Non-Quasi-Static (NQS) RF Model

For high-frequency modeling and fast transient simulations, a special version of the PSP model is available, which enables the simulation of non-quasi-static (NQS) effects, and includes several parasitic resistances.

Q_i is the charge density at the i-th collocation point and f_i are functions, which contain the complete PSP-charge model.

Parasitics Circuit

Additional NQS and RF Parameters

The PSP-NQS model has a few additional parameters, which are described in the tables below. The allowed values for the parameter SWNQS are 0, 1, 2, 3, 5, and 9. If SWNQS = 0, then NQS effects are switched off, i.e. the intrinsic MOS model is identical to the standard PSP-model (however, the parasitics-circuit is still in place). If SWNQS is nonzero, it indicates the number of collocation points to be used in the NQS-calculations. A higher value increases the accuracy, but leads to an increased computational burden.

Additional Parameters for Global NQS Model

Name	Unit	Default	Min	Max	Description
SWNQS	–	0	0	9	Switch for NQS effects / number of collocation points
MUNQSO	–	1	–	–	Relative mobility for NQS modeling
RGO	–	10-3	–	–	Gate resistance Rgate
RBULKO	–	10-3	–	–	Bulk resistance Rbulk
RWELLO	–	10-3	–	–	Well resistance Rwell
RJUNSO	–	10-3	–	–	Source-side bulk resistance Rjuns
RJUNDO	–	10-3	–	–	Drain-side bulk resistance Rjund

Geometrical Scaling Rules for the NQS RF Model

Although the parasitic resistances are (in general) dependent on geometry, the actual form of this dependency is be strongly influenced by the device layout. For this reason, L and W dependence of these resistances is currently not included in PSP; the correct values must be supplied manually for each geometry.

The following (trivial) scaling rules are included for the NQS-model.

Equations for the NQS RF Model

In this section, y denotes the (normalized) position along the channel (y = 0 is source side, y = 1 is drain side), while x denotes the surface potential (normalized to φ*T) at a certain position.

In PSP 101.0 and before, only SWNQS=0,1,2,3,5,9 are allowed.

Initial Values

First Loop

Second Loop (Back Substitution)

Position Independent Quantities

Position Dependent Surface Potential and Charge

Interpolated (quasi-static) surface potential along the channel:

Normalized bulk-charge and its first two derivatives as functions of surface potential:

Auxiliary Functions

Normalized right-hand-side of continuity equation

Cubic Spline Interpolation

Continuity Equation

x_0,0=x_s and x_n,0=x_d. Also, these values coincide with those in the quasi-static part of PSP.

The core of the NQS-model is the solution of q(y, t) from the charge continuity equation along the channel. By approximating the y-dependence by a cubic spline through a number of collocation points, the problem is reduced to solving the q_i(t) from the following set of coupled differential equations.

The boundary points q₀(t) = q(x_s) = q_is and q_n(t) = q(x_d) = q_id remain fixed to their quasi-static values; they are not solved from the equation above.

Non-Quasi-State Terminal Charges

Currently, only SWNQS = 0; 1; 2; 3; 5; 9 are allowed. For odd values of SWNQS, the gate charge is integrated along the channel using Simpson’s rule. If SWNQS = 2, Simpson’s 3=8-rule is used.

• If SWNQS is odd (that is, n is even),
  
  
• If SWNQS =2 (that is, n=3),
  
  

Converting back to conventional units:

Related Topics

PSP102 Model

Model Usage

History and Development

Structure of PSP102

Geometrical Scaling and Stress Model for Intrinsic MOSFET

Model Equations

Component Statements for PSP102 Models

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