Curve Tracer User's Manual and Examples

A.1 Command Line

Usage: tracer inputfile tracefile [outputfile]

  1. inputfile is the name of the PISCES input deck which defines the device structure to be simulated and specifies what physical models are to be used. Basically, it contains everything in a normal PISCES deck except the solve card specifications (Section A.7).

  2. tracefile is a file containing instructions on how to conduct the trace as well as specifying bias conditions for all electrodes (Sections A.2 through A.6).

  3. outputfile is an optional specification of the name of the file where the simulation data is to be written (Section A.8). If outputfile is not given, the name of the output file defaults to inputfile.out.

A.2 Trace File

The trace specification file, tracefile, is similar to a PISCES or SUPREM input deck. Each line begins with a word designating what type of statement, or "card", it is. The four possibilities are CONTROL, FIXED, OPTION, and SOLVE. Also, a line may start with a "$" for comments. Such lines are ignored. The cards may appear in any order, and a card may be continued on following lines by placing a "+" at the beginning of each subsequent line. The "+" should be separated from the parameters on the line by at least one space.

Each option in a card should have the following structure: "param = paramvalue". Spaces separating the "=" sign are optional. The parameters for each card are described in the fol- lowing four sections. As with PISCES syntax, parameter names and values are not case- sensitive and may be abbreviated provided they remain unambiguous. Square brackets, [], enclosing a parameter indicate that it is optional (note that some of these parameters are only optional in the sense that they will default to a certain value if not specified in tracefile). A vertical line, |, represents a logical OR--only one of a list of parameters separated by "|" signs can be specified.

All electrodes in the device must have representation in the tracefile. Each electrode must appear as one, and only one, of the following: the CONTROL electrode, a FIXED electrode, or an open contact (OPENCONT1 or OPENCONT2) on the SOLVE card.

A.3 CONTROL Card

A.3.1 Description
The CONTROL card is used to designate the electrode which will be swept through the trace as well as the boundaries of the trace. This electrode is referred to as the control electrode. To define the start of the simulation range, an initial voltage and an initial voltage step must be specified for the control electrode. The end of the trace is specified by either a maximum electrode voltage, a maximum electrode current, or the total number of simulated points to be found.

A.3.2 Syntax
NUM= CONTROL= [BEGIN=] [INITSTEP=] [ENDVAL=<- real> | STEPS=]
A.3.3 Parameters
  • NUM is the number of the electrode in the PISCES deck designated as the control electrode, whose voltage or current is swept through the trace. Its integer value must be between1 and 9, inclusive. Default: none.
  • CONTROL is either VMAX, IMAX, or STEP. VMAX denotes that a maximum voltage on the control electrode, specified by ENDVAL, is used as the upper bound on the trace. IMAX denotes that ENDVAL specifies a maximum control-electrode current for the trace. STEP signifies that the trace will proceed for a certain number of simulation points, specified by the STEPS parameter. In most cases VMAX or IMAX will be used because it is not known how many simulation steps it will take to reach a certain voltage or current. Default: none.
  • BEGIN is the value of the voltage, in volts, at the starting point of the curve trace for the electrode designated by NUM (the control electrode). If an initial solution is performed by Tracer, BEGIN should be 0.0. If a previous solution is loaded into the input deck at the start of Tracer (see SOLVE card below), BEGIN should be equal to the voltage of the control electrode in this solution. Default: 0.0V.
  • INITSTEP is the initial voltage increment, in volts, of the control electrode. Thus, at the second solution point the control electrode will have a voltage of BEGIN + INIT-STEP. A recommended initial step size is 0.1V. The sign of INITSTEP determines the direction in which the curve trace will initially proceed. If INITSTEP proves to be too large and PISCES cannot converge on the second solution point, Tracer will automatically reduce INITSTEP until convergence is attained, then proceed with the trace from this point. Default: 0.1V.
  • ENDVAL is used when CONTROL=VMAX or IMAX. Tracer stops tracing when the voltage (CONTROL=VMAX) or current (CONTROL=IMAX) of the specified electrode equals or exceeds the value specified by ENDVAL. Note that it is the absolute values of the voltage or current and of ENDVAL which are compared. Default: 10.0V (CONTROL=VMAX), 10.0A/mm (CONTROL=IMAX).
  • STEPS is used when CONTROL=STEP. It specifies the number of solution points Tracer should find. Default: 10.

A.3.4 Examples

  1. Electrode 3 is the control electrode. Tracer will initially proceed in the negative-volt- age direction with an initial step of -0.1V. Tracer will proceed until the absolute value of the control current equals or exceeds 3A/mm.

    control num=3 begin = 0.0 initstep=-0.1 control=IMAX end=-3.0

  2. Electrode 4 is the control electrode. Tracer will run until 65 solutions are found, start- ing at v4=0.0V with an initial v4 step of 0.5V.

    control num=4 begin=0.0 initstep=0.5 control=step steps = 65

A.4 FIXED Card
A.4.1 Description

A FIXED card is used to designate an electrode whose bias remains fixed throughout the simulation. There should always be at least one FIXED electrode and usually there are two or more. The two types of bias conditions available are voltage sources and current sources. The value of the bias is arbitrary, with one exception: a zero-current source (open contact) should be specified through the open-contact option on the SOLVE card and not on the FIXED card. If non-zero current sources are used for some electrodes in a simula- tion, in inputfile the user must create contact cards with the "current" option for each of these electrodes (see Section A.7).

A.4.2 Syntax
NUM= [TYPE=] [VALUE=] [RECORD=]
A.4.3 Parameters
  • NUM is the number of an electrode in the PISCES deck. Its integer value must be between1 and 9, inclusive. Default: none.

  • TYPE is either VOLTAGE or V for a voltage source or CURRENT or I for a current source. Default: VOLTAGE.

  • VALUE is the fixed value of the current or voltage for the electrode specified by NUM. VALUE has units of either volts or amps/mm, depending on the specification of TYPE. Note that the specification of VALUE is optional since it is merely for reference and is not used by Tracer. Default: 0.0.

  • RECORD is either YES or NO. For RECORD=YES, the simulated current is recorded in the output file for a fixed-voltage electrode, while the simulated voltage is recorded for a fixed-current electrode. Default: NO.

A.4.4 Examples
  1. In every Tracer solution, electrode 1 has a voltage of 0.0V. The current in this node is recorded in outputfile at every solution point.

    fixed num=1 type = voltage value=0.0 record =yes

A.5 OPTION Card

A.5.1 Description

An option card is used to specify convergence criteria and solution-method options for any open electrodes, parameters which affect the smoothness and step-size control of the trace, which PISCES solution files are saved, and whether extra solution data is saved in outputfile.

A.5.2 Syntax

Simulations with one or two open contacts:

[ABSMAX=] [RELMAX=] [DAMP=] [TRYCBC=]

Smoothness and step-size control:

[ANGLE1=] [ANGLE2= [ANGLE3=] [ITLIM=] [MIN- CUR=] [MINDL=]

Control of output files:

[FREQUENCY=] [TURNINGPOINTS=] [VERBOSE=]

A.5.3 Parameters
  • ABSMAX is the maximum current allowed in an open contact and is only relevant when open contacts are used and voltage biases are applied to these contacts. Conver- gence is satisfied when either the ABSMAX or RELMAX condition is met. Default: 1.0X10-19A/mm.

  • RELMAX is the maximum ratio of open-contact current to control-electrode current and is only relevant when open contacts are used and voltage biases are applied to these contacts. Convergence is satisfied when either the ABSMAX or RELMAX condition is met. Default: 1.0X10-9.

  • DAMP is a number between 0 and 1.0 determining how quickly Tracer will converge on an open-contact solution using voltage biasing. The closer DAMP is to 1.0, the more quickly Tracer will converge, but there is also an increased chance of slower convergence due to overshoot. Usually the user should not be concerned with the value of DAMP. Default: 0.9.

  • TRYCBC is used only if there is an open contact. Tracer will only attempt to use zero-current biasing when the current of the control electrode is greater than TRYCBC. Otherwise, voltage biasing is used. In most cases the user does not have to worry about this parameter. Default: 1.0X10-17A/mm.

  • ANGLE1, ANGLE2, and ANGLE3 are critical angles (in degrees) affecting the smoothness and step size of the trace. They are described in detail in [28]. If the differ- ence in slopes of the last two solution points is less than ANGLE1, the step size will be increased for the next projected solution. If the difference is between ANGLE1 and ANGLE2, the step size remains the same. If the difference is greater than ANGLE2, the step size is reduced. ANGLE3 is the maximum difference allowed, unless overrid- den by the MINDL parameter. ANGLE2 should always be greater than ANGLE1 and less than ANGLE3. Defaults: ANGLE1 = 5o, ANGLE2 = 10o, ANGLE3 = 15o.

  • ITLIM is the maximum number of Newton loops for a given solution as specified in the method card of the PISCES input deck. The user should make sure that the value of ITLIM specified here is the same as that in the input deck. In certain cases, a PISCES solution may be aborted in Tracer because the solution will not converge within the given number of iterations. In some of these cases Tracer will try to redo the solution with a doubled number of iterations. If ITLIM is specified here, such attempts will be made. If there is no itlim statement or ITLIM=0, no attempts will be made. It is recom- mended that ITLIM be set to a low value, around 10 or 15 (or at least high enough to allow convergence of the initial solution). However, for GaAs devices a larger ITLIM of 20 or 25 is recommended. Default: 0.

  • MINCUR is the value of the control current, in A/mm, above which Tracer carefully controls step size and guarantees a smooth trace. Below this current level, the program simply takes voltage steps as large as possible, i.e., as long as numerical convergence can be achieved, without regard for smoothness. If MINCUR is set to 0.0, Tracer will not begin smoothness control until it is past the first sharp turn in the I-V curve. This value should be used when the user is only interested in the rough location of a break in the curve, such as the breakdown voltage of a single-junction device. If smoothness is required, a lower value should be specified. Setting MINCUR below 1X10-15A/mm is not recommended because Tracer has problems controlling smoothness at such low currents. Default: 0.0A/mm.

  • MINDL is the minimum normalized step size allowed in the trace. Usually the user does not need to adjust this parameter. Increasing MINDL will reduce the smoothness of the trace by overriding the angle criteria, resulting in more aggressive projection and fewer simulation points. Reducing MINDL will enhance the smoothness and increase the number of points in the trace. Default: 0.1.

  • FREQUENCY specifies how often the binary output (solution) files of the trace are saved. All I-V points are saved in outputfile. However, the PISCES solution files corresponding to these points are saved only if they are designated by FREQUENCY. If FREQUENCY=0, none of the solutions is saved, except perhaps the turning points (see below). If FREQUENCY=5, e.g., the solution file of every fifth point will be saved to files named soln.5, soln.10, etc., along with its PISCES input file (input.5, input.10,...) and output I-V file (iv.5, iv.10,...). Default: 0.

  • TURNINGPOINTS is either YES or NO. If it is YES, the binary output (solution) file from PISCES will be saved whenever the slope of the I-V curve changes sign, i.e., there is a turning point. The name of the output file is soln.num, where num is the number of the current solution. For example, if the 25th point has a different sign than the 24th point, Tracer will save a file called soln.25. Default: NO.

  • VERBOSE is either YES or NO. If it is YES, certain information about each solution (which the user may not be interested in) is printed in outputfile. The information consists of the external control-electrode voltage, the load resistance on the control electrode, the slope (differential resistance) of the solution, the normalized projected distance of the next simulation I-V point, and the normalized angle difference between the last two simulation points. Default: NO.

A.5.4 Examples
  1. Step-size control will begin when the control electrode's current exceeds 1X10-14A/ mm. In the input deck itlim has been set to 12. Only essential information is saved in outputfile. The solution file of every tenth point, as well as any turning points, will be saved.

    option mincur=1e-14 itlim=12 verbose=no frequency=10 turningpoints=yes

  2. In a simulation with one or two open contacts, we want to keep the current through the open electrodes below 1X10-16A/mm, regardless of the current through the control electrode. Thus RELMAX is set to a very low value so that it will not be a factor in determining the current at the open contact(s).

    option absmax=1e-16 relmax=1e-25

A.6 SOLVE Card
A.6.1 Description
The solve card is used to specify how the initial solution is obtained, what simulator is used, and whether there are any open contacts (zero-current bias conditions). A Tracer run will start either with an initial solution or by loading a solution from a previous PISCES simulation. If such a previous simulation has one or two zero-current electrodes, the user has the option of either specifying the voltages on these electrodes or of simply designating them as open contacts.
A.6.2 Syntax
FIRSTSOLUTION= [OPENCONT1=] [OPENCONT2=] [SIMU- LATOR=] [VOPEN1=] [VOPEN2=]

A.6.3 Parameters
  • FIRSTSOLUTION is either INITIAL, LOAD, or CURRLOAD. In all cases a solve statement should be present in the PISCES input deck (inputfile). The parameters of this solve card in inputfile are not used but rather the card itself is used to mark where a PISCES solve card should be placed by Tracer in inputfile (see Section 4).

  • If FIRSTSOLUTION=INITIAL, a solution at thermal equilibrium will be solved by Tracer first. This implies that there cannot be any non-zero voltages or currents on a FIXED card. If the device has an open contact, i.e., a zero-current source, the user should not specify "current" on the contact line of the PISCES input deck to indicate a zero-current bias condition. Specifying OPENCONT1 or OPENCONT2 on the tracefile solve card is all that is needed.

  • If FIRSTSOLUTION=LOAD, a load statement should be present directly above the solve card in inputfile, and it should designate the infile (see Section 4). This option is used if the trace is to begin from a previously generated input solution file. The simulation which created this solution file must have used only voltage bias condi- tions. An open-contact trace can still be generated from such an input solution file if the voltage bias condition on the open electrode(s) results in near-zero current for that elec- trode (see VOPEN1, VOPEN2 below). Such an open-contact case would most likely arise if the user wanted to extend a previous Tracer run in which voltage bias condi- tions were used on the zero-current electrodes for the last simulation point.

    If the loaded solution is from a simulation using a zero-current bias condition, FIRST- SOLUTION=CURRLOAD should be used. In this case "current" should be specified on a contact card for each open electrode. As in the FIRSTSOLUTION=LOAD case, the existing inputfile load card is used by Tracer, which means the correct "infile" should be specified on a load card directly above the solve card in inputfile. Default: none.

  • OPENCONT1 and OPENCONT2 are the numbers of electrodes (between 1 and 9, inclusive) with a zero-current bias condition. There can be either zero, one, or two open contacts. When a device has an open contact, the user does not have to worry about convergence at low device-current levels. Tracer will automatically adapt the bias conditions to guarantee convergence. Default: none.

  • SIMULATOR is either PISC2ET (PISCES-IIET) or MD3200 or MD10000 (TMA- MEDICI). It designates the device simulator to be used by Tracer. Other additions may be made in the future. Default: PISC2ET.

  • VOPEN1 and VOPEN2 must be used if and only if there is an open contact and FIRSTSOLUTION=LOAD (voltage bias condition on open contact(s)). The values of VOPEN1 and VOPEN2 are the voltages of the open contacts OPENCONT1 and OPENCONT2, respectively, in the loaded solution file designated on the load card of inputfile. If there is only one open contact, VOPEN2 should not be specified. Defaults: 0.0.
A.6.4 Examples
  1. The trace starts by solving an initial solution at zero bias and uses PISCES-IIET as the simulator. Electrode 2 is an open contact.

    solve opencont1=2 firstsolution=init simulator=pisc

  2. The trace starts with a previous solution using only voltage bias conditions. In this loaded solution the open contacts 2 and 4 have voltages of 0.641V and 0.509V, respectively.

    solve firstsolution=load simulator=pisc opencont1=2 opencont2=4 + vopen1=0.641 vopen2=0.509

A.7 Input Deck Specifications
As of September 1994, Tracer works with PISCES-IIB [27], some in-house versions of Stanford PISCES, and to some extent md3200 or md10000, TMA-MEDICI Version 1.2.2 [29]. Use of MEDICI is not yet robust and thus Tracer may or may not complete a trace using this simulator; the ability to use MEDICI for simulations with open contacts has not yet been implemented. If Tracer is to use simulators which cannot perform ac analysis, the capability for calculating admittances using the difference method must be added (a previous version of Tracer had this capability, so it should not be hard to implement).

The input deck used by Tracer, inputfile, is a standard PISCES file, but Tracer has certain requirements. For understanding the basic flow of an input deck, consult the PISCES or TMA-MEDICI manual. The mesh, region, electrode, doping, and model cards must already be present in the input deck. Additionally, the Newton solution method must be specified in the symbolic card. Other requirements are described below.

A.7.1 Load and Solve Cards
In Tracer, the user specifies whether to start with an initial solution or to load a previous solution (see Section A.6). In either case, the user must mark a line in inputfile where the solve statement should go by starting the line with "solve". Any parameter specified in this solve statement is irrelevant. If Tracer is to start with a previous solution, inputfile must contain a standard load statement, above the solve line, containing the name of the input file to be used, i.e., load infil=. In the case of loading a solution with a zero-current bias condition, "current" should be specified on a contact card for the open electrode.
A.7.2 Contact Card
Contact cards are optional in inputfile except in the case of electrodes biased with a current source. The case of the zero-current source is noted in Section A.3 above. If there are any electrodes with a finite-current bias condition, a contact card with the "current" option should be placed in inputfile for each such electrode, regardless of whether Tracer is to begin with an initial solution or a loaded solution.

Even if no contact cards are required in inputfile, a line starting with "$contact" must be present so that Tracer will know where to add a contact statement. This contact card is necessary because this is where the load resistance of the control electrode is specified by Tracer. There is no problem with placing a contact card for the control electrode in the input deck as long as it does not specify a resistance value (which should never happen). Note that at least the first five letters of "contact" must appear for Tracer (and PISCES) to recognize it.

A.7.3 Method Card
In order to specify the maximum number of Newton iterations per solution, the itlim statement of the method card must be used in inputfile. If no method card is present, PISCES uses a default itlim of 20. However, in order to use the double-it limit option (see Section A.5.3), a method card must be present in the input deck and itlim must be set to some value.

Another option must be specified in the method card if TMA-MEDICI is used. In this simulator, if a solution is aborted MEDICI will try to solve for an intermediate solution and then retry the original solution. This is not desirable when using Tracer since Tracer needs to keep track of aborted solutions. Thus, "stack=0" should be specified in the method card of MEDICI so that it does not attempt intermediate solutions. Analogously, the "trap" option should not be specified on the method card in a PISCES-IIET deck.

A.7.4 Options Card
When using PISCES-IIET, "curvetrace" should be specified on the options card so that PISCES will abort nonconverging solutions. Additionally, "nowarning" can be specified to prevent PISCES from printing warning messages which clutter the output, especially the warning issued when the load resistance changes value from one solution to the next. (Note: these options may not be available in early releases of PISCES-IIET.)

A.8 Data Format in Output Files
As each solution is found, it is recorded in outputfile. Naming outputfile is described in Section 2. At the start of each line is the number of the solution. The second column of data contains voltage values of the control electrode, while the third column contains current values of the control electrode. If there is a zero-current electrode, the voltage and current values of OPENCONT1 will go in the next two columns, followed by the voltage and current of OPENCONT2 if there is a second open electrode.

Values in the next columns depend on which data are recorded. If requested in the FIXED statements of tracefile, current values of fixed-voltage electrodes and voltage values of fixed-current electrodes will be recorded for each solution point in outputfile. The order from left to right is from low to high electrode number.

After the electrode information is recorded, further columns contain information about each solution if VERBOSE=YES in the SOLVE card of tracefile. These columns are, from left to right, external control-electrode voltage, load resistance on the control electrode, differential resistance, normalized distance of the next projection, and the angle difference between the current and previous solution points (see [28] for a description of these parameters).

The FREQUENCY and TURNINGPOINTS parameters in the OPTION card allow data to be saved for certain specified solutions. In outputfile, those points which are saved are marked with an asterisk next to the solution number. The files saved are the input deck, input.i; the I-V data file, iv.i; and the solution file, soln.i; where i is the number of the solu- tion in outputfile.

A.9 Examples
In each of the Tracer examples below, a description of the simulation is given along with the command line used to invoke Tracer and figures with the listings of inputfile (the PISCES input deck), tracefile, and outputfile.

A.9.1 BVCEO
The BVCEO experiment is conducted by biasing an npn bipolar transistor's collector posi- tively with respect to the emitter while the base is left open. The PISCES input deck, bvceo.pis, shown in Fig. A.31, defines the mesh, region, electrodes, doping, emitter contact, physical models, and solution method. Even though the contact card is not for the collector, which will be the control electrode, the presence of the card ensures that Tracer will be able to find the correct place to insert a contact card for the collector when it needs to. If we did not wish to use the contact card in bvceo.pis, we would still have to insert a line beginning with "$contact" above the model and symbolic cards. Notice that "nowarn" and "curvetrace" are specified on the options card and "newton" is specified on the symbolic card, while nothing is specified on the solve card.

In the trace file bvceo.tra (Fig. A.32), the FIXED card sets the voltage on the emitter electrode (num=1, as defined by bvceo.pis) to a constant value of 0.0V and states that the cur- rent through this electrode will not be recorded in outputfile. Electrode 3, the collector electrode, is designated as the control electrode. The CONTROL card states that the first solution will have a collector voltage of 0.0V, while the second solution will have a collector voltage of 0.1V. Tracing will continue until the collector voltage equals or exceeds 20V. If the initial step of 0.1V proves to be too large for convergence, Tracer will cut the step size in half, possible more than once, until it converges on a solution, and then will proceed from this solution.

In the SOLVE card, we specify that the base electrode (num=2) is to be treated as an open contact during the trace. Also, tracing will begin with a thermal-equilibrium solution and PISCES-IIET will be used for the simulation. Finally, the OPTION card specifies that only essential I-V data will be saved in the output file; the PISCES iteration limit is set to 15, agreeing with the PISCES deck in the input file; PISCES solutions will be saved for any turning points as well as for every fifth solution point; smoothness of the I-V curve will not be enforced until the collector current is greater than 5X10-12A/mm; and while voltage biasing is used on the open base contact, a solution will be accepted only if the current through the base is less than 5X10-19A/mm (unless the RELMAX condition pre- dominates).

To run Tracer, the following command is typed at the prompt:

machine-prompt% tracer bvceo.pis bvceo.tra bvceo.out

While Tracer is running, the output of the PISCES runs are sent to the standard output, along with messages announcing when solutions are written to the output file. The output file, named bvceo.out in the command line, is shown in Fig. A.33, and a plot of the collector current vs. collector voltage is shown in Fig. A.34. In bvceo.out, we see that every fifth solution, along with solutions 24 and 36 (the turning points), has been saved in files named soln.5, soln.10, etc. Additionally, the last solution was saved in the file soln.last, although there is no asterisk marking the last solution in bvceo.out.

At the top of bvceo.out, column headings mark the solution number, control-electrode (collector) voltage, control-electrode current, open-contact (base) voltage, and open-con- tact current as Soln, Vctrl, Ictrl, Vcurr, and Icurr, respectively. We see that the collector voltages for the first, second, and last solutions are 0.0, 0.1, and 20.18V, respectively. The final solution does not have a collector voltage of exactly 20V, as specified in bvceo.tra, because Tracer only guarantees that the curve will be traced out to at least 20V, not exactly 20V.

Other information regarding the trace must be inferred from the PISCES output displayed while Tracer is running (not shown). From this output we can see that voltage biasing was used on the open base contact for the first few solutions, in which the collector current is too small to allow stable use of zero-current biasing. A few PISCES simulations are actually run for each I-V point, with minor adjustments on the base voltage being made until the base current is less than ABSMAX. When the collector current is large enough, Tracer places a zero-current bias on the base. We can also see that a variable load resistor is placed on the collector when the collector current exceeds MINCUR. After this, the step sizes are regulated to produce a smooth curve.

A.9.2 GaAs MESFET

In this example, the drain of a GaAs MESFET is biased with respect to the grounded source with the gate set at -0.5V and the substrate grounded. Before Tracer can be used to sweep the drain electrode, a solution must be created, using PISCES-IIET, to set up the gate bias. The input deck shown in Fig. A.35 and Fig. A.36 defines the device, finds the thermal-equilibrium solution, and then steps the gate bias to -0.5V while holding the other electrodes at 0V. The mesh and solution files are saved to the files mes.mesh and mes- vg.5.ini, respectively.

For Tracer, another PISCES input deck must be created to use as the input file (Fig. A.37). In mesvg.5.pis the mesh file generated by mes.pis, mes.mesh, is read in, preempt- ing the mesh, eliminate, region, electrode, and doping cards. Since Tracer will be starting with a previous solution, the name of the solution file to load must be given in mesvg.5.- pis. This load statement appears directly above the solve card with the file name mes- vg.5.ini, the solution file generated by mes.pis.

The trace file mesvg.5.tra is shown in Fig. A.38. In the three FIXED cards, the voltages of the source and substrate (num=1 and num=4, respectively, as defined by mes.pis) have been fixed at 0V, while the gate voltage (num=2) has been fixed at -0.5V. The current through the gate electrode will be recorded for each solution in the output file. The CON- TROL card of mesvg.5.tra specifies that the drain (num=3) will be swept from 0.0V to a voltage where the current is greater than or equal to 4.1X10-4A/mm, with an initial drain voltage step of 0.2V. On the SOLVE card, FIRSTSOLUTION is specified as LOAD, consistent with the input file mesvg.5.pis, and PISCES-IIET is designated as the simulator to use. Since VERBOSE is NO on the OPTION card, only the essential I-V data will be recorded in the output file. The iteration limit is 30, consistent with mesvg.5.pis, and every ninth solution, as well as those corresponding to turning points, will have its solution file saved.

To run Tracer, the following command is typed at the prompt:

machine-prompt% tracer mesvg.5.pis mesvg.5.tra mesvg.5.out

Fig. A.39 shows the output file, mesvg.5.out, in which the solution number, drain voltage, drain current, and gate current have been recorded as Soln, Vctrl, Ictrl, and I2, respec- tively. The solution files of points 9, 18, 27, and 29 (a turning point), as well as of the last point (not marked in the output file) were saved as soln.9, soln.18, soln.27, soln.29, and soln.last, respectively. A plot of the drain current vs. drain voltage is shown in Fig. A.40.