EE143 N. CheungIon Implantation Profile and Range DataIn EE143, we use a gaussian function to approximate the ion implantation concentration depthprofile:C(x) =2 Rpexp [- (x -Rp)22Rp2]where is the implantation dose ( in # /cm2), Rpis the projected range and Rpis the longitudinal straggle.This gaussian approximation is reasonably good for sheet resistance calculations because the integralquantity Rs(1q) is less sensitive to details of the distribution. However, the gaussian function has toorapid a decay with distances from Rpand can lead to smaller calculated junction depths xj.The rationales to choose the gaussian approximation are: (1) only two parameters (Rpand Rp)are used to describe the shape of the depth profile; (2) the gaussian function is a natural solution of thediffusion equation, which we have to deal with when further annealing steps are encountered afterimplantation. A better approximation for the implantation profile is the Pearson-IV distribution whichrequires the first four spatial moments of the distribution but such calculations will require numericalprocedures [see more advanced texts such as Plummer et al].Projected Range Rpand Longitudinal Straggle Rpfor common dopants used in IC technology, B,P and As implanted into Si are shown in the following graphs (solid lines). The ranges (in Å ) are also fittedto a polynomial (dashed lines) of the form:a0+a1*E+a2*E2+a3*E3+a4*E4with E in keV10 100 1000100100010000Rp=185.34201 +6.5308 E -0.01745 E2 +2.098e-5 E3 -8.884e-9 E4Rp=51.051+32.60883 E -0.03837 E2 +3.758e-5 E3 -1.433e-8 E4RpRpB11 into SiProjected Range & Straggle in AngstromIon Energy E in keV210 100 100010100100010000Rp=24.39576+4.93641 E -0.00697 E2 +5.858e-6 E3 -2.024e-9 E4Rp=-7.14745 +12.33417 E +0.00323 E2 -8.086e-6 E3 +3.766e-9 E4RpRpP31 into SiProjected Range & Straggle in AngstromIon Energy E in keV10 100 100010100100010000Rp=22.12602 +1.91541 x-0.0008444 E2+5.637e-7 E3 -2.322e-10 E4Rp=58.87725 +5.11177 x +0.0008995 E2 +1.173e-7 E3 -3.344e-10 E4RpRpAs75 into SiProjected Range & Straggle in AngstromIon Energy E in keVTransverse straggle RtFor common energies used in IC production (<200 keV), the transverse straggle (Rt) is alwayslarger than the longitudinal straggle (Rp). The Rtvalues for B, P, and As are also attached for yourreference.3For a line-shape mask opening of width 2a , the 2-D implantation profile is approximated by :C(x,y) =2 Rpexp [- (x -Rp)22Rp2] -12[ erfc (y-a2Rt) - erfc (y+a2Rt) ]Note that for an infinite opening (i.e., a ), C(x, y) reduces to the one-dimensional case C(x) =2 Rpexp [- (x -Rp)22Rp2], as expected.10 100 1000101001000AsPBRt in SiTraverse Straggle in AngstromsIon Energy E in keVIon ChannelingTo minimize ion channeling effect, the Si substrate is usually tilted by 7° with respect to the ionbeam but the cos 7° correction to projected depths is close to unity ( ~0.993) and is usually neglected incalculations.4Implantation into other SubstratesPoly-Si is pure Si, so it has identical ranges as single-crystal Si. Range in SiO2is about severalpercent smaller than that of Si. For IC processing designs, we are primary concerned with the dopant profilein Si. When we deal with problems involving implantation through SiO2into Si, we usually treat the SiO2having the same energy stopping power as Si to simplify the calculations. Detailed profile data of ions inmany substrates can be found in tables published by Gibbons et al or from Monte Carlo Simulators such asSRIM. [http://www.srim.org/index.htm]The following six plots show simulated values of Rpand Rpby SRIM for B, P and As into Photoresist, Si3N4and SiO2.Ion Energy in keVDRp in Angstroms1010010001000010 100 1000BPAsPhotoresistIon Energy in keVRp in Angstroms10010001000010000010 100 1000BPAsPhotore sistIon Energy in keVRp in Angstroms1010010001000010 100 1000Si3N4PBAsIon Energy in keVDRp in Angstroms10100100010 100 1000Si3N4BPAsIon Energy in keVRp in Angstroms10010001000010000010 100 1000SiO2BPAsIon Energy in ke VDRp in Angstroms1010010001000010 100 1000SiO2BPAs5Implantation profiles through multilayer structuresThe profile calculations generally require advanced techniques such as Boltzmann transportequation or Monte Carlo simulation. For implant masking calculations, most times we only care about thefraction of implant dose not passing through the mask thickness, not the detailed depth profile into theunderlying substrate. The transmission factor T is equal to:T =transmission=12erfc [d -Rp2 Rp]where d is the mask thickness, Rpand Rpcorrespond tovalues of the ion through the mask material, and transmissionis the dose of ions that penetrate pass through the mask. Thecomplementary error function erfc(x) is plotted in Figure 4.4 ofJaeger.Example:.SiO2is used as the implantation mask and we assume the SiO2stopping power is identical to that of Si. For200 keV Boron, find the required oxide thickness d such that the transmission factor T =12erfc [d -Rp2 Rp]is: (i) 10-5, (ii) 10-4, and (iii) 10-3.Transmitted fractionf=12erfc(z) where z =d - Rp2Rp(i)f= 10-5 z = erfc-1(2 10-5) = 3.02(ii)f= 10-4 z = erfc-1(2 10-4) = 2.64(iii) f= 10-3 z = erfc-1(2 10-3) = 2.20 d values are :(i) = 2Rp- z + Rp= 2 0.093 3.02 + 0.53 = 0.93 m(ii) = 2 0.093 2.64 + 0.53 = 0.877 m(iii) = 2 0.093 2.20 + 0.53 = 0.82 mSi3N4is more effective than SiO2in blocking implantation by about 15%. Since we use thephotoresist as an implantation mask, they are usually made sufficiently thick to completely block theimplanted dopants. For this reason, the ranges of dopants into photoresist are not given here but they can belooked up in tables. Roughly, a photoresist layer should be 1.8 times the thickness of a SiO2blocking layer.The rule-of-thumb to achieve sufficient blocking is to have the masking layer thickness larger than Rp+5Rpof that ion into the masking material.What happen to charges carried by the ions ?One common question asked is the charge state of the ions once they enter the solid. The answer ispositive ions will be neutralized by electrons in the solid instantaneously (e.g. Si) or after annealing steps(e.g. thick SiO2). We need the positive charge on the ions so that we can manipulate the acceleratingenergy. In principle, any particle with positive charge, negative charge, or in the
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