The Boundary Conditions are listed within a group located under the CHARGE solver, in the object tree. It allows the user to define voltage or surface recombination boundary conditions to their electrical simulation.
You can add a new boundary condition by selecting one from the Boundary Conditions section of the CHARGE tab. When using the "coupled" mode to perform electro-thermal simulations, the thermal boundary conditions will also be available in the same section of the CHARGE tab. Each boundary condition can be edited, renamed, deleted in the same way as any simulation object.
Electrical Boundary Condition
The Electrical boundary condition can be used to apply a DC, small-signal, or transient voltage to an electrical contact.
General
- BC MODE: The voltage set by the electrical boundary condition can be either steady-state (DC) or transient.
Steady-state bc mode:
SWEEP TYPE: In the steady state mode, the bias assigned to each contact can either be a fixed value or a sweep using one of the following three options:
- single: bias is fixed at a value set by the VOLTAGE (V) parameter.
- range: bias is swept over a range of DC values. The range is defined by a RANGE START (V) bias, a RANGE STOP (V) bias, and by either the bias RANGE INTERVAL (V) or the RANGE NUM POINTS (number of points in the sweep).
- RANGE BACKTRACKING: In the range sweep mode, the user can choose to use backtracking. If this option is enabled then the solver will automatically reduce the voltage step size, INTERVAL (V), by a factor of 2 in case it fails to converge at a certain bias point during the voltage sweep. It will keep reducing the step size down to the MIN INTERVAL (V) value. If the simulation still fails to converge with the minimum step size then the simulation will stop and the job manager will show an error message.
- RANGE MIN INTERVAL (V): The minimum voltage step size (magnitude) the solver will go down to in order to achieve convergence when using the backtracking option.
NOTE: The number of voltage points with range backtracking is not known ahead of time and will be determined by the convergence success of the IV curve and by the end of range or the last converged point. |
- values: bias is swept over a user defined range of values provided in the form of a table (VALUE TABLE).
- auto: bias is swept from a user defined AUTO START (V) value to a user defined AUTO STOP VOLTAGE (V) or AUTO STOP CURRENT (A) (can be either a voltage or a current value). The AUTO INITIAL INTERVAL (V) parameter defines the voltage step between the first and the second voltage points. From then on the interval (bias step size) is determined by the solver depending on the smoothness of the I-V characteristic and the convergence success.
- AUTO START (V): Starting bias voltage in the auto sweep mode.
- AUTO INITIAL INTERVAL (V): The voltage step between the first and the second bias points.
- AUTO STOP CONDITION: The type of the stop value. The options are VOLTAGE or CURRENT MAGNITUDE.
- AUTO STOP VOLTAGE (V): The voltage value of the end point for the bias sweep.
- AUTO STOP CURRENT (A): The current value (magnitude) at the end point for the bias sweep.
- AUTO SMOOTHNESS (º): Maximum allowed change in the slope-angle (degree) of the current-voltage (I-V) characteristic curve between two consecutive bias points (to ensure a smooth I-V curve).
- AUTO SMOOTHNESS SCALING: Determines whether the smoothness is measured using the linear I-V characteristic or the logarithmic I-V characteristic. If the entire IV curve (from low current region to high current region) can be clearly seen on a linear scale then the linear option can be used, otherwise the logarithmic option should be used. Most devices where current changes over several orders of magnitude require the logarithmic option.
NOTE:
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APPLY AC SMALL SIGNAL: This option is valid only during small-signal ac simulations. The value is set to NONE by default. When enabled it applies a small signal AC voltage to the DC bias voltage.
- all: SSAC voltage will be applied to all bias points.
- last: SSAC voltage will only be applied to the last bias point.
MAP CURRENT COLLECTION PROBABILITY: This option is available only during steady-state simulations. If enabled, the CHARGE solver will inject an impulsive generation rate source at each location in the mesh to calculate the fraction of charge collected at that contact at each bias point. The result will be available as a dataset (W) in the solver region. To see an application of this option go to the CMOS Greens Function IQE KB example page.
LUMPED IMPEDANCE: Series (rse) and shunt (rsh) resistors can also be added to the voltage source to model more complicated external circuits.
Transient bc mode:
In the transient mode, the bias is defined as a function of time. The values for each voltage point as well as the time point can be entered in a table. Series and shunt resistors (rse, rsh) and capacitors (cse, csh) can also be added to the voltage source to model more complicated external circuits. The resistance and capacitance for these elements can also be specified as a function of time. If only one point is specified in the table, then a constant value is assumed for that element.
- ENABLE: This box must be checked for the series and shunt resistors or capacitors to be included in the external circuit.
- UNITS: This drop-down menu option allows user to set the unit of the value provided for the bias voltage, resistance, and capacitance.
- FORCE OHMIC: The force ohmic option is enabled by default. When enabled, it creates an ohmic contact by matching the metals work-function with the semiconductors one. If disabled then a Schottky contact is formed based on the difference in their work-functions.
Note: The total simulation time for the transient mode is determined by the maximum time input in the simulation settings, either in the global source shutter, or in the transient boundary condition, whichever has larger final time input. It is common practice to use the boundary condition for setting the simulation time, by adding an additional time step at the intended final time. |
Geometry
The geometry option defines where the boundary condition can be applied.
Note: A list of domains will be available under the SIMULATION REGION object once the simulation region is partitioned. A list of solids (primitives) are available under the GEOMETRY Container Group. |
Volume, surface, line and point in 3D and 2D:
|
Volume |
Surface |
Point |
---|---|---|---|
3D |
Volume |
Surface or Line |
Point |
2D |
Surface |
Line |
Point |
Surface Type
- DOMAIN:EXTERIOR : Select the target domain. The reference geometry is the common surface(s) shared by the uttermost surface(s) of the selected domain and the simulation region. The selected domain has to have at least a surface that is shared with one of the simulation region surfaces.
- DOMAIN:DOMAIN : Select the target domains. The reference geometry is the common surface(s) shared by the two selected domains.
- DOMAIN : Select the target domain. The reference geometry is the surfaces of the selected domain.
- SOLID : Select the target solid. The reference geometry is the surfaces that enclose the selected volume if the solid is a 3D shape, or the surface if the solid is a 2D plane.
- SIMULATION REGION : Select one or more simulation region boundaries. The reference geometry is the selected boundaries.
- SOLID:SIMULATION REGION : Select one or more simulation region boundaries and the target solid. The reference geometry is the common surface(s) shared by the simulation region and the target solid.
- MATERIAL:MATERIAL : Select the target materials. The reference geometry is the surface(s) that is shared by the two selected materials. This is only available in some boundary conditions.
- SURFACE : Type the identifier of the partition surface. If the target partition surface is SURFACE 3, type 3. If the target partition surfaces are SURFACE 3 and SURFACE 5, enter 3,5.
Surface Recombination
Two types of interfaces can exist with a semiconductor in the simulation region: interfaces with conductors, and interfaces with insulators. while both are subject to the same physical process, certain restrictions on the boundary conditions limit the application of the model to conductor interfaces.
The surface recombination process that models the charge behavior at the interface acts effectively like a current source or sink. Electrons and holes interact with impurity trap states at the surface, and recombine. Therefore, a surface recombination rate specifies a Neumann (or derivative) boundary condition on the charge density. For details on the surface recombination model used in CHARGE and the procedure for calculating the model parameters from the trap state properties, please consult the "Trap-Assisted Surface Recombination Model" section below.
Trap-Assisted Surface Recombination Model
Like bulk Shockley-Read-Hall (SRH) recombination, the presence of deep-level trap states at the semiconductor surface catalyzes recombination. The surface recombination process is modeled by a formula similar to that of the bulk case,
$$R_{surf}=\frac{np-n_i^2}{\frac{1}{s_p}(n+n_{ls})+\frac{1}{s_n}(p+p_{ls})}$$
but differs slightly from the bulk process since it is occurs on a two-dimensional surface. The trap density Nts is now given per unit area, such that the carrier lifetime of the bulk case is replaced by a surface recombination velocity,
$$s_{n,p}=\sigma_{n,p}N_{ts}\sqrt{\frac{3k_BT}{m_{n,p}^\ast}}$$
The surface recombination velocity is treated as an input parameter in CHARGE, chosen to reflect the non-ideal nature of the material surface. The surface recombination velocity may be temperature dependent. Like the bulk case, the constants n1s and p1s are calculated as
$$n_{ls}=n_{ie}e^{\frac{E_{ts}}{k_BT}}$$
$$p_{ls}=n_{ie}e^{\frac{-E_{ts}}{k_BT}}$$
General
SURFACE RECOMBINATION VELOCITY: The surface recombination property is usually defined by a parameter called surface recombination velocity. If there are no surface recombinations at an interface then the net movement of carriers toward that surface is zero which refers to a surface recombination velocity of zero. On the other hand, if the surface recombination at an interface is infinitely large then the carriers will move toward that surface at maximum velocity (~107 cm/s) which is limited by the material property of the semiconductor.
- ELECTRON (cm/s)
- HOLES (cm/s)
ENABLE MODEL: Enables the temperature dependent surface recombination velocity model
$$A(T)=A(300)(\frac{T}{300})^\eta$$
where, A(T) is the surface recombination velocity at temperature T and ETA is the index of the power law.
- APPLY TO MAJOR CARRIERS: Enabling this options applies the surface recombination for both majority and minority carriers. If disabled then surface recombination is applied to minority carriers only.
- TRAP Ei OFFSET (eV): Energy offset of the trap level from the mid-gap energy level (Ei).
Geometry
The geometry option defines where the boundary condition can be applied.
Note: A list of domains will be available under the SIMULATION REGION object once the simulation region is partitioned. A list of solids (primitives) are available under the GEOMETRY Container Group. |
Volume, surface, line and point in 3D and 2D:
|
Volume |
Surface |
Point |
---|---|---|---|
3D |
Volume |
Surface or Line |
Point |
2D |
Surface |
Line |
Point |
Surface Type
- DOMAIN:EXTERIOR : Select the target domain. The reference geometry is the common surface(s) shared by the uttermost surface(s) of the selected domain and the simulation region. The selected domain has to have at least a surface that is shared with one of the simulation region surfaces.
- DOMAIN:DOMAIN : Select the target domains. The reference geometry is the common surface(s) shared by the two selected domains.
- DOMAIN : Select the target domain. The reference geometry is the surfaces of the selected domain.
- SOLID : Select the target solid. The reference geometry is the surfaces that enclose the selected volume if the solid is a 3D shape, or the surface if the solid is a 2D plane.
- SIMULATION REGION : Select one or more simulation region boundaries. The reference geometry is the selected boundaries.
- SOLID:SIMULATION REGION : Select one or more simulation region boundaries and the target solid. The reference geometry is the common surface(s) shared by the simulation region and the target solid.
- MATERIAL:MATERIAL : Select the target materials. The reference geometry is the surface(s) that is shared by the two selected materials. This is only available in some boundary conditions.
- SURFACE : Type the identifier of the partition surface. If the target partition surface is SURFACE 3, type 3. If the target partition surfaces are SURFACE 3 and SURFACE 5, enter 3,5.
Semiconductor-Conductor Interface
In a CHARGE simulation, conductors specify both charge and electrostatic boundary conditions. Due to the nature of the equations required to describe the physical behavior of the semiconductor, the charge density for both electrons and holes must be specified explicitly on at least on surface in the system. Generally, this is accomplished by specifying the majority carrier concentration.
On conductor surfaces where an interface model (surface recombination) is specified, the model should not be applied to the majority carriers. This is accomplished by un-checking the "Apply to majority carriers" option, which is the default for a newly added interface. This assumption is appropriate at a conductor interface where the doping concentration is large: the relative change in the carrier densities due to recombination may be large in for the minority carriers, but will typically be negligible for the majority carriers. Therefore, the physical behavior of the interface is correctly modeled by applying the surface recombination model to the minority carriers, while fixing the majority carriers at their equilibrium density, which in turn specifies a necessary boundary condition.
Semiconductor-Insulator Interface
Unlike conductors, insulator (e.g. oxide) boundaries are not used to specify charge boundary conditions in a CHARGE simulation. In addition, insulator interfaces may not be associated with large doping concentrations. Therefore, when specifying the properties for an insulator interface, it is correct to ensure that the "Apply to majority carriers" box is checked. This will ensure that the density of both the majority and minority carriers at the insulator interface are adjusted according to the surface recombination model.
Surface Charge Density
General
CONCENTRATION (C/cm^2): The concentration of the constant surface charge at the interface. Positive values represent electron surface density and negative values represent hole surface density.
Geometry
The geometry option defines where the boundary condition can be applied.
Note: A list of domains will be available under the SIMULATION REGION object once the simulation region is partitioned. A list of solids (primitives) are available under the GEOMETRY Container Group. |
Volume, surface, line and point in 3D and 2D:
|
Volume |
Surface |
Point |
---|---|---|---|
3D |
Volume |
Surface or Line |
Point |
2D |
Surface |
Line |
Point |
Surface Type
- DOMAIN:EXTERIOR : Select the target domain. The reference geometry is the common surface(s) shared by the uttermost surface(s) of the selected domain and the simulation region. The selected domain has to have at least a surface that is shared with one of the simulation region surfaces.
- DOMAIN:DOMAIN : Select the target domains. The reference geometry is the common surface(s) shared by the two selected domains.
- DOMAIN : Select the target domain. The reference geometry is the surfaces of the selected domain.
- SOLID : Select the target solid. The reference geometry is the surfaces that enclose the selected volume if the solid is a 3D shape, or the surface if the solid is a 2D plane.
- SIMULATION REGION : Select one or more simulation region boundaries. The reference geometry is the selected boundaries.
- SOLID:SIMULATION REGION : Select one or more simulation region boundaries and the target solid. The reference geometry is the common surface(s) shared by the simulation region and the target solid.
- MATERIAL:MATERIAL : Select the target materials. The reference geometry is the surface(s) that is shared by the two selected materials. This is only available in some boundary conditions.
- SURFACE : Type the identifier of the partition surface. If the target partition surface is SURFACE 3, type 3. If the target partition surfaces are SURFACE 3 and SURFACE 5, enter 3,5.