1DiffusionD. W. Parent2Impurity Diffusion• Diffusion: An old concept whose mathematics have been worked out for a long time.• Diffusion: A concentration gradient will cause a force to redistribute particles until there is no concentration gradient.• Uses: Drain and Source regions for MOS, active regions for BJTs3Impurity Diffusion• It is ideal for batch processes.• It does not induce crystal damage• Diffusion is very useful for p and n type doping in Si.• Diffusion in III-V(GaAs, InP) is limited to Zn diffusions for p+ layers for ohmic contacts.4Impurity Diffusion• Diffusion does not give you as exact control over doping concentration and junction depth as does ion-implantation, but it is an inexpensive process.• Ion-implantation can place oxygen ions under the surface of Si which can be turned into SiO2.• Ion-implantation can place a buried layer of dopant atoms in silicon.5Impurity Diffusion (How does it work?)• At elevated temperatures impurity atoms move around the lattice in a random series of jumps.– Three dimensional in nature– Only net movement if there is a concentration gradient.6Impurity Diffusion (How does it work?)• Random series of jumps?– Interstitial Diffusion: Impurity atoms jump between the empty spaces in the semiconductor lattice. This is a fast process that Na+and Li+use to move around the lattice (Bad).– Substitutional Diffusion: Impurity atoms jump from one vacant lattice site to an adjacent lattice site. There are not many of these vacant sites so this type of diffusion is slow.7Dopants used for Si diffusion•Arsenic– Low misfit factor which leads to high n-type concentrations. Also has an abrupt doping profile.• Phosphorus– Most common diffusion dopant source. It does not make as abrupt junctions as arsenic.8Dopants used for Si diffusion• Boron– Used for p and p+ diffusions•Aluminum– Annealed into Si to make p+/p(boron) ohmic contacts.9Lateral diffusion• At the beginning of the diffusion process, there is no concentration gradient in the Si.• As soon as there are impurity atoms in the Si, there is an impurity gradient in all directions thus diffusion occurs in all directions.• This causes impurities to diffusion underneath the mask. (not so the ion-implantation)10Types of Diffusion• “Infinite Source” or Pre-depositionx(cm)Doping concentrationNCNot3>t2>t1 t(s) x(cm),/s),D(cm ),No(cmDt2xNoerfct)N(x,23−⎟⎠⎞⎜⎝⎛=11Types of Diffusion• “Limited Source” or Drive-inx(cm)Doping concentrationNCNot3>t2>t12111122),(2⎟⎠⎞⎜⎝⎛==⎟⎠⎞⎜⎝⎛−ππtDNQoeDtQotxNoDtx12Average Diffusivities for P and B-14.00-13.50-13.00-12.50-12.00-11.50-11.00-10.50-10.000.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775 0.8Temperature 1000/T (K-1)Log(D (cm2/s))13Solubility limits of B and P2020.220.420.620.82121.2900 950 1000 1050 1100 1150 1200Temperature (oC)Impurity concentration (cm-3)PB14Z erf(Z) Z erf(Z) Z erf(Z) Z erf(Z)0.00 0.000000000 0.50 0.520499878 1.00 0.842700793 1.50 0.9661051460.01 0.011283416 0.51 0.529243620 1.01 0.846810496 1.51 0.9672767480.02 0.022564575 0.52 0.537898630 1.02 0.850838018 1.52 0.9684134970.03 0.033841222 0.53 0.546464097 1.03 0.854784211 1.53 0.9695162090.04 0.045111106 0.54 0.554939250 1.04 0.858649947 1.54 0.9705856900.05 0.056371978 0.55 0.563323366 1.05 0.862436106 1.55 0.9716227330.06 0.067621594 0.56 0.571615764 1.06 0.866143587 1.56 0.9726281220.07 0.078857720 0.57 0.579815806 1.07 0.869773297 1.57 0.9736026270.08 0.090078126 0.58 0.587922900 1.08 0.873326158 1.58 0.9745470090.09 0.101280594 0.59 0.595936497 1.09 0.876803102 1.59 0.9754620160.10 0.112462916 0.60 0.603856091 1.10 0.880205070 1.60 0.9763483830.11 0.123622896 0.61 0.611681219 1.11 0.883533012 1.61 0.9772068370.12 0.134758352 0.62 0.619411462 1.12 0.886787890 1.62 0.9780380880.13 0.145867115 0.63 0.627046443 1.13 0.889970670 1.63 0.9788428400.14 0.156947033 0.64 0.634585829 1.14 0.893082328 1.64 0.9796217800.15 0.167995971 0.65 0.642029327 1.15 0.896123843 1.65 0.9803755850.16 0.179011813 0.66 0.649376688 1.16 0.899096203 1.66 0.9811049210.17 0.189992461 0.67 0.656627702 1.17 0.902000399 1.67 0.9818104420.18 0.200935839 0.68 0.663782203 1.18 0.904837427 1.68 0.9824927870.19 0.211839892 0.69 0.670840062 1.19 0.907608286 1.69 0.9831525870.20 0.222702589 0.70 0.677801194 1.20 0.910313978 1.70 0.9837904590.21 0.233521923 0.71 0.684665550 1.21 0.912955508 1.71 0.9844070080.22 0.244295912 0.72 0.691433123 1.22 0.915533881 1.72 0.9850028270.23 0.255022600 0.73 0.698103943 1.23 0.918050104 1.73 0.9855785000.24 0.265700059 0.74 0.704678078 1.24 0.920505184 1.74 0.9861345950.25 0.276326390 0.75 0.711155634 1.25 0.922900128 1.75 0.9866716710.26 0.286899723 0.76 0.717536753 1.26 0.925235942 1.76 0.9871902750.27 0.297418219 0.77 0.723821614 1.27 0.927513629 1.77 0.9876909420.28 0.307880068 0.78 0.730010431 1.28 0.929734193 1.78 0.9881741960.29 0.318283496 0.79 0.736103454 1.29 0.931898633 1.79 0.9886405490.30 0.328626759 0.80 0.742100965 1.30 0.934007945 1.80 0.9890905020.31 0.338908150 0.81 0.748003281 1.31 0.936063123 1.81 0.9895245450.32 0.349125995 0.82 0.753810751 1.32 0.938065155 1.82 0.9899431560.33 0.359278655 0.83 0.759523757 1.33 0.940015026 1.83 0.9903468050.34 0.369364529 0.84 0.765142711 1.34 0.941913715 1.84 0.9907359480.35 0.379382054 0.85 0.770668058 1.35 0.943762196 1.85 0.9911110300.36 0.389329701 0.86 0.776100268 1.36 0.945561437 1.86 0.9914724880.37 0.399205984 0.87 0.781439845 1.37 0.947312398 1.87 0.9918207480.38 0.409009453 0.88 0.786687319 1.38 0.949016035 1.88 0.9921562230.39 0.418738700 0.89 0.791843247 1.39 0.950673296 1.89 0.9924793180.40 0.428392355 0.90 0.796908212 1.40 0.952285120 1.90 0.9927904290.41 0.437969090 0.91 0.801882826 1.41 0.953852439 1.91 0.9930899400.42 0.447467618 0.92 0.806767722 1.42 0.955376179 1.92 0.9933782250.43 0.456886695 0.93 0.811563559 1.43 0.956857253 1.93 0.9936556500.44 0.466225115 0.94 0.816271019 1.44 0.958296570 1.94 0.9939225710.45 0.475481720 0.95 0.820890807 1.45 0.959695026 1.95 0.9941793340.46 0.484655390 0.96 0.825423650 1.46 0.961053510 1.96 0.9944262750.47 0.493745051 0.97 0.829870293 1.47 0.962372900 1.97 0.9946637250.48 0.502749671 0.98 0.834231504 1.48 0.963654065 1.98 0.9948920000.49 0.511668261 0.99 0.838508070 1.49 0.964897865 1.99 0.99511141315Z erf(Z) Z erf(Z) Z erf(Z) Z erf(Z)2.00 0.995322265 2.50 0.999593048 3.00 0.999977910 3.50 0.9999992572.01 0.995524849 2.51 0.999614295 3.01 0.999979261 3.51 0.9999993092.02