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Calculating a hysteresis

  1. Dec 28, 2009 #1
    Hey All happy holidays,

    Some time back I took electrical measurements on a ferroelectric capacitors in which I would apply sin or triangle waves for a certain amplitude (typically 4-5volts) and I collected/mointered/measured the current. I then was hoping to take that current and calculate the polarization of the ferroelectric capacitors and create a hysteresis but my loops were coming out garabage.

    At any rate I know was looking at someone elses data collected in the same manner, but their device was able to caculate polarization on the spot. They obtained hystersis loops. Looking at their raw current data and voltage data the trends are exactly the same as mine! Which has given me hope that my data is good and i was just calculating polarization wrong.

    To caculate polarization I was using taking the current and multplying it by the difference in time between each step.

    Does anyone know the correct way to take current with respect to voltage and calculate polarization electrical hystersis loops?


  2. jcsd
  3. Dec 28, 2009 #2


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    Staff: Mentor

    Could you please provide a pointer to info on "ferroelectric capacitors"? What are they used for?
  4. Dec 28, 2009 #3
    Hey Berkeman,

    Ferroelectric capacitors are used for mostly nonvolatile memory devices. My particular ferroelectric capacitors are comprised of SRO top and bottom electrodes with PZT material inbetween.

    I am using a simple 3 probe station to collect my data. I use triangular or sin waves sweeping through -5 to 5 volts and back. I am mointering the change in current as the wave sweeps through.

    My capacitor structures are about 30 micron in diameter.

    They capacitor structures are seeing more and more in materials reseach papers as they are getting smaller and smaller. They can also be used as gates but I am not familar with that application. I am studying the material properties of these structures.

  5. Dec 28, 2009 #4
    For my calculations I am taking the current obtained (amperes) and mutilpying by the difference in time. I then divide by by the area of my capacitors and I believe that will yeild (C/m^2) or polarization.

    But looking at the data obtained by some colleagues from a machine that does the calculation for them I cannot take their raw data and use this method and obtian the same machine generated results!
  6. Dec 29, 2009 #5
    Based on my knowledge of magnetic hysteresis loops, I have a suggestion on analysis of your data.
    The objective is to measure the energy loss (joules) for going through a complete hysteresis cycle, from zero to + 5 V, back through zero to -5 V, and back to zero. You will need many points, at least 100 if possible for a single loop. This goes through all four quadrants of coulombs plotted against volts. For each point, multiply voltage (volts) times current (amps) times time interval (seconds) from previous point. This gives volts times coulombs, which is energy (joules). You need to sum this product, point by point, for the complete hysteresis cycle, going around the loop in a counterclockwise direction, keeping track of the sign of each volt x coulomb product. If the hysteresis loop has zero area, the sum should equal zero. Any residual represents the joules lost per hysteresis cycle. I hope this helps.
    Bob S
  7. Dec 29, 2009 #6
    Thanks Bob S,

    I will give it a shot.

    Its actually really interesting how these electrical probe stations actually work. I dont what is actual data or what is derived data.

    i have spoken to a few of them on the phone asking how to calculate the polarization from the current obtained. It shouldnt be that difficult.

    Thanks again Bob I will post how it went later tonight

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