Doping and diffusion I Motivation Faster MOSFET requires Requires shallower source, drain Ar P* poly snorter channel Al A source drai Shorter channel but with Shallower source, drain depth same source, drain depth demands better control drain field dominates gate field in doping diffusion. =>drain-induced barrier lowering"DIBL CHANNEL ASPECT RATIO=>p 6.155/3.155J9/29/03
6.155/ 3.155J 9/29/03 1 P + Poly Al Al P + Poly Al Al Doping and diffusion I Motivation Shorter channel but with same source, drain depth => drain field dominates gate field =>”drain-induced barrier lowering” DIBL source drain Faster MOSFET requires shorter channel Requires shallower source, drain Shallower source, drain depth demands better control in doping & diffusion. CHANNEL ASPECT RATIO =>rs
How are shallow doped layers made? 1)Predeposition: controlled number of dopant species at surface 60s: film or gas phase of dopant at surface c(x) Surface concentration is limited by equilib, solubility Now: lon implant(non-equilibrium), heat substrate to diffuse dopant but ions damage target. requires anneal, changes doping, C(z) Soon: film or gas phase of dopant at surface 2) Drive-in process: heat substrate+predep diffusion determines junction depth, sharpness c(x) Need sharper diffusion profiles: depth 6.155/3.155J9/29/
6.155/ 3.155J 9/29/03 2 Need sharper diffusion profiles: C depth How are shallow doped layers made? 1) Predeposition: controlled number of dopant species at surface ‘60s: film or gas phase of dopant at surface Surface concentration is limited by equilib . solubility Now: Ion implant (non-equilibrium) , heat substrate to diffuse dopant but ions damage target…requires anneal, changes doping, C (z ) Soon: film or gas phase of dopant at surface C (x) x 2) Drive-in process: heat substrate+predep, diffusion determines junction depth, sharpness C (x) x
DopIng and diiuslon apparatus Putnam Soine Rat Shonn Carrier Slices an carier 三 lo ve Nalyea and flw myors Valves and Flow Meters Siceson carmer armer Gases Oart Difusin Tthe Valyes and flow meters Te- enrolled Eath In vent Later lon Implantation 6.155/3.155J9/2903
6.155/ 3.155J 9/29/03 4 Doping and diffusion apparatus Later… Ion implantation x Later… Ion implantation x
Doping, Diffusion I Initial state a) Gas diffusion F=U-TS If no chem'l interaction with air H2s Later time F=-7S der C Gas disperses, fills all possible states randomly dfusⅰon b)I J=gE R 0 P E=-Vc Electric potential gradient large Tiow Electrons drift down potential gradient ere p is imposed from outside 6.155/3.155J9/29/03 what about solids
6.155/ 3.155J 9/29/03 5 Doping, Diffusion I a) Gas diffusion F =U - T S. If no chem’l interaction with air: F = - T S H2S b) I = V R J =sE = s - ,f ,z Ê Ë ˆ ¯ Electric potential gradient fi charge flow Initial state Gas disperses, fills all possible states randomly. diffusion Later time order C(z) z - Electrons drift down potential gradient: here f is imposed from outside f r E = - r —f what about solids…
C(3,t) J=0 Diffusing c)Mass(or heat)flow J, specles must be due to concentration gradient soluble C Fick I area·t C △x=+J()-/(x+△ # (z+△x) area·t sout 7+△x dt 7 dc( C Fick‖ d t d he dep. Schrodinger Eq DVC 方2 Vy+vy d 2, These Eqs = time evolution of some initial conditions, boundary conditions 6.155/3.155J9/29/03
6.155/ 3.155J 9/29/03 6 c) Mass (or heat) flow J, due to concentration gradient J # area u t ( ) = D -,C,z ÊËÁ ˆ¯˜ Fick I t > 0 J = 0 C ( z, t ) z d) Dz z Jin = J z( ) Jout = J z( ) + Dz z z+Dz dC z( ) dt Dz = +J z( ) - J z( ) + Dz # areau t dC dt = J z( ) - J z( ) + Dz Dz æ Æ ææ DzÆ æ - 0 dJ dz These Eqs => time evolution of some initial conditions, boundary conditions dC(z) dt = - d dz D - ,C ,z Ê Ë ˆ ¯ …or if D is constant dC z( ) ,t dt = D—2C z( ) ,t Fick II Time dep. Schrödinger Eq. +ih ,y ,t = - h2 2m —2y + Vy Diffusing species must be soluble
Atomistic picture of diffusion See web site for movies. http://www.tf.uni-kiel.de/matwis/amat/def_en/index.htm En 4 most important is vacancy diffusion. ○○○○○○ ●○00○ Initial and final states have same energy Also possible is direct exchange (x =broken bond) Higher energy barrier or break more bonds = lower value of d= d ex T Atoms that bond with si are substitutional impurities p, b, As, Al, Ga, Sb, Ge 6.155/3.155J9/29/
6.155/ 3.155J 9/29/03 7 Atomistic picture of diffusion See web site for movies: http://www.tf.uni-kiel.de/matwis/amat/def_en/index.html Most important is vacancy diffusion. Ea i f En Initial and final states have same energy Also possible is direct exchange (¥ = broken bond) Higher energy barrier or break more bonds => lower value of D = D0 exp -E kT ( ) Atoms that bond with Si are substitutional impurities P, B, As, Al, Ga, Sb, Ge ¥ ¥ ¥ ¥
Atomistic picture of diffusion eps for diffusion: 1) create vacancy 2)achieve energy ea 2.6 ex Vo ex KT AG E VF一 S EVE eM→>e kT = ee k o kT e +e daxv=a'voexpl kT Vacancy diffusion D=d ex kT Contains vo= Debye frequency 9×10 10 6.155/3.155J9/29/
6.155/ 3.155J 9/29/03 8 2 steps for diffusion: 1) create vacancy 2) achieve energy Ea nv = Nv N0 = exp - 2.6 kT È ÎÍ ˘˚˙ nv = n0 exp - Ea kT ÊËÁ ˆ¯˜ D = D0 exp - EVD kT È Î ˘ ˚ D ~ a x v = a2n 0 exp - Ev + Ea kT ÈÎÍ ˘˚˙ cm2 s Ê ËÁ ˆ¯˜ Contains n0 § Debye frequency ª 3 2 kBT h = 9 ¥1012 s-1 @1013 s-1 e - DG kT Æ e - EVF -TS kT = e S k e - EVF kT Ê ËÁ ˆ¯˜ Atomistic picture of diffusion EVD a n0 Vacancy diffusion
Analytic Solution to Diffusion Equations, Fick ll: ac dt 0 Steady state dC/at=0 Conversely, C(z C(z=a+b if C(z)is curved dc/dt≠0 We assumed this to be the case in oxidation 02 diffusion through SiO2, where flux J C -Dd-=-Db, is same everywhere 6.155/3.155J9/29/
6.155/ 3.155J 9/29/03 9 Analytic Solution to Diffusion Equations, Fick II: ,C ,t = D ,2C ,z 2 Steady state, dC/dt = 0 C(z) = a + bz 0 z C(z) We assumed this to be the case in oxidation: O2 diffusion through SiO2 , where flux ,J = -D is same everywhere ,C,z = -Db, Conversely, if C(z) is curved, dC/dt 0
For other solutions, consider classical experiment Diffusion couple: thin dopant layer on rod face press 2 identical pieces together, heat Then study diffusion profile in sections symmetry dC(o. =0 C(x0)=0(x≠ 6.155/3.155J9/29/
6.155/ 3.155J 9/29/03 10 Diffusion couple: thin dopant layer on rod face, press 2 identical pieces together, heat. Then study diffusion profile in sections. For other solutions, consider classical experiment: symmetry 0 z t = 0 dC( ) 0,t dz = 0 C( ) •,t = 0 C z( ) ,0 = 0 ( ) z 0 C z( ) ,t -• • Ú dz = Q = const. (# /area)
Analytic Solution to Diffusion Equations J=-Dco d-c ot dz ."Drive in"of small, fixed amount of dopant, solution is Gaussian dC(o. _o d Predeposition is C(∞,)=0 delta function, 8(2). Xt=0 c(i a)=exp Units lTDt 4DE Width of Gaussian= a=2Dt=diffusion length a (a is large relative to width of predeposition) Dose, Q, amount of dopant in sample, is constant. 6.155/3.155J9/29/
6.155/ 3.155J 9/29/03 11 Analytic Solution to Diffusion Equations J = -D,C,z , ,C,t = D,2C,z 2 t = 0 dC( ) 0,t dz = 0 C( ) •,t = 0 C z( ) ,0 = 0 ( ) z 0 0 z I. “ Drive in” of small, fixed amount of dopant, solution is Gaussian Predeposition is delta function, d(z). C z( ) ,t = Q pDt exp - z 2 4Dt È ÎÍ ˘ ˚˙ t > 0 Units Width of Gaussian = = diffusion length a (a is large relative to width of predeposition) 1 2 a = 2 Dt Dose, Q, amount of dopant in sample, is constant