COMSOL 6.4 - Schottky Contact

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Schottky Contact

This benchmark simulates the behavior of an ideal Schottky barrier diode made of a tungsten contact deposited on a silicon wafer. The resulting J–V (current density versus applied voltage) curve obtained from the model under forward bias is compared with experimental measurements found in the literature.

When a metal is brought in contact to a semiconductor, a potential barrier forms at the contact. This is mainly a consequence of the work function difference between the metal and the semiconductor.

In this model, the ideal Schottky contact is used to model the behavior of a simple Schottky barrier diode. The use of the word “ideal” implies here that surface states, image force lowering, tunneling, and diffusion effects are neglected in the computation of the current transferred between the semiconductor and the metal at the interface.

Note that ideal Schottky contacts are characterized by a thermionic current that depends mostly on the applied bias and barrier height of the metal–semiconductor contact. These contacts usually occur in nondegenerate semiconductors with doping concentrations less than 1 × 1016 cm-3 at room temperature.

Model Definition

This model simulates the behavior of a tungsten–semiconductor Schottky barrier diode. Figure 1 shows the geometry of the modeled devices. It consists of an n-doped silicon wafer (Nd=1 × 1016 cm-3) on top of which a tungsten contact has been deposited.

The model computes the current density obtained under forward bias (from 0 to 0.25 V) and compares the resulting J–V curve with experimental measurements presented in Ref. 1.

This model uses the default silicon material properties as well as an ideal barrier height defined by:

Where ΦB is the barrier height, Φm is the metal work function, and χ0 is the electron affinity of the semiconductor.

The work function of the tungsten contact has been chosen to be Φm = 4.72 V, which gives a barrier height of ΦB = 0.67 V.

Figure 1: Schematic of the geometry. The Schottky contact is displayed in red and the silicon wafer in white. The thickness of the n-doped silicon wafer is 254 μm (0.01 inches) and the diameter of the diode is twenty times larger than its thickness.

Results and Discussion

Figure 2 shows the current density obtained under forward bias with our model (solid line) and compares it with the experimental measurements presented in Ref. 1 (circles).

Figure 2: The current density obtained with the model (solid line) and the measurements (circles) presented in Ref. 1 under forward bias.

1. C.R. Crowell, J.C. Sarace, and S.M. Sze, “Tungsten-Semiconductor Schottky-Barrier Diodes,” Transaction of the Metallurgical Society of AIME, vol. 233, pp. 478–481, 1965.

Semiconductor_Module/Device_Building_Blocks/schottky_contact

Modeling Instructions

From the menu, choose .

In the window, click

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In the window, click

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In the tree, select > .

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In the tree, select > .

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Global Definitions

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In the window, under click .

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In the window for , locate the section.

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In the table, enter the following settings:


Name	Expression	Value	Description
Va	0[V]	0 V	Voltage
phim	4.72[V]	4.72 V	Work function
th	0.01[in]	2.54E-4 m	Thickness
w	th	2.54E-4 m	Radius
T0	298[K]	298 K	Temperature

Choose um as default length units.

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

Rectangle 1 (r1)

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In the toolbar, click

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In the window for , locate the section.

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In the text field, type w.

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In the text field, type th.

Rectangle 2 (r2)

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Right-click and choose .

Create another rectangle in order to resolve the depletion region near the Schottky contact.

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In the window for , locate the section.

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In the text field, type 1[um].

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Locate the section. In the text field, type th-1[um].

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In the toolbar, click

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Create an integration coupling variable. This will be used to display the normal current density at the boundary.

Integration 1 (intop1)

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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Select Boundary 5 only.

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Locate the section. Clear the checkbox.

Load the material properties of silicon.

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In the toolbar, click

to open the window.

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Go to the window.

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In the tree, select > .

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Click the button in the window toolbar.

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In the toolbar, click

to close the window.

Si - Silicon (mat1)

Set the lattice temperature to T0.

Semiconductor (semi)

Semiconductor Material Model 1

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In the window, under > click .

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In the window for , locate the section.

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In the T text field, type T0.

Add a doping model. Keep the default values, that is, n-type with impurity concentration of 1E16 cm^-3.

Analytic Doping Model 1

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. From the list, choose .

Since the doping feature adds a highly nonlinear contribution to the equation system, it is better to ramp the impurity concentration up from a small value. First set the continuation option to use the interface continuation parameter.

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Click to expand the section. Next set the interface continuation parameter as a parameter "ramp" at the main physics node.

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In the window, click .

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In the window for , click to expand the section.

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In the Cp text field, type ramp.

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From the list, choose .

Finally enter the parameter "ramp" in the parameter table. Later on this can be used in an auxiliary sweep in a study step to ramp the impurity concentration up from a small value.

Global Definitions

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In the window, under click .

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In the window for , locate the section.

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In the table, enter the following settings:


Name	Expression	Value	Description
ramp	1	1

Semiconductor (semi)

Metal Contact 1

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In the toolbar, click

and choose .

Add an ideal Schottky contact. Set the metal work function to phim and the applied voltage to Va.

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Select Boundary 5 only.

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In the window for , locate the section.

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From the list, choose .

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Locate the section. In the V0 text field, type Va.

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Locate the section. In the Φ text field, type phim.

Metal Contact 2

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In the toolbar, click

and choose .

Set the potential on the ohmic side of the silicon wafer to V = 0 V.

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button in the toolbar.

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Select Boundary 2 only.

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button in the toolbar.

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In the toolbar, click

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In the window for , locate the section.

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From the list, choose .

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Right-click and choose .

Add a fine mesh along the thickness of the top rectangle where the depletion region will occur.

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Select Boundaries 3 and 7 only.

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In the window for , locate the section.

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From the list, choose .

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In the text field, type 40.

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In the text field, type 50.

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From the list, choose .

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Select the checkbox.

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In the window, right-click and choose .

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Select Boundaries 1 and 6 only.

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In the window for , locate the section.

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From the list, choose .

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In the text field, type 50.

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In the text field, type 100.

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From the list, choose .

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Select the checkbox.

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button in the toolbar.

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Right-click and choose .

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Select Boundary 5 only.

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In the window for , locate the section.

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In the text field, type 10.

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In the window, right-click and choose .

Step 1: Stationary

Set up an auxiliary continuation sweep for the ’ramp’ parameter.

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In the window, under click .

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In the window for , click to expand the section.

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Select the checkbox.

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In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
ramp	10^range(-6,2,0)

Add a second study step to perform an auxiliary continuation sweep for the ’Va’ parameter.

Step 2: Stationary 2

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In the toolbar, click

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In the window for , click to expand the section.

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Select the checkbox.

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In the dialog, type 0.01 in the text field.

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In the text field, type 0.01.

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In the text field, type 0.25.

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In the window for , locate the section.

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From the list, choose .

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From the list, choose .

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In the toolbar, click

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Net Dopant Concentration (semi)

The model has a uniform n-doping therefore, we remove the generated default plot, Net Dopant Concentration.

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In the window, under right-click and choose .

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In the toolbar, click

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Load the measurements from the reference in a table.

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In the window for , locate the section.

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Browse to the model’s Application Libraries folder and double-click the file schottky_contact_1d_ref.txt.

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In the toolbar, click

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In the window for , type J vs. V in the text field.

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Click to expand the section. From the list, choose .

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Locate the section.

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Select the checkbox. In the associated text field, type Va (V).

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Select the checkbox. In the associated text field, type J (A/cm^2).

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Locate the section. From the list, choose .

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Right-click and choose .

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In the window for , locate the section.

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Find the subsection. From the list, choose .

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From the list, choose .

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From the list, choose .

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Find the subsection. From the list, choose .

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Click to expand the section. Select the checkbox.

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From the list, choose .

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In the table, enter the following settings:


Legends
Reference

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button in the toolbar.

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In the window, right-click and choose .

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In the window for , locate the section.

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In the table, enter the following settings:


Expression	Unit	Description
-intop1(semi.nJ)/intop1(1)	A/cm^2

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Click to expand the section. From the list, choose .

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In the table, enter the following settings:


Legends
Model

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In the toolbar, click

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