Contacts

1. Overview

Electrical, thermal and electrothermal contacts can be assigned to any edge (or combination of edges) along the perimeter of a region. A single contact may span multiple edges, and contacts can also be distributed across different regions, including junctions between regions. To successfully simulate a device, at least two contacts must be defined. A maximum of eight contacts can be added to a single device model.

2. Usage Instructions

To define a contact:

1. From the Menu, select Define → Contact.

2. Using the cursor, hover the cursor over the geometric edges that make up the contact. When the edge is highlighted in green and the cursor changes to indicate a selectable element, left-click to select the edge.

3. After defining all the contact edges, right-click anywhere to open the properties dialog for the contact. Use this dialog to set the contact's properties.

3. Parameters

3.1. General

Name	Description	Unit
Name	A unique identifier for the contact.	-
Type	Used to define how contact will interact with the semiconductor. Options: [Electrical, Thermal, Electro-thermal]	-
Colour	Used to define visual colour of the contact (Not used in the solver).	-

3.2. Thermal

Name	Description	Unit
Resistance	Used to define the thermal resistance.	K/W
Capacitance	Used to define the thermal capacitance.	J/K
Ambient Temperature	Used to define the ambient temperature used in the simulation.	K

3.3. Electrical

Name	Description	Unit
Type	Used to define the electrical contact type Options: [Ohmic, Schottky]	-
Material	Used to specify the material used for the contact.	-
Work Function	Defines the work function of the contact material. This value is automatically filled in when you choose a predefined material. If the material you need is not listed, select “Other” and manually enter a custom value.	eV
P Richardson	If set to a non-zero, the value is used as the Richardson constant to calculate the thermionic emission current for holes. See Thermionic Emission for details.	Acm-2K-2
N Richardson	If set to a non-zero, the value is used as the Richardson constant to calculate the thermionic emission current for electrons. See Thermionic Emission for details.	Acm-2K-2
Barrier Lowering	Enables or disables field‑induced barrier lowering. Used together with the dipole barrier‑lowering coefficient. See Barrier Lowering for details. [On, Off]	-
Dipole Alpha	Coefficient used to calculate dipole‑induced barrier lowering at Schottky contacts. See Barrier Lowering for details.	cm

3.3.1. Thermionic Emission

The thermionic emission current densities for electrons ($J_n$) and holes ($J_p$) are given by:

$$\begin{equation} J_n = A_n^* \cdot T^2 \cdot e^{-\frac{q (\phi_B-\Delta\phi_B)}{k_B T}} \qquad/\qquad J_p = A_p^* \cdot T^2 \cdot e^{-\frac{q (\phi_B-\Delta\phi_B)}{k_B T}} \end{equation}$$

where:

• $A_n^*$, $A_p^*$ = Richardson constants (electrons and holes) [Acm^-2K^-2]
• $T$ = Temperature [K]
• $q$ = Elementary charge [C]
• $\phi_B$ = Barrier height [eV]
• $\Delta\phi_B$ = Barrier height lowering [eV]
• $k_B$ = Boltzmann constant [eV/K]

3.3.2. Barrier Lowering

The total barrier lowering is given by:

$$\begin{equation} \Delta \phi_B = \sqrt{\frac{qE}{4\pi\varepsilon}} +\alpha E \end{equation}$$

where:

• $\Delta \phi_B$ = Total barrier lowering [eV]
• $q$ = Elementary charge [C]
• $E$ = Electric field at the interface [Vcm^-1]
• $ε$ = Permittivity of the semiconductor [Fcm^-1]
• $α$ = Dipole lowering coefficient [cm]

The first term is Schottky barrier lowering, and the second term is dipole‑induced barrier lowering.

note

The dipole term typically corresponds to an effective dipole layer thickness < 2 nm.