Example of Multiple Superimposed Doping Profiles
This example uses multiple Gaussian profiles to demonstrate how to create an intricate doping distribution using a combination of several doping features. Figure 2-6 shows the geometry along with a line graph of the dopant concentrations. The geometry shows the location of the contacts and the line cut along which the line graph is plotted.
To create the doping profile three Analytic Doping Model nodes and one Geometric Doping Model node are used. The line graph shows the total resultant dopant concentration as well as the individual contribution from each node.
 
Care should be taken when specifying multiple doping profiles in the same domains as the resultant dopant concentration is the sum of all coincident doping models.
Figure 2-6: Top: Geometry in which the example dopant concentration is created. Bottom: Line graphs of the total doping distribution and the individual contributions from each of the steps in the instructions. The numbered circles highlight the overlap points of the different distributions due to the junction depth specified in the corresponding step.
To create the doping profile:
The following example is similar to the model Bipolar Transistor, which is available in the Semiconductor Applications Libraries (Semiconductor_Module/Devices/bipolar_transistor).
1
Constant background: a constant n-type doping of 1017 cm−3 is added using an Analytic Doping Model that specifies a User defined profile with constant Donor Concentration.
2
Top surface: a Box dopant distribution that decays away from the top surface with a Gaussian profile is added using a second Analytical Doping Model. The uniformly doped region is set to cover the entire width of the model at the top surface but to have zero depth, thus the profile decays away from the surface.
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Acceptor doping is applied with a maximum concentration of 1019 cm−3.
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The donor concentration defined in the previous step, semi.adm1.Nd, is selected for the Background doping concentration.
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The Junction depth is set to 2 μm below the top surface. Since the background doping is of a different type, semi.adm2.Na has equal magnitude to semi.adm1.Nd at this depth, as indicated by point 2 shown in Figure 2-6. Thus the overall contribution to semi.Nd-semi.Na due to the first two distributions is zero at a depth of 2 μm. This is an example of doping distribution into a constant background distribution of the opposite type.
3
Emitter contact: a Geometric Doping Model is used to define a Gaussian profile which decays away from the emitter contact.
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The boundary that represents the emitter contact is selected in Boundary Selection for Doping Profile node and a Gaussian Dopant profile away from the boundary is selected.
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The Junction depth is set to 1.5 μm.
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The Background doping concentration must account for the effect of both of the two preceding steps. To achieve this, choose a User defined background concentration and set it to semi.adm2.Na-semi.adm1.Nd. This causes the resulting distribution, semi.gdm1.Nd, to be equal magnitude to semi.adm2.Na at the desired junction depth of 1.5 μm, as can be seen at point 3 labeled in Figure 2-6.
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This is an example that demonstrates the need to carefully consider the cumulative effects of coincident dopant distributions when placing junction depths.
4
Collector contact: another Box distribution is defined with a third Analytic Doping Model. This is used to create a Gaussian profile that decays away from the collector contact. The uniformly doped region is set to cover the entire width of the model at the bottom surface but to have zero depth.
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Donor doping is applied with a maximum concentration of 1022 cm−3.
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The Junction depth is set to 0.2 μm, which produces a junction at a depth of 4.8 μm from the top surface.
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In this case the constant donor concentration defined in step 1 (1017 cm−3), semi.adm1.Nd, is selected for the Background doping concentration. Since donors are being doped into donors the concentration due to this final distribution (semi.adm3.Nd) is 2·1017 cm−3 at the junction depth, which is double the background level as indicated a point 4 shown in Figure 2-6. This is because at the junction depth semi.adm3.Nd has equal magnitude to the constant background and, because it is the same doping type, the sum of the contribution from both distributions results in double the concentration. This is an example of doping one type into a constant background of the same type.