (cap) 69 Ga 121 Sb 71 Ga 123 Sb 71 Ga 69 Ga 123 Sb 121 Sb nat GaSb Depth (microns) 32

33 GaSb Self-Diffusion using Stable Isotopes Simultaneous isotope diffusion experiments revealed that Ga and Sb self-diffusion coefficients in GaSb differ by 3 orders of magnitude 33

34 GaAs Self-Diffusion using Stable Isotopes Temperature dependence of Ga self-diffusion in GaAs under intrinsic (x), p-type Be doping ( ), and n-type Si doping ( ). Ga self-diffusion is retarded under p-type doping and enhanced under n-type doping due to Fermi level effect on Ga self-interstitials 34 Bracht, et al., Solid State Comm (1999)

35 Diffusion in AlGaAs/GaAs Isotope Structure Ga self-diffusion coefficient in AlGaAs found to decrease with increasing Al content. Activation energy for Ga self-diffusion ± 0.1 ev Bracht, et al., Appl. Phys. Lett (1999). 35

36 Diffusion in Ge Stable Isotope Structure Ge self-diffusion coefficient determined from 74 Ge/ 70 Ge isotope structure Annealed 586 C for hours D Ge = ( ( ) ) 3.0 ± cm s exp k B T 36 ev Fuchs, et al., Phys. Rev B (1995)

37 Diffusion in GaP Stable Isotope Structure Ga self-diffusion coefficient in GaP determined from 69 GaP/ 71 GaP isotope structure Annealed 1111 C for 231 min D Ga eV ( 2.0cm s ) exp = k B T 37 Wang, et al., Appl. Phys. Lett (1997).

38 Diffusion in Si 1-x Ge x SiGe will be used as next generation material for electronic devices Will face same device diffusion issues as Si Currently, limited knowledge of diffusion properties 38 SiGe HBTs with cut-off frequency of 350 GHz Rieh, J.-S.; Jagannathan, B.; Chen, H.; Schonenberg, K.T.; Angell, D.; Chinthakindi, A.; Florkey, J.; Golan, F.; Greenberg, D.; Jeng, S.-J.; Khater, M.; Pagette, F.; Schnabel, C.; Smith, P.; Stricker, A.; Vaed, K.; Volant, R.; Ahlgren, D.; Freeman, G.; Intl. Electron Devices Meeting, IEDM '02. Digest. International, 8-11 Dec. 2002, Page(s):

39 Previous Results on Diffusion in Si 1-x Ge x Strohm, et al., (2001) 71 Ge diffusion in SiGe alloys McVay and DuCharme (1975) 71 Ge diffusion in poly-sige alloys 39

40 Stable Isotope Diffusion in Si 1-x Ge x 200 nm nat. Si 1-x Ge x 400 nm 28 Si 1-x 70 Ge x 200 nm nat. Si 1-x Ge x SiGe graded buffer layer Use isotope heterostructure technique to study Si and Ge self-diffusion in relaxed Si 1-x Ge x alloys. (0.05 x 0.85) No reported measurements of simultaneous Si and Ge diffusion in Si 1-x Ge x alloys Si substrate Si 0.75 Ge 0.25 (900C 2days) simulation Fitting of SIMS diffusion profile to simulation result of simultaneous Si and Ge self-diffusion will yield self-diffusion coefficients of Si and Ge Concentration (cm -3 ) Si Conc. 76Ge Conc. Simulation result of simultaneous Si and Ge self-diffusion Depth (nm)

41 Conclusions Diffusion in semiconductors is increasingly important to device design as feature level size decreases. Device processing can lead to non-equilibrium conditions which affect diffusion. Diffusion using stable isotopes yields important diffusion parameters which previously could not be determined experimentally. 41