5.4.4 Optimization of the Doping Profiles

Starting from an initial guess for the 25 parameters listed in Table 5.4, the optimization was performed. A comparison of the donor doping profile of the simulated device and the analytical profile in the source region is shown in Figure 5.16 and Figure 5.17. The modeled donor profile consists of two Pearson/Error-function distributions (S/D 1 and S/D 2). This profile has a good coincidence with the results of the process simulation. The peak located $0.1 \ {\rm\mu m}$ away from the top of the device which is caused by coupled diffusion is not modeled by the resulting profile, but it is negligible for the electrical characterization.

**Figure 5.16:** Donor doping delivered by *Tsuprem4*.
$\includegraphics[width=0.75\linewidth]{graphics/donorsource.epsi}$

**Figure 5.17:** Fitted analytical donor doping profile.
$\includegraphics[width=0.75\linewidth]{graphics/donortarget.epsi}$

Table 5.4: The initial guess for the device model.

Name	Nominal	Minimum	Maximum
$\Delta_l$	0.0	-0.005	0.005
N_sub,don	14.65	14.0	15.0
N_sub,acc	5.0	0.0	15.0
N₁	19.5	18.5	19.8
x_0,1	-0.0023	-0.02	0.01
y_0,1	0.015	0.01	0.02
$\sigma_{x,1}$	0.0095	0.0085	0.012
$\sigma_{y,1}$	0.029	0.015	0.042
$\gamma_{1}$	-4.47	-5.6	5.6
$\beta_{1}$	1735.64	0.0	2000.
N₂	20.4	19.8	21.0
x_0,2	0.00031	0.00	0.0006
y_0,2	0.011	0.005	0.02
$\sigma_{x,2}$	0.011	0.0114	0.05
$\sigma_{y,2}$	0.061	0.015	0.12
$\gamma_{2}$	-3.79	-5.6	5.6
$\beta_{2}$	245.45	10.0	1000.0
N₃	17.7	16.5	18.5
y_0,3	0.075	0.07	0.17
$\sigma_{y,3}$	0.106	0.08	0.3
$\gamma_{3}$	-5.59	-5.6	5.6
$\beta_{3}$	17.3	8.0	100.0
N₄	16.8	16.0	17.5
y_0,4	1.10	0.5	1.5
$\sigma_{y,4}$	1.99	0.4	2.5