GaAs Full Coupled Diffusion

DESCRIPTION

The input file for the simulation is in the "examples/exam17" directory, in the file example17.in. In this example, the full.coupled method of diffusion is illustrated.

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
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
interstitial gaas beryllium neu.0=0 pos.0=0 neg.0=0 dneg.0=0 dpos.0=0
interstitial gaas beryllium tneg.0=0 tpos.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
vacancy gaas beryllium neu.0=0 pos.0=0 neg.0=0 dneg.0=0 dpos.0=0
vacancy gaas beryllium tneg.0=0 tpos.0=0

method full.fac
diffuse time=.00001 temp=800 argon
    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 full.cpl init=1e-5
diffuse time=15 temp=800 continue 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

Here Example 13 is repeated, but using the full.coupled diffusion method rather than the fermi method. In this method, non-equilibrium levels of interstitials or vacancies can be produced by the diffusion process itself, without adding non-equilibrium levels of defects at the beginning, as was done in Example 16. This is because in the diffusion process, the dopant diffuses as a dopant/defect pair, and defects are carried along with the dopant. This can result in local regions of non-equilibrium concentrations of defects and can in turn effect the dopant diffusion. (If one believes that the "kick-out" mechanism is occurring rather than the pair mechanism, the same effect occurs as the interstitial dopant kicks-out a matrix atom, creating an interstitial.) The method statement is now:

method full.cpl init=1e-5

Note that there is an initial very short diffuse statement:

diffuse time=.00001 temp=800 argon

In this first diffusion step, a short time anneal is done to establish the equilibrium defect concentrations in case you want to plot the initial values of these (since they are temperature dependent). In the second diffuse statement:

diffuse time=15 temp=800 continue argon

the continue parameter is used to maintain the initial defect values. Therefore, the initial diffuse uses the fermi method, and the defect levels are initially set at their equilibrium values. (Since the interstitials are set at the +1 charge state, the equilibrium interstitial concentration is fermi level dependent and therefore the initial interstitial profile follows the beryllium profile). The main diffusion step uses the full.cpl method. The dopant/defect pairing parameters are specified by the following statements.

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

These are all normally set to 0 if one assumes that the pair concentration is much less than the defect concentration (non-equilibrium levels of defects will still occur, since the defect flux equation in the full-coupled mode still takes into account the extra defects produced by the diffusion process). In Figure 1, the as-implanted and diffused beryllium and interstitial profiles generated are shown. One can see that, compared to Example 13, a kink in the profile occurs due to this defect non-equilibrium effect. If one increases the interstitial diffusivity in the statement:

interstitial gaas D.0=5e-14 D.E= 0.

from 5.0E-14 to 1.0E-11 for example, the interstitials are able to diffuse back to their equilibrium levels everywhere, and normal "Example 13 type" diffusion occurs.