Semiconductor
Next define the physics settings. Start with the carrier statistics and doping.
1
In the Model Builder window, click Semiconductor .
2
In the Settings window for Semiconductor, locate the Model Properties section. From the “Carrier statistics” list, choose Fermi–Dirac.
Analytic Doping Model 1
First a constant background acceptor concentration is defined.
1
On the Physics ribbon/toolbar, click the Domains menu and choose Analytic Doping Model .
2
In the Settings window for Analytic Doping Model locate the Domain Selection section. From the Selection list, choose All domains.
3
Locate the Impurity section. In the NA0 text field, type 1e17[1/cm^3].
Analytic Doping Model 2
Add a second doping feature to define the implanted doping profile for the source.
1
On the Physics ribbon/toolbar click the Domains menu and choose Analytic Doping Model .
2
In the Settings window for Analytic Doping Model, locate the Domain Selection section. From the Selection list, choose All domains.
3
Locate the Distribution section. From the list, choose Box.
When defining a Box doping distribution, a rectangular region of constant doping is defined, with a Gaussian drop off away from the edges of this rectangular region.
Define the location of the lower-left corner of the uniformly doped rectangular region.
1
Locate the Uniform Region section.
-
Specify the Base position: r0 vector as
0[um]
x
0.6[um]
y
2
Then define the width and height of the uniformly doped region.
-
In the Width: W text field, type 0.6[um].
-
In the Depth: D text field, type 0.1[um].
Choose the dopant type and the doping level in the uniformly doped region.
3
Locate the Impurity section.
-
From the “Impurity type” list, choose “Donor doping (n-type)”.
-
In the ND0 text field, type 1e20[1/cm^3].
Next, specify the length scale over which the Gaussian drop off occurs. If doping into a background dopant distribution of opposite type (as in this case), this setting specifies the junction depth. In this model, different length scales are used in the x and y directions.
4
Locate the Profile section. Select the “Specify different length scales for each direction” checkbox.
5
Specify the dj vector as
0.2[um]
x
0.25[um]
y
Finally specify the constant background doping level.
6
From the Nb list, choose “Acceptor concentration (semi/adm1)”.
7
You can visualize doping profiles by clicking the preview buttons before solving the model. Two buttons named as Plot Doping Profile for Selected and Plot Net Doping Profile for All are available both in the toolbar and the context menu. The doping profile will be shown in a separate plot window named as Doping Profile Plot. Note that p-type and n-type domains are shown in red and blue color, respectively.
Analytic Doping Model 3
Add a similar Gaussian doping profile for the drain.
1
Right-click Analytic Doping Model 2 and choose Duplicate .
2
In the Settings window for Analytic Doping Model, locate the Uniform Region section.
-
Specify the r0 vector as
2.4[um]
x
0.6[um]
y
Next set up boundary conditions for the contacts and gate.
Metal Contact 1
First add a contact for the source.
1
On the Physics ribbon/toolbar click the Boundaries menu and choose Metal Contact .
The Metal Contact feature is used to define Metal–Semiconductor interfaces of various types. In this instance use the default Ideal Ohmic contact type to define the source.
2
Select Boundary 3 only.
Note: The Metal Contact feature in COMSOL Multiphysics is a so called Terminal boundary condition. By default a fixed potential of 0 V is applied, which is appropriate in this instance, since the source is grounded. The terminal can also be set up to specify an input current, input power, or to connect to a voltage or current source from an external circuit.
Metal Contact 2
Add a second Metal Contact feature to define the drain.
1
On the Physics ribbon/toolbar click the Boundaries menu and choose Metal Contact .
2
Select Boundary 7 only.
Set the drain voltage to be specified by the previously defined parameter.
3
In the Settings window for Metal Contact, locate the Terminal section. In the V0 text field, type Vd.
Metal Contact 3
Add a third Metal Contact to set the body voltage to 0 V.
1
On the Physics ribbon/toolbar click the Boundaries menu and choose Metal Contact .
2
Select Boundary 2 only.
Thin Insulator Gate 1
Set up the Gate. The Gate dielectric is not explicitly represented in the model, instead the Thin Insulator Gate boundary condition represents both the gate contact and the thin layer of oxide.
1
On the Physics ribbon/toolbar click the Boundaries menu and choose Thin Insulator Gate .
The Thin Insulator Gate feature is also a terminal, but in this instance it is possible to fix the voltage or charge on the terminal, as well as to connect it to a circuit.
Note: The charge setting determines the charge on the conductor and does not relate to trapped charge at the oxide–semiconductor interface.
The voltage applied to the gate is specified by the parameter added previously.
2
In the Settings window for Thin Insulator Gate, locate the Terminal section. In the V0 text field, type Vg.
3
Locate the Gate Contact section.
-
In the εins text field, type 4.5.
-
In the dins text field, type 30[nm].
4
Select Boundary 5 only.
Trap-Assisted Recombination 1
A range of generation–recombination mechanisms are available to be added to the model. In this case, we simply add trap-assisted recombination, using the default Shockley–Read–Hall model.
1
On the Physics ribbon/toolbar click the Domains menu and choose Generation–Recombination section > Trap-Assisted Recombination .
2
In the Settings window for Trap-Assisted Recombination, locate the Domain Selection section. From the Selection list, choose All domains.