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