Method for measuring ultrafast ferroelectric hysteresis loop of ferroelectric capacitor

Abstract

The invention belongs to the technical field of solid dielectric material testing, and particularly relates to a method for measuring an ultrafast ferroelectric hysteresis loop of a ferroelectric capacitor. According to the equivalent circuit provided by the invention, the stray inductance in a line and the change of the partial voltage of the stray inductance along with time can be solved; meanwhile, a ferroelectric capacitor ferroelectric hysteresis loop correction method is provided. The method comprises the following steps: firstly, applying electric pulses with different polarities to a standard capacitor or a ferroelectric capacitor, and measuring partial voltages in a circuit in nanosecond magnitude time through a high-bandwidth oscilloscope, including the partial voltage of a circuit total resistor and the partial voltage of the ferroelectric capacitor; by correcting the influence of stray inductance, the circuit current at each moment is obtained, then the charging and discharging current and the electric domain reversal current of the ferroelectric capacitor are obtained, the charging and discharging current and the electric domain reversal current are converted into a ferroelectric hysteresis loop within the nanosecond magnitude time range, and the ferroelectric polarization intensity and the coercive field under different periods are obtained from the ferroelectric hysteresis loop. According to the method, the ferroelectric hysteresis loop with the nanosecond-level period is accurately measured by establishing the equivalent circuit model.

Description

Technical Field

[0001] The invention belongs to the technical field of solid dielectric material testing, and in particular relates to a method for measuring an ultrafast hysteresis loop of a ferroelectric capacitor with a nanosecond period. Background Art

[0002] Ferroelectric materials have high spontaneous polarization and large dielectric constant, and can be used in non-volatile random access memory (FeRAM), dynamic random access memory (DRAM), uncooled infrared detectors, thin film dielectric capacitors, electric field modulated microwave devices, AC electroluminescent devices and thin film sensors. With the increase of device integration density, the size of device units has been greatly reduced, approaching the atomic or molecular level. It is expected that the storage density of FeRAM and DRAM in the future can reach ~Tb / in 2 The quantum tunneling current of this ultra-thin film will increase exponentially with the decrease of film thickness, and the magnitude of the tunneling current will change significantly with the change of the polarization direction of the electric domain, that is, a polarization modulated electroresistance effect (TER) will be generated [References 1-5], which can be used for high-density information non-volatile storage. However, how to quantitatively measure the spontaneous polarization intensity of ferroelectric leakage films based on the TER principle has become an international problem. In addition, commercial FeRAM products generally use insulating ferroelectric films and charge integration methods for information destructive reading, such as lead zirconate titanate and hafnium oxide films, with a read and write time of 10-20ns and a storage capacity of 64Mb [References 6,7]. However, current measurement technology cannot measure its ferroelectric hysteresis loop within nanoseconds, which affects the development of ferroelectric memory devices with high-speed read and write performance.

[0003] Applying square pulse or triangular pulse signals to ferroelectric capacitors is the most commonly used method to study the basic process of polarization reversal of ferroelectrics. However, the test principles of current commercial ferroelectric testers (such as the Premier series of Radiant Corporation in the United States and the TF 2000 series of aixACCT in Germany) are based on Sawyer-Tower or Virtual Ground circuits, with low measurement frequencies, and can only measure some highly insulating ferroelectric film capacitors. The measurement frequency is lower than 1MHz, and it is impossible to characterize insulating / leaky ferroelectric films or two-dimensional ferroelectric semiconductor materials with nanosecond read and write speeds, which affects the development of ferroelectric functional devices with ultrafast response.

[0004] Different from the Sawyer-Tower or Virtual Ground circuit, Jiang et al. have greatly expanded the limitations of the pulse measurement method and greatly improved the accuracy of the pulse measurement method by continuously improving the electric pulse measurement method (Chinese patent CN200910054686.1; Chinese patent CN200910195455.2; Chinese patent CN201110000987.3; Chinese patent CN201210038180.3; Chinese patent CN201180002911.2; US patent US9354192B2). For example, Jiang et al. proposed a relatively accurate domain reversal current density J based on the domain reversal current density J. SW and the evaluation method of the domain reversal dynamic mechanism of the domain reversal coercive field Ec; at the same time, Jiang et al. realized the conversion of the domain reversal current curve into a hysteresis loop by the electric pulse method, and the hysteresis loop measurement period was greatly reduced to the domain reversal time; in addition, Jiang et al. also realized the distinction between the conduction current and the reversal current of the leakage ferroelectric film by the electric pulse method, and realized the ultrafast measurement of the hysteresis loop of the leakage ferroelectric film. Although the above pulse measurement technology can realize the measurement of hysteresis loops with a period of more than 100ns, which is 10-100 times faster than the measurement speed of Sawyer-Tower or Virtual Ground circuits, it is limited by the influence of the parasitic effects of the line and cannot accurately characterize the ferroelectric hysteresis loop with a period of less than 100ns. The present invention proposes an effective equivalent circuit, which can calculate the stray inductance in the circuit by measuring the signal with an oscilloscope, and deduct the influence of the above stray inductance from the measurement signal of the sample, so as to realize the measurement of the hysteresis loop of the nanosecond ferroelectric film, which is equivalent to the reading and writing speed of FeRAM, filling the gap in international metrology. Summary of the invention

[0005] The purpose of the present invention is to provide a method for measuring the ultrafast hysteresis loop of a ferroelectric capacitor, so as to improve the measurement accuracy of the hysteresis loop based on the previous pulse measurement technology and realize the measurement of the hysteresis loop of the ferroelectric film under the ultrafast polarization period of nanosecond level.

[0006] The method for measuring the ultrafast hysteresis loop of a ferroelectric capacitor provided by the present invention first constructs a test circuit and its equivalent circuit; wherein:

[0007] The test circuit is composed of a signal generator, a ferroelectric capacitor to be tested / standard capacitor, a high-frequency data acquisition card or a high-bandwidth oscilloscope, and a standard resistor in series; the standard resistor and the high-frequency data acquisition card or the high-bandwidth oscilloscope are connected in series or in parallel; see Figure 1 As shown;

[0008] The equivalent circuit is composed of a signal generator, a ferroelectric capacitor to be tested / standard capacitor, stray inductance and a total circuit resistance connected in series; the electric pulse signal emitted by the signal generator is V std (t) represents; the ferroelectric capacitor to be tested / standard capacitor voltage is divided by V s (t) represents; the stray inductance is represented by L, and the voltage division is represented by V L (t) represents; the total resistance of the circuit is represented by R tot Indicates that the voltage is divided by V R (t) represents; the sum of the divided voltages of the stray inductance and the total circuit resistance is directly measured by the high-frequency data acquisition card or the high-bandwidth oscilloscope, and is represented by V Osc (t); the loop current corrected by the iterative formula is represented by I(t), and the loop current obtained by the standard capacitor charging and discharging formula is represented by i(t); the equivalent circuit can calculate the stray inductance in the circuit and obtain the corrected ferroelectric capacitor hysteresis loop; see Figure 2 shown.

[0009] The method for measuring the ultrafast hysteresis loop of a ferroelectric capacitor provided by the present invention comprises the following specific steps:

[0010] (1) Connect the standard capacitor to the test circuit, apply an electric pulse, and measure the total resistance R of the circuit using an oscilloscope or data acquisition card. tot The voltage across the stray inductance L changes with time, and the stray inductance L inside the circuit is calculated; the specific process is:

[0011] Step a: Connect a standard capacitor to the test circuit. The standard capacitor size is C. s , the total circuit resistance R tot It is composed of the internal resistance of the signal generator, the internal resistance of the oscilloscope and the standard resistance connected in parallel with the oscilloscope, which is known; a bipolar electrical pulse signal V is generated by the signal generator. std (t), record the relationship between the total circuit resistance and the voltage across the stray inductance over time using an oscilloscope or acquisition card V Osc (t);

[0012] Step b, according to the formula:

[0013]

[0014] The estimated stray inductance L is obtained, where i(t) is the circuit current based on the standard capacitance, which is calculated by the following formula:

[0015]

[0016] Step c, fine-tune the estimated stray inductance L and arrange the V Osc(t) The corrected circuit current I(t) is obtained according to an iterative formula; the iterative formula is a differential formula obtained by converting the following formula:

[0017]

[0018] Step d, integrating the corrected circuit current I(t) in step c according to time can obtain the charge Q(t) stored in the standard capacitor, that is, At the same time, the voltage V across the standard capacitor S (t) can be obtained using the following formula:

[0019] V S (t) = V std (t)-V Osc (t); (4)

[0020] Step e, the charge Q(t) stored in the standard capacitor in step d and the voltage V across the standard capacitor S (t) According to Q(t)~V S (t) Plotting, when the curve composed of the data points is a line passing through the origin and with a slope of the standard capacitance value C s If the curve formed by the data points is not a straight line passing through the origin and with a slope of the standard capacitance value C, it means that the correct stray inductance L is obtained; otherwise, s When the straight line is obtained, repeat steps c to e;

[0021] (2) Connecting the ferroelectric capacitor to be tested to the test circuit, calibrating the domain reversal current curve and converting it into a ferroelectric hysteresis loop; the specific process is as follows:

[0022] Step a: connect the ferroelectric capacitor to be tested to the same test circuit and use a signal generator to generate a bipolar electrical pulse signal V std (t), the relationship between the total circuit resistance and the voltage across the stray inductance over time is recorded by an oscilloscope V Osc (t);

[0023] Step b: V in the form of an array arranged in time Osc (t), and calculate the corrected circuit current I(t) according to the iterative formula; the iterative formula is a differential formula obtained by converting the following formula;

[0024]

[0025] The corrected circuit current I(t) is the domain reversal current curve formula of the ferroelectric film;

[0026] Step c, integrating the corrected circuit current I(t) in step b with respect to time to obtain the polarization intensity P(t) of the ferroelectric film:

[0027]

[0028] Where S is the electrode area; the voltage V across the ferroelectric capacitor is s (t) is obtained by the following formula:

[0029] V s (t) = V std (t)-V Osc (t); (7)

[0030] Step d, the polarization intensity P(t) of the ferroelectric film in step c and the voltage V across the ferroelectric capacitor s (t) According to P(t)~V S (t) After plotting, the curve composed of the obtained data points is the final corrected hysteresis loop of the ferroelectric capacitor.

[0031] Furthermore, the differential formula can be converted into a first-order, second-order or higher-order differential formula according to the required accuracy requirements. For example, the first-order differential formula includes but is not limited to one of the following forms:

[0032]

[0033] Furthermore, without changing the test circuit settings, the stray inductance L will not change due to the pulse signal width, pulse signal size, or different samples being tested;

[0034] Furthermore, the voltage magnitude and pulse width of the bipolar pulse signal are not limited, for example, the voltage magnitude is -100V to 100V, and the pulse width time is greater than or equal to 0.1ns and less than or equal to 100s;

[0035] Furthermore, the resistance value of the standard resistor is not limited, for example, greater than or equal to 1Ω and less than or equal to 100MΩ;

[0036] Furthermore, the standard capacitor has no limitation on size, and is greater than or equal to 0.1 pF and less than or equal to 10 nF.

[0037] The present invention improves the calculation method of the previous domain reversal current curve, corrects the error caused by the stray inductance in the circuit, greatly broadens the limitation of the electric pulse measurement method for measuring the domain reversal current curve of the ferroelectric film, and after correction, the domain reversal current curve can be correctly read out below 100ns, and the hysteresis loop of the nanosecond period of the ferroelectric film can be accurately obtained. When the test circuit is not changed, the stray inductance L will not change, which greatly facilitates the subsequent testing of different ferroelectric capacitors. Based on this method, the measurement of the hysteresis loop of the nanosecond-level ferroelectric film can be realized, which is conducive to the development of ferroelectric functional devices with ultrafast polarization response. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is the schematic diagram of the pulse method measurement circuit.

[0039] Figure 2 This is the equivalent circuit diagram of the pulse method measurement circuit.

[0040] Figure 3 The bipolar electrical pulse signal used to measure standard capacitance and the voltage curve across the total circuit resistance and stray inductance recorded by an oscilloscope.

[0041] Figure 4 It is the measured uncorrected QV curve of the standard capacitor and the ideal QV curve of the standard capacitor.

[0042] Figure 5 The QV curve of the standard capacitor is correctly corrected for the measured data.

[0043] Figure 6 The uncorrected QV curve obtained by taking stray inductance into consideration using software simulation and the QV curve corrected using the correction algorithm provided by the present invention are shown.

[0044] Figure 7 The bipolar electric pulse signal used to measure the ferroelectric film and the voltage curve across the total circuit resistance and stray inductance recorded by the oscilloscope.

[0045] Figure 8 This is the uncorrected ferroelectric hysteresis loop of the hafnium zirconium oxide ferroelectric capacitor.

[0046] Fig. 9 This is the ferroelectric hysteresis loop of the hafnium zirconium oxide ferroelectric capacitor after correct correction. DETAILED DESCRIPTION

[0047] The present invention is further described below by way of embodiments in combination with the accompanying drawings. Based on the embodiments, all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection of the present invention.

[0048] Example:

[0049] In this embodiment, the pulse signals required for the test are provided by an Agilent 81110A pulse generator, and the total circuit resistance R tot The voltage across the stray inductance L is recorded by a LeCroy 6200A oscilloscope, R tot =100Ω.

[0050] Figure 1The test circuit diagram used in the present invention is shown in FIG. The capacitance value of the standard capacitor selected in this embodiment is 30 pf, and the ferroelectric capacitor is a hafnium zirconium oxide film capacitor (HZO) sample (electrode area: square 20 μm×20 μm).

[0051] 1. Connect the standard capacitor to the test circuit, apply an electric pulse, and measure R using an oscilloscope or data acquisition card. tot The voltage across L changes with time, and the internal stray inductance L of the circuit is calculated:

[0052] Step a: Connect a 30pf standard capacitor to the test circuit. The total resistance of the circuit is R tot =100Ω; Use the pulse generator to send out bipolar electrical pulses V std (t) (bipolar pulse width is 40ns, voltage is ±1.5V), use an oscilloscope to record the change of the total resistance and stray inductance of the circuit over time V Osc (t), V std (t) and V Osc The waveform of (t) is as follows Figure 3 As shown;

[0053] Step b, according to the formula The stray inductance L is initially guessed. The i(t) in the formula is the circuit current based on the standard capacitance. Find; In this example, the calculated result is 0.39μH;

[0054] Step c, fine-tune the estimated stray inductance L and arrange the V Osc (t) according to the iterative formula to obtain the corrected circuit current I(t); the iterative formula is given by The difference formula obtained by conversion;

[0055] Step d, integrating the corrected circuit current I(t) in step c according to time can obtain the charge Q(t) stored in the standard capacitor, that is, At the same time, the voltage V across the standard capacitor S (t) can be obtained using the formula V S (t) = V std (t)-V Osc (t) obtain;

[0056] Step e, when L=0.48 μH, the charge Q(t) stored in the standard capacitor in step d and the voltage V across the standard capacitor are S (t) According to Q(t)~V S (t) Plot the data points to form a straight line that passes through the origin and has a slope close to the standard capacitance value of 30 pf (e.g. Figure 5The uncorrected QV curve (as shown in Figure 4 The solid line shows that the capacitor deviates significantly from the ideal QV curve of the standard capacitor (shown as Figure 4 dotted line).

[0057] At the same time, in this embodiment, the bipolar pulse with a width of 20ns and a voltage of ±3V are used to simulate the same stray inductance effect, and the uncorrected QV curve is obtained by simulation (such as Figure 6 solid line), and Figure 4 The actual measured results shown by the solid line are relatively close; using the same stray inductance value and the same steps c to e, the correct QV curve is also obtained (such as Figure 6 The dashed line shows the correctness of considering the stray inductance effect.

[0058] 2. Connect the ferroelectric capacitor to be tested to the test circuit, calibrate the domain reversal current curve and convert it into a ferroelectric hysteresis loop:

[0059] Step a: connect the ferroelectric capacitor to be tested to the same test circuit and use a pulse generator to send a bipolar electrical pulse signal V std (t) (the pulse width increases logarithmically from 20ns to 10μs, and the voltage is ±3V). Use an oscilloscope to record the change of the voltage across the total resistance and stray inductance over time. Osc (t), and obtain V of 240ns std (t) and V Osc (t) waveform (respectively as Figure 7 Solid and dotted lines);

[0060] Step b: V in the form of an array arranged in time Osc (t), and the corrected circuit current I(t) is obtained according to the iterative formula; the iterative formula is given by The differential formula obtained by conversion; the corrected circuit current I(t) is the domain reversal current curve formula of the ferroelectric film;

[0061] Step c, integrating the corrected circuit current I(t) in step b with respect to time can obtain the polarization intensity P(t) of the ferroelectric film, that is, The S in the formula is the area of ​​the ferroelectric film (S = 20 μm × 20 μm); at the same time, the voltage V across the ferroelectric capacitor is s (t) can be obtained using the formula V s (t) = V std (t)-V Osc (t) obtain;

[0062] Step d, the polarization intensity P(t) of the ferroelectric film in step c and the voltage V across the ferroelectric capacitor s (t) According to P(t)~V S (t) After plotting, the curve composed of the obtained data points is the final corrected hysteresis loop of the ferroelectric capacitor; Figure 8 The ferroelectric hysteresis loop of the hafnium zirconium oxide ferroelectric capacitor that has not been corrected is shown in Figure 2. The shape of its high-frequency hysteresis loop is abnormal due to the stray inductance effect. For example, under different period changes, as the period increases (gradually from 69ns to 2.11us), the positive and negative coercive voltages obtained obviously violate the Merz law. The ferroelectric hysteresis loop after correct correction is shown in Figure 2. Fig. 9 As shown, it can be clearly observed that both the positive and negative coercive voltages are corrected. As the period increases (gradually from 69ns to 2.11us), the positive and negative coercive voltages gradually decrease (at higher frequency periods, the maximum voltage emitted by the pulse generator is 3V, so the actual size is not shown), which is in line with Merz's law. At the same time, the shape of the hysteresis loop is significantly improved.

[0063] References:

[0064] [1]MYZhuravlev, et al. Giant Electroresistance in Ferroelectric Tunnel Junctions. Phys. Rev. Lett. 94, 246802 (2005).

[0065] [2]EYTsymbal and H.Kohlstedt, Tunneling Across a Ferroelectric.Science313,181(2006).

[0066] [3]V.Garcia,et al.Giant tunnel electroresistance for non-destructivereadout of ferroelectric states.Nature 460,81(2009).

[0067] [4] A. Gruverman, et al. Tunneling electroresistance effect inferroelectric tunnel junctions at the nanoscale. Nano Lett. 9, 3539 (2009).

[0068] [5]P.Maksymovych,et al.Polarization Control ofElectron Tunneling intoFerroelectric Surfaces.Science 324,1421(2009).

[0069] [6]J.F.Scott,Ferroelectric Memories.Springer.Heidelberg,Germany 2000.

[0070] [7]Y.Shimojo,et al.High-density and high-speed 128Mb chain FeRAM TM withSDRAM-compatible DDR2 interface.Symp.VLSI Tech.Dig.p.218-219,2009。

Claims

1. A method for measuring ultrafast hysteresis loop of ferroelectric capacitor, characterized in that: First, build the test circuit and its equivalent circuit; where: The test circuit is composed of a signal generator, a ferroelectric capacitor to be tested / a standard capacitor, a high-frequency data acquisition card or a high-bandwidth oscilloscope, and a standard resistor in series; the standard resistor and the high-frequency data acquisition card or the high-bandwidth oscilloscope are connected in series or in parallel; The equivalent circuit is composed of a signal generator, a ferroelectric capacitor to be tested / standard capacitor, a stray inductance and a total circuit resistance connected in series; the electric pulse signal emitted by the signal generator is V std (t) represents; the ferroelectric capacitor to be tested / standard capacitor voltage is divided by V s (t) represents; the stray inductance is represented by L, and the voltage division is represented by V L (t) represents; the total resistance of the circuit is represented by R tot Indicates that the voltage is divided by V R (t) represents; the sum of the divided voltages of the stray inductance and the total circuit resistance is directly measured by the high-frequency data acquisition card or the high-bandwidth oscilloscope, and is represented by V Osc (t); the loop current corrected by the iterative formula is represented by I(t), and the loop current obtained by the standard capacitor charging and discharging formula is represented by i(t); the equivalent circuit can calculate the stray inductance in the circuit and obtain the corrected ferroelectric capacitor hysteresis loop; The specific steps for measuring the ultrafast hysteresis loop of a ferroelectric capacitor are as follows: (1) Connect the standard capacitor to the test circuit, apply an electric pulse, and measure the total resistance R of the circuit using an oscilloscope or data acquisition card. tot The voltage across the stray inductance L changes with time, and the stray inductance L inside the circuit is calculated; the specific process is: Step a: Connect a standard capacitor to the test circuit. The standard capacitor size is C. s , the total circuit resistance R tot It is composed of the internal resistance of the signal generator, the internal resistance of the oscilloscope and the standard resistance connected in parallel with the oscilloscope, which is known; a bipolar electrical pulse signal V is generated by the signal generator. std (t), record the relationship between the total circuit resistance and the voltage across the stray inductance over time using an oscilloscope or acquisition card V Osc (t); Step b, according to the formula: The estimated stray inductance L is obtained, where i(t) is the circuit current based on the standard capacitance, which is calculated by the following formula: Step c, fine-tune the estimated stray inductance L and arrange the V Osc (t) The corrected circuit current I(t) is obtained according to an iterative formula; the iterative formula is a differential formula obtained by converting the following formula: Step d, integrating the corrected circuit current I(t) in step c according to time can obtain the charge Q(t) stored in the standard capacitor, that is, At the same time, the voltage V across the standard capacitor S (t) can be obtained using the following formula: V S (t)=V std (t)-V Osc (t) ; (4) Step e, the charge Q(t) stored in the standard capacitor in step d and the voltage V across the standard capacitor S (t) According to Q(t)~V S (t) Plotting, when the curve composed of the data points is a line passing through the origin and with a slope of the standard capacitance value C s If the curve formed by the data points is not a straight line passing through the origin and with a slope of the standard capacitance value C, it indicates that the correct stray inductance L is obtained; otherwise, s When the straight line is obtained, repeat steps c to e; (2) Connecting the ferroelectric capacitor to be tested to the test circuit, calibrating the domain reversal current curve and converting it into a ferroelectric hysteresis loop; the specific process is as follows: Step a: connect the ferroelectric capacitor to be tested to the same test circuit and use a signal generator to generate a bipolar electrical pulse signal V std (t), the relationship between the total circuit resistance and the voltage across the stray inductance over time is recorded by an oscilloscope V Osc (t); Step b: V in the form of an array arranged in time Osc (t), and calculate the corrected circuit current I(t) according to the iterative formula; the iterative formula is a differential formula obtained by converting the following formula; The corrected circuit current I(t) is the domain reversal current curve formula of the ferroelectric film; Step c, integrating the corrected circuit current I(t) in step b with respect to time to obtain the polarization intensity P(t) of the ferroelectric film: Where S is the electrode area; the voltage V across the ferroelectric capacitor is s (t) is obtained by the following formula: V s (t)=V std (t)-V Osc (t); (7) Step d, the polarization intensity P(t) of the ferroelectric film in step c and the voltage V across the ferroelectric capacitor s (t) According to P(t)~V S (t) After plotting, the curve composed of the obtained data points is the final corrected hysteresis loop of the ferroelectric capacitor.

2. The method for measuring the ultrafast hysteresis loop of a ferroelectric capacitor according to claim 1, characterized in that: The differential formula is converted into a first-order, second-order or higher-order differential formula according to the required accuracy requirements; wherein the first-order differential formula is one of the following:

3. The method for measuring the ultrafast hysteresis loop of a ferroelectric capacitor according to claim 1, characterized in that: The voltage of the bipolar pulse signal is between -100V and 100V, and the pulse width is greater than or equal to 0.1ns and less than or equal to 100s.

4. The method for measuring the ultrafast hysteresis loop of a ferroelectric capacitor according to claim 1, characterized in that: The standard resistor has a resistance greater than or equal to 1Ω and less than or equal to 100MΩ.

5. The method for measuring the ultrafast hysteresis loop of a ferroelectric capacitor according to claim 1, characterized in that: The standard capacitance is greater than or equal to 0.1 pF and less than or equal to 10 nF.

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