Method for measuring ultrafast hysteresis loop of ferroelectric capacitor

Abstract

The application belongs to the technical field of solid-state dielectric material testing, and particularly relates to a ferroelectric capacitor ultrafast hysteresis loop measuring method. The application proposes an equivalent circuit, which can obtain the stray inductance in the circuit and the voltage division of the stray inductance changing with time; and proposes a ferroelectric capacitor hysteresis loop correction method; first, different polarity electric pulses are applied on a standard capacitor or a ferroelectric capacitor, the voltage division in the circuit in the nanosecond time is measured by a high-bandwidth oscilloscope, including the voltage division of the total resistance of the circuit and the voltage division of the ferroelectric capacitor; then, the influence of the stray inductance is corrected to obtain the circuit current at each moment, and then the charging and discharging current and the domain reversal current of the ferroelectric capacitor are obtained, and they are converted into the ferroelectric hysteresis loop in the nanosecond time range, and the ferroelectric polarization intensity and the coercive field size under different periods are obtained from the ferroelectric hysteresis loop. The application accurately measures the ferroelectric hysteresis loop with a period of nanoseconds by establishing an equivalent circuit model.

Description

Technical Field

[0001] This invention belongs to the field of solid dielectric material testing technology, specifically relating to an ultrafast hysteresis loop measurement method for nanosecond-level periods of ferroelectric capacitors. Background Technology

[0002] Ferroelectric materials possess high spontaneous polarization intensity and large dielectric constant, making them suitable for applications such as 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 increasing device integration density, the size of device units is shrinking dramatically, approaching the atomic or molecular level. It is projected that future FeRAM and DRAM storage densities will reach ~Tb / in. 2 The read / write speeds are on the order of nanoseconds (ns-ps), approaching the level of current magnetic recording hard drives manufactured using vertical technology. With increasing density, the quantum tunneling current of this ultrathin film increases exponentially with decreasing film thickness, and the magnitude of the tunneling current changes significantly with the change in domain polarization direction, generating a polarization-modulated electroresistivity (TER) effect [References 1-5]. This can be applied to high-density non-volatile information storage. However, quantitatively measuring the spontaneous polarization intensity of ferroelectric leakage films based on the TER principle has become an international challenge. Furthermore, commercial FeRAM products generally use insulating ferroelectric films and charge integration methods for destructive information reading, such as lead zirconate titanate and hafnium oxide films, achieving read / write times of 10-20 ns and storage capacities of up to 64 Mb [References 6,7]. However, current measurement techniques cannot measure the ferroelectric hysteresis loop within nanosecond timeframes, hindering the development of ferroelectric storage devices with high-speed read / write performance.

[0003] Applying square or triangular pulse signals to ferroelectric capacitors is the most common method for studying the fundamental process of polarization reversal in ferroelectric materials. However, current commercial ferroelectric testing instruments (such as the Premier series from Radiant Corporation in the United States and the TF 2000 series from AixACCT in Germany) are based on Sawyer-Tower or Virtual Ground circuits. They have low measurement frequencies and can only measure some highly insulating ferroelectric thin-film capacitors. The measurement frequency is below 1MHz, which cannot characterize insulating / leakage ferroelectric thin films or two-dimensional ferroelectric semiconductor materials with nanosecond-level read / write speeds, thus affecting the development of ferroelectric functional devices with ultrafast responses.

[0004] Unlike Sawyer-Tower or Virtual Ground circuits, Jiang et al. significantly expanded the limitations of pulse measurement methods and greatly improved their accuracy by continuously refining the electrical 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 more accurate method based on domain reversal current density J... SW This invention provides an evaluation method for the domain reversal dynamics mechanism of the domain reversal coercive field Ec. Simultaneously, Jiang et al. achieved the conversion of the domain reversal current curve into a hysteresis loop using an electric pulse method, significantly reducing the hysteresis loop measurement period to the domain reversal time. Furthermore, Jiang et al. also used the electric pulse method to distinguish between the conduction current and reversal current of leakage ferroelectric thin films, achieving ultrafast measurement of the hysteresis loop of leakage ferroelectric thin films. While the above pulse method measurement techniques can achieve the measurement of hysteresis loops with periods exceeding 100 ns, which is 10-100 times faster than Sawyer-Tower or Virtual Ground circuits, they are limited by the parasitic effects of the circuit and cannot accurately characterize ferroelectric hysteresis loops with periods below 100 ns. This invention proposes an effective equivalent circuit that can calculate the stray inductance in the circuit by measuring the signal with an oscilloscope and subtract the influence of the stray inductance from the sample's measurement signal, achieving nanosecond-level measurement of the hysteresis loop of ferroelectric thin films, comparable to the read / write speed of FeRAM, filling a gap in international metrology. Summary of the Invention

[0005] The purpose of this invention is to propose an ultrafast hysteresis loop measurement method for ferroelectric capacitors, so as to improve the measurement accuracy of hysteresis loops based on pulse measurement technology and realize the measurement of hysteresis loops of ferroelectric thin films under nanosecond-level ultrafast polarization cycles.

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

[0007] The test circuit consists of a signal generator, a ferroelectric capacitor under test / standard capacitor, a high-frequency data acquisition card or a high-bandwidth oscilloscope, and a standard resistor connected in series; the standard resistor is connected in series or parallel with the high-frequency data acquisition card or high-bandwidth oscilloscope; see [link to documentation]. Figure 1 As shown;

[0008] The equivalent circuit consists of a signal generator, a ferroelectric capacitor / standard capacitor under test, stray inductance, and total circuit resistance connected in series; the electrical pulse signal emitted by the signal generator is V std (t) represents the voltage divider between the ferroelectric capacitor under test and the standard capacitor, which is determined by V. s (t) represents the value; the magnitude of the stray inductance is represented by L, and the voltage division is represented by V. L (t) represents the total resistance of the circuit, which is determined by R. tot This means that the voltage divider is determined by V. R (t) indicates that the sum of the voltage divisions of the stray inductance and the total circuit resistance is directly measured by the high-frequency data acquisition card or high-bandwidth oscilloscope, and is determined by V. Osc (t) represents the loop current corrected by the iterative formula, and I(t) represents the loop current obtained by the standard capacitor charging and discharging formula. The equivalent circuit can calculate the stray inductance in the circuit and obtain the corrected hysteresis loop of the ferroelectric capacitor. See also Figure 2 As shown.

[0009] The method for measuring the ultrafast hysteresis loop of ferroelectric capacitors provided by this invention includes the following specific steps:

[0010] (1) Connect a standard capacitor to the test circuit, apply an electrical pulse, and measure the total resistance R of the circuit using an oscilloscope or data acquisition card. tot The stray inductance L inside the circuit is calculated by varying the voltage across it over time. The specific process is as follows:

[0011] Step a: Connect a standard capacitor to the test circuit. The standard capacitor has a value of C. s The total resistance R of the circuit tot The signal generator consists of the internal resistance of the signal generator, the internal resistance of the oscilloscope, and a standard resistor connected in parallel with the oscilloscope, which are known. A bipolar electrical pulse signal V is generated using the signal generator. std (t), record the relationship between the total resistance and the voltage across the stray inductance of the circuit and time using an oscilloscope or data acquisition card. 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 capacitor, and is calculated using the following formula:

[0015]

[0016] Step c: Fine-tune based on the estimated stray inductance L, and arrange V in array form according to time. Osc(t) Calculate the corrected circuit current I(t) according to the iterative formula; the iterative formula is a difference formula derived from the following equation:

[0017]

[0018] Step d: By integrating the corrected circuit current I(t) from step c over time, the charge Q(t) stored in the standard capacitor can be obtained, i.e. 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 are... S (t) according to Q(t)~V S (t) Plot the data points so that the curve formed by the data points passes through the origin and has a slope equal to the standard capacitance value C. s If the curve is a straight line, it indicates that the correct stray inductance L has been obtained; otherwise, if the curve formed by the data points is not a straight line passing through the origin and has a slope equal to the standard capacitance value C, then the correct stray inductance L has been obtained. s When the line is straight, repeat steps c to e;

[0021] (2) Connect the ferroelectric capacitor under test to the test circuit, correct the domain reversal current curve and convert it into a ferroelectric hysteresis loop; the specific process is as follows:

[0022] Step a: Connect the ferroelectric capacitor under test 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 resistance and the voltage across the stray inductance of the circuit and time is recorded using an oscilloscope. Osc (t);

[0023] Step b, V is in array form, sorted by time. Osc (t), the corrected circuit current I(t) is obtained according to the iterative formula; the iterative formula is a difference formula obtained by transforming the following formula;

[0024]

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

[0026] Step c: Integrate the corrected circuit current I(t) from step b over time to obtain the polarization intensity P(t) of the ferroelectric thin film:

[0027]

[0028] In the formula, S is the electrode area; and V is the voltage across the ferroelectric capacitor. s (t) is obtained from 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 thin film and the voltage V across the ferroelectric capacitor mentioned in step c are... s (t) according to P(t)~V S After plotting (t), the curve formed by the obtained data points is the final corrected hysteresis loop of the ferroelectric capacitor.

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

[0032]

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

[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 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 size limit, but is greater than or equal to 0.1pF and less than or equal to 10nF.

[0037] This invention improves upon previous methods for calculating domain reversal current curves, corrects errors caused by stray inductance in the circuit, and significantly expands the limitations of the electric pulse measurement method for measuring domain reversal current curves of ferroelectric thin films. After calibration, the domain reversal current curve can be correctly read out below 100 ns, and the hysteresis loop of the ferroelectric thin film with nanosecond-level period can be accurately obtained. Without changing the test circuit, the stray inductance L remains unchanged, greatly facilitating subsequent testing of different ferroelectric capacitors. Based on this method, the measurement of the hysteresis loop of ferroelectric thin films at the nanosecond level can be achieved, contributing to the development of ferroelectric functional devices with ultrafast polarization response. Attached Figure Description

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

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

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

[0041] Figure 4 The measured QV curves of the standard capacitor (uncorrected) and the ideal QV curves of the standard capacitor are shown.

[0042] Figure 5 The QV curve is the standard capacitor whose measured data has been correctly calibrated.

[0043] Figure 6 The uncorrected QV curve obtained by considering stray inductance in software simulation and the corrected QV curve obtained by using the correction algorithm provided in this invention.

[0044] Figure 7 The bipolar electrical pulse signal used to measure ferroelectric thin films and the voltage curves across the total circuit resistance and stray inductance recorded by an oscilloscope.

[0045] Figure 8 This refers to the uncorrected ferroelectric hysteresis loop of a hafnium-zirconium ferroelectric capacitor.

[0046] Figure 9 This is the ferroelectric hysteresis loop of a hafnium-zirconium ferroelectric capacitor after proper calibration. Detailed Implementation

[0047] The present invention will be further described below with reference to the embodiments and accompanying drawings. All other embodiments obtained by those skilled in the art based on these embodiments without inventive effort are within the scope of protection of the present invention.

[0048] Example:

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

[0050] Figure 1This is a schematic diagram of the test circuit used in this invention. The standard capacitor used in this embodiment has a capacitance of 30pF, and the ferroelectric capacitor is a hafnium zirconium oxide thin film capacitor (HZO) sample (electrode area: square 20μm×20μm).

[0051] 1. Connect a standard capacitor to the test circuit, apply an electrical pulse, and measure R using an oscilloscope or data acquisition card. tot The stray inductance L inside the circuit is calculated by varying the voltage across L over time.

[0052] Step a: Connect a 30pF standard capacitor to the test circuit. The total resistance of the circuit is R. tot =100Ω; a bipolar electrical pulse V is generated using a pulse generator. std (t)(bipolar pulse width 40ns, voltage ±1.5V), use an oscilloscope to record the change in voltage across the total resistance and stray inductance of the circuit over time. 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 initial estimate of the stray inductance L is obtained. In the formula, i(t) represents the circuit current obtained based on a standard capacitor. The result is calculated to be 0.39 μH in this example.

[0054] Step c: Fine-tune based on the estimated stray inductance L, and arrange V in array form according to time. Osc (t) The corrected circuit current I(t) is obtained according to the iterative formula; the iterative formula is derived from... The difference formula obtained from the transformation;

[0055] Step d: By integrating the corrected circuit current I(t) from step c over time, the charge Q(t) stored in the standard capacitor can be obtained, i.e. 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) is obtained;

[0056] Step e, when L = 0.48 μH is adjusted, the charge Q(t) stored in the standard capacitor described in step d and the voltage V across the standard capacitor are... S (t) according to Q(t)~V S (t) Plot the graph; the curve formed by the data points is a straight line passing through the origin with a slope close to the standard capacitance value of 30pF (e.g., ...). Figure 5As shown in the figure, this indicates that the correct value of the stray inductance L has been obtained. The uncorrected QV curve (as shown in the figure) Figure 4 As shown by the solid line), it deviates significantly from the ideal QV curve of a standard capacitor (as shown by the solid line). Figure 4 (As shown by the dashed line).

[0057] In this embodiment, a bipolar pulse with a width of 20 ns and a voltage of ±3V is used to simulate the same stray inductance effect, and the uncorrected QV curve is obtained through simulation (e.g., Figure 6 (as shown by the solid line), and Figure 4 The measured results shown by the solid lines are quite close; using the same stray inductance value and the same steps c to e, the correct QV curves are also obtained (e.g., Figure 6 (As shown by the dashed line), this verifies the correctness of considering stray inductance effects.

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

[0059] Step a: Connect the ferroelectric capacitor under test to the same test circuit, and use a pulse generator to generate a bipolar electrical pulse signal V. std (t)(pulse width increases logarithmically from 20 ns to 10 μs, voltage ±3 V), use an oscilloscope to record the change in voltage across the total resistance and stray inductance over time. Osc (t), yielding a V of 240 ns. std (t) and V Osc The waveforms of (t) are shown below (as shown below). Figure 7 (Shown by solid lines and dashed lines);

[0060] Step b, V is in array form, sorted by time. Osc (t), the corrected circuit current I(t) is obtained according to the iterative formula; the iterative formula is derived from The difference formula obtained by conversion; the corrected circuit current I(t) is the formula for the domain reversal current curve of the ferroelectric thin film;

[0061] Step c, integrating the corrected circuit current I(t) from step b over time yields the polarization intensity P(t) of the ferroelectric thin film, i.e. In the formula, S represents the area of ​​the ferroelectric thin film (S = 20 μm × 20 μm); simultaneously, the voltage V across the ferroelectric capacitor... s (t) can be obtained using the formula V s (t)=V std (t)-V Osc (t) is obtained;

[0062] Step d: The polarization intensity P(t) of the ferroelectric thin film and the voltage V across the ferroelectric capacitor mentioned in step c are... s (t) according to P(t)~V S (t) After plotting, the curve formed by the obtained data points is the final corrected hysteresis loop of the ferroelectric capacitor. Figure 8 The uncorrected ferroelectric hysteresis loop of the hafnium-zirconium ferroelectric capacitor exhibits an abnormal high-frequency hysteresis loop shape due to stray inductance effects. For example, under different period changes, as the period increases (gradually increasing from 69 ns to 2.11 μs), the obtained positive and negative coercive voltages significantly violate Merz's law. In contrast, the correctly corrected ferroelectric hysteresis loop... Figure 9 As shown, it can be clearly observed that the magnitudes of both positive and negative coercive voltages have been corrected. As the period increases (gradually increasing from 69ns to 2.11us), the magnitudes of both positive and negative coercive voltages gradually decrease (at higher frequency periods, the maximum voltage emitted by the pulse generator is 3V, so the actual magnitude is not shown), which conforms to 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 aFerroelectric.Science 313,181(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 the ultrafast hysteresis loop of a ferroelectric capacitor, characterized in that, First, construct the test circuit and its equivalent circuit; where: The test circuit consists of a signal generator, a ferroelectric capacitor under test / standard capacitor, a high-frequency data acquisition card or a high-bandwidth oscilloscope, and a standard resistor connected in series; the standard resistor is connected in series or in parallel with the high-frequency data acquisition card or high-bandwidth oscilloscope. The equivalent circuit consists of a signal generator, a ferroelectric capacitor / standard capacitor under test, stray inductance, and total circuit resistance connected in series; the electrical pulse signal emitted by the signal generator is... Indicates; the voltage divider of the ferroelectric capacitor / standard capacitor under test is composed of The stray inductance is represented by L, and the voltage divider is represented by... Indicates; the total resistance of the circuit is determined by R. tot This indicates that the partial pressure is determined by... This indicates that the sum of the voltage divisions of the stray inductance and the total circuit resistance is directly measured by the high-frequency data acquisition card or high-bandwidth oscilloscope. Indicates; the loop current corrected by the iterative formula is... This indicates that the loop current obtained from the standard capacitor charging and discharging formula is... The equivalent circuit can calculate the stray inductance in the circuit and obtain the corrected hysteresis loop of the ferroelectric capacitor. The specific steps for measuring the ultrafast hysteresis loop of a ferroelectric capacitor are as follows: (1) Connect a standard capacitor to the test circuit, apply an electrical pulse, and measure the total resistance R of the circuit using an oscilloscope or data acquisition card. tot The stray inductance L inside the circuit is calculated by varying the voltage across it over time. The specific process is as follows: Step a: Connect a standard capacitor to the test circuit. The standard capacitor has a value of C. s The total resistance R of the circuit tot The signal generator consists of the internal resistance of the signal generator, the internal resistance of the oscilloscope, and a standard resistor connected in parallel with the oscilloscope, which are known. A bipolar electrical pulse signal is generated using the signal generator. Record the relationship between the total resistance and the voltage across the stray inductance of the circuit over time using an oscilloscope or data acquisition card. ; Step b, according to the formula: ， （1） The estimated stray inductance L is obtained from the formula. The circuit current, obtained based on the standard capacitor, is calculated using the following formula: ； （2） Step c: Fine-tune based on the estimated stray inductance L, and arrange the data in array form according to time. The corrected circuit current is calculated using the iterative formula. The iterative formula is a difference formula derived from the following equation: ； （3） Step d: Adjust the corrected circuit current described in step c. The charge stored in a standard capacitor can be obtained by time integration. ,Right now At the same time, the voltage across the standard capacitor It can be obtained using the following formula: ； （4） Step e, the charge stored in the standard capacitor described in step d. and the voltage across the standard capacitor according to Plot the data points so that the curve passes through the origin and has a slope equal to the standard capacitance value C. s When the curve is a straight line, it indicates that the correct stray inductance L has been obtained; otherwise, when the curve formed by the data points is not a straight line passing through the origin and with a slope equal to the standard capacitance value C, it indicates that the correct stray inductance L has been obtained. s When the line is straight, repeat steps c to e; (2) Connect the ferroelectric capacitor to be tested to the test circuit, correct the domain reversal current curve and convert it into a ferroelectric hysteresis loop; the specific process is as follows: Step a: Connect the ferroelectric capacitor under test to the same test circuit, and use a signal generator to generate a bipolar electrical pulse signal. Record the relationship between the total resistance and the voltage across the stray inductance of the circuit over time using an oscilloscope. ; Step b, sort the data into an array format according to time. The corrected circuit current is calculated using the iterative formula. The iterative formula is a difference formula derived from the following equation; ; （5） The corrected circuit current This is the formula for the domain reversal current curve of ferroelectric thin films; Step c, the corrected circuit current described in step b The polarization intensity of the ferroelectric thin film is obtained by integrating over time. : ， （6） In the formula, The electrode area; and the voltage across the ferroelectric capacitor. It is obtained from the following formula: ； （7） Step d: The polarization intensity of the ferroelectric thin film described in step c. and the voltage across the ferroelectric capacitor according to After plotting, the curve formed by 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 difference formula is converted into a first-order, second-order, or higher-order difference formula according to the required accuracy; the first-order difference formula is one of the following: ； （8） ； （9）。 3. The method for measuring the ultrafast hysteresis loop of a ferroelectric capacitor according to claim 1, characterized in that, The bipolar electrical pulse signal has a voltage range of −100 V to 100 V and a pulse width of greater than or equal to 0.1 ns and less than or equal to 100 s.

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 value greater than or equal to 1 Ω and less than or equal to 100 MΩ.

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

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