ION IMPLANTATION We saw how dopants were introduced into a wafer by using diffusion (‘predeposition’ and ‘drive-in’). This process is limited: -cannot exceed solid solubility of dopant -difficult to achieve light doping Ion implantation is preferred because: -controlled, low or high dose can be introduced (1011 - 1018 cm-2) -depth of implant can be controlled. Used since 1980, despite substrate damage; low throughput, and cost. Plummer Ch. 8, Campbell Ch. 5 3.155J/6.152J, 2003 1 Reminder: Analytical Solutions to Diffusion Equations Solution for a limitless source of dopant (constant surface concentration): Bound cond: 2 ∂C ∂ C C (0, t ) = C Const C = D surf surf Bound cond: ∂t ∂z 2 C (∞, t ) = 0 t È ˘ ( ) = z Cz, t Csurf erfcÍ ˙, t > 0 Î2 Dt ˚ Initial cond: C (z, 0) = 0 z where erfc(x) = 1-erf(x) and tp = predep time p) Dose Q = (2/√ Csurf √Dtp Dose in sample increases as t1/2 3.155J/6.152J, 2003 2 Diffusion of a thin surface layer into a solid When a thin surface layer diffuses into a solid, what is C(z,t)? Q = initial amount of dopant (‘dose’), • assumed to be a delta-function Ú C (z , t)dz = Q = const. (# /area) -• C t = 0 Bound cond: t dC(0, t) 1 Bound cond: = 0 Solution is a Gaussian. dz C(•,t) = 0 t2 Q È z 2 ˘ C( z, t) = exp - p Í ˙ Dt Î 4 Dt˚ 0 z Initial cond: Cz( ,0) = 0 ( z ≠ 0) diffusion length a = 2 Dt Dose in sample constant in time 3.155J/6.152J, 2003 3 Example: wafer originally has a uniform dopant level, e.g. donor. Predep plus drive-in introduces a second dopant, an acceptor. At a certain depth, a p-n junction is formed. A third pre-dep of donor can then be done to make an npn transistor. Problem: can only make profiles consisting of superposed Gaussians centered at the substrate surface. 3.155J/6.152J, 2003 4 Since the maximum amount of a dopant that can dissolve in the Si is given by the solid solubility, you may be limited in the amount of dopant that can be incorporated. 3.155J/6.152J, 2003 5 Ion Implantation Beam of energetic dopant ions is fired into surface of wafer. Energies are 5 - 200 keV. This leads to implantation (burial) of the ions into the substrate. What happens at the substrate? Ions can: bounce off absorb sputter atoms (10 eV - 10 keV) implant into surface (5 keV - 200 keV)… and do tremendous damage 3.155J/6.152J, 2003 Ion Implantation Equipment Ions generated in a source (from feed gas, e.g. BF3, AsH3, PH3 ... or heated solid source, then ionized in arc chamber by electrons from hot filament) select desired species by q/m, using a magnet, accelerated by an E-field and focused using electrostatic lenses and impact substrate (a bend removes neutrals) in raster pattern. 3.155J/6.152J, 2003 7 What happens to ions inside the material? Ions lose energy, dE/dx, interacting elastically with nuclei and inelastically with electrons dE =-N [ S (E ) + S (E)] dx n e 2 Si (E) is Stopping power (eVcm ) E R 1 0 dE Ion range in target: R = Ú dx = Ú ( ) + ( ) 0 N 0 Sne E S E What can we say about nuclear and electronic stopping… 3.155J/6.152J, 2003 8 Nuclear stopping power: Coulomb scattering (assumed elastic) Incident ion interacts with nucleus of stationary ion b = impact parameter 1.0 E , M 1 1 0.8 dE/E b q 0.4 f 0.2 M2 0.0 0 2 4 6 8 10 M /M Energy lost by incoming ion (microscopic) 2 1 Ï sin2 f ¸ DE = E Ì1 - ˝ 1 Ó cosq sinf + cosf sinq ˛ The angles depend on masses and on b. 4 M M DE = E 1 2 Max. energy loss is when b = 0, f = 0: 1 ( + )2 M1 M2 3.155J/6.152J, 2003 9 Nuclear stopping power: Coulomb scattering (assumed elastic) At 100 keV an ion of 15 amu has velocity , v ≈106 m/s! Q Q ion µ 1 2 F 2 E1, M1 r This is 1000 times faster than speed of sound in solids… b q So ion is far past nucleus f before nucleus can displace M2 in response to Coulomb force So nuclear scattering is not strong at high ion velocity; There are also only significant inelastic collisions when ion slows down. that transfer energy… 3.155J/6.152J, 2003 10 Electronic stopping power: also Coulomb interactions , but inelastic) Non-local: ion experiences drag due to “free” or polarizable electrons: incident ion attracts electron polarization, Ion velocity=> charge separation, drag E Local: passing ion causes internal electronic transitions => energy and moment transfer e - e - e - Because electrons can follow fields up to optical frequencies, 5 (velocities of 10 m/s - 100 times faster than phonons) S ( E) = cv = kE 1 2 electronic losses dominate at higher ion velocities. e ion 3.155J/6.152J, 2003 11 Stopping power in Ion Implantation At each impact, the ion loses some energy. It travels through a vertical projected range Rp before stopping. It transfers energy to target via both electronic and nuclear interactions Viscosity, Transitions, Nuclear non-local local Coulomb electrons electrons collisions velocity Rp More effective at larger vion More effective at smaller vion substrate R 1 E0 dE R = Ú dx = Ú p ( ) + ( ) 0 N 0 Sn E Se E 3.155J/6.152J, 2003 12 Stopping power in Ion Implantation Most damage is done by nuclear interactions About 15 eV needed to displace Si from lattice site, create vacancy/interstitial pair (Frankel defect) Viscosity, Transitions, Nuclear non-local local Coulomb electrons electrons collisions velocity Rp MoreMilMMtl effective effectiffti i e at t larger l g vioni MoreMiM effectieffectiveff ti i e att smallerll vion substrate Most damage occurs near limit of Rp. 3.155J/6.152J, 2003 13 D From Se and Sn, Rp and Rp can be calculated: in Si in Si D D Rp Rp Rp Rp (Å) (Å) in Si in GaAs D D Rp Rp Rp Rp (Å) (Å) 3.155J/6.152J, 2003 15 Composition profile for ion implantation If the depth is x, the impurity concentration C(x) is approximated by a gaussian Ê - 2 ˆ Á (x Rp ) ˜ Cx( ) = C exp - p Á D 2 ˜ Ë 2 Rp ¯ D where Cp is the peak concentration, Rp the projected range and Rp the standard deviation of the projected range (vertical straggle). The implanted dose is given by Q (Number/area) • = Ú ( ) = pD Q C x dx Q 2 RP CP -• So a given dose will determine the peak concentration. 3.155J/6.152J, 2003 16 200 keV implants in Si Why do light atoms have greater vertical projected range Rp and D standard deviation Rp ? 3.155J/6.152J, 2003 17 B in Si gaussian The composition profiles are not always perfect Gaussians: there can be a skew or distortion (kurtosis) making the profile asymmetric. 3.155J/6.152J, 2003 18 Channeling If the ions are incident parallel to a major crystal direction, they can pass through the structure with less scattering, so the range is much larger than expected. 3.155J/6.152J, 2003 19 Nuclear Stopping Need to sum the effects of all the scattering events, e.g. using Monte Carlo modeling. Nuclear stopping, Sn, can be modeled by Coulomb scattering (so it depends on impact parameter, relative masses, and E). 3.155J/6.152J, 2003 20 Modeling Distributions of ions after implant can be modeled using a Monte Carlo calculation to give projected range. Can include both nuclear and electronic stopping Ion implantation can be modeled using SUPREM, which calculates dopant profiles vs. implant conditions and annealing. 3.155J/6.152J, 2003 21 Ion implantation through a mask D Range, Rp* and standard deviation , R p * are for ions in mask Ê (x - R* )2 ˆ C* (x ) = C* expÁ- m P ˜ £ C For an efficient mask: m P D *2 B Ë 2 RP ¯ Mask thickness: Background Ê ˆ concentration C * = **+D Á P ˜ = *+ D * in substrate xm RP RP 2lnÁ ˜ RP m RP ËCB ¯ xm = range + some multiple, m, of std dev’n Dose penetrating mask: È 2˘ • Ê - * ˆ Q Í Á x RP ˜ ˙ Q = Ú expÍ-Á ˜ ˙dx P pD * Ë 2DR* ¯ 2 RP x m Î P ˚ Ê ˆ Q x - R* Q = erfcÁ m P ˜ P D * 2 Ë 2 RP ¯ 3.155J/6.152J, 2003 22 In SiO2 In GaAs In Photoresist Vacancy Damage in Ion Implantation Most damage is done by nuclear interactions V-I pair = About 15 eV needed to displace Si from lattice site, Frankel defect Self create vacancy/interstitial pair interstitial Viscosity, Transitions, Nuclear non-local local Coulomb electrons electrons collisions velocity Rp MoreMffilMfftitl effective effectiff i e at larger g vioni MoreMffiMffti effectieffectiveff i e attll smallerll vion substrate Most damage occurs near limit of Rp. 3.155J/6.152J, 2003 24 Implantation damage The ions damage the crystal structure, and might cause amorphization. Dose needed to amorphize a silicon substrate Need solid-phase epitaxy to recrystallize the amorphous regions How many Si atoms does an implant displace? 3.155J/6.152J, 2003 25 Implantation damage A post-implant anneal (e.g. >850˚C) must be done to restore atoms to lattice sites and ‘activate’ the dopant. This causes diffusion of the dopant profile, and formation of defect clusters. Transient effect on diffusion are very important! Effective transient diffusion distance for B in Si after implantation with Si ions.