CN112816790A - Quantum capacitance measuring system and measuring method thereof - Google Patents
Quantum capacitance measuring system and measuring method thereof Download PDFInfo
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Abstract
The invention discloses a quantum capacitance measuring system and a measuring method thereof. The measuring bridge is integrated on the sample table, so that the influence of parasitic capacitance is reduced as much as possible; the excitation signal of the bridge is kept small, and meanwhile, the measurement frequency is improved to obtain enough measurement precision, the measurement heating is reduced, and the quantum state of a sample is prevented from being influenced; the invention combines a superheterodyne structure with a phase-locked measuring method, converts a high-frequency signal output by a bridge into a low-frequency signal by using local oscillation signal mixing, and measures the amplitude and phase of the low-frequency signal by using a low-frequency phase-locked measuring technology, thereby realizing the detection of the amplitude and phase of a high-frequency small signal; the invention adopts the resistance-capacitance bridge which can normally work in the extremely low temperature environment, and amplifies and reduces the frequency of the high-frequency signal generated by the resistance-capacitance bridge through the superheterodyne frequency reduction circuit, thereby finally realizing the accurate measurement of the quantum capacitance.
Description
Technical Field
The invention relates to a quantum capacitance measuring technology, in particular to a quantum capacitance measuring system and a quantum capacitance measuring method.
Background
The capacitance measurement researches the charge and discharge process of the current carrier under the external electric field, and is a practical measurement technology for representing materials and devices. In quantum material research, the change of state density of a carrier Fermi surface can be reflected by detecting the small change of a capacitance value, namely quantum capacitance. Quantum capacitance measurements are much more difficult than conventional capacitance measurements due to: the sample volume is small, and the capacitance value is generally as small as fF magnitude; the sample is generally positioned in a measuring device such as a vacuum measuring device, a low-temperature measuring device or a strong magnetic field measuring device, and is far away from a measuring instrument, and the measured parasitic capacitance is far larger than the capacitance value to be measured; when the sample is in a very low temperature environment (typically-100 mK or below), very low excitation is required for the measurement.
The primary principle of quantum capacitance measurement is that the measurement signal cannot affect the quantum state of the device itself. By evaluating conventional quantum materials, the general measurement conditions for quantum capacitance can be known. Suppose that the area of a GaAs two-dimensional electron gas sample for quantum transport measurement is A ═ (100 μm)2Electron density n-1011cm-2The dielectric layer thickness d is 500 nm. It carries a charge of 1.6 × 10 ═ Ane ═ Q-12C, where e is the electron charge amount. Since the charge variation Δ Q of the measurement signal in each cycle is much smaller than Q, Δ Q < 0.01Q is generally required to be 1.6 × 10-15C. At the same time, because the measuring frequency ω is equal to IinA,/Δ Q, wherein IinIn order to excite current, the conventional measurement requires more than I-10 nA magnitude to be more convenient for extracting and amplifying subsequent measurement signals, so the measurement frequency must be more than MHz magnitude to meet the requirement.
The geometric capacitance value of the sample is
Wherein epsilonr13 is the relative dielectric constant, ε, of the GaAs dielectric layer0A capacitor C to be measured having a vacuum dielectric constantDUTSatisfy the requirement of
Wherein C isQIs the quantum capacitance value of the sample to be measured,
of the order of magnitude of
0.01 of (1). Therefore, the measurement of the quantum capacitance not only needs to measure an extremely small capacitance value, but also needs to be more than 1% in measurement accuracy.
In addition, because the sample to be measured is arranged in the low-temperature equipment and is connected with the measuring instrument at the room temperature end by the connecting wire with the length of several meters,the parasitic capacitance of the connecting wire is 200pF and far larger than the capacitance C to be measuredDUTTherefore, the conventional capacitance measuring instrument cannot directly measure the capacitance of the sample to be measured.
At present, the main method for measuring the quantum capacitance at low temperature is to directly place a preamplifier near a capacitance bridge, reduce the influence of cable capacitance and achieve the purposes of coupling and transmitting output voltage. However, the operating temperature is known to be 50mK at the lowest because the power consumption of the preamplifier is too high. However, the appearance of some quantum states often requires lower temperature, such as 5/2 fractional quantum hall effect, so that the measurement methods have strong limitation on quantum capacitance which can only appear at lower temperature.
Disclosure of Invention
In order to solve the technical problem, the invention provides a quantum capacitance measuring method and a corresponding measuring system. The method adopts a signal measurement method of a balance bridge and superheterodyne demodulation to realize the measurement of the quantum capacitance.
In order to reduce the influence of parasitic capacitance as much as possible, the measuring bridge is integrated on the sample stage; in order to reduce the measurement heating and avoid influencing the quantum state of the sample, the measurement frequency is increased to obtain enough measurement precision while keeping the excitation signal of the bridge small; in order to realize accurate measurement of the bridge output signal of the high-frequency small signal, the invention combines a superheterodyne structure with a phase-locking measurement method, converts the high-frequency signal output by the bridge into a low-frequency signal by using local oscillator signal mixing, and measures the amplitude and the phase of the low-frequency signal by using a low-frequency phase-locking measurement technology, thereby realizing the detection of the amplitude and the phase of the high-frequency small signal.
One object of the present invention is to provide a quantum capacitance measurement system.
The quantum capacitance measuring system of the present invention comprises: the system comprises a low-temperature bridge circuit, a room-temperature end interface circuit and a superheterodyne phase-locking measurement system; the low-temperature bridge circuit is integrated on a sample table in a refrigerator; the room temperature end interface circuit and the superheterodyne phase-locking measuring system are positioned outside the refrigerator; the input and output of the low-temperature bridge circuit are connected to the superheterodyne phase-locking measuring system through a room-temperature end interface circuit;
the low-temperature bridge circuit comprises a standard resistor, a standard capacitor, a capacitor to be detected, a balancing resistor, a control end current limiting resistor, a third current limiting resistor and a fourth current limiting resistor; the balancing resistor is a voltage controllable resistor, a control voltage end of the balancing resistor is connected to a control voltage through a control end current limiting resistor, and the size of the resistance of the balancing resistor is controlled through the control voltage; the balancing resistor and the standard resistor are connected in series to form a resistor arm of a bridge; the standard capacitor and the capacitor to be measured are connected in series to form a capacitor arm of the bridge: the second end of the balancing resistor is connected with the first end of the standard capacitor and then used as a radio frequency input positive end; the first end of the standard resistor is connected with the second end of the capacitor to be detected and then serves as the negative end of the radio frequency input; the second end of the standard capacitor is connected with the first end of the capacitor to be measured and then is used as the output positive end of the low-temperature bridge to be connected outside the refrigerator through the core layer of the coaxial line; the first end of the balancing resistor is connected with the second end of the standard resistor and then is used as the output negative end of the low-temperature bridge, and the output negative end of the low-temperature bridge is connected to the outside of the refrigerator through a coaxial shielding layer and is connected with a measuring ground through a room-temperature interface circuit; the radio frequency input positive end of the low-temperature bridge is connected to a low-frequency voltage measuring positive end of a room temperature interface circuit positioned outside the refrigerator through a third current-limiting resistor; the radio frequency input negative end of the low-temperature bridge is connected to a low-frequency voltage measurement negative end of a room temperature interface circuit outside the refrigerator through a fourth current-limiting resistor;
the room temperature interface circuit includes: the device comprises a radio frequency excitation input end, an excitation coupling transformer, an isolation capacitor, a first low-frequency current input end, a second low-frequency current input end, a low-frequency voltage measuring positive end, a low-frequency voltage measuring negative end, a first current limiting resistor and a second current limiting resistor; the radio frequency excitation input end is connected to a first port of the excitation coupling transformer, a second port of the excitation coupling transformer is grounded, a third port and a fourth port of the excitation coupling transformer are respectively connected to a radio frequency input positive end and a radio frequency input negative end of the low-temperature bridge circuit, and the isolation capacitor is connected in series between the third port of the excitation coupling transformer and the radio frequency input positive end or between the fourth port of the excitation coupling transformer and the radio frequency input negative end; the first low-frequency current input end is connected to the positive end of the radio frequency input through a first current-limiting resistor; the second low-frequency current input end is connected to the negative end of the radio frequency input through a second current-limiting resistor;
the superheterodyne phase-locked measuring system comprises a signal source, a high-frequency low-noise pre-amplifier, a frequency mixer, a low-pass filter and a low-frequency phase-locked amplifier; the signal source is used for generating a bridge measurement excitation signal, a mixer local oscillation signal and a low-frequency phase-locked reference signal; the output positive end of the low-temperature bridge circuit is connected to the input end of a high-frequency low-noise preamplifier, the output end of the high-frequency low-noise preamplifier is connected to the signal input end of a frequency mixer, a local oscillation signal generated by a signal source is connected to the local oscillation signal input end of the frequency mixer, the output end of the frequency mixer is connected to the input end of a low-pass filter, and the output end of the low-pass filter is connected to the signal input end of a low-frequency phase; a low-frequency phase-locked reference signal generated by a signal source is accessed to a reference signal input end of a low-frequency phase-locked amplifier;
an excitation signal generated by the signal source is input to the input end of the room temperature interface circuit and is coupled to the low-temperature bridge circuit through the excitation coupling transformer;
in the measuring process, low-frequency alternating currents with different angular frequencies are respectively input from a first low-frequency current input end and a second low-frequency current input end of a room temperature interface circuit, the currents respectively flow into an output negative end of a low-temperature bridge circuit after passing through a balancing resistor and a standard resistor of the low-temperature bridge circuit, differential voltage is generated between a low-frequency voltage measuring positive end and a low-frequency voltage measuring negative end, and the differential voltage is respectively measured by using a low-frequency phase locking technology, so that the real-time measurement of the standard resistor and the balancing resistor is realized;
a voltage signal output from the output positive end of the low-temperature bridge circuit is connected to a superheterodyne phase-locking measuring system for measurement, is pre-amplified by a high-frequency low-noise pre-amplifier and then is input into a mixer together with a local oscillation signal for frequency mixing, the mixed frequency signal comprises a sum frequency signal and a difference frequency signal of the output voltage signal and the local oscillation signal, and the mixed frequency signal is filtered by a low-pass filter, so that the sum frequency signal is filtered, and only the difference frequency signal of the low frequency is left; accurate reading phase-locked amplifier of low-frequency phase-locked amplifier measures difference frequency signalAmplitude of | VdfL, and the difference frequency signal VdfReference signal V output from signal sourcerefA phase difference θ between;
the bridge measurement is divided into two modes: the method comprises the steps of measuring a balanced bridge and a non-balanced bridge, wherein the balanced bridge is used for measuring the absolute value of a capacitor, the non-balanced bridge is used for measuring the variation of the capacitor, and the capacitor to be measured is obtained through calibration.
The balancing resistor is a voltage-controlled variable resistor and is realized by using a source-drain resistor of an ultrahigh-mobility transistor in order to work in a low-temperature environment. The first end of the balancing resistor is a source electrode or a drain electrode of the ultrahigh mobility transistor; the second end of the balancing resistor is a drain electrode or a source electrode of the ultrahigh mobility transistor; the gate of the ultra-high mobility transistor is the control voltage terminal. As the quantum system is arranged in low-temperature equipment, the balancing resistor is required to be an electric control device capable of working at low temperature, and a conducting channel of an ultra-high mobility transistor (HEMT) is two-dimensional electron gas in a heterojunction, so that the quantum system can normally work at low temperature. Control voltage VgThrough a current limiting resistor RgAnd the control voltage is changed to adjust the size of the source-drain resistance.
The signal source is used for generating a bridge measurement excitation signal, a mixer local oscillation signal and a low-frequency phase-locked reference signal; the frequencies of the three signals are respectively fin、fLoAnd fDAnd satisfy fD＝|fin-fLoL. The signal source is realized by a signal generator with clock synchronization, a digital frequency synthesizer or a phase-locked loop.
In the invention, a measuring circuit in the refrigerator has no device with overhigh power consumption, and the low-temperature power consumption is as low as 10nW under the conventional measurement, so that the refrigerator can work at the temperature of 10mK or even lower.
Another objective of the present invention is to provide a method for measuring quantum capacitance.
In the quantum capacitance measuring method, bridge measurement is divided into two modes: the balance bridge measurement and the unbalance bridge measurement, the former is suitable for measuring the absolute value of the capacitance, the latter is suitable for measuring the variable quantity of the capacitance, thereby obtaining the capacitance to be measured:
firstly, balance bridge measurement:
1) an excitation signal generated by the signal source is input to the input end of the room temperature interface circuit and is coupled to the low-temperature bridge circuit through the excitation coupling transformer;
2) the control end changes the resistance value of the balancing resistor through controlling the voltage so as to change the balance state of the bridge and generate corresponding output voltage;
3) in the measuring process, alternating currents with different angular frequencies are respectively input from a first low-frequency current input end and a second low-frequency current input end of a room temperature interface circuit, the currents respectively flow into an output negative end of a low-temperature bridge circuit after passing through a balancing resistor and a standard resistor of the low-temperature bridge circuit, differential voltage is generated between a low-frequency voltage measuring positive end and a low-frequency voltage measuring negative end, and the differential voltage is respectively measured by using a low-frequency phase locking technology, so that the real-time measurement of the standard resistor and the balancing resistor is realized;
4) an output voltage signal at the positive output end of the low-temperature bridge circuit is transmitted to a superheterodyne frequency-reducing circuit through a room-temperature interface circuit, pre-amplified by a high-frequency low-noise pre-amplifier and then input to a mixer together with a local oscillation signal for frequency mixing, the mixed frequency signal comprises a sum frequency signal and a difference frequency signal of the output voltage signal and the local oscillation signal, and the mixed frequency signal is filtered through a low-pass filter, so that the sum frequency signal is filtered, and only the difference frequency signal of the low frequency is left; amplitude | V of difference frequency signal measured by accurate reading phase-locked amplifier of low-frequency phase-locked amplifierdfL, and the difference frequency signal VdfReference signal V output from signal sourcerefA phase difference θ between;
5) measuring amplitude | V of output difference frequency signaldfThe minimum indicates the bridge balance, using the balance relationship
Obtaining the capacitance C to be measuredDUTWherein R isrefIs a standard resistance, CrefIs a standard capacitance and RhIs a trim resistance;
secondly, unbalanced bridge measurement:
1) an excitation signal generated by the signal source is input to the input end of the room temperature interface circuit and is coupled to the low-temperature bridge circuit through the excitation coupling transformer;
2) the control end changes the resistance value of the balancing resistor through controlling the voltage so as to change the balance state of the bridge and generate corresponding output voltage;
3) in the measuring process, alternating currents with different angular frequencies are respectively input from a first low-frequency current input end and a second low-frequency current input end of a room temperature interface circuit, the currents respectively flow into an output negative end of a low-temperature bridge circuit after passing through a standard resistor and a balancing resistor of the low-temperature bridge circuit, differential voltage is generated between a low-frequency voltage measuring positive end and a low-frequency voltage measuring negative end, and the differential voltage is respectively measured by using a low-frequency phase locking technology, so that the real-time measurement of the standard resistor and the balancing resistor is realized;
4) an output voltage signal at the positive output end of the low-temperature bridge circuit is transmitted to a superheterodyne frequency-reducing circuit through a room-temperature interface circuit, pre-amplified by a high-frequency low-noise pre-amplifier and then input to a mixer together with a local oscillation signal for frequency mixing, the mixed frequency signal comprises a sum frequency signal and a difference frequency signal of the output voltage signal and the local oscillation signal, and the mixed frequency signal is filtered through a low-pass filter, so that the sum frequency signal is filtered, and only the difference frequency signal of the low frequency is left; amplitude | V of difference frequency signal measured by accurate reading phase-locked amplifier of low-frequency phase-locked amplifierdfL, and the difference frequency signal VdfReference signal V output from signal sourcerefThe phase difference θ of (a);
5) from the amplitude | V of the difference signaldfThe measurement of | and the phase difference θ yields a quadrature component V that does not vary with the change in the trim resistancexAnd a signal component V which varies with the change in the trimming resistancey：
Wherein
Is | VdfThe value of theta at the point of equilibrium is the minimum |;
6) signal component V varying with changes in trim resistanceyThe relation of the bridge balance satisfies:
wherein S is the measurement sensitivity and represents V corresponding to unit capacitance changeyFrom which is obtained a change of
And a signal component V varying with the change of the trimming resistanceyAnd the capacitor C to be measuredDUTCalibration relation of RrefIs a standard resistance, CrefIs a standard capacitance and RhIs a trim resistance;
7) the control end sets the resistance value of the balancing resistor through controlling the voltage to enable the low-temperature bridge circuit to be in a balanced state, and the signal component V changing along with the change of the balancing resistor is measuredyAnd obtaining the capacitor C to be measured by using the calibration relation curve obtained in the previous stepDUTA change in (c).
Wherein, in step 3), the current i is respectively input into the first and the second low-frequency current input terminals1sin(ω1t) and i2sin(ω2t)，i1Is the amplitude of the alternating current at the first low-frequency current input terminal i2Is the amplitude, omega, of the alternating current at the second low-frequency current input1Is the angular frequency, omega, of the alternating current at the first low-frequency current input2Is the angular frequency of the alternating current at the second low-frequency current input end, and t is time; the current respectively passes through the balancing resistors R of the low-temperature bridge circuithAnd a standard resistance RrefThen flows into the output negative terminal of the low-temperature bridge circuit, and generates a differential voltage i between the low-frequency voltage measuring positive terminal and the low-frequency voltage measuring negative terminal1Rhsin(ω1t)-i2Rrefsin(ω2t), respectively measuring the amplitude i of the differential voltage by using a low-frequency phase-locking technology1RhAnd i2RrefTherefore, real-time measurement of the standard resistance and the balancing resistance is realized.
The invention has the advantages that:
the invention adopts the resistance-capacitance bridge which can normally work in the extremely low temperature environment, and amplifies and reduces the frequency of the high-frequency signal generated by the resistance-capacitance bridge through the superheterodyne frequency reduction circuit, thereby finally realizing the accurate measurement of the quantum capacitance.
Drawings
FIG. 1 is a circuit diagram of one embodiment of a superheterodyne demodulation bridge method quantum capacitance measurement system of the present invention, in which (a) is a circuit diagram of a bridge measurement circuit and a room temperature termination circuit, and (b) is a circuit diagram of a superheterodyne down-conversion circuit;
fig. 2 is a comparison graph of a measurement result of a voltage-controlled variable capacitor and a reference value of the variable capacitor obtained according to an embodiment of the superheterodyne demodulation bridge method quantum capacitor measurement system of the present invention;
FIG. 3 is a calibration curve diagram obtained by one embodiment of a superheterodyne demodulation bridge method quantum capacitance measurement system according to the present invention;
fig. 4 is a graph of a capacitance real-time change measurement result obtained by one embodiment of the superheterodyne demodulation bridge method quantum capacitance measurement system according to the present invention.
Detailed Description
The invention will be further elucidated by means of specific embodiments in the following with reference to the drawing.
As shown in fig. 1, the quantum capacitance measurement system of the present embodiment includes: the system comprises a low-temperature bridge circuit, a room-temperature end interface circuit and a superheterodyne phase-locking measurement system; the low-temperature bridge circuit is integrated on a sample table in a refrigerator; the room temperature end interface circuit and the superheterodyne phase-locking measuring system are positioned outside the refrigerator; the input and output of the low-temperature bridge circuit are connected to the superheterodyne phase-locking measuring system through a room-temperature end interface circuit;
the low-temperature bridge circuit comprises a standard resistor RrefStandard capacitor CrefTo be treatedCapacitance CDUTBalancing resistance RhControl end current limiting resistor RgAnd a third current limiting resistor R3And a fourth current limiting resistor R4(ii) a Wherein, the balancing resistor adopts a voltage controllable resistor, and the control voltage end of the balancing resistor is connected to the control voltage V through a control end current limiting resistorgControlling the resistance of the balancing resistor by controlling the voltage; the balancing resistor and the standard resistor are connected in series to form a resistor arm of a bridge; the standard capacitor and the capacitor to be measured are connected in series to form a capacitor arm of the bridge: the second end of the balancing resistor is connected with the first end of the standard capacitor and then used as a radio frequency input positive end; the first end of the standard resistor is connected with the second end of the capacitor to be detected and then serves as the negative end of the radio frequency input; the second end of the standard capacitor is connected with the first end of the capacitor to be measured and then used as the output positive end V of the low-temperature bridgeoutThe core layer is connected to the outside of the refrigerator through a coaxial line COAX; the first end of the balancing resistor is connected with the second end of the standard resistor and then serves as the output negative end of the low-temperature bridge, and the output negative end of the low-temperature bridge is connected to the outside of the refrigerator through a shielding layer of a coaxial line COAX and is connected with a measuring ground through a room temperature interface circuit; the radio frequency input positive end of the low-temperature bridge is connected to a low-frequency voltage measurement positive end V of a room temperature interface circuit positioned outside the refrigerator through a third current-limiting resistorR+(ii) a The radio frequency input negative end of the low-temperature bridge is connected to a low-frequency voltage measurement negative end V of a room temperature interface circuit outside the refrigerator through a fourth current-limiting resistorR-The portion of fig. 1(a) within the dashed box is within the refrigerator;
the room temperature interface circuit includes: radio frequency excitation input terminal VinExciting coupling transformer TinAnd an isolation capacitor CinA first low-frequency current input terminal I1A second low-frequency current input terminal I2Low frequency voltage measuring positive terminal VR+Negative end V for measuring low-frequency voltageR-A first current limiting resistor R1And a second current limiting resistor R2(ii) a The radio frequency excitation input end is connected to the first port of the excitation coupling transformer, the second port of the excitation coupling transformer is grounded, the third port and the fourth port of the excitation coupling transformer are respectively connected to the radio frequency input positive end and the radio frequency input negative end of the low-temperature bridge circuit, and the isolation capacitor is connected in series to the third port of the excitation coupling transformerThe port is connected between the positive end of the radio frequency input or connected between the fourth port of the excitation coupling transformer and the negative end of the radio frequency input in series; the first low-frequency current input end is connected to the positive end of the radio frequency input through a first current-limiting resistor; the second low-frequency current input end is connected to the negative end of the radio frequency input through a second current-limiting resistor;
the superheterodyne phase-locked measuring system comprises a signal source, a high-frequency low-noise pre-amplifier, a frequency mixer, a low-pass filter and a low-frequency phase-locked amplifier; the signal source is used for generating a bridge measurement excitation signal, a mixer local oscillation signal and a low-frequency phase-locked reference signal; the output positive end of the low-temperature bridge circuit is connected to the input end of a high-frequency low-noise preamplifier, the output end of the high-frequency low-noise preamplifier is connected to the signal input end of a frequency mixer, a local oscillation signal generated by a signal source is connected to the local oscillation signal input end of the frequency mixer, the output end of the frequency mixer is connected to the input end of a low-pass filter, and the output end of the low-pass filter is connected to the signal input end Sig of a low-frequency phase; the low-frequency phase-locked reference signal generated by the signal source is accessed to a reference signal input end Ref of the low-frequency phase-locked amplifier.
The signal source is used for generating a bridge measurement excitation signal, a mixer local oscillation signal and a low-frequency phase-locked reference signal, wherein the signal source uses a reference clock signal CLK, so that the phase difference of the generated three signals cannot drift along with time; the frequencies of the three signals are respectively fin、fLoAnd fDAnd satisfy fD＝|fin-fLoL. The signal source is realized by a signal generator with clock synchronization, a digital frequency synthesizer or a phase-locked loop.
In order to simulate the variation of the quantum capacitance, the capacitor C to be measured is selected in this embodimentDUTIs a voltage-controlled variable capacitor with a regulated voltage of VcIt is known that V is accompanied bycThe variation range of the capacitance is 15-35 pF. Selecting a standard capacitance CrefIs 10pF, standard resistance R ref50 omega, 1: 1 turn ratio of exciting coupling transformer, and input capacitor CinIs 100 nF. The passband of the high frequency low noise preamplifier, which determines the generation of the bridge measurement excitation signal V, is 10-100 MHzinFrequency f ofinSelection of (2). Selection finThe measurement is carried out for three values of 10.1MHz, 27MHz and 49MHz, and the frequencies of the local oscillation signals of the corresponding mixers are respectively set to be 10.1MHz +233Hz, 27MHz +233Hz and 49MHz +233 Hz. Frequency-reduced difference frequency signal VdfHas a frequency of 233 Hz.
As shown in the inset of FIG. 2, the capacitor C to be measured is selectedDUTVoltage V ofcScanning RhGate voltage V ofgTo change RhWhile scanning, recording the amplitude V of the down-converted difference signaldfAfter scanning is finished, the difference frequency signal amplitude | V after frequency reduction can be readdfR corresponding to when | is minimumhAccording to equilibrium conditions
The value of the capacitor to be measured can be obtained. Different frequencies, different VcThe measurement result of (2) is shown in FIG. 2, with the abscissa of VcThe ordinate is the capacitance value, the solid line is the reference value curve given in the capacitance model data table, and the scatter point is the actual result of the measurement, so that the measurement results of different frequencies are well matched with the approximate value curve.
It can be seen that there is a slight difference between the measurement data with the measurement frequency of 27MHz and the measurement data of 10MHz and 49MHz, because 10MHz and 49MHz are both the signals V to be measured of the whole measurement systemdfThe frequency of the maximum amplitude is the frequency of the maximum amplitude, and the maximum amplitude exists because the inductance of the excitation coupling transformer and the equivalent capacitance of the system generate resonance effect, so that the V output at the resonance pointdfThe amplitude will be much higher than the non-resonant point, so the measurement accuracy of the frequency chosen at the resonant point will be higher.
In the quantum capacitance measurement system method of the present embodiment, the bridge measurement is divided into two modes: the former is suitable for measuring the absolute value of the capacitance, and the latter is suitable for measuring the variation of the capacitance, thereby obtaining the capacitance to be measured:
firstly, balance bridge measurement:
1) an excitation signal generated by the signal source is input to the input end of the room temperature interface circuit and is coupled to the low-temperature bridge circuit through the excitation coupling transformer;
2) the control end changes the resistance value of the balancing resistor through controlling the voltage so as to change the balance state of the bridge and generate corresponding output voltage;
3) in the measuring process, alternating currents with different angular frequencies are respectively input from a first low-frequency current input end and a second low-frequency current input end of a room temperature interface circuit, the currents respectively flow into an output negative end of a low-temperature bridge circuit after passing through a balancing resistor and a standard resistor of the low-temperature bridge circuit, differential voltage is generated between a low-frequency voltage measuring positive end and a low-frequency voltage measuring negative end, and the differential voltage is respectively measured by using a low-frequency phase locking technology, so that the real-time measurement of the standard resistor and the balancing resistor is realized;
4) an output voltage signal at the positive output end of the low-temperature bridge circuit is transmitted to a superheterodyne frequency-reducing circuit through a room-temperature interface circuit, pre-amplified by a high-frequency low-noise pre-amplifier and then input to a mixer together with a local oscillation signal for frequency mixing, the mixed frequency signal comprises a sum frequency signal and a difference frequency signal of the output voltage signal and the local oscillation signal, and the mixed frequency signal is filtered through a low-pass filter, so that the sum frequency signal is filtered, and only the difference frequency signal of the low frequency is left; amplitude | V of difference frequency signal measured by accurate reading phase-locked amplifier of low-frequency phase-locked amplifierdfL, and the difference frequency signal VdfReference signal V output from signal sourcerefA phase difference θ between;
5) measuring amplitude V of output difference frequency signaldfThe minimum indicates the bridge balance, using the balance relationship
Obtaining the capacitance C to be measuredDUTThe capacitance value of (a);
secondly, unbalanced bridge measurement:
1) an excitation signal generated by the signal source is input to the input end of the room temperature interface circuit and is coupled to the low-temperature bridge circuit through the excitation coupling transformer;
2) the control end changes the resistance value of the balancing resistor through controlling the voltage so as to change the balance state of the bridge and generate corresponding output voltage;
3) in the measuring process, alternating currents with different angular frequencies are respectively input from a first low-frequency current input end and a second low-frequency current input end of a room temperature interface circuit, the currents respectively flow into an output negative end of a low-temperature bridge circuit after passing through a standard resistor and a balancing resistor of the low-temperature bridge circuit, differential voltage is generated between a low-frequency voltage measuring positive end and a low-frequency voltage measuring negative end, and the differential voltage is respectively measured by using a low-frequency phase locking technology, so that the real-time measurement of the standard resistor and the balancing resistor is realized;
4) an output voltage signal at the positive output end of the low-temperature bridge circuit is transmitted to a superheterodyne frequency-reducing circuit through a room-temperature interface circuit, pre-amplified by a high-frequency low-noise pre-amplifier and then input to a mixer together with a local oscillation signal for frequency mixing, the mixed frequency signal comprises a sum frequency signal and a difference frequency signal of the output voltage signal and the local oscillation signal, and the mixed frequency signal is filtered through a low-pass filter, so that the sum frequency signal is filtered, and only the difference frequency signal of the low frequency is left; amplitude | V of difference frequency signal measured by accurate reading phase-locked amplifier of low-frequency phase-locked amplifierdfL, and the difference frequency signal VdfReference signal V output from signal sourcerefThe phase difference θ of (a);
5) from the absolute value | V of the difference signaldfThe measurement of | and the phase difference θ yields a quadrature component V that does not vary with the change in the trim resistancexAnd a signal component V which varies with the change in the trimming resistancey：
Wherein
Is | VdfThe phase difference theta value when | is minimum, namely the balance point;
6) signal component V varying with changes in trim resistanceyIn relation to bridge balanceSatisfies the following conditions:
wherein S is the measurement sensitivity, and represents the V corresponding to the unit capacitance or unit resistance changeyFrom which is obtained a change of
And a signal component V varying with the change of the trimming resistanceyAnd the capacitor C to be measuredDUTThe calibration relation curve of (1). The measurement result is shown in FIG. 3, and the obtained sensitivity S is 9.98 mV/%, i.e. when the signal V to be measured isdfEvery time the change is 9.98mV,
1% change; therefore, the signal V to be measured can be known from the above formuladfCun corresponding to each variation of 9.98mV
-1% variance of;
7) the control end sets the resistance value of the balancing resistor through controlling the voltage to enable the low-temperature bridge circuit to be in a balanced state, and the signal component V changing along with the change of the balancing resistor is measuredyAnd obtaining the capacitor C to be measured by using the calibration relation curve obtained in the previous stepDUTA change in (c).
In order to simulate the real-time change of the quantum capacitance, the capacitance C to be measured is selectedDUTVoltage V ofcWhich is a square wave with an amplitude of 2V 10mV, and a frequency of 10mhz, it can be predicted from fig. 2 that a variation of 10mV with respect to 2V is equivalent to a variation of 0.23% of the capacitance C. The measurement signal V obtained with a sensitivity S of 9.98 mV/% is useddfThe measurement results obtained by the processing are shown in fig. 4, and the average value of the change in the capacitance change Δ C/C is calculated to be ± 0.221%, which corresponds to the prediction results.
Finally, it is noted that the disclosed embodiments are intended to aid in further understanding of the invention, but those skilled in the art will appreciate that: various substitutions and modifications are possible without departing from the spirit and scope of the invention and the appended claims. Therefore, the invention should not be limited to the embodiments disclosed, but the scope of the invention is defined by the appended claims.
Claims (5)
1. A quantum capacitance measurement system, comprising: the system comprises a low-temperature bridge circuit, a room-temperature end interface circuit and a superheterodyne phase-locking measurement system; the low-temperature bridge circuit is integrated on a sample table in a refrigerator; the room temperature end interface circuit and the superheterodyne phase-locking measuring system are positioned outside the refrigerator; the input and output of the low-temperature bridge circuit are connected to the superheterodyne phase-locking measuring system through a room-temperature end interface circuit;
the low-temperature bridge circuit comprises a standard resistor, a standard capacitor, a capacitor to be detected, a balancing resistor, a control end current limiting resistor, a third current limiting resistor and a fourth current limiting resistor; the balancing resistor is a voltage controllable resistor, a control voltage end of the balancing resistor is connected to a control voltage through a control end current limiting resistor, and the size of the resistance of the balancing resistor is controlled through the control voltage; the balancing resistor and the standard resistor are connected in series to form a resistor arm of a bridge; the standard capacitor and the capacitor to be measured are connected in series to form a capacitor arm of the bridge: the second end of the balancing resistor is connected with the first end of the standard capacitor and then used as a radio frequency input positive end; the first end of the standard resistor is connected with the second end of the capacitor to be detected and then serves as the negative end of the radio frequency input; the second end of the standard capacitor is connected with the first end of the capacitor to be measured and then is used as the output positive end of the low-temperature bridge to be connected outside the refrigerator through the core layer of the coaxial line; the first end of the balancing resistor is connected with the second end of the standard resistor and then is used as the output negative end of the low-temperature bridge, and the output negative end of the low-temperature bridge is connected to the outside of the refrigerator through a coaxial shielding layer and is connected with a measuring ground through a room-temperature interface circuit; the radio frequency input positive end of the low-temperature bridge is connected to a low-frequency voltage measuring positive end of a room temperature interface circuit positioned outside the refrigerator through a third current-limiting resistor; the radio frequency input negative end of the low-temperature bridge is connected to a low-frequency voltage measurement negative end of a room temperature interface circuit outside the refrigerator through a fourth current-limiting resistor;
the room temperature interface circuit includes: the device comprises a radio frequency excitation input end, an excitation coupling transformer, an isolation capacitor, a first low-frequency current input end, a second low-frequency current input end, a low-frequency voltage measuring positive end, a low-frequency voltage measuring negative end, a first current limiting resistor and a second current limiting resistor; the radio frequency excitation input end is connected to a first port of the excitation coupling transformer, a second port of the excitation coupling transformer is grounded, a third port and a fourth port of the excitation coupling transformer are respectively connected to a radio frequency input positive end and a radio frequency input negative end of the low-temperature bridge circuit, and the isolation capacitor is connected in series between the third port of the excitation coupling transformer and the radio frequency input positive end or between the fourth port of the excitation coupling transformer and the radio frequency input negative end; the first low-frequency current input end is connected to the positive end of the radio frequency input through a first current-limiting resistor; the second low-frequency current input end is connected to the negative end of the radio frequency input through a second current-limiting resistor;
the superheterodyne phase-locked measuring system comprises a signal source, a high-frequency low-noise pre-amplifier, a frequency mixer, a low-pass filter and a low-frequency phase-locked amplifier; the signal source is used for generating a bridge measurement excitation signal, a mixer local oscillation signal and a low-frequency phase-locked reference signal; the output positive end of the low-temperature bridge circuit is connected to the input end of a high-frequency low-noise preamplifier, the output end of the high-frequency low-noise preamplifier is connected to the signal input end of a frequency mixer, a local oscillation signal generated by a signal source is connected to the local oscillation signal input end of the frequency mixer, the output end of the frequency mixer is connected to the input end of a low-pass filter, and the output end of the low-pass filter is connected to the signal input end of a low-frequency phase; a low-frequency phase-locked reference signal generated by a signal source is accessed to a reference signal input end of a low-frequency phase-locked amplifier;
an excitation signal generated by the signal source is input to the input end of the room temperature interface circuit and is coupled to the low-temperature bridge circuit through the excitation coupling transformer;
in the measuring process, low-frequency alternating currents with different angular frequencies are respectively input from a first low-frequency current input end and a second low-frequency current input end of a room temperature interface circuit, the currents respectively flow into an output negative end of a low-temperature bridge circuit after passing through a balancing resistor and a standard resistor of the low-temperature bridge circuit, differential voltage is generated between a low-frequency voltage measuring positive end and a low-frequency voltage measuring negative end, and the differential voltage is respectively measured by using a low-frequency phase locking technology, so that the real-time measurement of the standard resistor and the balancing resistor is realized;
a voltage signal output from the output positive end of the low-temperature bridge circuit is connected to a superheterodyne phase-locking measuring system for measurement, is pre-amplified by a high-frequency low-noise pre-amplifier and then is input into a mixer together with a local oscillation signal for frequency mixing, the mixed frequency signal comprises a sum frequency signal and a difference frequency signal of the output voltage signal and the local oscillation signal, and the mixed frequency signal is filtered by a low-pass filter, so that the sum frequency signal is filtered, and only the difference frequency signal of the low frequency is left; amplitude | V of difference frequency signal measured by accurate reading phase-locked amplifier of low-frequency phase-locked amplifierdfL, and the difference frequency signal VdfReference signal V output from signal sourcerefA phase difference θ between;
the bridge measurement is divided into two modes: the method comprises the steps of measuring a balanced bridge and a non-balanced bridge, wherein the balanced bridge is used for measuring the absolute value of a capacitor, the non-balanced bridge is used for measuring the variation of the capacitor, and the capacitor to be measured is obtained through calibration.
2. The quantum capacitance measurement system of claim 1, wherein the trim resistance is implemented using source-drain resistance of an ultra-high mobility transistor; the first end of the balancing resistor is a source electrode or a drain electrode of the ultrahigh mobility transistor; the second end of the balancing resistor is a drain electrode or a source electrode of the ultrahigh mobility transistor; the gate of the ultra-high mobility transistor is the control voltage terminal.
3. The quantum capacitance measurement system of claim 1, wherein the signal source is implemented using a clock-synchronized signal generator, a digital frequency synthesizer, or a phase-locked loop.
4. A measurement method of a quantum capacitance measurement system according to claim 1, characterized in that the measurement method is divided into balanced bridge measurement and unbalanced bridge measurement:
firstly, balance bridge measurement:
1) an excitation signal generated by the signal source is input to the input end of the room temperature interface circuit and is coupled to the low-temperature bridge circuit through the excitation coupling transformer;
2) the control end changes the resistance value of the balancing resistor through controlling the voltage so as to change the balance state of the bridge and generate corresponding output voltage;
3) in the measuring process, alternating currents with different angular frequencies are respectively input from a first low-frequency current input end and a second low-frequency current input end of a room temperature interface circuit, the currents respectively flow into an output negative end of a low-temperature bridge circuit after passing through a balancing resistor and a standard resistor of the low-temperature bridge circuit, differential voltage is generated between a low-frequency voltage measuring positive end and a low-frequency voltage measuring negative end, and the differential voltage is respectively measured by using a low-frequency phase locking technology, so that the real-time measurement of the standard resistor and the balancing resistor is realized;
4) an output voltage signal at the positive output end of the low-temperature bridge circuit is transmitted to a superheterodyne frequency-reducing circuit through a room-temperature interface circuit, pre-amplified by a high-frequency low-noise pre-amplifier and then input to a mixer together with a local oscillation signal for frequency mixing, the mixed frequency signal comprises a sum frequency signal and a difference frequency signal of the output voltage signal and the local oscillation signal, and the mixed frequency signal is filtered through a low-pass filter, so that the sum frequency signal is filtered, and only the difference frequency signal of the low frequency is left; amplitude | V of difference frequency signal measured by accurate reading phase-locked amplifier of low-frequency phase-locked amplifierdfL, and the difference frequency signal VdfReference signal V output from signal sourcerefA phase difference θ between;
5) measuring amplitude | V of output difference frequency signaldfThe minimum indicates the bridge balance, using the balance relationship
Obtaining the capacitance C to be measuredDUTWherein R isrefIs a standard resistance, CrefIs a standard capacitance and RhIs a trim resistance;
secondly, unbalanced bridge measurement:
1) an excitation signal generated by the signal source is input to the input end of the room temperature interface circuit and is coupled to the low-temperature bridge circuit through the excitation coupling transformer;
2) the control end changes the resistance value of the balancing resistor through controlling the voltage so as to change the balance state of the bridge and generate corresponding output voltage;
3) in the measuring process, alternating currents with different angular frequencies are respectively input from a first low-frequency current input end and a second low-frequency current input end of a room temperature interface circuit, the currents respectively flow into an output negative end of a low-temperature bridge circuit after passing through a standard resistor and a balancing resistor of the low-temperature bridge circuit, differential voltage is generated between a low-frequency voltage measuring positive end and a low-frequency voltage measuring negative end, and the differential voltage is respectively measured by using a low-frequency phase locking technology, so that the real-time measurement of the standard resistor and the balancing resistor is realized;
4) an output voltage signal at the positive output end of the low-temperature bridge circuit is transmitted to a superheterodyne frequency-reducing circuit through a room-temperature interface circuit, pre-amplified by a high-frequency low-noise pre-amplifier and then input to a mixer together with a local oscillation signal for frequency mixing, the mixed frequency signal comprises a sum frequency signal and a difference frequency signal of the output voltage signal and the local oscillation signal, and the mixed frequency signal is filtered through a low-pass filter, so that the sum frequency signal is filtered, and only the difference frequency signal of the low frequency is left; amplitude | V of difference frequency signal measured by accurate reading phase-locked amplifier of low-frequency phase-locked amplifierdfL, and the difference frequency signal VdfReference signal V output from signal sourcerefThe phase difference θ of (a);
5) from the amplitude | V of the difference signaldfThe measurement of | and the phase difference θ yields a quadrature component V that does not vary with the change in the trim resistancexAnd a signal component V which varies with the change in the trimming resistancey：
Wherein
Is | VdfThe value of theta at the point of equilibrium is the minimum |;
6) signal component V varying with changes in trim resistanceyThe relation of the bridge balance satisfies:
wherein S is the measurement sensitivity and represents V corresponding to unit capacitance changeyFrom which is obtained a change of
And a signal component V varying with the change of the trimming resistanceyAnd the capacitor C to be measuredDUTCalibration relation of RrefIs a standard resistance, CrefIs a standard capacitance and RhIs a trim resistance;
7) the control end sets the resistance value of the balancing resistor through controlling the voltage to enable the low-temperature bridge circuit to be in a balanced state, and the signal component V changing along with the change of the balancing resistor is measuredyAnd obtaining the capacitor C to be measured by using the calibration relation curve obtained in the previous stepDUTA change in (c).
5. A measuring method according to claim 4, characterized in that in step 3), the current i is respectively input to the first and second low-frequency current input terminals1sin(ω1t) and i2sin(ω2t)，i1Is the amplitude of the alternating current at the first low-frequency current input terminal i2Is the amplitude, omega, of the alternating current at the second low-frequency current input1Is the angular frequency, omega, of the alternating current at the first low-frequency current input2Is the angular frequency of the alternating current at the second low-frequency current input end, and t is time; the current respectively passes through the balancing resistors R of the low-temperature bridge circuithAnd a standard resistance RrefRear-inflow low-temperature bridge circuitBetween the low-frequency voltage measuring positive terminal and the low-frequency voltage measuring negative terminal, a differential voltage i is generated1Rhsin(ω1t)-i2Rrefsin(ω2t), respectively measuring the amplitude i of the differential voltage by using a low-frequency phase-locking technology1RhAnd i2RrefTherefore, real-time measurement of the standard resistance and the balancing resistance is realized.
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