Two.Dim Diffusion With File Input Interstitials

DESCRIPTION

Here the two.dim method for diffusion is illustrated. The input file for the simulation is in the "examples/exam16" directory, in the file example16.in.

option quiet
set echo

mode one.dim
line x loc=0.0 spacing=0.01 tag=top
line x loc=1.0 spacing=0.01
line x loc=20 spacing=0.25 tag=bottom

region gaas      xlo=top  xhi=bottom
boundary exposed xlo=top  xhi=top
boundary backside xlo=bottom xhi=bottom

init carbon conc=1e15
implant beryllium dose=1e14 energy=100 pearson
profile infile=file1 inter
deposit nitride thick=.3

interstitial gaas D.0=5e-14     D.E= 0.
interstitial gaas Kr.0=1e-18    Kr.E= 0.
interstitial gaas Cstar.0= 1.0e16    Cstar.E= 0.
interstitial gaas  /nitride  Ksurf.0= 1e-3   Ksurf.E=0.
interstitial gaas neu.0=0 pos.0=1 neu.E=0 neg.0=0 pos.E=0 dneg.0=0
interstitial gaas dpos.0=0 dpos.E=0 neg.E=0 tpos.0=0 tneg.0=0

vacancy gaas D.0= 1e-15      D.E= 0.
vacancy gaas Kr.0=1e-18      Kr.E= 0.
vacancy gaas Cstar.0=1e16    Cstar.E=0.
vacancy gaas  /nitride  Ksurf.0=1e-3   Ksurf.E=0.
vacancy gaas neu.0=0 pos.0=0 neu.E=0 neg.0=0 pos.E=0 dneg.0=0
vacancy dpos.0=0 dpos.E=0 neg.E=0 tpos.0=0 tneg.0=1
method full.fac

    select z=log10(beryllium)
    plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20 line.type=4
    select z=log10(inter)
    plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20 cle=f axi=f line.type=2

method two.dim init=1e-5
diffuse time=15 temp=800 argon
    select z=log10(beryllium)	
    plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20 cle=f axi=f line.type=4
    select z=log10(inter)	
    plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20 cle=f axi=f line.type=2

quit

In Example 13, the Fermi method for diffusion was used, in which it is assumed that interstitial and vacancy concentrations are at their equilibrium values throughout the simulation. Therefore, the diffusivities are only dependent on temperature and the local doping concentrations (n or p). In Example 14, the two.dim method for diffusion is used, in which extrinsic interstitials or vacancies (i.e. added from some source, such as implant damage, or from oxidation in the case of silicon technology) are taken into account in the diffusion of dopants. In this case I/I* or V/V* may not equal one, and these terms are included in the diffusion equations. In this example, the interstitial profile is input by the statement:

profile infile=file1 inter

where file1 contains the x concentration values for the interstitials that might be caused by implantation damage. Now the statement:

method two.dim init=1e-5

is used, rather than the fermi method statement. Parameters for various interstitial and vacancy properties are also included. For example, only +1 charge state interstitials are used, according to the statements:

interstitial gaas neu.0=0 pos.0=1 neu.E=0 neg.0=0 pos.E=0 dneg.0=0
interstitial gaas dpos.0=0 dpos.E=0 neg.E=0 tpos.0=0 tneg.0=0

The as-implanted and diffused profiles of beryllium and interstitials are shown in Figure 1. The diffused beryllium profile is much different than that in Example 13, where the fermi method was used (with no added interstitials). The simulation predicts the famous "uphill diffusion" of implanted p-type dopants often observed.