Keithley 4200 functionality range can be directly measured by thickness of the manual it is shipped with - its close to 5cm! It is fantastic tool and it has a  built-in programming interface, where you can set almost arbitrary sweep with high number of points (regarding your first question). 

Regarding the second one, I have a feeling, that it unfortunately is beyond standard interface of 4200. However, you may use external control of the device e.g. with LabVIEW. I have worked extensively with LabVIEW interface to Keithley for organic solar cell characteristics (with similar requirements as yours 0->v+->0->v-->0. 

If you would be interested in developing an application to perform test you specified, please feel free to contact me here, or through [email protected]

best regards, 

 dr Michal Radziwon

For the 1st question, just do a double sweep. That is sweep from say -10V to +10V and then opt for double sweep. As for the second question, I don't know how to do it without appending.

If the time of signal application is not a Problem in your measurements, then you can try to use DC Voltage setting mode instead of sweep mode. Computer which controls the SMU should have  all voltage values which you need for your sweep and then you set these voltages at the output of SMU and read the value of the current and so on. In most cases the simple drivers for Keithley and Agilent instruments are functioning in this way and do not use inner SMU memory for storage of the data points.

We also had a problem with the sweep 0->v+->0->v-->0 for memristor cycling. The only way we've found in KITE interface is to use the Voltage List Sweep option and manually wright the sequence of voltage values. For example, we used Excel to form the voltage list. Note, there is a limit on number of points.

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I agree with Sergey Bychikhin. Thanks