A transient current correction method for CELIV measurement

Abstract

The present invention discloses a transient current correction method for CELIV measurement, comprising the following steps: A current sampling circuit is formed by using a waveform signal generator, a sampling resistor, a standard resistor, and a digital storage oscilloscope; The digital storage oscilloscope records the voltage change curve of the sampling resistor over time, performs a non-linear fitting on the voltage change curve over time, obtains the parallel value R of the sampling resistor and the oscilloscope input resistor and the capacitor in parallel with the sampling resistor, replaces the standard resistor with a diode structure sample, and again measures the voltage change curve of the sampling resistor over time under linear bias voltage by the digital oscilloscope, calculates the current change curve passing through the sample, corrects it to the CELIV transient current curve under this linear voltage, and obtains the time corresponding to the peak value. By adopting the present invention, the influence of the sampling resistor voltage drop and the RC parameters of the measurement circuit is corrected, and a normal transient current curve is obtained, so that the electric field drift mobility can be determined according to the current peak time and the semiconductor thickness.

Description

Technical Field

[0001] The present invention relates to a current measurement method, and particularly to a transient current correction method for CELIV measurement. Background Art

[0002] The research and development in the field of semiconductor materials and devices have always had relatively rapid development. The transport ability of carriers in a semiconductor is a crucial factor affecting the performance of semiconductor devices. Mobility is the main parameter reflecting the electrical properties of carriers in a semiconductor. It has a direct impact on the working speed and high-frequency characteristics of semiconductor devices. Therefore, the measurement of carrier mobility is an important content in the research of semiconductor materials.

[0003] So far, there have been various methods for measuring mobility. Among them, the more commonly used ones are the Hall effect method, the time-of-flight method (TOF), the linear ramp carrier extraction transient method (CELIV), etc. Each method has its own advantages and disadvantages. The CELIV measurement system has a relatively simple structure and operation and low cost, and it is a new measurement technology for low-conductivity materials. Later, methods such as photo-CELIV and i-CELIV (injected-CELIV) were developed to measure mobility by increasing the number of carriers and current through light illumination or artificial injection. After more than 20 years of development, the CELIV technology has become an important means for measuring the carrier mobility of organic semiconductor materials. In its actual measurement, due to the involvement of transient processes, it is necessary to eliminate the influence of circuit distribution parameters and some AC impedances to improve the measurement accuracy. Generally, the solution is to select sufficiently small circuit R and C parameters to achieve this, and no other methods are recorded in the literature.

[0004] The existing solution is strictly speaking an approximation, and there are certain systematic errors and inaccuracies in the obtained transient current results; how to select R and C parameters brings inconvenience to the measurement of different samples. The main reason for this is that since the measurement object is the current transient spectrum, the transient characteristics of the measurement circuit must be considered. Therefore, the improper selection of the RC parameters of the measurement circuit is an important source of error. The current general method is to require the entire circuit to select sufficiently small R and C parameters. However, since the distributed capacitance in the circuit and some input impedances of the instrument are inevitable and difficult to clarify, and too small a sampling resistance value will cause the signal-to-noise ratio of the sampling voltage to be too weak and be easily interfered with and introduce errors. Therefore, this solution sometimes fails to meet the actual requirements and has limitations, resulting in problems with the accuracy of the transient current measurement results. In addition, with the differences in samples, the rate of increase of the applied bias voltage with time during measurement often needs to be changed, and the originally used R and C parameters may become inappropriate and need to be adjusted accordingly, which will all bring errors and inconvenience to the measurement. Summary of the Invention

[0005] The technical problem to be solved by the embodiments of the present invention is to provide a transient current correction method for CELIV measurement. On the basis of not strictly requiring the circuit R and C parameters, the correction formula and the improvement of the measurement method can be obtained through the equivalent circuit and semiconductor theory, so as to reasonably correct the measured current result.

[0006] To solve the above technical problem, the embodiments of the present invention provide a transient current correction method for CELIV measurement, including the following steps:

[0007] S1: Use a waveform signal generator, a sampling resistor, a standard resistor, and a digital storage oscilloscope to form a current sampling circuit;

[0008] S2: Make the waveform signal generator output a linearly increasing voltage with a slope of A, and the digital storage oscilloscope records the voltage change curve of the sampling resistor over time V 1 ~t ;

[0009] S3: Perform non-linear fitting on the voltage change curve over time V 1 ~t to obtain the parallel value R of the sampling resistor and the oscilloscope input resistor and the capacitance C in parallel with the sampling resistor;

[0010] S4: Replace the standard resistor with a Schottky diode structure sample, and measure the voltage change curve V1~t of the sampling resistor over time under a linearly reverse-biased voltage by the digital oscilloscope again, and calculate the change rate at each moment dV 1 / dt ;

[0011] S5: The waveform emitter outputs a stepped DC voltage, and the leakage current of the sample under different reverse-biased voltages is obtained by combining the sampling resistor voltage read by the digital oscilloscope with the Newton interpolation method I L ;

[0012] S6: Calculate the current change curve through the sample I(t) , and correct it to the CELIV transient current curve under this linear voltage by the following formula I R (t) , and obtain the time corresponding to the peak t m

[0013]

[0014] where the second term on the right side is the correction term, dV1 / dt is the oscilloscope reading V 1 the time rate of change; d and S represent the thickness and cross-sectional area of the semiconductor layer, respectively;

[0015] and the measurement result of the semiconductor mobility is obtained by the following formula:

[0016] .

[0017] Wherein, the S3 and S6 also include calculating the current passing through the standard resistor or the sample by the following formula:

[0018] .

[0019] Wherein, the S6 also includes calculating V 1( t ) the current density passing through the sample:

[0020]

[0021] Wherein is the conductivity of the material to be measured, E d is the electric field in the electrically neutral region inside the semiconductor, l = l(t) is the width of the charge depletion layer formed by the carriers being extracted by the bias electric field.

[0022] Implementing the embodiments of the present invention has the following beneficial effects: The present invention proposes an equivalent circuit for measurement and adds a calibration step during the measurement process. By fitting the measurement results of the current (voltage) when a known resistor is used as a sample through the circuit transient equation, the impedance and distributed capacitance values of the sampling circuit are obtained, so that the CELIV transient current measurement can be further corrected to obtain the accurate current value passing through the sample, rather than usually obtaining the transient current passing through the sample by simply dividing the voltage across the sampling resistor by the value of the sampling resistor, and also reduces the stringent requirements for the R and C parameters of the measurement circuit; According to the CELIV measurement principle, the formula for the transient current is deduced, and the influence of the sampling resistor voltage drop and the R and C parameters of the measurement circuit is corrected accordingly, obtaining a normal transient current curve with obvious peak position changes, so that the electric field drift mobility can be determined according to the current peak time and the semiconductor thickness μ . BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 is the measurement system of the present invention;

[0024] Figure 2It is a schematic diagram of the electric field distribution in the semiconductor layer;

[0025] Figure 3 It is the current (V1 / Rs) directly obtained from the voltage of the sampling resistor and the corrected transient current when the sample is under the condition that the bias voltage rising slope is 21.73 mV / ns. I R Schematic diagram of the curve. Specific implementation mode

[0026] To make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings.

[0027] Establish a measurement system as Figure 1 , which is composed of an AFG-2225 arbitrary waveform signal generator, a GDS-2104 digital storage oscilloscope, a sample holder with a fixture and a computer. The sample is a Schottky structure diode. Set a linearly increasing sawtooth voltage waveform on the Arbitrary Waveform Software-V3220 of the computer and transmit it to the waveform generator. Control the magnitude of the output bias voltage and the value of the rising slope A through the waveform generator. Observe and record the voltage signal on the sampling resistor and the bias voltage waveform output by the signal generator with the oscilloscope, and then record the signal data on the computer through the Freewave3-V323 software.

[0028] The experimental sample is a Schottky structure diode. When using an oscilloscope to measure the sample current, there will be obvious errors in the general method of directly obtaining the current by dividing the oscilloscope voltage reading by the sampling resistance value. Because from Figure 1 the equivalent circuit, it can be seen that the current passing through the sample should include the current flowing through the sampling resistor, the distributed capacitance and the internal impedance of the oscilloscope. Only considering the sampling resistor current is biased, and this influence will be more obvious in the measurement of the transient current that changes rapidly with time.

[0029] In order to obtain the internal resistance R 1 of the oscilloscope, the distributed capacitance C and the distributed inductance of the oscilloscope input cable L specific numerical values of the parameters, this method adds a pre-measurement calibration step, replacing the Schottky diode with a resistor R 2 (in this example ), so that the total current passing through the measured sample is divided into two parts. One part is the current R S flowing through the sampling resistor I S , and the other part I 1Via the input cable to the oscilloscope. Thus, the total current I has the following expression:

[0030] (1)

[0031] Because the voltage across the sampling resistor V S = At - IR 2 = L(dI 1 / dt) + V 1 , I 1 = CdV 1 / dt + V 1 / R 1 , where V 1 、V S is the oscilloscope reading and the voltage across the sampling resistor R S (330 Ω in this example), R 1 is the input resistance of the oscilloscope, A is the rising rate of the linearly rising voltage output by the signal source. Since the cable length used in the experiment is short, the influence of its inductance can be ignored. Substitute V 1 = At - I(t)R 2 into (1) to get:

[0032] (2)

[0033] Integrating gives:

[0034] (3-1)

[0035] From the above equation, we have

[0036] V 1 = At -(Equation 3-1)• R 2 (3-2)

[0037] According to this equation, performing a non-linear fit on the V 1 ~t data obtained by the oscilloscope can yield the distributed capacitance C , the resistance R and I, the capacitor C includes the distributed capacitance of the connecting cable and the input capacitance of the oscilloscope, R is the sampling resistor R S in parallel with the input resistance of the oscilloscope R 1 . In this example, the obtained C and R are 1.17×10 -10 F and 319.19 Ω respectively, which are consistent with the actual measured values using an RLC meter. When they are used in the calibration of the current, the current passing through the sample should be:

[0038] (4)

[0039] On the other hand, since a sampling resistor is added during the measurement, the linearly increasing voltage At output by the signal source is not fully loaded on the sample, which is different from the theoretical requirement of CELIV that the voltage is fully loaded on the sample. This is also an important factor causing errors. Under this actual situation and ignoring the leakage current condition, it is deduced that V 1( t ) the current density of the reverse-biased Schottky diode structure sample:

[0040] (5)

[0041] where is the conductivity of the material to be measured, E d is the electric field in the electrically neutral region inside the semiconductor, l=l(t) is the depletion layer width formed by the extraction of carriers by the bias electric field. The derivation process of equation (5) is as follows (combining Figure 1 and 2 ):

[0042] At-V1- Ф =V2 (6)

[0043] The third term on the left Ф is the contact potential, and V2 is the voltage drop across the semiconductor layer. From the Figure 2 displayed electric field distribution inside the semiconductor layer, it can be seen that

[0044] V 2 =E d d+(l 2 / 2)(eN / εε 0 ) (7)

[0045] eN is the charge density in the depletion region,N represents the ionized impurity concentration, εε 0 is the dielectric constant of the semiconductor material.

[0046] According to the Poisson equation, the electric field distribution in the depletion region:

[0047] (8)

[0048] From equations (6) and (7), we get

[0049] (9)

[0050] So the current density through the sample

[0051] (10)

[0052] where . From the cross-sectional area of the semiconductor layer S , we have jS = I - I L =(Equation 4) - leakage current. Further, the CELIV transient current curve without the voltage drop of the sampling resistor is obtained by correction through the following formula I R :

[0053] (11)

[0054] where the second term on the right side is the correction term, and dV1 / dt is the time derivative of the oscilloscope reading V 1 in this example εε 0 S / d = 2.97 pF .

[0055] Replace the standard resistor with the sample of the diode structure, measure the curve of the voltage across the sampling resistor versus time V1~t under the linear voltage by the digital oscilloscope, calculate the derivative d(V1) / dt at each moment; calculate the curve of the current through the sample versus time I(t) , according to the CELIV theory, through the corrected I R （t） curve, the time corresponding to the current peak can be read t m , and the carrier electric field drift mobility is obtained using the common formula for CELIV measurement:

[0056] (12)

[0057] Based on considering the circuit distributed capacitance and the oscilloscope input impedance, the present invention proposes an equivalent circuit for measurement and adds a calibration step during the measurement process. By fitting the measurement results of the current when a known resistor is used as a sample through the circuit transient equation, the impedance and distributed capacitance values of the sampling circuit are obtained, so that the measurement results of the CELIV transient current can be further corrected, improving the accuracy of the measured current in terms of principle and method, thus making the mobility measurement results more reliable, rather than simply obtaining the current value through the voltage on the sampling resistor in the prior art, and also reducing the stringent requirements for the R and C parameters of the measurement circuit and the inconvenience brought by selecting the RC parameters in the current technology.

[0058] The above-disclosed is only a preferred embodiment of the present invention, and of course, it cannot be used to limit the scope of the rights of the present invention. Therefore, equivalent changes made according to the claims of the present invention still fall within the scope covered by the present invention.

Claims

1. A transient current correction method for CELIV measurement, characterized in that Including the following steps: S1: A current sampling circuit is formed by using a waveform signal generator, a sampling resistor, a standard resistor, and a digital storage oscilloscope; S2: Make the waveform signal generator output a linearly increasing voltage with a slope of A, and the digital storage oscilloscope records the curve of the voltage across the sampling resistor changing with time. V 1 ~t ; S3: Perform non-linear fitting on the voltage-time curve V 1 ~t to obtain the parallel value R of the sampling resistor and the oscilloscope input resistor, and the capacitance C in parallel with the sampling resistor; S4: Replace the standard resistor with a Schottky diode structure sample, and measure the curve of the voltage across the sampling resistor changing with time V1~t under linearly reverse-biased voltage again by a digital oscilloscope, and calculate the change rate at each moment. dV 1 / dt ; S5: The waveform signal generator outputs a stepped DC voltage, and the leakage current of the sample under different reverse bias voltages is obtained by combining the voltage of the sampling resistor read by the digital storage oscilloscope with the Newton interpolation method. I L ; S6 : Calculate the curve of the current passing through the sample versus time I(t) , which is corrected by the following formula to the CELIV transient current curve at this linear voltage I R (t) , and obtain the time corresponding to the peak t m , Among them, the second term on the right is the correction term. dV 1 / dt is the oscilloscope reading V 1 of the time rate of change; d and S respectively represent the thickness and cross-sectional area of the semiconductor layer; And the measurement result of the semiconductor mobility is obtained through the following formula: 。 2. The transient current correction method for CELIV measurement according to claim 1, characterized in that The S3 and S6 also include calculating the current passing through the standard resistor or the sample through the following formula: 。 3. The transient current correction method for CELIV measurement according to claim 2, characterized in that, The S6 also includes calculating through the following formula V 1( t ) the current density passing through the diode structure sample: wherein is the conductivity of the material to be measured, E d is the electric field in the electrically neutral region inside the semiconductor, l = l (t) is the width of the charge depletion layer formed by carriers being extracted by the bias electric field.

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