EE143 profile C x N Cheung Ion Implantation Profile and Range Data In EE143 we use a gaussian function to approximate the ion implantation concentration depth x Rp 2 exp 2 Rp2 2 Rp where is the implantation dose in cm2 Rp is the projected range and Rp is the longitudinal straggle This gaussian approximation is reasonably good for sheet resistance calculations because the integral 1 quantity Rs is less sensitive to details of the distribution However the gaussian function has too q rapid a decay with distances from Rp and can lead to smaller calculated junction depths xj The rationales to choose the gaussian approximation are 1 only two parameters Rp and Rp are used to describe the shape of the depth profile 2 the gaussian function is a natural solution of the diffusion equation which we have to deal with when further annealing steps are encountered after implantation A better approximation for the implantation profile is the Pearson IV distribution which requires the first four spatial moments of the distribution but such calculations will require numerical procedures see more advanced texts such as Plummer et al Projected Range Rp and Longitudinal Straggle Rp for common dopants used in IC technology B P and As implanted into Si are shown in the following graphs solid lines The ranges in are also fitted to a polynomial dashed lines of the form a0 a1 E a2 E2 a3 E 3 a4 E4 with E in keV Rp 51 051 32 60883 E 0 03837 E2 3 758e 5 E3 1 433e 8 E4 Projected Range Straggle in Angstrom Rp 185 34201 6 5308 E 0 01745 E2 2 098e 5 E3 8 884e 9 E4 B11 into Si 10000 Rp 1000 Rp 100 10 100 Ion Energy Ein keV 1000 Rp 7 14745 12 33417 E 0 00323 E2 8 086e 6 E3 3 766e 9 E4 Projected Range Straggle in Angstrom Rp 24 39576 4 93641 E 0 00697 E2 5 858e 6 E3 2 024e 9 E4 P31 into Si 10000 Rp 1000 Rp 100 10 10 100 1000 Ion Energy Ein keV Projected Range Straggle in Angstrom Rp 58 87725 5 11177 x 0 0008995 E2 1 173e 7 E3 3 344e 10 E4 Rp 22 12602 1 91541 x 0 0008444 E2 5 637e 7 E3 2 322e 10 E4 As75 into Si 10000 Rp 1000 Rp 100 10 10 100 1000 Ion Energy Ein keV Transverse straggle Rt For common energies used in IC production 200 keV the transverse straggle Rt is always larger than the longitudinal straggle Rp The Rt values for B P and As are also attached for your reference 2 For a line shape mask opening of width 2a the 2 D implantation profile is approximated by C x y x Rp 2 1 y a y a exp erfc 2 2 erfc 2 R 2 Rp 2 Rt 2 Rt p Traverse Straggle in Angstroms Note that for an infinite opening i e a C x y reduces to the one dimensional case C x x Rp 2 exp as expected 2 Rp2 2 Rp Rt in Si 1000 B P As 100 10 10 100 1000 Ion Energy Ein keV Ion Channeling To minimize ion channeling effect the Si substrate is usually tilted by 7 with respect to the ion beam but the cos 7 correction to projected depths is close to unity 0 993 and is usually neglected in calculations 3 Implantation into other Substrates Poly Si is pure Si so it has identical ranges as single crystal Si Range in SiO2 is about several percent smaller than that of Si For IC processing designs we are primary concerned with the dopant profile in Si When we deal with problems involving implantation through SiO2 into Si we usually treat the SiO2 having the same energy stopping power as Si to simplify the calculations Detailed profile data of ions in many substrates can be found in tables published by Gibbons et al or from Monte Carlo Simulators such as SRIM http www srim org index htm The following six plots show simulated values of Rp and Rp by SRIM for B P and As into Photoresist Si3 N4 and SiO2 10000 100000 Photoresist Photoresist B B 1000 Rp in Angstroms P As 100 As 1000 P DRp in Angstroms 10000 10 10 100 10 100 Ion Energy in keV 10000 1000 1000 B B Si3N4 100 Ion Energy in keV 1000 P Si3N4 P DRp in Angstroms Rp in Angstroms 1000 As As 100 100 10 10 10 100 1000 10 100 Ion Energy in keV 1000 Ion Energy in keV 100000 10000 Rp in Angstroms P As 1000 B SiO2 1000 B P DRp in Angstroms SiO2 10000 As 100 100 10 10 100 1000 10 Ion Energy in keV 100 Ion Energy in keV 4 1000 Implantation profiles through multilayer structures The profile calculations generally require advanced techniques such as Boltzmann transport equation or Monte Carlo simulation For implant masking calculations most times we only care about the fraction of implant dose not passing through the mask thickness not the detailed depth profile into the underlying substrate The transmission factor T is equal to transmission 1 d Rp T erfc 2 2 R p where d is the mask thickness Rp and Rp correspond to values of the ion through the mask material and transmission is the dose of ions that penetrate pass through the mask The complementary error function erfc x is plotted in Figure 4 4 of Jaeger Example SiO2 is used as the implantation mask and we assume the SiO2 stopping power is identical to that of Si For d Rp 1 200 keV Boron find the required oxide thickness d such that the transmission factor T erfc 2 2 R is i 10 5 ii 10 4 p 10 3 and iii f 1 d Rp Transmitted fraction erfc z where z 2 2 Rp f 10 5 z erfc 1 2 10 5 3 02 f ii 10 4 z erfc 1 2 10 4 2 64 f iii 10 3 z erfc 1 2 10 3 2 20 d values are i 2 Rp z Rp 2 0 093 3 02 0 53 0 93 m i ii 2 0 093 2 64 0 53 0 877 m iii 2 0 093 2 20 0 53 0 82 m Si3N4 is more effective than SiO2 in blocking implantation by about 15 Since we use the photoresist as an implantation mask they are usually made sufficiently thick to completely block the implanted dopants For this reason the ranges of dopants into photoresist are not given here but they can be looked up in tables Roughly a photoresist layer should be 1 8 times the thickness of a SiO2 blocking layer The rule of thumb to achieve sufficient blocking is to have the masking layer thickness larger than Rp 5 Rp of 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 …
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