Numerical Command (Compute menu)

This command opens a dialog box which allows you to set the following parameters which affect the numerical computation algorithm. These parameters do not alter the definition of either the device or the excitation, but they will influence the accuracy of the solution and the speed with which the solution converges to an answer. Improper settings of these parameters can cause the program to fail to converge even for simple problems, so the default values of each parameter are listed here for reference.

Element Size Factor This value determines the size of the finite elements used to partition the device. A smaller element size factor produces smaller elements, which improves accuracy but takes more time. The default value is 0.5. Values greater than 1.0 can produce elements so large that converge problems may arise. Once the factor is small enough that all 500 available elements are used, making it smaller will have no further effect.
Normalized Error Limit This value determines when the solution is said to have converged. Iterations will continue until the largest change in any of the three potentials (electron or hole quasi-Fermi potential, or electrostatic potential) at any node is less than this factor times the thermal voltage, kT/q (which is about 26 mV at room temperature). The default value is 1E-6, and will rarely need modification.
Normalized Potential Clamp This value determines the maximum change in one iteration that is allowed for any potential at any node, as a multiple of the thermal voltage, kT/q. The default value is 1, which is rather conservative, favoring robustness over speed. Increase this value for more speed if convergence is not a problem. In particular, a higher value may be desirable to increase speed when large reverse-bias voltages are imposed. Note that you can change the clamp value during a solution, for those times when you need a small value for steady state but a larger value will do for subsequent transient steps.
Clamping Phi/Psi These check boxes determine how the Normalized Potential Clamp is imposed. Selecting Psi clamping prevents the electrostatic potential from changing by more than the clamp amount with each iteration. Selecting Phi prevents the separation between each quasi-Fermi potential and the electrostatic potential from changing too much. AT LEAST ONE OF THESE BOXES SHOULD BE SELECTED, as many problems will “blow up” very quickly without some form of clamping imposed. The default is for both boxes to be selected.
Maximum Time This value determines how long (in seconds) a solution is permitted to continue before it is judged to be non-convergent. The default value is 60 seconds. Some problems involving internal shunt elements may take longer than this to converge, but most problems that haven't converged after a minute never will.
Renode These three check boxes determine when the finite-element nodes are reallocated. When initialized, the problem has 100 elements in each defined region. It is usually desirable to renode during the equilibrium solution, since the initial node allocation does not yet know where the critical junction regions are located. Selecting renode for the steady-state solution serves to refine the previous node allocation based on the equilibrium solution, and allows the program to do an emergency renode if the quasi-Fermi potential step across any one element exceeds 32 times the thermal voltage. Renoding for a transient solution should only be invoked when the excitation significantly alters the space-charge regions, and it should especially be avoided during fast transients where time derivatives are important. The default is to renode during equilibrium and steady state solutions, but not during transient solutions.
Display graphs after every iteration This check box is provided for those who are interested in observing the numerical computation performed by PC1D. When checked, the plots on screen are updated after every iteration, not just when the solution has converged. This slows the solution considerably, so should be chosen only when the convergence behavior is of interest.
Total velocity saturation This check box is provided for those who need to impose rigid saturation of the total velocity of the carriers, due to both drift and diffusion. Normally, when this box is not selected, the mobility of the carriers is reduced only in response to a high electric field. When this box is selected, the mobility is reduced in response to a high gradient in the quasi-Fermi potential. Although checking this box invokes the more-correct physical limitation, convergence is more difficult and solutions can take more than twice as long to complete. It is recommended only for heterostructure devices in which the current is limited by thermionic emission over an energy barrier.