Table of Contents - Ferroelectric and Multiferroic Testing · 2010-11-09 · TABLE OF CONTENTS ......

Updated 10/11/06

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Table of Contents

TABLE OF CONTENTS .................................................................................................. I

TABLE OF FIGURES....................................................................................................III

A - DISCUSSION...............................................................................................................1

B - MAIN SETUP...............................................................................................................3

B.1 - Setup Dialog ...............................................................................................................4 B.2 - Description .................................................................................................................5 B.3 - Controls ......................................................................................................................6

C - PLOT SETUP...............................................................................................................8

C.1 - Setup Dialog ...............................................................................................................9 C.2 - Description .................................................................................................................9 C.3 - Controls ....................................................................................................................10

D - EXECUTION, ARCHIVE REGRAPH AND EXPORTING ................................12

D.1 - Execution..................................................................................................................12 D.2 - Archive Regraph ......................................................................................................15 D.3 - Data Exporting .........................................................................................................19 D.4 - Export Setup.............................................................................................................21

E - EXAMPLES ...............................................................................................................29

E.1 - Standard Plots ...........................................................................................................29 E.1.1 - No Filter .....................................................................................................................29 E.1.2 - Centering ....................................................................................................................29 E.1.3 -Capacitance Vs Voltage...............................................................................................30 E.1.4 - Normalized Capacitance Vs Voltage..........................................................................31 E.1.5 - dP/dT Vs Voltage .......................................................................................................32

E.2 - Plots Vs Time ...........................................................................................................33 E.2.1 - No Filter Vs Time.......................................................................................................34 E.2.2 - Centering Vs Time .....................................................................................................35 E.2.3 - Capacitance Vs Time..................................................................................................36 E.2.4 - Normalized Capacitance Vs Time ..............................................................................37

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E.2.5 - dP/dT Vs Time ...........................................................................................................38

F - MATHEMATICAL DESCRIPTION.......................................................................39

G - CHANGE AND VERSION RECORD ....................................................................46

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Table of Figures Figure B.1.1 - Hysteresis Filter Task Configuration Dialog............................................... 4 Figure B.1.2 - Hysteresis Filter Task Configuration Dialog. Import a Vision Data File.... 5 Figure C.1.1 - Hysteresis Filter Task Plot Configuration Dialog. ...................................... 9 Figure D.1.1 - Multi-Volt Centered Hysteresis Data. Data are Recalled from a DataSet

Archive.................................................................................................................. 12 Figure D.1.2 - Multi-Volt Normalized C/V Data. Data are Recalled from a DataSet

Archive.................................................................................................................. 13 Figure D.1.3 - 7.0-Volt Data. Four Appended Traces. Data are Recalled from a DataSet

Archive.................................................................................................................. 14 Figure D.1.4 - 7.0-Volt Data. Four Accumulated Traces. Data are Recalled from a

DataSet Archive. ................................................................................................... 15 Figure D.2.1 - Recall the Hysteresis Filter Task from a DataSet Archive........................ 16 Figure D.2.2 - Main Hysteresis Filter Dialog Recalled from a DataSet Archive. ............ 17 Figure D.2.3 - Hysteresis Filter Plot Dialog Recalled from a DataSet Archive. Some

Labels are Adjusted............................................................................................... 18 Figure D.2.4 - Hysteresis Filter Centered Data Recalled from a DataSet Archive. ......... 19 Figure D.3.1 - Export Configuration Dialog..................................................................... 20 Figure D.3.2 - Standard Windows File Browser Dialog................................................... 20 Figure D.4.1 - Standard Windows Printer Configuration Dialog. .................................... 22 Figure D.4.2 - Sample Hysteresis Filter Text Export File. Upper Portion. ...................... 23 Figure D.4.3 - Sample Hysteresis Filter Text Export File. Lower Portion....................... 23 Figure D.4.4 - Sample Hysteresis Filter Excel Export Output. Upper Portion................. 24 Figure D.4.5 - Sample Hysteresis Filter Excel Export Output. Lower Portion. ............... 25 Figure D.4.6 - Sample Hysteresis Filter Word Export Output. Upper Portion................. 26 Figure D.4.7 - Sample Hysteresis Filter Word Export Output. Lower Portion. ............... 27 Figure E.1.1.1 - No Filter Applied.................................................................................... 29 Figure E.1.2.1 - Centered Hysteresis Loops. .................................................................... 30 Figure E.1.3.1 - Derivative Capacitance Vs Voltage........................................................ 31 Figure E.1.4.1 - Normalized Capacitance Vs Voltage...................................................... 32 Figure E.1.5.1 - Polarization Derivative with Respect to Time........................................ 33 Figure E.1.1. - Polarization Vs Time with no Filtering. ................................................... 34 Figure E.2.2.1 - Centered Polarization Vs Time............................................................... 35 Figure E.2.3.1 - Derivative Capacitance Vs Time. ........................................................... 36 Figure E.2.4.1 - Normalized Capacitance Vs Time. ......................................................... 37 Figure E.2.5.1 - Time Derivative Vs Time. ...................................................................... 38 Figure F.1a - Subsampling-Induced Noise Around a Critical Point................................. 42 Figure F.b1 - Subsampling-Induced Noise Around a Critical Point................................. 43 Figure F.2 - Nine-Point Smoothing Using Savitszky-Golay Coefficients........................ 44

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A - Discussion The Hysteresis Filter belongs to a class of Tasks known as Filters. A Filter is a Task that performs one or more of the following operations...

Collects data from one or more Tasks preceding the Filter in the Test Definition. Performs some operation on the collected data. Stores the collected and altered data. Optionally plots the data during execution.

The Filter must be associated with one or more Tasks, of the same type, that precede it in the Test Definition. It takes its data from those Tasks. Most Filters operate on measured data, so that only the measurement subset of Tasks is available to the Filter. Often a Filter Task is included in the Test Definition to allow data display during execution of the Cur-rent Test Definition (CTD). Measurement Tasks do not normally plot themselves during Test Definition execution. Filters are included to perform this operation so that the num-ber and type of plots that appear during execution can be limited and under the user's control. Exceptions to this rule are those Tasks that execute over extended periods of time. These plot themselves and do not require a Filter. Such Tasks include Fatigue, Re-sist and Retain. The Hysteresis Filter performs all of the four Filter functions listed above. It operates only on Hysteresis Task input, placing it in a Filter sub-category known as Task-Specific Filters. The operations performed by this Filter can be mimicked by one or more mem-bers of the Generic category of Filters that operate on any (or nearly any) Measurement Task. These usually perform general math functions that could be chained to arrive at the same results achieved immediately by the Hysteresis Filter. The operations performed by the Hysteresis Filter are also available directly in the Hysteresis Task when the Task is executed under the QuikLook menu. The operations include:

None - The Hysteresis data are not altered before saving or displaying them. This is the standard mode for QuikLook Hysteresis Task execution. Setting this Filter is essentially the same as selecting the Pass-Through Filter and associating it with the Hysteresis Tasks.

Centering - Polarization is a relative quantity whose value can only be specified as related to some reference value. For a Hysteresis measurement made on a sin-gle capacitor, no such reference exists. Instead, the first sample point is arbitrarily set to 0.0 µC/cm2 and used as the reference for all other measured points. As a re-sult, the a positive-going Hysteresis loop is shifted upwards relative to the voltage axis. (A negative-going loop is shifted downwards.) Traditionally Hysteresis loops are displayed as centered about the voltage axis. The Centering filter ac-complishes this. This is accomplished by simply subtracting the average of the

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polarizations at the maximum and minimum (maximum negative) applied volt-ages from every point in the loop. This is a necessary operation for the proper cal-culation of ±Vc and ±Pr. This operation has been available as a switch during DataSet execution of the Hysteresis Task. With the introduction of this Filter, that operation will eventually be disabled.

Capacitance Vs Voltage - The non-linear capacitance of a ferroelectric material can be derived from the Hysteresis loop by differentiating the loop (δPolarization/δVoltage) at every point. When the derivative is displayed as a function of voltage, a clearer picture of the nature of the sample can be derived than that afforded by the Hysteresis loop alone. The derivative displays the distri-bution of polarization over its switching voltage, so that the amount of polariza-tion that will switch at the application of a particular voltage can be inferred. This representation also provides a more correct view of the coercive voltages, ±Vc. To provide this display, a simple numerical derivative is calculated, and the re-sults smoothed.

Normalized Capacitance Vs Voltage - This filter performs the identical opera-tion to Capacitance Vs Voltage. It then performs the single additional step of scaling the resulting derivative by the inverse of the sample area in cm2. The ad-vantage of this filter is that the results from capacitors of varying sizes can be di-rectly compared.

δP/δT - This is a derivative filter in which the change of polarization as a function of the change in time between two points is calculated. This will give a very simi-lar representation to Capacitance Vs Voltage, though scaled. However, while dV can produce a negative value, dT is always positive. For this reason, dP/dT can have negative values on the plot while dV/dT is always positive for a quality Hysteresis loop.

Normally, the filtered measured values are plotted as a function of the stimulus voltage that induced them. However, an option exists to plot the values as a function of the time in milliseconds, relative to the first measured value, at which they were acquired. This same option in the QuikLook version of the Hysteresis measurement will plot both meas-ured values and drive voltage as a function of time. For the Hysteresis Filter Task, only the measured values are plotted. Note that if this option is enabled, any Filter Task that takes its data from the Hysteresis Filter Task (for example, the Pass-Through Filter Task) will still plot the incoming data as a function of voltage. See Mathematical Discussion for a more detailed description of each of these Filters. See Examples for a sample of the results of each Filter.

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B - Main Setup

Task Name: Hysteresis Filter Version: 4.0.0 Last Update: 6 January 2006 In QuikLook Menu: No Folder: Filter Subfolder: Task-Specific Subsubfolder: None Window Name: Hysteresis Filter Setup::Main Setup Change Record: Go to Change Record Known Bugs: None User Variables Added: None

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B.1 - Setup Dialog

Figure B.1.1 - Hysteresis Filter Task Configuration Dialog.

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Figure B.1.2 - Hysteresis Filter Task Configuration Dialog. Import a Vision Data File.

B.2 - Description

For those familiar with the Pass-Through Filter, the configuration of the Hysteresis Filter is a greatly simplified version of the same process. Missing from this dialog is the selec-tion of the Task type (since only Hysteresis Tasks may be selected) and the controls asso-ciated with Single-Point data. The dialog's two main functions are to select a Filter type

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and to associate the Filter with a subset of all of the Hysteresis Tasks that precede the Fil-ter in the Test Definition. The Accumulate control relates to how the data are gathered and plotted. The Export control is disabled during configuration, but available as the re-sult of the Filter being recalled from the DataSet Archive. Archived data can be exported. See the table below for a detailed description of each of the controls. With the release of Version 4.0.0, a new exporting option has been introduced. Once a Collect/Plot Filter Task has been executed it can have its configuration parameters and data exported to a Vision data file. Subsequent Collect/Plot Filter Tasks can be config-ured to read from the data file in lieu of gathering new data. This feature allows data taken from diverse places, including multiple DataSets to be imported into other Data-Sets, where Filters can then be applied as though the Task were taking new data. Con-figuration of the Collect/Plot Filter Task to import Vision Data File data is shown in Fig-ure B.1.2, above. For details, see the exporting tutorial.

B.3 - Controls

Name Type Default Description Task Name Text "" 30-Characters Maximum. A unique identifier for the particular instance

of the Hysteresis Filter Task. Accumulate Check

Box Disabled This check box only applies to the filter if it and/or the associated Hys-

teresis Tasks are located in a Branch Loop. With the control enabled, each successive iteration of the Filter will collect data from the entire history of the associated Tasks' executions. The first iteration will take the first measurement, the second iteration will collect the first and sec-ond measurement, and so on. From a plotting viewpoint, with a single associated Task, the first iteration will plot a single Hysteresis loop, the second iteration will plot two loops, and so on. With the control dis-abled, only the most recent measurement of the associated Task(s) is (are) collected. With the control enabled, the volume of data gathered can increase very quickly, especially if multiple Hysteresis Tasks are associated with the Filter. It is recommended that this control only be used when the number of loop iterations is small and when the size and/or shape of the Hysteresis loop is expected to change as a result of other operations within the loop.

Filter List Box

"<None>>" This control selects the type of filter that is to be applied to the collected Hysteresis data.

Read Data from Vision

File

Check Box

Unchecked Checking this box configures the Single-Trace Math Filter Task to read its configuration parameters and measured data from a Vision data file, exported by another Hysteresis Task, rather than making a new meas-urement. When the box is checked, File Name and Browse to File, nor-mally hidden, are shown. Since the configuration parameters are read from the file, most controls are disabled when this control is checked. Task Name, Comments, Help, OK and Cancel/Plot remain enabled.

Browse to File

Button Unpressed This control is normally hidden. It appears when Read Data From Vi-sion File is checked. Clicking this button opens a standard windows file browser configured to look for files with a *.vis file extension. The

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browser is to be used to identify the location and name of a Vision Data File, exported by a previous execution of the Sensor Collect/Plot Filter Task, whose configuration parameters and measured data are to be taken on by the current Task. Once the file is identified and the browser is closed, the file path and name are reflected in File Name.

File Name Text "" This control is read-only. It is normally hidden. It appears when Read Data From Vision File is checked. This control displays the Sensor Col-lect/Plot Filter Vision Data File, identified by the browser using Browse to File, that is to provide the formatted configuration parameters and measured data to the Task on execution. A file name must be identified or the configuration may not proceed.

Task Selec-tor

List Box

N/A This control displays, by name, all of the Hysteresis Tasks that precede the Hysteresis Filter Task in the Test definition. Using the <Shift> and/or <Ctrl> keys, one or more of the Tasks can be selected (high-lighted). The selected Tasks can then be associated with the Filter using the Add Task button. When this is done, the Task names in the control will have "(X)" appended to them.

Add Task Button Unpressed Clicking this button causes the Task whose names are highlighted in Task Selector to be associated with the Filter. When this is done, the Task names in Task Selector will have "(X)" appended to them.

Comments Text "" 511-Characters maximum. This control allows the user to describe the inclusion of the Hysteresis Filter Task in the Test Definition in some detail.

Export Button Unpressed This control is disabled when the Filter is being configured for execu-tion. It is enabled, when the Filter is recalled for review from the Data-Set Archive. Clicking this button opens an export dialog as discussed below. The dialog allows the Task data to be exported to a printer, a text file or an Excel file.

Help Button Unpressed Open this help page for reading. OK Button Unpressed Accept the current configuration and add the Task to the Test Defini-

tion. This control closes the configuration dialog. Cancel Button Unpressed Close the configuration dialog. Do not add the Task to the Test Defini-

tion. Apply Button Unpressed This control is always disabled.

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C - Plot Setup

Task Name: Hysteresis Filter Version: 4.0.0 Last Update: 6 January 2006 In QuikLook Menu: No Folder: Filter Subfolder: Task-Specific Subsubfolder: None Window Name: Hysteresis Filter Setup::Plot Setup Change Record: Go to Change Record Known Bugs: None User Variables Added: None

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C.1 - Setup Dialog

Figure C.1.1 - Hysteresis Filter Task Plot Configuration Dia-log.

C.2 - Description

The plot setup dialog is used to configure the appearance of the presented data if data are

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to be plotted at configuration time. It will also establish the appearance of data that are recalled from the DataSet Archive. Plotting during execution is enabled from this dialog. Note that this dialog differs from most Task configuration dialogs when recalled from the DataSet Archive. The controls of this dialog remain active. This is primarily done to al-low the user to enable or disable the Plot Vs Time control to alter the way the recalled data are displayed. All other controls are also active and main be changed at will. How-ever, enabling or disabling the Plot These Data control has no effect. Data will always be plotted, when recalled from the Archive, once the dialog is close. With the release of Version 4.0.0, the Plot Vs Time control has been renamed Plot Time (ms) and changed to a radio button grouped with the Plot Volts and Plot Field (kV/cm) controls. This is clearer and more appropriate since the controls are mutually exclusive.

C.3 - Controls

Name Type Default Description Plot These

Data Check Box

Disabled When checked, indicates that data are to be plotted when the Hys-teresis Filter Task executes in a DataSet. Example of the plots gen-erated are shown in the Examples page.

Append Data Check Box

Disabled This control applies when the Filter is located within a Branch Loop. When enabled, a single plot will be generated and updated at every loop iteration. If disabled, a new plot will be generated each loop iteration.

Check Box

Disabled Indicates that the data are to be plotted as a function of time, in mil-liseconds, with 0 being the first measured point in the Hysteresis loop. This control adjusts the Plot X-Axis Label default time. Values are "Voltage" or "Time (ms)".

Plot Title Text "" 60 Characters Maximum. A description of the plot on which the Title appears.

Plot Subtitle Text "" 60 Characters Maximum. A second line to help describe the plot, providing more room for detail.

Plot X-Axis Label

Text "" 60 Characters Maximum. A description of the value of the inde-pendent plot axis. This value is first under the control of the set of controls grouped under X-Axis Plot Option. As the option is changed between Plot Volts, Plot Field (kV/cm) and Plot Time (ms), the label in this control will be adjusted automatically from "Voltage" to "Field (kV/cm)" to "Time (ms)". Once the selection in the X-Axis Plot Option list is finalized, the value in this control can be manually adjusted by the user to any text string.

Plot Volts Radio Button

Checked This is the default selection. In this selection the Filter-manipulated data, recovered from the input Task(s) are displayed as a function of the drive voltage recovered from the input Task(s). When this button is checked, the text value in Plot X-Axis Label is automatically set to "Voltage". It can then be overwritten by the user.

Plot Field (kV/cm)

Radio Button

Unchecked In this selection the Filter-manipulated data, recovered from the in-put Task(s) are displayed as a function of the scaled drive voltage

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recovered from the input Task(s). The voltage is scaled by dividing by the sample thickness. Thickness is also scaled to units of cm. When this button is checked, the text value in Plot X-Axis Label is automatically set to "Field (kV/cm)". It can then be overwritten by the user.

Plot Time (ms) Radio Button

Unchecked In this selection each Filter-manipulated data point, recovered from the input Task(s) is displayed as a function of time, in milliseconds, at which the data point was sampled. The first data point is assigned a value of 0.0 ms. The final data point will be very near the assigned Hysteresis period given by the input Task. When this button is checked, the text value in Plot X-Axis Label is automatically set to "Time (ms)". It can then be overwritten by the user.

Data Label Text "" Not currently used. Help Button Unpressed Open this help page for reading. OK Button Unpressed Accept the current configuration and add the Task to the Test Defi-

nition. This control closes the configuration dialog. Cancel Button Unpressed Close the configuration dialog. Do not add the Task to the Test

Definition. Apply Button Unpressed This control is always disabled.

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D - Execution, Archive Regraph and Exporting

D.1 - Execution

When the Hysteresis Filter Task executes, it gathers the data from the associated Hystere-sis and/or Remanent Hysteresis Tasks, applies the appropriate mathematical conversion to the data and stores the accumulated and filtered data to the DataSet. The Task may also display the gathered and altered data when the Task executes. Regardless of whether data are displayed during execution, they may always be displayed by recalling them from the DataSet Archive. Figure D.1.1 shows the Hysteresis Filter Task centering Hysteresis data from 5.0 and 7.0-Volt Hysteresis Task measurements. Figure D.1.2 shows the Normal-ized C/V derivative computed on the same data. A 2600 Å 1e-4 cm2 20/80 PZT sample was measured. Note that it cannot be determined from the plot alone that the data, in both cases, are displayed as a result of a DataSet Archive recall and not directly from the Task execution. Plots in both cases are identical.

Figure D.1.1 - Multi-Volt Centered Hysteresis Data. Data are Recalled from a DataSet Archive.

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Figure D.1.2 - Multi-Volt Normalized C/V Data. Data are Re-called from a DataSet Archive.

If the Hysteresis source Tasks are programmed into a Branch Loop, the behavior of the Filter as a result of multiple executions of the source Task (and perhaps of the Filter) be-comes significant. If no action is taken, a Filter, set to plot its data, programmed within a Branch Loop will generate a new plot each Branch iteration. The newest plot will show the most recently acquired data. If the Filter is placed after the Branch Loop, a single plot will be produced that shows only the most recently acquired data. A "Append" option is available for data that are to be plotted. In this case, a single plot is generated at the first iteration. At each new iteration i, m new plots will be appended, where m is the number of associated Hysteresis Tasks. At any given iteration, the number of traces is given as i x m. Figure D.1.3 shows a single 7.0-Volt Hysteresis measurement plotted over four iterations. Only a single plot is evident because the traces overlay. However, notice that there are four labels above the plot.

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Figure D.1.3 - 7.0-Volt Data. Four Appended Traces. Data are Recalled from a DataSet Archive.

An "Accumulate" option is available whether or not the plot is shown during execution. Accumulate will generate a new plot at each Branch iteration if programmed within a Branch. Each new plot will include the most recently acquired data as well as the entire history of previous data. Therefore, each new plot will resemble an "Append" plot for that iteration, but the advantage of a single plot is lost. Although this may seem impracti-cal, the utility is in placing the Accumulate-enabled Task after the Branch Loop so that it executes only once, generating a single plot. Being associated with Hysteresis Tasks that are programmed within the Branch Loop, the Task will recall all data from the Tasks, displaying the entire history of Task execution within the Branch Loop. Figure D.1.4 shows a 7.0-Volt centered example.

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Figure D.1.4 - 7.0-Volt Data. Four Accumulated Traces. Data are Recalled from a DataSet Archive.

D.2 - Archive Regraph

Once accumulated and filtered data are stored in an Archive Regraph, they can be easily recalled for review. Both the original Task configuration and the generated data can be reviewed. Data can also then be exported to a source outside of Vision for more analysis. To recall the data, open the desired DataSet, open the Archive, open the desired Executed Test Definition (ETD), open the "Experiment Data" folder and double-click on the de-sired Hysteresis Filter Task.

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Figure D.2.1 - Recall the Hysteresis Filter Task from a DataSet Archive.

The Task configuration dialog will appear. Many controls are disabled and for review only. When the Task is recalled from the DataSet, the entire Test Definition is not recon-structed. As a result, the Task Selector control is empty and does not show the associated Tasks. Export is available as discussed in the next section. Help is available. OK and Cancel perform the identical functions of closing the dialog and allowing the recalled data to be plotted.

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Figure D.2.2 - Main Hysteresis Filter Dialog Recalled from a DataSet Archive.

The "Plot Setup" tab can also be accessed. In this case the controls are enabled, though they are preset with the original configuration value. The purpose is to allow changes to the plot labels. Note that adjusting Plot These Data and/or Append Data will have no ef-fect. Recalled data will be plotted regardless. Plot Vs Time is functional.

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Figure D.2.3 - Hysteresis Filter Plot Dialog Recalled from a DataSet Archive. Some Labels are Adjusted.

Once the dialog is closed the recalled data are plotted.

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Figure D.2.4 - Hysteresis Filter Centered Data Recalled from a DataSet Archive.

D.3 - Data Exporting

In order to allow data to be exported when they are recalled from the DataSet Archive, an Export button appears on the recalled Task configuration dialog. Clicking the button pro-duces the new dialog that appears below. Figure D.3.1 shows the Export configuration dialog in which the default "Export Text" option is selected and the browser button dis-abled. Figure D.3.2 shows the browser dialog that appears when any option other than Print is selected in the Select Option control.

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Figure D.3.1 - Export Configuration Dialog.

Figure D.3.2 - Standard Windows File Browser Dialog.

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D.4 - Export Setup

Name Type Default Description Select Option List

Box "Print" Select between the "Print", "Export Text", "Export Word", "Export Ex-

cel" and "Export Vision" options. This control enables the Browse for File Name button for all selections except the "Print" option.

Header Only Check Box

Checked This control appears when Select Option is set to "Print" or "Export Word". Otherwise it is hidden. When checked, the output of the point-by-point drive voltage and measured data is suppressed. This shortens the document and eliminates what is likely to be superfluous data.

Line Spacing Integer 100 This control appears when Select Option is set to "Print". Otherwise it is hidden. Increasing or decreasing this value will increase or decrease the vertical spacing of lines on the printed page. Experimentation will fix the value for any given printer.

Left Margin Integer 100 This control appears when Select Option is set to "Print". Otherwise it is hidden. Increasing or decreasing this value will increase or decrease the left start point of text on the printed page. Experimentation will fix the value for any given printer.

Tab Spacing Integer 200 This control appears when Select Option is set to "Print". Otherwise it is hidden. Increasing or decreasing this value will increase or decrease the horizontal spacing of tabbed sections of text on the printed page. Ex-perimentation will fix the value for any given printer.

Browse for File Name

Button Unpressed This control is enabled for all export options except "Print". For the re-maining options, this control must be selected. The browser dialog will appear where a path and filename must be specified for the export out-put.

File Name Text "" This control is always disabled and cannot be used to specify the file name or path for Text, Word or Excel export. Once the browser is used to selected a path and file name, those will be displayed in this control for review. Note that a path and file name MUST be specified for the "Text" and "Vision" export options and may be specified for "Excel" or "Word".

Help Button Unpressed Open this help document for review. OK Button Unpressed Accept the configured export and close the dialog. Exporting will occur

when the main data regraph dialog is closed. Cancel Button Unpressed Close the export dialog. Do not export.

Data can be exported to one of five targets:

Printer - Pre-formatted text is sent to the printer when the configuration dialog is closed. Before printing a printer setup dialog will appear, allowing printer options to be adjusted. With the release of Version 4.0.0, printer text can be formatted from within Vision by adjusting the Line Spacing, Left Margin and Tab Spacing integer values. Experimentation will show the proper settings for all exporting to

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the attached printer. These controls are hidden unless the printer is specified as the target. Version 4.0.0 also includes the addition of the Header Only check box. When checked, appropriate configuration parameters and measured values are sent to the printer, but the point-by-point exporting of the filtered data are omit-ted. This option saves many pages of paper and eliminates information that is likely superfluous in printed form.

Figure D.4.1 - Standard Windows Printer Configuration Dia-log.

Text File - Selecting this option enables the Browse for File Name button. Click-

ing this button will open a standard browser dialog in which a file name and path must be selected. If the file already exists, the output will be appended to existing text. An output file name must be specified for this export. Figures D.4.2 and D.4.3 show a partial sample of the text export from a file generated using differ-entiated Hysteresis Task data.

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Figure D.4.2 - Sample Hysteresis Filter Text Export File. Up-per Portion.

Figure D.4.3 - Sample Hysteresis Filter Text Export File. Lower Portion.

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Excel - Selecting this option enables the Browse for File Name button. Clicking this button will open a standard browser dialog in which a file name and path may be selected. Specifying a file name is optional. However, if specified, a unique file name/file path must be created or an overwrite situation will occur. Data are not appended to existing files. When the configuration dialog is closed, the Excel program will be started and a spread sheet created. When Excel is closed, the data will be written to the specified file name, or the user will be prompted to save if the file is not specified. Programmatic techniques for producing the Excel file were provided by Lacoude and Ketema2. Office '97 or Office 2000 must be loaded for this option. Office is not provided with the tester or Vision software. Utilities to write to Office 2003 or Office XP are not yet available. Figures D.4.4 and D.4.5 show a partial sample of the Excel export from a file generated using differentiated Hysteresis data.

Figure D.4.4 - Sample Hysteresis Filter Excel Export Output. Upper Portion.

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Figure D.4.5 - Sample Hysteresis Filter Excel Export Output. Lower Portion.

Word - Selecting this option enables the Browse for File Name button. Clicking

this button will open a standard browser dialog in which a file name and path may be selected. Specifying a file name is optional. The Word program will be opened and written when the regraph dialogs have been closed. If a new file name is specified, the document will be saved immediately. Word export to Office '97 de-pends on two template files - "Template.doc" and "Template2.doc"- located in "D:\DataSets" (C:\DataSets for the Precision LC tester family.). These are blank Word files. Template.doc is in portrait orientation with tabs at 1", 2.5", and 4". Template2.doc is in landscape orientation with tabs at 1", 2.5", 4" and 6". Both pages are set to Times New Roman 12 pt font. Word export output is formatted to align properly with these settings. Care must be taken not to overwrite the tem-plates. If no file name is specified, the user will be prompted to save the docu-ments when closed. If the documents are saved, the template file will be overwrit-ten. In this event, the file should be renamed appropriately and a new template file created with the specifications given above. Exporting to Word 2000 does not de-pend on the template files. Office '97 or Office 2000 must be loaded for this op-tion. Office is not provided with the tester or Vision software. Utilities to write to Office 2003 or Office XP are not yet available. The Word export option has been added as of Version 3.1.0. Office 2000 exporting is available as of Ver-sion 4.0.0.

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Figure D.4.6 - Sample Hysteresis Filter Word Export Output. Upper Portion.

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Figure D.4.7 - Sample Hysteresis Filter Word Export Output. Lower Portion.

Vision Data File - In this option, added as of Version 4.0.0., the Task configura-

tion parameters and measured data are written to a formatted binary file. Subse-quent instances of the Two-Trace Math Filter Task can be configured to import the data from the file, on execution, rather than making a new measurement. In this way, data can be moved from one DataSet to another where they can be grouped with other data and filtered. This utility is demonstrated in Figure D.4.8. Selecting this option enables the Browse for File Name button. Clicking this but-ton will open a standard browser dialog in which a file name and path may be se-lected. Specifying a file name is required.

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Figure D.4.8 - Utility of Vision Data File Exporting.

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E - Examples This page shows ten sample plots covering each data combination. The five Filters are each shown plotted as a function of Drive Voltage and as a function of Time in millisec-onds. Data were gathered on an actual ferroelectric sample. The Hysteresis speed was 1.0 ms and the voltages ranged over 3.0 Volts, 5.0 Volts, 7.0 Volts and 9.0 Volts. The 5.0-Volt and 7.0-Volt traces were selected for accumulation and filtering by the Hysteresis Filter Task. Standard plots as a function of voltage are shown first. These are followed by the plots represented as a function of Time.

E.1 - Standard Plots

E.1.1 - No Filter - The plot below shows the data with no filtering applied. The Hysteresis Filter, in this case, simply serves to gather the data from multiple Hys-teresis Tasks into a single plot. This is identical to using the Pass-Through Filter. Note that the first point for the traces is plotted at the origin.

Figure E.1.1.1 - No Filter Applied.

E.1.2 - Centering - Polarization is a relative value that, much like voltage, re-quires a reference for quantization. In a Hysteresis loop, no such reference exists.

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Instead, the first measured value is arbitrarily set to 0.0 µC/cm2 and used as the reference for all subsequent values. This produces a loop that begins at the origin and is shifted upward (downward for negative-starting loops) in polarization as shown in Figure E.1.1.1. A more classic representation is a loop that is balanced about the voltage axis. This representation is required to accurately compute and display PMax, ±Vc and ±Pr. To achieve this the average of the polarizations at the maximum absolute positive and negative voltages is subtracted from every meas-ured point in the loop. This is accomplished by the Centering filter and shown in the Figure below. A more complete mathematical description is found in Mathe-matical Discussion.

Figure E.1.2.1 - Centered Hysteresis Loops.

E.1.3 -Capacitance Vs Voltage - An alternative method of showing the response of a non-linear device such as a ferroelectric capacitor to a drive voltage profile is to represent the capacitance as a function of voltage. The capacitance can be de-fined as the derivative of the polarization with respect to voltage. The Capacitance Vs Voltage Filter performs this operation, along with noise reduction processing as shown in the figure below. This representation show can be used to infer the distribution of domains over the voltage required to switch them. It also provides an accurate determination of the coercive voltages. These are the voltages at

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which the plot peaks occur.

Figure E.1.3.1 - Derivative Capacitance Vs Voltage.

E.1.4 - Normalized Capacitance Vs Voltage - The Capacitance Vs Voltage rep-resentation described above can be extended to allow the direct comparison of several capacitors of varying electrode areas simple by dividing out the sample area that is part of the polarization term and remains in the calculation of Capaci-tance Vs Voltage. The effect of this is to scale the data and make it independent of sample area. This scaling is represented in the Figure below.

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Figure E.1.4.1 - Normalized Capacitance Vs Voltage.

E.1.5 - dP/dT Vs Voltage - In this plot the derivative of the polarization with re-spect to time is shown. Time is in milliseconds counted from the initial measure-ment point, that is given as zero. As with voltage, the magnitude of delta time is approximately constant throughout the Hysteresis loop, so that the dP/dT Vs Volt-age plot is a scaled version of the Capacitance Vs Voltage plot. However, time throughout the trace increases monotonically, whereas the sign of dV is normally the sign of dP. As a result, while the Capacitance Vs Voltage plot normally re-mains positive throughout the trace, dP/dT will go negative over those portions of the Hysteresis loop where dP is negative.

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Figure E.1.5.1 - Polarization Derivative with Respect to Time. E.2 - Plots Vs Time

With Plot Vs Time enabled, the five filters shown above can be plotted, not as function of voltage, but as as function of time in milliseconds, where the time at which each point was sampled serves as the independent variable. In this case, the first measured point is used as the reference, 0.0 ms point. The plots shown above are reiterated below with the Plot Vs Time control enabled.

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o E.2.1 - No Filter Vs Time

Figure E.1.1. - Polarization Vs Time with no Filtering.

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o E.2.2 - Centering Vs Time

Figure E.2.2.1 - Centered Polarization Vs Time.

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o E.2.3 - Capacitance Vs Time

Figure E.2.3.1 - Derivative Capacitance Vs Time.

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o E.2.4 - Normalized Capacitance Vs Time

Figure E.2.4.1 - Normalized Capacitance Vs Time.

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o E.2.5 - dP/dT Vs Time

Figure E.2.5.1 - Time Derivative Vs Time.

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F - Mathematical Description The Hysteresis Filter Tasks collects raw measured data, as reported by the measurement hardware, collected from one or more associated Hysteresis Tasks. The measured data are normally taken from a non-linear sample and represent the sample response, in polariza-tion (µC/cm2) to a stepped series of stimulus voltages applied to the sample and known collectively as a Hysteresis loop. Measured data collected by the Hysteresis Filter Task are then altered mathematically by the Task before plotting, exporting or storing. The math applied to the data depends on the filter. In many cases, once the initial filter is ap-plied, additional math is performed on the data to reduce its noise content. This section describes, in detail, the mathematical manipulation of the input data performed by each of the filters.

No Filter (<None>) -- This option performs no manipulation of the data, but re-ports them exactly as presented to the software by the measurement hardware.

Centering - Polarization is a relative value. Much like Voltage it requires a com-mon (zero) reference in order to assign a quantitative value. In the Hysteresis data reported, no such reference exists. Instead, the first measured polarization value is arbitrarily assumed to be 0.0 µC/cm2 and used as the reference for the remaining measured points in the Hysteresis loop. The result is a loop that begins at the Po-larization/Voltage origin and is vertically shifted in the direction of the sign of VMax, or the sign of the voltages of the first half of the Hysteresis loop (for nor-mal bipolar voltage profiles). The polarization is asymmetric about the voltage axis. A more common representation is a Hysteresis loop that is centered horizon-tally and vertically about the Polarization/Voltage origin. This representation is required to properly compute ±Pr, ±Vc and PMax. To arrive at this representation, the Centering filter compute the centered value at loop point t (Pc(t)) by subtracting the average of the uncentered polarizations at the maximum positive and negative voltages from the uncentered value a point t (P0(t)).

(F.1) Capacitance Vs Voltage - Considering the simple relationship:

(F.2) the non-linear capacitance of a ferroelectric sample can be derived from the Hys-teresis measurement by performing the numerical derivative, given by:

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(F.3) This is a very simple calculation. However it is also highly subject to noise. The noise primarily results from the very small denominator in the calculation. Volt-age steps from one measurement point to another can be very small. Even minute errors in the dV calculation, due for example to one-bit errors or round-off errors, can results in significantly large changes in the division represented in (F.3). Two noise reduction processes are applied during the calculation represented in (F.3). A third post-processing filter is applied to reduce noise that was generated by the calculation. The first process is to try to eliminate variations in the dV due to digitally-introduced error. To accomplish this, the denominator in (F.3) is replaced by a single constant value that is the average of the dV's over the entire Hysteresis trace. The average is simply given as:

(F.4) This renders (3) as:

(F.5) Both the calculation of the average dV given in (4) and the differentiation of (F.5) are further modified by reducing the total number of points differentiated. This is done by subsampling the points by selecting a subset that is incrementally extracted from the original data. This has the effect of increasing the voltage step size between selected points, thereby increasing the size of the denominator in (F.3) or the value of the average in (F.4). The subsample increment term is cur-rent 1 for traces of 400 points or less and 4 for Hysteresis loops of more than 400 points. That means that for traces of 400 points or less, (F.6) does not differ from (F.5). For traces of more than 400 points, every fourth point in the original data is selected to be applied to the subsampled data.

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(F.6)

Critical points are never differentiable. However, by considering a critical point as the end of one smooth series of data and the beginning of another, the point can be included in two smooth differentiations. This normally is represented by a separation of "smooth" portions of the differential representation at the end points. Subsampling can greatly exacerbate noise near a critical point and even result in an improper change of sign for the differentiation. Consider the three figures below.

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Figure F.1a - Subsampling-Induced Noise Around a Critical Point.

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Figure F.b1 - Subsampling-Induced Noise Around a Critical Point.

In these figures the polarization trace in red is simply a synthetic data representa-tion and is not intended to simulate expected sample data of any sort. However, as the polarization term for the calculation appears in the numerator of (F.6) it is not of real concern. The Voltage trace could be taken to represent the top of the positive leg of a standard bipolar drive profile. In any case, it well represents the discussion. In the first figure, the critical point occurs at the subsample point. In this case no new error is introduced. However, in the second figure, two sequen-tial subsample points straddle the measurement point. Both dP and dV are re-duced. In the synthetic, symmetric case presented, the reduction should scale for them. However, for real data, the symmetry in dP cannot be assumed. Further-more, the digital error due to round-off or truncation and bit-error becomes a lar-ger proportion of the smaller dV, introducing more significant error The most extreme case is shown in the third figure. Here the subsample points evenly straddle the critical point. In the representation both dP and dV are ideally zero. However for real data, dP, with no noise, will generally be non-zero. Equa-

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tion (F.3) traps dV = 0.0. But round-off and bit errors can make dV non-zero, with its value entirely due to error. Further more, with error acting on both sam-ple points, the sign of dV cannot be predicted. Large errors that may cross the voltage axis can result from (F.3). These are essentially eliminated in (F.6) by us-ing the constant average in the denominator. However, the calculation of the de-nominator itself is subject to the slight introduction of error as of dV around critical points is added into the sum in (F.4). Once the derivative is calculated with the error-reducing methods described above, it is not assumed that the data are error free. Instead the data are passed through an additional 9-point weighted moving average smoothing filters. This technique replaced Capt with a weighted average of itself and its nine nearest neighbors. For optimal smoothing, the Savitszky-Golay coefficients for a nine-point symmetric moving average were used as described in [1]. In steady state, the smoothing is given by:

(F.7)

Figure F.2 - Nine-Point Smoothing Using Savitszky-Golay Co-

efficients.

Note that near the trace endpoints (F.7) is modified to discard points within the window that lie past the end points. In this case the total weight must be divided from the sum. The divided weight does not appear in (F.7) since the weights sum

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to 1.0. Note that the weights used are not altered near the end points, so that non-optimal coefficients are introduced at the boundaries. Furthermore, the algorithm given in (F.7) disregards critical points, continuing its calculation through and past them. This calculation may introduce additional error. Note that this filtering occurs after the calculation of the derivative and is done in the dependent Capaci-tance domain.

Normalized Capacitance Vs Voltage - The entire discussion above applies to the Normalized Capacitance Vs Voltage filter as well. The only difference is that the Normalized version does not multiply out the Area term from the polarization de-nominator as shown in figures (F.3), (F.5) and (F.6). Instead the applicable equa-tion is:

dP/dT - The discussion of the Capacitance Vs Voltage filter applies in its entirety

to this filter. In this case, however, the polarization is differentiated with respect to time instead of voltage. Furthermore, the Area in the denominator of the polari-zation term is left in. Equation (3) becomes:

and Equation (F.6) becomes:

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G - Change and Version Record

Version 3.0.0 - 17 December 2001 1. Set to Version 3.0.0 for development of the next release. 17 December 2001 -

SPC. Version 3.1.0 - 14 March 2002

1. Set to Version 3.1.0 for release - 3/14/02 - SPC. 2. Initial Word Export feature was added. 5 April 2002 - SPC. 3. Add Plot Vs Field X-Axis option. 18 July 2002 - SPC. 4. Installed an update that correctly handles data that vary in number of points as pa-

rameters are adjusted in a Branch Loop. 29 July 2002 - SPC. Version 3.1.1 - 4 October 2002

1. Set to Version 3.1.1 to account for various changed in the Task - 10/04/02 - SPC. 2. Eliminated the "Eye" icon - 10/04/02 - SPC. 3. Adjusted plot dialog text control sizes - 10/04/02 - SPC. 4. Eliminated the Data Label control - 11/04/02 - SPC. 5. Added Tool Tips - 12/06/02 - SPC.

Version 3.2.0 - 30 April 2003

1. Set to Version 3.1.1 to account for various changed in the Task - 4/30/03 - SPC. 2. Added Normalized Capacitance Vs Polarization filtering - 4/30/03 - SPC. 3. Added customized text spacing to printer exporting - 4/30/03 - SPC. 4. Added the Check Hysteresis Task as an input Task - 3/19/04 - SPC. 5. Added the Header-Only option to Word and printer exporting - 5/07/04 - SPC.

Version 4.0.0 - 18 October

1. Set to Version 4.0.0 for release - 10/18/04 - SPC. 2. Added Vision Data File I/O - 10/18/04 - SPC. 3. Adjusted icons of associated Hysteresis data Tasks to indicate their association

with a Filter Task - 5/02/05 - SPC.

Table of Contents - Ferroelectric and Multiferroic Testing · 2010-11-09 · TABLE OF CONTENTS ......

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