ECE 416/516 IC Technologies

Transcription

1 ECE 416/516 IC Technologies Professor James E. Morris Spring 1 4/9/1 ECE 416/516 Spring 1 1

2 Spin-on doped glass Solid Liquid (bubbler) Gaseous Ion Implant Planar Sources solid silica tube gas Carrier gas Source boat wafers dopant liquid Planar sources Heated bath

3 Boron B O 3 + 3Si <--> 4B+3SiO at surface Liquid: (CH 3 O 3 )B+9O --9ºC--> B O 3 +6CO +9H O 4BBr 3 +3O --> B O 3 +6Br Gaseous: B H + 3O --3ºC--> B O 3 + 3H O TMB - trimethylbromate Phosphorus P O 5 + 5Si <--> 4P+5SiO at surface Liquid: 4POCl 3 +3O --> P O 5 +6Cl Gaseous: PH 3 + 4O --4ºC--> P O 5 + 3H O DIFFUSION Doping profiles determine many short channel characteristics in MOS devices. Resistance impacts drive current. Scaling implies all lateral and vertical dimensions scale by the same factor. Generally doping levels need to increase and x J values need to decrease. R contact V S x W V G Silicide R poly R source R ext R chan Sidewall Spacers V D x J Year of Production Technology N ode (half pitch) 5 nm 18 nm 13 nm 9 nm 65 nm 45 nm 3 nm nm 18 nm MPU Printed Gate Leng th 1 nm 7 nm 53 nm 35 nm 5 nm 18 nm 13 nm 1 nm Contact Resi stiv ity r C (ž cm ) x x1-7 1x1-7 6x x x1-9 5x1-9 S/D Extens ion Abruptness (nm/decdade ) S/D Extens ion Sheet Resistance TBD TBD TBD TBD (PMOS) (ž /sq) S/D Extens io n x J (nm) Min Supply Voltage (volts)

4 The resistivity of a cube is given by a) b) x j J nqv nq 1 cm (1) J R = S = /x j The sheet resistance of a shallow junction is R x j / Square S () Depth For a non uniformly doped layer, s x j q x j nx 1 N dx Eqn. (3) has been numerically integrated by Irvin for simple analytical profiles (example later). B (3) Sheet resistance can be experimentally measured by a four point probe technique. Doping profiles can be measured by SIMS (chemical) or spreading R (electrical). 7 n(x) N B x Figure 3.1 Typical concentration plot of impurities or carriers as a function of depth into the wafer. Note that these profiles are typically much less than 1% of the total wafer thickness. Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. 4

5 "Predep" controlled dose Silicon Drive-in constant dose Diffusion is the redistribution of atoms from regions of high concentration of mobile species to regions of low concentration. It occurs at all temperatures, but the diffusivity has an exponential dependence on T. Predeposition: doping often proceeds by an initial predep step to introduce the required dose of dopant into the substrate. Drive In: a subsequent drive in anneal then redistributes the dopant giving the required x J and surface concentration. Ion Implantation and Annealing Solid/Gas Phase Diffusion Advantages Room temperature mask No damage created by doping Precise dose control Batch fabrication atoms cm - doses Accurate depth control Problems Implant damage enhances diffusion Dislocations caused by damage may cause junction leakage Implant channeling may affect profile Usually limited to solid solubility Low surface concentration hard to achieve without a long drivein Low dose predeps very difficult 9 1 Solid Solubility (atoms cm -3 ) As P 11 B Sb 1 Sn Ga Al Temperature (ÞC) Dopants are soluble in bulk silicon up to a maximum value before they precipitate into another phase. As + Si As V Dopants may have an electrical solubility that is different than the solid solubility defined above. One example As 4 V electrically inactive complex. 1 5

6 (see Runyan & Bean, Fig 8.5) (a) Interstitial (b) Substitutional Exchange (c) Substitutional vacancy (d) Interstitiality mechanism (substitutional site) OR Interstitial Frank-Turnbull Kickout (e) Conversion mechanism from interstitial to substitutional Dissociative mechanism: -generally mixture of interstitial and substitutional Significant movement by interstitial only -substitutional requires adjacent vacancy Interchange diffusion -Direct interchange -Cooperative interchange: more than atoms involved Self-diffusion: -Lattice atoms also diffuse Dislocation / Grain Boundary diffusion: -easier at crystal edges -Diffusion parallel to dislocation or along grain boundary -more than 3 orders faster than bulk 6

7 To move from one interstitial site to next, must squeeze past lattice atoms. Requires energy E m So jump freq = 4 o exp - (E m /kt) Vibr freq with E>E m 4 adjacent sites for Si Lattice vibration freq o ( / sec) - Approx. 1 jump/minute at room temp. (interstitial in Si) e.g. FCC Movement requires vacant site - Schottky defect - atom fraction: exp - (E s /kt) - potential barrier: break bond E n = 4 o (exp - E n /kt ) (exp - E s /kt) E s to form vacancy less adjacent to impurity -E n + E s about 3-4eV for impurity diffusion -E n + E s = 5.13eV for Si self-diffusion About 1 jump/1 45 years at room temperature (compare interstitial one/min) 7

8 Impurities dissolve as both Substitutional & Interstitial - Substitutional solubility N s - Interstitial solubility N i - Usually N s > N i but I >> s Given atom spends (at equilibrium): -N i / ( N i + N S ) time in interstitial site -N S / ( N i + N S ) time in substitutional site Therefore: eff = ( s N S+ i N i ) / (N i + N S ) I / (1+ N S / N i ) Interaction since: S I + V Substitution Interstitial Vacancy Group III / V impurities: Substitutional diffusers: B,Al,Ga,In,Sb,As,P (B also interstitial) Group I / VIII impurities: Interstitial diffusers H,Na,L,K,Ar,He Transition: substitutional/interstitial: Co,Cu,Au,Fe,Ni,Pt,Ag 8

9 Interstitial/Substitutional Diffuses Ns cm /s D i ' N i D s ' /T ( x 1-13 ) ( x 1-13 ) (1/ 1/) z (1/4 1/4 1/4) ( 1/ 1/) y n 1,n impurity atoms in layers 1, Concentrations N 1 = n 1 / (Ad/3), N = 3 n / Ad Atom on boundary P jumps every -1 sec. Net impurity flow across P to right = n/t = (n 1 / - n /) / ( -1 ) and N/x = (N -N 1 )/(d/3) x a/ (1/ 1/ ) Tetrahedral Si lattice Site separation d = bond length = 3a / 4 Projection on axes = d / 3 = a /4 1 d/3 P A x n/t = (/)(Ad/3) (N 1 -N ) = - ( /)(Ad/3) (d/3) (N/x) = - A (d / 6) (N/x) Flux density j=(n/t)/a, Define diffusion constant D=d / 6 j = - D ( N / x ) (Fick s First Law) D i = i d /6=(4 o d /6) exp -E m /kt = D o exp -E m /kt D S = S d /6=(4 o d /6) exp -( E n + E S ) = D o exp -( E n + E S ) / kt 9

10 Fick s Second Law of Diffusion J 1 J J dx x Figure 3. A differential volume element in a bar of cross sectional area A, where J 1 and J are the flux of an impurity into and out of the volume element. dn C J In element A. dx. A( J J1) A. dx. dt t x C J t x Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. x Concentration Fin C x t 1 t F = - D dc/dx Distance Fout J 1 J c/s area A Macroscopic dopant redistribution is described by Fick s first law, which describes how the flux (or flow) of dopant depends on the doping gradient. F C J D x (4) D is the diffusivity (cm sec 1 ). D is isotropic in the silicon lattice. Fick s second law describes how the change in concentration in a volume element is determined by the fluxes in/out of the volume. C F t x C D x x (5) If D is a constant this gives C C (6) t D x D. This is rarely true in practice but this is the only form of Fick's second law which can be solved analytically. C 1

11 Analytic Solutions Of Fick s Laws 1. Limited Source: Consider a fixed dose Q, introduced as a delta function at the origin. Dose Q The solution that satisfies Fick s second law is 1 t=t Diffused Gaussian x Cx,t Q x exp (7) Dt 4Dt Important consequences: 1. Dose Q remains constant. Peak concentration decreases as 3. Diffusion distance increases as 1 1/ t Dt.8 t=4t.1.6 t=9t.1 Concentration t=t t=4t t=9t X (Units of Diffusion Distance Dt ) X (Units of Diffusion Distance Dt ) 1. Constant Source Near A Surface: Imaginary Delta Function Dose Q Delta Function Dose Q (Initial Profile) Virtual Diffusion Diffused Gaussian x This is similar to the previous case except the diffusion only goes in one direction. Cx,t Q x exp C,t exp x (8) Dt 4Dt 4Dt 11

12 3. Infinite Source: C Dose C² x Initial Profile ²x Diffused Profile C Dt C x 1 erf where erf Dt C x erfc Dt x 4Dt x x i The infinite source is made up of small slices each diffusing as a Gaussian. n C x xi C x, t xi exp (9) Dt 4Dt i1 exp d z C x / Dt z x exp d where Dt exp d The solution which satisfies Fick s second law is C(x,t) C x x 1 erf C S erfc (1) Dt Dt 3 erf(x/ Dt) t=9t t=4t Initial t=t X (Units of Dt ) Important consequences of error function solution: Symmetry about mid point allows solution for constant surface concentration to be derived. Error function solution is made up of a sum of Gaussian delta function solutions. Dose beyond x = continues to increase with annealing time. (See text Appendix Plummer/A9 or Campbell/V for properties of erfc.) 4. Constant Surface Concentration: Just the right hand side of the above figure. x Cx,t C S erfc (11) Dt Note that the total dose is given by x C S (1) Q CS 1 erf dx Dt Dt 4 1

13 Figure 3.8 Typical profile for a high concentration boron diffusion. Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. A. Infinite source B. Limited source Figure 3.7 Concentration as a function of depth for (A) predeposition and (B) drive in diffusions for several values of the characteristic diffusion length. Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. 13

14 Intrinsic Dopant Diffusion Coefficients Intrinsic dopant diffusion coefficients are found to be of the form: D D exp E A (13) kt Si B In As Sb P Units D cm sec -1 E A ev Sb As B, In P Note that n i is very large at process temperatures, so "intrinsic" actually applies under many conditions. Note the "slow" and "fast" diffusers. Solubility is also an issue in choosing a particular dopant Diffusivity (cm -sec -1 ) vs 1 4 /T(K) 7 Figure 3.4 Intrinsic carrier concentration of silicon and GaAs as a function of temperature. Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. 14

15 Effect Of Successive Diffusions If a dopant is diffused at temperature T 1 for time t 1 and then is diffused at temperature T for time t, the total effective Dt is given by the sum of all the individual Dt products. Dt eff Dt D 1 t 1 D t... (14) The Gaussian solution only holds if the Dt used to introduce the dopant is small compared with the final Dt for the drive in; i.e. if an initial delta function approximation is reasonable. Example: In a bipolar transistor, if the emitter profile is formed by a predep and the base profile by an implant + drive in, then the junctions occur where: Base Emitter x C S erfc Dt Q x exp Dt 4Dt Base (Emitter Dt) (Base+Emitter Dt) Collector Q x exp C B Dt 4Dt 9 Surface Concentration (cm -3 ) C B = 1 15 C B = 1 14 C B = 1 16 C B = 117 Design Of Diffused Layers C B = 1 18 Eqn. (3) has been numerically integrated for specific cases (erfc and Gaussian). Example of Irvin s curves, in this case for P type Gaussian profiles Effective Conductivity (ohm-cm) -1 N Well P Well We can now consider how to design a boron diffusion process (say for the well or tub of a CMOS process, such that: P { 9 / square x C S j 3 m BC 1x1 15 cm -3 (substrate concentration) 3 15

16 The average conductivity of the layer is _ 1 S x j 1 (9 /sq)(31 4 cm) 3.7 cm 1 From Irvin s curve we obtain C S /cm 3 We can surmise that the profile is Gaussian after drive in. C BC Q Dt exp x j 4Dt C S exp x j 4Dt so that If the drive in is done at 11 C, then the boron diffusivity is The drive in time is therefore Dt X j 4ln C s C bc 3x x1 9 cm 4ln 4x D cm sec cm t drive in 6.8 hours cm / sec 31 Given both the surface concentration and Dt, the initial dose can be calculated for this Gaussian profile. Q C S Dt cm This dose could easily be implanted in a narrow layer close to the surface, justifying the implicit assumption in the Gaussian profile that the initial distribution approximates a delta function. If a gas/solid phase pre deposition step at 95 C were used, i.e. infinite source,then { B solid solubility at 95 C is.5 1 cm 3 B diffusivity is cm sec 1 The dose for an erfc profile is Q C s Dt So that the time required for the predeposition is t predep 5.5sec Check delta function approximation: Dt predep 5.5x4.x1.31 Dt drive in 3.7x

17 Concentration As + -field No Electric Field Depth.5 microns.5 microns As e - Modifications Of Fick's Laws A. Electric Field Effects When the doping is higher than n i, field effects become important. field induced by higher mobility of electrons and holes compared with dopant ions. field enhances the diffusion of dopants causing the field (see derivation in text). C JhD A (16) x C (See next slide) where h 1 C (17) 4n i With Electric Field SUPREM simulation at 1 C. Note the boron profile (h 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. As electric field pulls low density B back into the n+ region, it depletes B at the junction B 33 C Total flux F D Cv where v velocity in electric field x C F C C D v, t x x x x or using q q kt n n v. D. D. n D n kt x kt x q ni x n i C n 1 C n F D DC n DC n x x ni C x x ni n n -DC nc n DC n C x x ni x ni or using N D p N A n n ni 1 n C 1 gives n np ni and C N D N x ni n ni x x C 4ni A n C n i get n C, i.e. n Cn ni, and F J D DC n n x x ni C C 1 C C 4ni dn dn dc D DC giving n and n C n x x dx dx dx C 4ni dc dc n n C C dn i.e. dx dx D1 x dx n C C n i C 4n 4 i C 4/9/1 ECE 416/516 Spring 1 hd 34 x 17

18 Ionized impurities driven by field AND conc n gradient Field generated by diffusion process at high doping levels N >> n i - i.e. effect increases at high N or low T N.type impurity --> donor ion + electron (e - ) - electrons diffuse rapidly (out-run ions) - creates space charge and field - field enhances ion diffusion, i.e. increases D 1. For N-type: J= - D N/x + ( N). (N-type still) Einstein relation for electrons = - (kt/q)(1/n)dn/dx n = (N D /) + [(N D /) +n i ] 1/ Substitute D = (kt/q) for ions dn/dn D = ½ + ½ [(N D /) +n i ] -1/ (N D /) / J = - D N/x - (q/kt) D.N. (kt/q) n -1 dn/dx = ½ {1 + [1+(n i / N D ) ] -1/ } = - D dn/dx - D (N/n) dn/dx max 1 as n i /N D ---> = - D (1+ dn / dn) (dn/dx) for n N D eff D D eff = D (1+dn / dn) D Substitutional diffusion Impurity ion / vacancy interaction Vacancies have associated charge state Represent as V +,V,V -,V -,3 3-,etc... Diffusion due to various vacancies D i+, D i, D i-, D - i, D 3- i, etc Intrinsic diffusivity: D i = D i+ + D i + D i- + D - i + conventional Extrinsic Diffusivity ln n high T intrinsic incr N D High doping, low T low T extrinsic E F shifts, defect concentrations change D=D + i [V + ]/[V + ] i + D i [V ]/[V ] i + D i- [V - ]/[V - ] i +... EC Ef ED EFi EV 18

19 [V ] = [V ] i not charge dependent V + h + V + (h + = hole) k 1 =[V + ] / p [V ] = [V + ] / p [V ] i & for the intrinsic case: k 1 =[V + ] i / n i [V ] i [V + ] / [V + ] i = p / n i Generalize for V -r V + re - V -r K r =[V -r ] / n r [V ] = [V -r ] I / n r i [V ] [V -r ]/[V -r ] i = (n / n i ) r D= D + i (p/n i ) + D i + D i- (n/n i ) + D - i (n/n i ) +... D eff = [D + i (p/n i ) + D i + D i- (n/n i ) + ] h where field enhancement h=1+ [1+(n i / N) ] -1/ N type impurity diffusion: D i- D - i,... dominant P type impurity diffusion: D i+ dominant GaAs vacancies neutral: D i hd i B. Concentration Dependent Diffusivity Concentration (cm -3 ) D = constant D (n/n i ) D (n/n i ) Depth (µm) D D eff A eff A At high doping concentrations, the diffusivity appears to increase. Fick's equation must then be solved numerically since D constant. C t x D eff C A x Isoconcentration experiments indicate the dependence of D on concentration; e.g. isotopes B 1 in a B 11 background. n i Often, D is well described by D D D D n n i p n i D D n n i i p n for n - type, and for p - type (5) (18) The n and n (p and p for P type dopants) terms are due to charged defect diffusion mechanisms

20 For intrinsic ( n p n ) : and D where D - D and D i D D A eff A D D D A D n 1 ni 1 D D.exp D.E kt Si B In As Sb P D. cm sec D.E ev D +. cm sec D +.E ev D -. cm sec D -.E ev D =. cm sec D =.E ev 4.37 n n i (19) D (cm /s) (Ghandhi Fig 4.7) Es + En similar D i + D i P As Sb B Al Ga D E D E Al others Sb - D i - D i D E D 44. E (Ghandhi Table 4.1) cm /s & ev x Di (cm /s) Asi Pi 14C 11C 9C Pi Pi - Asi T (C)

21 DP Di D ( D D) i n n i Figure 3.9 Typical profile for a high concentration phosphorus diffusion. Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. Concentration (cm-3 ) Polysilicon As Deposited after 3min 1 C epi anneal Epi B Substrate Distance (µm) P Concentration (cm-3 ) E B C Distance (µm) SUPREM simulation including field and concentration dependent D effects. Note: 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. Segregation effects 4 1

22 C. Segregation F k CA kc C k Dopants segregate at interfaces. B 1 ko Recall from Lecture, CA k This gives an interface flux of 1 B in equilibrium k C F 1.5x118 A C k B O () (1) Microns SiO Si 3 N 4 Boron Microns Oxidation of a uniformly doped boron substrate depletes the boron into the growing SiO (SUPREM simulation). k C Si CSiO.3 (B) &1 (As, Sb, & P) Concentration (cm -3 ) x x1 18 1x118 5x117 Oxide Arsenic Boron Phosphorus Distance (µm) N type dopants tend to pile up while boron depletes (SUPREM simulation). 43 D. Interfacial Dopant Pile up Dopants may also segregate to an interface layer, perhaps only a monolayer thick. Interfacial dopant dose loss or pile up may consume up to 5% of the dose in a shallow layer. Oxide Dose lost in interfacial layer 11 1 Dose = 1 x 115 cm- Dose = 6.8 x 114 cm- Normal segregation 1 19 Arsenic 118 Concentration ( cm -3 ) 3sec, 15ÞC RTA As implanted Depth (nm) Kasnavi et. al. In the experiment (right) 4% of the dose was lost in a 3 sec anneal. 44

23 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 Mechanism: Kick out and Interstitial(cy) Assisted Mechanisms (Identical from a mathematical viewpoint.) A V AV A I AI Mobile vacancy assisted dopant Mobile interstitial assisted dopant OED: oxidation enhanced diffusion; TED: transient enhanced diffusion 45 Figure 3.3 Diffusion of an impurity atom by direct exchange (A) and by vacancy exchange (B). The latter is much more likely owing to the lower energy required. Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. 3

24 Figure 3.5 In interstitialcy diffusion, an interstitial silicon atom displaces a substitutional impurity, driving it to an interstitial site, where it diffuses some distance before it returns to a substitutional site. Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. Figure 3.6 The kick out (left) and Frank Turnbull mechanisms (right). Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. 4

25 A. Modeling I And V Components Of Diffusion O Inert Diffusion Surface Recombination Bulk Recombination Buried Dopant Marker Layer G Stacking Faults Grow I R Oxidation provides an I injection source. Nitridation provides a V injection source. Stacking faults serve as "detectors" as do dopants which diffuse. Experiments like these have "proven" that both point defects are important in silicon. Therefore, OED D eff A D, C, C A CI C V DA f I f V CI C () V I V equilibrium values Thus dopant diffusion can be enhanced or retarded by changes in the point defect concentrations. ( f I + f V = 1 ) Silicon.6.4 Boron 1. Phosphorus 1. Arsenic.4.6 Antimony..98 f I f V 49 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 C I /C I and reduces C V /C V through I V recombination in the bulk silicon. Nitridation does exactly the opposite. Concentration ( cm -3 ) Inert Depth (µm) O C I /C I C V /C V 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 antimony, the two deeper profiles are boron. Note that the C I /C I and C V /C V profiles are relatively flat indicating the stiff source characteristic of the oxidation process. Point defect supersaturation ratio 5 5

26 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 A I pairs and enhancing the dopant D. A I AI (3) Concentration (cm -3 ) Phosphorus F I C I /C I = 1 F AI C I /C I Depth (µm) Phosphorus diffuses with I, and releases them in the bulk. This enhances the tail region D. 1 1 Interstitial Supersaturation Ratio Base Emitter Collector Emitter push "Emitter push" is also explained by this mechanism. 51 If we assume chemical equilibrium between dopants and defects in Eqn. (3), then from the law of mass action, C AI kc A C I (4) C Applying Fick s law to the mobile species F AI d AI (5) AI x C Applying the chain rule from calculus, F AI d AI kc A I x kc C I A (6) x Thus, gradients in defects as well as gradients in dopant concentrations can drive diffusion fluxes. The overall flux equation solved by simulators like SUPREM is F tot BI D BI 1 p n i C I o 1 C C B I o x ln C C I B p o C I o n i (written for boron diffusing with neutral and positive interstitials as an example). (7) 5 6

27 F tot BI D BI 1 p n i C I o 1 C C B I o x ln C C I B p o C I o n i (7) 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 x ln p n i C I o /C I o 1 p / 1 n i D BI Compare the above expression with Fick s Law, which is where we started. F D C x (4) 53 Concentration (cm -3 ) Concentration (cm -3 ) No coupling Phosphorus profile Arsenic profile C I /C I Full coupling Distance (µm) C I /C I.1..3 Depth (µm) Interstitial Supersaturation Ratio TSUPREM IV simulations of boron diffused from a polysilicon source for 8 hours at 85 C, with experimental data (diamonds) from [7.9]. The simulations use identical coefficients, but with and without full coupling between dopants and defects. The C I /C I curve (right axis) is for the fully coupled case. Without full coupling, C I /C I = 1. No coupling produces a boxier profile because of concentration dependent diffusion. 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 C I /C I than the slow diffusing arsenic profile. 54 7

28 micron. Microns -. Concentration (cm -3 ).5 micron 1. micron Microns D 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 Depth (microns) Result is that V TH depends on channel length (the "reverse short channel effect" only recently understood). (See text for more details on these examples.) 55 Zn in GaAs Figure 3.1 Predeposition diffusions of zinc into GaAs at 6 C for 5,, and 8 min (after Field and Ghandi, used with permission, Electrochemical Society). (Solid solubility limited) Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. 8

29 Zn Figure 3.11 Comparison of the multiple charge model for zinc diffusion and experimental results (after Kahen, used with permission, Materials Research Society). Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. Figure 3.1 Diffusion of silicon in GaAs (after Kahen et al., used with permission, Materials Research Society). Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. 9

30 Figure 3.18 Plot of impurity as a function of depth for phosphorus drive in. (Simulation) Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. Surface Property Measurements R S q ( C). C ( z). dz 1 e 4 3 Figure 3.13 Four point probe (A) and Van der Pauw (B) methods for determining the resistivity of a sample. Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. 1 4 I-V measurement combinations 1 V1 V3 V34 V 41 R 4 I34 I 41 I1 I 3 R RS F( Q) n F( Q) is geometric correction (1for square) 3

31 Junction depth Figure 3.14 In junction staining, a cylinder is used to groove the wafer. A doping sensitive etch then removes part of the top layer. The junction depth can be found from the known diameter of the cylinder and the measured width of the lower abraded groove. Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. Hall effect N, μ Figure 3.15 The Hall effect is able to simultaneously measure the carrier type, mobility, and sheet concentration. qx R C 1, R from Van der Pauw j S e Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. S 31

32 C-V measurement for N(z) Spreading resistance profilometry: shallow lapped samples Figure 3.16 Typical spreading resistance profile showing measured carrier concentration as a function of depth (used with permission, Solecon Labs). Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. Secondary Ion Mass Spectroscopy (SIMS) for C(z) Figure 3.17 A typical SIMS arrangement. The sample is bombarded by high energy ions. The sputtered material is mass analyzed to determine the composition of the substrate. Fabrication Engineering at the Micro and Nanoscale Campbell Copyright 9 by Oxford University Press, Inc. 3

33 Sidewall Spacer Future Projections Shallow Junctions Poly Gate Accumulation Layer Inversion Layer ITRS Roadmap 3 ITRS - NMOS 3 ITRS - PMOS 1 S qc S x J R contact Rext Racc R chan x j S 1 1. q C S Sheet Resistance (ž /sq) Assuming N D or N A x 1 cm 3 and µ 5 cm volt 1 sec 1 an ideal box shaped profile limits the x J S 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 > x 1 cm Future Projections Shallow Junctions Flash annealing ramp to intermediate T ( 8 C) then msec flash to high T ( 13 C). Recent flash annealing results with boron are much better than RTA. = flash data points We ll see why this works in ion implantation and damage annealing. Overall, the shallow junction problem seems manageable through process innovation. msec Flash Spike Anneal RTA Furnace 66 33

34 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. 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. 67 Campbell: Problems (Use text data rather than lecture slides) /9/1 ECE 416/516 Spring

35 Low concentrations: - surface concentration in equilibrium with ambient gas High concentrations (e.g. emitter diffusion) : - surface concentration = solid solubility in wafer - supplied from surface film Limited source diffusions(e.g. base diffusion) - Finite thickness film on wafer surface - all consumed, typically less than monolayer - ion implantation - Infinite source diffusion for short time (pre-deposition) to establish limited source quantity Q - low surface concentration and deep diffusion Generally needs computer simulation Constant/infinite source diffusion --> profile more abrupt than for constant D D =D =D swp D 1 =K 1 D N=D swp (N/N swp ) as for As in Si D =K D N =D swp (N/N swp ) 1 D 3 =K 3 D N 3 =D swp (N/N swp ) 3 x j when N =, steep slope independent of background Dsup (Ghandhi Fig 4.1) x j = (Dsup t) 1/ N 3 N N N/ t= / x(d N/ x) Have recurring normalization factor x/t 1/ above Define z = x/t 1/ z=(1+t 1/ )dx N/ x=( N/ z)/t 1/ z=(x/)(-t -3/ /)dt N/ t =-x( N/ z)/4t 3/ Substitute gives -z (dn/dz) =d / dz (D (dn/dz) ) i.e. ordinary differential equation y = x / (Dsup t) 1/ Solve for different situations and boundary conditions e.g. for constant source diffusion (D varying) At x=, N=N swp and z= for all t At t=, z= for all x, and initial N=N 1 35

36 Si Si N ox D ox x ox M = impurity segregation coefficient at interface For short times x ox --> 4(Dt), For approx constant source i.e. oxide still supplies impurities as t--> N(x,t)N ox [D ox /D (1+k)] 1/ exfc x / (4Dt) 1/ where k=(dox/d) 1/ Diffusion into semi-infinite substrate with initial distribution N(x,)=f(x) Assume D constant ---> N/t=D N/x Separation of variables: N(x,t) = X(x)T(t) --> (XT)/t = D (XT)/x --> X(T/t) = DT( X/x ) --> (1/DT) T/t = (1/X) ( X/x ) = - T/T= - D t & X/ x = - X T(t)= exp - Dt & X(x)= cos x + sin x N(x,t)= exp - Dt (Acos x + Bsin x ) General solution = all possible solutions N(x,t) = - exp - Dt (Acosx + Bsinx) and at t=, N(x,)= - (A cos x + B sin x)d = f(x) Compare Fourier Integral Theorem: f(x) = (1/) - - f(). cos (-x) d d =(1/) - { [ - f().cos d] cosx + [ - f(). sin d] sinx} d By comparison:a = (1/) - f() cos d, B = (1/) - f() sin d N(x,t)=(1/) - f()[ - exp-( /4Dt)cos (-x)d]d = (Dt ) -1 f() exp-((-x) /4Dt) d = (Dt ) -1 N(,) exp-((-x) /4Dt) d 36

37 If D=D(t), e.g. for T=T(t) e.g. furnace insertion/withdrawl write =D(t) t i.e. = t D(t)dt = (Dt) eff and D -1 (N / t) = N / x --> N / = N / x Assume linear T(t) variation - i.e. T=T -Ct (ramp down) T -1 = (T -C t ) -1 = T -1 (1 - C t / T ) -1 T -1 (1+ C t / T ) for T >> C t (Dt) eff = t D(t)dt = t D exp -E /kt(t) dt = t D exp -(E /kt )(1+Ct/T ) dt = t D (T ) exp -(CE /kt )t. dt = D(T ) [(1-exp-(CE /kt )t )]/(CE /kt ) D(T )[kt / CE ] if t --> Additional effective time kt / CE at temp T due to a slow ramp-down Note: ramp-up --> symmetrical effective time e.g. for T =9 C, E =4eV, C=9 C/min t=1.38x1-3 (1173) /9.4(1.6x1-5 ) 45s Account for ramp-down: extra 45sec at 9 C (Mixed diffusion revisited) S <--> I + V Substitutional Interstitial Vacancy Interstitial D i >> D s substitutional, assume substitutional impurities immobile Region of high concentration Interstitials move out faster, Equation driven L-->R many substitutional impurities convert to interstitial & also move out High apparent D Two extreme cases for low concn. region (S <-- I + V): Semiconductor highly dislocated lots of vacancies, reaches equilibrium quickly More Interstitials moving in than substitutionals eff i N i /(N i +N s ) --> D eff D i N i /(N i +N s ) Region of low concentration: Low dislocation density More Interstitials moving in than substitutional Equilibrium slow & equation R-->L Equation driven R-->L Interstitials convert to substitutionals (limited by low vacancy conc n) & move more slowly N i is equilibrium value Low apparent D eff v n v /(n v +n s ) ---> D eff D n v /n s where D v = self-diffusivity of Si atoms 37

38 (N s +N i )/t = (D s/.n s /x + D i/.n i /x)/x for N s >> N i ---> N s /t [(D s/ + D i/.n i /N s )(N s /x)]/x i.e. for substitutional impurity diffusion effective D D s/ + D / i (N i / N s ) (D i/ )(N i /N s ) for D i/ >> D / S and N i /N s depends on the dissociation mechanism D eff = h [D i + D i+ (p/n i ) + D - (n/n i ) + D - (n/n i ) ] For As, there are As(I-V ) & As(I-V - ) levels D = h[d i + D i- (n/n ie )] n ie =intrinsic electron concentration at high N D (solid solubility limited, i.e. N D >> n ie ) & h =, D D i- (N D /n ie ) This is 1st-order conc n dependent diffusion [see back; compare D=K 1 D N=D surf (N/N surf )] EITHER use previous result x j =D i- (N surf /n ie ) x j = (D surf t) ½ x j = (D i- (N surf /n ie )t) ½ x j =.9 (N surf /n ie ) ½ (D i- t) ½ where D i1 =.9 exp - 4.1eV/kT OR solve D=D i- (N/n ie ) in closed form --> N=N surf (1-.87y-.45y ) where y=x(4d surf t) 1/ 38

39 Low surface conc n --> use constant D High conc n --> B(I-V ), B(I-V + ) levels D=h[D i + D i+ (p/ n i ) n i not significantly affected by N A usually h ~ 1, D=3.17 exp -(3.59eV/kT) EMPIRICALLY: x j.45(n surf /n i ) 1/ (Dt) 1/ OR: N N surf (1 - y /3 ), where y=(x /6D surf t) 3/ 1 N/Nsurp 1-.87Y -.45Y.1.1 B 1- Y /3 erfc As Y/Yj B, As doping profiles with inclusion of defect charge effects (Note similarity to diffusion with D N) 39

40 Anomalous behavior Experimental 1 1 Total concn Kink at 1 / cm Elec. active concn Depth 1 N D =n+.4x1 41 n 3 for 1 19 N D 1 1 Anomalous behavior Log concn P + V - concn ns surface ne P + V - dissociation region P + V - P + V - + e - B) Concentration falls to n e (E F falls to E - ) Here P + V - pair tends to dissociate - releases many vacancies tail P + V - P + V - - vacancies move more readily to tail P(I V ), P(I V ), P(I V ), so D=h[D i +D i (n/n i )+D i (n/n i ) ] D tail =D i + D i- [V - ]/[V - ] I ---> D i + D i- (n s3 /n e n i ) (1+ exp.3/kt) with D i =3.85exp-3.66/kT, D i -=4.44exp-./kT A) At high concentration --> P(I-V - ) dominant -negligible concentration gradient --> no field enhancement, h1 Ef Ec E - E - D i D - i (n/ni) where n=n, D - i =44.exp-4.37/kT - D i has form D N, profile very abrupt N=ne Ev Depth 4