5.4.3 Profile Extraction

In the first subproblem an analytical doping profile is fitted to the simulated doping profile from the process simulation. This is done by modeling the acceptor and donor dopant profiles by analytical two-dimensional function.

The required parameters for modeling the analytical dopant profiles shown in Figure 5.15 are listed in Table 5.3.

Table 5.3: Parameters of the first subproblem.

Parameter	Description	Doping Type	Parameters	Number
S/D Wells
S/D 1	Pearson/Error-function	Donor	N1, $\sigma_{x,1}$, x0,1, y0,1, $\sigma_{y,1}$, $\gamma_{1}$, $\beta_{1}$	7
S/D 2	Pearson/Error-function	Donor	N2, $\sigma_{x,2}$, x0,2, y0,2, $\sigma_{y,2}$, $\gamma_{2}$, $\beta_{2}$	7
Channel Implant
C 1	Pearson-function	Acceptor	N3, y0,3, $\sigma_{y,3}$, $\gamma_{3}$, $\beta_{3}$	5
C 2	Gauß-function	Acceptor	N4, y0,4, $\sigma_{y,4}$	3
Background Doping
Acceptor Background	Constant Distribution	Acceptor	Nsub,acc	1
Donor Background	Constant Distribution	Donor	Nsub,don	1
Geometric Parameter
Gate-length			$\Delta_l$	1

Figure 5.15: Analytical doping profiles of the generated device.

The extraction of the doping profiles is done in the first optimization loop in Figure 5.13. The comparison between the profiles from the process simulation and the generated analytical doping profile is a critical point.

In the device simulated by the process simulation are several thousand discrete points with their donor and acceptor concentrations. To reduce the number of discrete points a grid refinement (adaption) has to be done. In regions with a flat profile the number of grid points has to be reduced. In regions where the first or second derivatives have a large absolute value the number of grid points has to be increased. This regridding is carried out with the tool triangle [3].

The regions of interest are completely different for the acceptor the donor profiles so they have to be regridded separately.

In order to model various gate lengths, a parameter l_G is also included in the device model, but will be fixed during optimization. Additionally, to account for a difference between the drawn channel length and the actual one, a parameter $\Delta_l$ is included.

The two doping profiles were compared with an extra developed tool called tridiff. This program is able to compare the attributes in the overlapping area or in an arbitrary sub-area of two devices. The attributes of one of the input devices have to be assigned on a triangular grid. The grid on this input device is usually created using the triangle program. The number of grid-points generated during the regridding of the device determines the dimension of the residual vector. In the first step both devices are read and the matching regions are searched. In the second step for all grid-points of a region a point location and attribute interpolation has to be performed. The difference -- absolute or logarithmic -- is stored in a residuum file and can be written in an extra output file. In this file the locations of the error can be visualized during the optimization process.