(Experiment) TMR data for a low product tunnel junction before and after correction for the negative resistance artifact. The correction reduces the measured TMR from 6.2% to 3.4% due to the overall increase in the resistance. 1 standard deviation of the measurement uncertainty is for the resistance and for the magnetic field.
(a) Typical schematic diagram of a four-point measurement where the current is driven from source to drain while measuring the voltage drop between and . This is often used, but poor model for CWDs; the diagram shown in (b) is a minimum representative diagram where the from (a) is expanded to two parallel resistor elements representing the device separated by a resistor element on the top and the bottom representing the finite size of the electrode across the device size. The voltage drops across these latter two resistors always contribute error, which can exceed the voltage drop across the device resistors when is small.
(Model) Voltage contour plots of CWD devices when the DUT resistance is large (top) and small (bottom) compared to the electrode resistance. The plots mirror the geometry of experimental devices and the height and width are noted in the upper plot. The colors represent the local voltage and the lines within the colors are contours marking 1/100 of the difference between and . In the upper plot nearly all the voltage is dropped across the DUT (which is obscured into the plane of the figure) and the measurement error is about 1%. At bottom, the voltage profile is dominated by the voltage drop across the electrodes so that and the measured resistance is negative. Even though the DUT has a resistance of , the measured resistance , a −230% error.
Schematic representation of the computation model. Each wire is represented as a two-dimensional array of resistors that are connected to form the DUT at a rectangular grid of nodes. In the DUT, the nodes on the upper wire are connected to a corresponding node on the lower wire by an additional “device” resistor .
(Model) The absolute measurement error as a function of device resistance and (inset) the corresponding relative error . When the relative error falls below −100%, the measured resistance is a negative number. The four traces model the error for a device that is symmetric (a), has geometric asymmetry (b), has resistive asymmetry (c), and has both asymmetries designed to match our experimental devices (d). The points shown for are calculated from Eq. (5). The parameters are given in Table I.
(Model) The absolute resistance error is shown as a function of asymmetry in geometry or resistivity. The junction resistance in all cases, so . The parameter ranges for each case are shown in Table II. for the geometric asymmetry and for the resistive asymmetries considered.
(Model) The relative error is shown for nonlinear tunnel devices due to varying voltage (, , and ). The ordinate axis voltage is . A voltage difference in the range −2.5 to 2.5 V was applied between and for all cases of , with most of the voltage drop occurring across the electrodes for .
(Model) Relative error of the correction compared to the computer model as a function of device resistance with no correction (uncorrected), by simply adding the constant to all measured values , and using the suggested correction method (corrected). The vertical line at is the point where .
(Experiment) Uncorrected differential resistance vs bias voltage data for an ultrathin barrier MTJ is shown, and then after correction. The three fit parameters obtained by fitting the data with Chow’s (Ref. 17) asymmetric tunneling model are superimposed for each case. The correction dramatically affects the best fit values. The standard deviation due to measurement error of the resistance is , and in bias is . Uncertainties in the fits are 1 standard deviation.
(Experiment) Uncorrected and corrected resistances vs temperature data for a MTJ is shown along with the calculated estimated for an ideal device with the same electrodes. For all three cases, the trends are fitted to estimate the contribution to the 78 K conductance due to the defect states . The negative resistance causes the ideal resistor to appear to have of the current at 78 K carried by defect states. For the experimental data, the correction reduces the estimate of defect state conduction from 14.5% to 3.6% (every 20th data shown). 1 standard deviation of uncertainty is in resistance and 0.1 K in temperature.
Model parameters for cases shown in Fig. 5.
Model parameters for the center and extrema of each curve shown in Fig. 6.
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