Resistivity Measurement System

Abstract

To provide a resistance rate measurement system that can highly accurately and quickly measure a resistance rate of a measured object and a resistance rate distribution in the measured object by non-destruction.SOLUTION: A resistance rate measurement system comprises: a voltage generation unit that generates a voltage having a cyclical waveform between a protection electrode 23 and a substrate supporting body 31; a current voltage conversion unit that, when a voltage is applied between the protection electrode 23 and the substrate supporting body 31 in a state where a capacitance probing needle part 20 is put into close with a substrate W, and a gap G is formed between the capacitance probing needle part and the substrate, converts a current flowing to a probing needle electrode 21 to the voltage; a Fourier transformation unit that Fourier-transforms digital data obtained by converting an analog voltage to be output from the current voltage conversion unit; an amplitude phase calculation unit that calculates an amplitude component and phase component from a real number component and imaginary number component to be obtained by the Fourier transformation; and a resistance rate calculation unit that calculates a resistance rate on the basis of at least one frequency dependence of the real number component, imaginary number component, amplitude component and phase component.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a resistivity measurement system. [Background technology]

[0002] Among compound semiconductors such as GaAs, InP, and SiC, those having semi-insulation properties are widely used as semiconductor substrates for fabricating integrated circuits and power devices. Such semi-insulating semiconductor substrates (hereinafter sometimes abbreviated as substrates) are manufactured by slicing an ingot of compound semiconductor, which is crystal-grown by a method such as pulling from a melt or sublimation, into thin slices and then polishing them. Since the characteristics of electronic devices such as FETs formed on the substrate are greatly affected by the resistivity of the substrate, it is required that the resistivity be within a predetermined range and that the resistivity distribution over the entire substrate is uniform. For this reason, it is essential to measure the average resistivity and standard deviation of the resistivity of the substrate, as well as the resistivity distribution over the entire substrate.

[0003] Conventional methods for measuring the resistivity of a substrate include a method in which the substrate is placed on a conductive substrate support, a conductive probe is brought into contact with the substrate surface, and the current flowing when a voltage is applied between the conductive probe and the conductive substrate support (see, for example, Patent Document 1), a method in which multiple ohmic electrodes are formed on the substrate surface and the resistivity is measured using a four-terminal method (see, for example, Patent Document 2), and a method in which multiple conductive probes are brought into contact with the substrate surface and the current flowing between the probes is measured (see, for example, Patent Document 3).

[0004] However, these methods have the problem that the substrate surface is damaged or destroyed by contacting the conductive probe with the substrate surface or forming an ohmic electrode. In addition, there is a problem that resistivity cannot be measured with high accuracy and stability due to electrical instability at the interface between the conductive probe and the substrate surface or the difficulty of forming an ohmic electrode on a semi-insulating semiconductor substrate. Furthermore, there is a problem that it takes a relatively long time to measure the resistivity distribution over the entire substrate surface.

[0005] In contrast, there are non-destructive measurement methods using a capacitance probe as a measurement method that does not damage or destroy the substrate (see, for example, Non-Patent Documents 1 and 2). In these non-destructive measurement methods, a substrate is placed in contact with one side of a conductive substrate support, and a capacitance probe consisting of a conductive probe electrode and a protective electrode that insulates and surrounds the side of the probe electrode is brought close to the other side of the substrate. With the protective electrode maintained at ground potential and the probe electrode connected to a terminal of a charge amplifier as a pseudo-ground potential, the output voltage output from the output terminal of the charge amplifier when a voltage having a certain waveform is applied to the substrate support is measured.

[0006] In particular, Non-Patent Document 1 discloses that when a voltage having a single-step waveform with a single polarity is applied to a substrate support, the equation Q(τ)=Q(∞)-(1 / e)(Q(∞)-Q(0)) is theoretically derived for the charge amount Q(t) representing the output voltage of the charge amplifier, where Q(0) is the charge amount at time t=0, Q(∞) is the charge amount at time t=∞, and Q(τ) is the charge amount at time t=τ, and the resistivity ρ can be obtained from the dielectric relaxation time τ. However, in an actual measurement of the charge amount Q(t), the rise of the single-step waveform does not occur instantly but takes a certain amount of time, and the charge amplifier is not ideal, and its gain and phase are frequency-dependent and are also affected by DC drift, etc. For this reason, the non-destructive measurement method disclosed in Non-Patent Document 1 has problems with measurement accuracy and measurement time. In particular, when the resistivity ρ is large, it takes a relatively long time to measure Q(∞) and the effect of the DC drift of the charge amplifier becomes large, reducing the measurement accuracy of Q(∞). On the other hand, when the resistivity ρ is small, there is a problem that the measurement accuracy of Q(0) decreases due to the influence of the rise time of the single-shot staircase waveform and the frequency dependence of the gain and phase of the charge amplifier.

[0007] In order to solve the problems with the nondestructive measurement methods described above, as shown in Non-Patent Document 2, the present inventors proposed applying a bipolar, periodically repeating square wave voltage to the substrate support rather than a single unipolar step-wave voltage, and further proposed analyzing the frequency response rather than analyzing the time response of the output voltage from the charge amplifier. They have already shown that this will be an extremely useful substrate evaluation technique in the field of semi-insulating semiconductor substrate manufacturing. [Prior art documents] [Patent documents]

[0008] [Patent Document 1] Japanese Patent Application Publication No. 63-33666 [Patent Document 2] Japanese Patent Application Publication No. 02-24573 [Patent Document 3] Japanese Patent Application Publication No. 05-164795 [Non-patent literature]

[0009] [Non-Patent Document 1] R. Stibal, J. Windscheif, W. Janz, Semicond. Sci. Technol. Vol. 6, 1991, pp. 995-1001. [Non-Patent Document 2] M. Fukuzawa, M. Yamada, Institute of Physics, Conference Series Number174, Paper presented at 29th International Symposium Compound Semiconductors, Lausanne, Switzerland, 7-10 October 2002, pp. 85-88 Summary of the Invention [Problem to be solved by the invention]

[0010] However, Non-Patent Document 2 does not disclose a specific method for solving the above-mentioned problems, a method for measuring resistivity, or a specific configuration of a system for measuring resistivity.

[0011] The present invention has been made in consideration of the above-mentioned circumstances, and has an object to provide a resistivity measurement system that can non-destructively measure the resistivity of an object to be measured and the resistivity distribution in the object to be measured with high accuracy and high speed. [Means for solving the problem]

[0012] In order to achieve the above object, a resistivity measurement system according to the present invention comprises: A conductive substrate support for supporting the object to be measured; a capacitive probe portion having a columnar probe electrode, a cylindrical protective electrode disposed so as to surround the probe electrode, and a cylindrical insulator portion interposed between the probe electrode and the protective electrode, wherein an end of the probe electrode on the side of the substrate support and an end of the protective electrode on the side of the substrate support are disposed on the same imaginary plane; a voltage generating unit that generates, between the protective electrode and the substrate support, a voltage having a periodic waveform with a preset period, with the protective electrode at a ground potential; a current-voltage converter that converts into a voltage a current flowing into the probe electrode when the voltage generating unit applies a voltage having the periodic waveform between the protective electrode and the substrate support and the probe electrode is maintained at a pseudo-ground potential while the capacitance probe unit is brought close to the object to be measured that is supported by the substrate support and a gap is formed between the object and the capacitance probe unit; an analog / digital conversion unit that samples the analog voltage output from the current-voltage conversion unit in synchronization with the set period and at a time interval of 1 / N of the set period to convert the analog voltage into digital data; a Fourier transform unit that performs a Fourier transform on the digital data from the analog / digital conversion unit; an amplitude / phase calculation unit that calculates an amplitude component and a phase component from the real component and the imaginary component obtained by the Fourier transform; and a resistivity calculation unit that calculates a resistivity based on the frequency dependence of at least one of the real component, the imaginary component, the amplitude component, and the phase component.

[0013] Further, the resistivity measurement system according to the present invention comprises: The resistivity calculation unit may calculate the resistivity based on a frequency dependence of at least one of the real component, the imaginary component, the amplitude component, and the phase component based on a predetermined frequency transfer function of the current-voltage conversion unit.

[0014] Further, the resistivity measurement system according to the present invention comprises: The frequency transfer function may be determined based on real and imaginary components obtained by Fourier transforming digital data output by the analog / digital conversion unit when a voltage having the periodic waveform is applied between the substrate support and the protected electrode while the object to be measured is not supported by the substrate support.

[0015] Further, the resistivity measurement system according to the present invention comprises: The periodic waveform may be a sawtooth wave that fluctuates at the set period.

[0016] Further, the resistivity measurement system according to the present invention comprises: The periodic waveform may be a square wave that fluctuates at the set period.

[0017] Further, the resistivity measurement system according to the present invention comprises: The periodic waveform may be a triangular wave that fluctuates at the set period.

[0018] Further, the resistivity measurement system according to the present invention comprises: the object to be measured is a semi-insulating semiconductor substrate, The set period may be longer than a dielectric relaxation time of the object to be measured.

[0019] Further, the resistivity measurement system according to the present invention comprises: a moving mechanism for relatively moving the capacitance probe unit and the substrate support; A control unit for controlling the moving mechanism, The control unit may control the moving mechanism so as to measure the resistivity at a plurality of points on the object to be measured. Effect of the Invention

[0020] According to the present invention, the capacitance probe portion, the object to be measured, and the substrate support are arranged in the order of the conductive probe electrode, the gap, the object to be measured, and the conductive substrate support, so that the capacitance probe portion does not come into contact with the object to be measured. Therefore, problems such as damage or destruction of the object to be measured, and further the influence of electrical instability at the contact portion with the object to be measured do not occur. Therefore, the resistivity and resistivity distribution of the object to be measured can be measured nondestructively, highly accurately, and stably.

[0021] Furthermore, according to the present invention, since the protective electrode of the capacitance probe portion is at ground potential and the probe electrode is connected to the terminal of the current-voltage converter, the probe electrode is at pseudo-ground potential, and the electric field distribution between the capacitance probe portion and the substrate support becomes non-uniform at the outer periphery of the protective electrode of the capacitance probe portion due to the end face effect. However, the electric field distribution in the probe electrode portion, i.e., the target area measured by the capacitance probe portion, is uniform, and is not affected by undesirable currents such as leakage currents flowing from the protective electrode to the probe electrode. Therefore, highly accurate resistivity measurement is possible.

[0022] Furthermore, according to the present invention, the current-voltage converter and the analog-to-digital converter are operated in synchronization with the set period of the voltage generated by the voltage generator, and the electrical noise components during measurement can be reduced by performing an addition process on the digital data for each set period, thereby suppressing the variation in the measured resistivity value caused by electrical noise during measurement.

[0023] Furthermore, according to the present invention, the digital data obtained at a time interval of 1 / N of the set period of the voltage generated by the voltage generating unit is Fourier transformed, so that the real and imaginary components of the angular frequency, as well as the amplitude and phase components can be instantly calculated from the real and imaginary components. Therefore, the frequency dependence of each of the real, imaginary, amplitude and phase components can be calculated at once at high speed, so that the influence of current generation that is undesirable for measurement, such as DC drift in the object to be measured, can be eliminated. Therefore, resistivity measurement can be performed quickly and with high accuracy. [Brief description of the drawings]

[0024] [Figure 1] 1 is a schematic configuration diagram of a mechanical system of a resistivity measurement system according to an embodiment. [Diagram 2] 3 is a schematic enlarged cross-sectional view showing the arrangement of a capacitance probe portion, a substrate, a substrate support, and an insulating support according to the embodiment. FIG. [Diagram 3] 3 is an electrical equivalent circuit diagram formed by a probe electrode, a gap, a substrate, and a substrate support according to the embodiment. FIG. [Figure 4] FIG. 2 is a block diagram of a measurement calculation control system of the resistivity measurement system according to the embodiment. [Diagram 5] 5A and 5B show examples of waveforms of voltages generated by a voltage generating unit in an embodiment, where (A) is a sawtooth wave, (B) is a square wave, and (C) is a triangular wave. [Figure 6] 11 is a diagram illustrating the relationship between a sampling interval, the number of samplings, and a period when a square wave response is performed in the embodiment. FIG. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0025] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, a specific description will be given of an embodiment of the present invention with reference to the drawings, with a mechanical system and a measurement control system of the resistivity measurement system of the present invention being separated.

[0026] FIG. 1 is a schematic diagram of the mechanical system of the resistivity measurement system of the present invention. The mechanical system of the resistivity measurement system includes a capacitance probe unit 20, a substrate W, a substrate support 31, an insulating support 32, and a moving mechanism 90. The moving mechanism 90 has an X-axis stage 91, a Y-axis stage 92, and a Z-axis stage 93. The Z-axis stage 93 raises and lowers a moving stage (not shown) to which the capacitance probe unit 20 is attached along the Z-axis direction as shown by an arrow AR13. That is, the capacitance probe unit 20 can be moved up and down by the Z-axis stage 93. The X-axis stage 91 moves a moving stage 91a to which the insulating support 32 is attached along the X-axis direction as shown by an arrow AR11. The Y-axis stage 92 moves a moving stage 92a to which the X-axis stage 91 is attached along the Y-axis direction as shown by an arrow AR12. The Y-axis stage 92 is fixed to a base (not shown).

[0027] The insulating support 32 is formed in a flat plate shape from an insulating material. The substrate support 31 is formed in a flat plate shape from a conductive material, and is disposed vertically above the insulating support 32. This allows the substrate support 31 to move in a horizontal plane by the X-axis stage 91 and the Y-axis stage 92. The capacitance probe unit 20 can move in a horizontal plane while maintaining a gap G between the probe surface 24 and the upper surface of the substrate W.

[0028] The substrate W, which is the object to be measured, is placed on the upper surface of the substrate support 31 and is supported by the substrate support 31. The substrate W is generally shaped like a thin disk, but may have other shapes.

[0029] 2 is a schematic enlarged cross-sectional view showing the arrangement of the capacitance probe section 20, the substrate W, and the substrate support 31. The capacitance probe section 20 has a conductive cylindrical probe electrode 21, a cylindrical conductive protective electrode 23 arranged so as to surround the probe electrode 21, and a cylindrical insulator section 22 interposed between the probe electrode 21 and the protective electrode 23. Here, the end of the probe electrode 21 on the substrate support 31 side and the end of the protective electrode 23 on the substrate support 31 side are arranged on the same imaginary plane VP1. In other words, the capacitance probe section 20 has the conductive probe electrode 21, the conductive protective electrode 23, and the insulator section 22 interposed between the probe electrode 21 and the protective electrode 23 to insulate them. The probe electrode 21, the insulator portion 22, and the protected electrode 23 are integrally formed such that the end face of the probe electrode 21 on the substrate support 31 side and the end face of the protected electrode 23 on the substrate support 31 side form a probe surface 24 that exists in the same imaginary plane VP1. Here, the central axis of the probe electrode 21, the cylindrical axis of the insulator portion 22, and the cylindrical axis of the protected electrode 23 are aligned. The shape of the probe electrode 21 is not limited to a cylindrical shape, and may be, for example, a rectangular column or other shapes. The shapes of the insulator portion 22 and the protected electrode 23 are also not limited to a cylindrical shape, and may be a rectangular column or other shapes. The probe electrode 21, the protected electrode 23, and the substrate support 31 are connected to terminals a, b, and c, respectively, via conductors.

[0030] As described later, the probe electrode 21 and the protected electrode 23 of the capacitance probe portion 20 are used at a pseudo-equal potential. Therefore, no leakage current flows from the protected electrode 23 to the probe electrode 21 or vice versa. When the gap G is narrowed and a voltage is applied between the substrate support 31 and the protected electrode 23, the electric field lines between the capacitance probe portion 20 and the substrate W are as shown by the arrows in FIG. 2. The electric field lines are nonuniform below the outer periphery of the protected electrode 23 due to the end effect, but are uniform in the measurement target area below the probe electrode 21.

[0031] Assuming that there is a virtual electrode on the upper surface of the substrate W in the measurement target area, the capacitance and resistance formed by the virtual electrode and the substrate support 31 sandwiching the substrate W are respectively expressed as C s , Rs The capacitance formed by the virtual electrode and the probe electrode 21 across the gap G is C a Then, the electrical equivalent circuit diagram formed by the probe electrode 21, the gap G, the substrate W and the substrate support 31 is as shown in Fig. 3. Note that the capacitance between the protected electrode 23 of the capacitive probe portion 20 and the virtual electrode or the probe electrode 21 is omitted.

[0032] As shown in FIG. 2, the distance between the probe surface 24 and the substrate support 31 is d 0 , the thickness of the substrate is d s , the distance of the gap G is d a Let the resistivity and dielectric constant of the semi-insulating semiconductor substrate be ρ and ε, respectively. r , the dielectric constant of vacuum is ε 0 If the electrode area of ​​the virtual electrode is A, then C s =ε 0 ε r A / d s , R s =ρd s / A. In addition, the dielectric relaxation time is τ s Then, τ s =C s R s =ε 0 ε r ρ, where τ s is a material-specific property that does not depend on the geometric shape of the electrode area or electrode spacing. a is C a =ε 0 A / d a In order to simplify the following equations, we use τ a =C a R s In addition, τ s , τ a has a unit of time and is called a time constant in the field of electrical circuit engineering. r If the dielectric relaxation time τ is known, s This is equivalent to measuring

[0033] 4 is a schematic diagram of a measurement, calculation and control system of the resistivity measurement system of the present invention. The measurement, calculation and control system of the resistivity measurement system includes a voltage generating section 40, a current-voltage converting section 50, an analog / digital converting section 60, an X-axis driver 96, a Y-axis driver 97, a Z-axis driver 98, and a personal computer (hereinafter referred to as "PC") 100.

[0034] The voltage generating section 40 has a waveform memory 41, a digital / analog conversion circuit 42, and a power amplifier circuit 43, and generates a voltage having a periodic waveform with a preset period between the guard electrode 23 and the substrate support 31, with the guard electrode 23 at ground potential. clk The waveform data recorded in the waveform memory 41 is sequentially sent to the digital / analog conversion circuit 42 in synchronization with the power amplifier circuit 43, and a periodic voltage V in The voltage generated by the voltage generating unit 40 is supplied to a terminal c' connected to the output of the power amplifier circuit 43 and to a terminal b' at ground potential. The terminals c' and b' are respectively connected to the terminals c and b shown in FIG. 1. The voltage generating unit 40 generates a periodic voltage having the aforementioned set period, such as a sawtooth wave, a rectangular wave, or a triangular wave, as shown in FIGS. 5(A) to 5(C), in response to a waveform clock W. clk In the following explanation, the set period is T.

[0035] Returning to FIG. 4, the current-voltage conversion unit 50 converts into a voltage the current flowing into the probe electrode 21 when the voltage generator 40 applies a voltage having a periodic waveform between the protective electrode 23 and the substrate support 31 and the probe electrode 21 is maintained at a pseudo-ground potential, with the capacitance probe unit 20 being brought close to the substrate W supported by the substrate support 31 and a gap G being formed between the substrate W and the capacitance probe unit 20. The current-voltage conversion unit 50 has an operational amplifier 52 and a feedback passive element 51. The input terminals of the current-voltage conversion unit 50 are terminals a' and b'. The terminals a' and b' are connected to the terminals a and b of the capacitance probe unit 20 shown in FIG. 1, respectively. The feedback passive element 51 may be called a charge amplifier when it is only a capacitance component, and may be called a current amplifier when it is only a resistance component. The operational amplifier 52 is preferably one having a large gain, a small phase delay, a large input impedance, and a small input bias current or input bias voltage.

[0036] The current flowing into the terminal of the current-voltage conversion unit 50 is the sum of the current flowing out to the feedback passive element 51 and the current flowing into the negative terminal of the operational amplifier 52. Since the input impedance of the operational amplifier 52 is extremely large, the current flowing into the negative terminal of the operational amplifier 52 is extremely small, and the current flowing into the terminal of the current-voltage conversion unit 50 is equal to the current flowing out to the feedback passive element 51. Since the positive terminal of the operational amplifier 52 is maintained at ground potential, the terminal of the current-voltage conversion unit 50, i.e., the negative terminal of the operational amplifier 52, becomes pseudo-ground potential. The gain and phase of the operational amplifier 52 and the impedance of the feedback passive element 51 generally have frequency dependence. The frequency dependence of the current-voltage conversion unit 50 is expressed by a frequency transfer function having a real component and an imaginary component.

[0037] The analog / digital conversion section 60 has a sampling / hold circuit 61 and an analog / digital conversion circuit 62, and samples the analog voltage output from the current / voltage conversion section 50 in synchronization with the above-mentioned set period and at a time interval of 1 / N of the set period to convert it into digital data. The input of the analog / digital conversion section 60 is connected to the voltage output of the current / voltage conversion section 50 and a terminal g. If the output of the current / voltage conversion section 50 is disconnected and an external analog voltage output is connected to the terminal g, an analog voltage other than the output voltage of the current / voltage conversion section 50 can also be measured. FIG. 6 shows the timing of sampling the voltage output from the current / voltage conversion section 50 when the voltage generation section 40 is generating a rectangular wave voltage. As shown in FIG. 6, the control section 95 generates a sampling clock S at every time interval Δt obtained by dividing the set period T of the periodic waveform voltage generated by the voltage generation section 40 by N, that is, at time t=nΔt (n=1, 2, 3, . . .). clk to the analog / digital conversion unit 60. The analog / digital conversion unit 60 converts the output sampling clock S clk In synchronization with the above, the voltage output from the current-voltage converter 50 is sampled and held by the sampling / hold circuit 61, and then converted by the analog / digital converter 62 into time-series digital data D n (n=1, 2, 3, . . . ) is output to an interface of PC 100, which will be described later.

[0038] The PC 100 is a general-purpose PC and includes a CPU (Central Processing Unit), a main memory, an auxiliary memory, an interface, and a bus connecting each unit. The main memory is made up of a volatile memory and is used as a working area for the CPU. The auxiliary memory is made up of a non-volatile memory and stores programs executed by the CPU. The CPU loads the programs stored in the auxiliary memory into the main memory and executes them, thereby functioning as a preprocessing unit 81, a Fourier transform unit 70, an amplitude / phase calculation unit 82, a resistivity calculation unit 83, and a control unit 95.

[0039] The control unit 95 outputs a waveform clock W to the voltage generating unit 40 in synchronization with the system clock. clk The analog / digital converter 60 receives the sampling clock S clk Furthermore, the control unit 95 sends position command pulses to an X-axis driver 96, a Y-axis driver 97, and a Z-axis driver 98 to position the X-axis stage 91, the Y-axis stage 92, and the Z-axis stage 93.

[0040] The preprocessing unit 81 converts the time-series digital data D input from the analog / digital conversion unit 60 into n (n=1,2,3,...) is divided into periods (n=1,2,3,...,N) and the averaging process for M periods is performed. n (n=1,2,3,...) is the data obtained by sampling the complex output voltage output from the circuit represented by the electrical equivalent circuit diagram shown in Figure 3. Time-series digital data D n (n=1,2,3,...) is divided into periods (n=1,2,3,...,N) and the digital data for M periods is D n、m (n=1,2,3,···,N, m=1,2,3,···,M), i.e., D 1,1 ,D 2,1 ,D 3,1 ,···,D N,1 , D 1,2 ,D 2,2 ,D 3,2 ,···,D N,2 , D 1,3 ,D 2,3 ,D 3,2 ,···,D N,3 , D 1,M ,D 2,M ,D 3,M ,···,D N,M The weighted average processed periodic digital data is expressed as E n (n=1,2,3,...,N), then E 1 =(D 1,1 +D 1,2 +D 1,3 +···+D 1,M ) / M,E 2 =(D 2,1 +D2,2 +D 2,3 +···+D 2,M ) / M,E 3 =(D 3,1 +D 3,2 +D 3,3 +···+D 3,M ) / M,...,E N =(D N,1 +D N,2 +D N,3 +···+D N,M ) / M. If this pre-processing is performed over many periods, noise in the digital data can be reduced, i.e., the resistivity measurement can be made more accurate, but the measurement time becomes longer. Therefore, the number of periods for which this pre-processing is performed can be determined by the trade-off between the high accuracy and high speed of the resistivity measurement. The pre-processing unit 81 then performs the weighted averaging process described above to generate the digital data E n (n=1, 2, 3, . . . , N) is notified to the Fourier transform unit 70.

[0041] The Fourier transform unit 70 performs a Fourier transform on the digital data input from the analog / digital conversion unit 60. More specifically, the Fourier transform unit 70 performs a Fourier transform on the digital data input from the analog / digital conversion unit 60 and subjected to weighted average processing in the preprocessing unit 81. The Fourier transform unit 70 performs a Fourier transform on the digital data E n For (n=1,2,3,...,N), if N is a power of 2, the Fast Fourier Transform (FFT) algorithm is used to perform the Fourier transform, and if N is not a power of 2, the Discrete Fourier Transform (DFT) algorithm is used to perform the Fourier transform. Note that the transformation speed of the FFT is much faster than that of the DFT. As a result of this Fourier transform, the angular frequency nω n For (n=1,2,3,...,N), the real component P n , the imaginary component Q n get.

[0042] Here, the Fourier series analysis performed by the Fourier transform unit 70 will be described in detail. in(t) can be expanded in a Fourier series, with the period being T and the angular frequency being ω n = 2πn / T, then it can be expressed as the following equation (1).

[0043]

number

[0044] In addition, the Fourier coefficient a in Eq. (1) n and b n is expressed by the following formula (2) and formula (3). 0 is the voltage V in (t) is the average value, i.e., the DC component. In the following, in order to simplify the handling of the formula, 0 = 0. This means that V in This corresponds to the case where (t) is a bipolar, positive-negative symmetrical waveform.

[0045]

number

[0046]

number

[0047] The Fourier series using sine waves and cosine waves as in formulas (1) to (3) may be expressed as a complex Fourier series using complex numbers and complex Fourier coefficients, which are alternative expressions. Specific formulas are omitted here.

[0048] Since the voltage actually output from the voltage generating unit 40 has a finite rise time and fall time, it is appropriate to use the partial sums of up to N terms in equations (1) to (3). When using partial sums, an oscillatory phenomenon called the Gibbs phenomenon occurs near discontinuous points. To alleviate this, a Hamming window or the like is used to weight each term, that is, the coefficient a of each term is n and b n Alternatively, as will be described later, the voltage output from the voltage generating unit 40 may be actually measured, and the coefficient a n and b n can be calculated in advance.

[0049] As shown in FIGS. 5A to 5C, the voltage output from the voltage generating unit 40 has an amplitude of |V in Let us consider three types of voltage: a sawtooth wave voltage, a square wave voltage, and a triangular wave voltage. When the waveform of the voltage output from the voltage generating unit 40 is a sawtooth wave as shown in FIG. 5(A), the above-mentioned formula (1) becomes the following formula (4).

[0050]

number

[0051] From equation (4), we can see that the sawtooth voltage is composed only of the sum of sine wave voltages, its frequency has odd and even components, the amplitude of the odd components is positive and the amplitude of the even components is negative, and the absolute value of the amplitude decreases by an odd multiple as the frequency increases.

[0052] When the waveform of the voltage output from the voltage generating unit 40 is a square wave as shown in FIG. 5(B), the formula (1) becomes the following formula (5).

[0053]

number

[0054] From equation (5), we can see that the square wave voltage is composed only of the sum of sine wave voltages, its frequency only has odd wave components, and the amplitude decreases by an odd multiple as the frequency increases.

[0055] When the waveform of the voltage output from the voltage generating unit 40 is a triangular wave as shown in FIG. 5(C), the formula (1) becomes the following formula (6).

[0056]

number

[0057] From equation (6), we can see that the triangular wave voltage is composed only of the sum of cosine wave voltages, its frequency only has odd wave components, and as the frequency increases, the amplitude decreases as a square of an odd multiple, that is, the harmonic components decrease rapidly.

[0058] Here, the angular frequency ω n Complex voltage V in n (ω n ) is applied between terminals a and c in the electrical equivalent circuit diagram shown in Figure 3. Let Z n (ω n ), where j is the imaginary unit, the complex admittance Z is the inverse of the complex impedance. n -1 (ω n ) is expressed by the following formula (7).

[0059]

number

[0060] If the complex current flowing between terminal a and terminal c is In(ωn), the following relational expression (8) is obtained.

[0061]

number

[0062] Voltage V in The complex voltage of the nth term when (t) is expanded into a complex Fourier series is V in n (ω n ), and the real component of the frequency transfer function of the current-voltage conversion unit 50 is G(ω n ), and the imaginary component is F(ω n ), the complex current I n (ω n ) is input, the complex output voltage V n (ω n ) is substituted into the above equation (8) to obtain the following equation (9).

[0063]

number

[0064] In addition, the real component of the complex output voltage Re[V n (ω n )] and the imaginary component Im[V n (ω n )] are expressed by the following equations (10) and (11), respectively.

[0065]

number

[0066]

number

[0067] Returning to FIG. 4, the amplitude and phase calculation unit 82 calculates the real component Pn and the imaginary component Q n Specifically, the amplitude / phase calculation unit 82 uses the fact that the angular frequency components are orthogonal to each other to calculate the amplitude and phase components of the angular frequency ω n The amplitude and phase calculation unit 82 calculates the real component P n and the imaginary component Q n In the case of , the amplitude component is S n =[P n 2 +Q n 2 ] 1 / 2 , the phase component is U n =arctan(Q n / P n ) is calculated as follows.

[0068] Here, the amplitude component of the complex output voltage |V n (ω n )| and the phase component φ n (ω n ) are expressed by the following formulas (12) and (13), respectively.

[0069]

number

[0070]

number

[0071] In addition, in the formulas (10) to (13), γ=τ a / τ s =d s / ε r d a It was decided.

[0072] Next, the resistivity measurement system 10 according to the present embodiment is used to measure the periodic voltage V in Complex voltage V when (t) is expanded into a complex Fourier seriesin n (ω n 4, the output of the current-voltage conversion unit 50 is disconnected, and the terminal c' which is the output terminal of the voltage generation unit 40 is connected to the input terminal g of the sampling / hold circuit 61 of the analog-to-digital conversion unit 60. The voltage output by the voltage generation unit 40 is converted into digital data by the analog-to-digital conversion unit 60, and the digital data is Fourier-transformed by the Fourier transformation unit 70, to obtain a complex voltage V in n (ω n ) is obtained.

[0073] Next, the resistivity measurement system according to the present embodiment is used to measure the real component G(ω n ) and the imaginary component F(ω n 4, terminal c', which is the output terminal of voltage generating section 40, is connected to terminal a', which is the terminal of current-voltage converting section 50, and the voltage output from voltage generating section 40 is converted to digital data by analog-to-digital converting section 60, and the digital data is Fourier-transformed by Fourier transforming section 70, whereby the real component G(ω n ) and the imaginary component F(ω n ) can be obtained directly.

[0074] 2 and 3, in a state where the substrate W is not placed on the substrate support 31, that is, d s =0, d a =d 0 When C a =C 0 =ε 0 A / d 0 , τ s →∞, and if the voltage output by voltage generating unit 40 is converted to digital data by analog / digital conversion unit 60 and the digital data is Fourier transformed by Fourier transform unit 70, the following equation (14) can be obtained from the above-mentioned equations (8) and (9).

[0075]

number

[0076] Therefore, in advance, jω n C 0 V in n (ω n ) is measured, the real component G(ω n ) and the imaginary component F(ω n ) is obtained.

[0077] In the resistivity measurement system according to the present embodiment, when the substrate W is not placed on the substrate support 31, d s =0, d a =d 0 When C a =C 0 , τ s 4 is connected to the input side of the sampling / hold circuit 61 of the analog / digital conversion unit 60, the voltage output by the voltage generation unit 40 is converted into digital data by the analog / digital conversion unit 60, and the digital data is then Fourier-transformed by the Fourier transformation unit 70, thereby obtaining jω n C 0 V in n (ω n ) is obtained.

[0078] The resistivity calculation unit 83 calculates the resistivity based on the frequency dependence of at least one of the real component, the imaginary component, the amplitude component, and the phase component of the complex output voltage. As described above, the distance between the probe surface 24 of the capacitance probe unit 20 and the substrate support 31 is d 0 , the thickness of the substrate is d s , the distance of the gap G is d a Let the resistivity and relative dielectric constant of the semi-insulating semiconductor substrate to be measured be ρ and ε, respectively. r , the dielectric constant of vacuum is ε 0If the electrode area of ​​the virtual electrode is A, then C s =ε 0 ε r A / d s , R s =ρd s / A. And the dielectric relaxation time is τ s Then, τ s =C s R s =ε 0 ε r Therefore, the resistivity calculation unit 83 calculates the dielectric relaxation time τ s Calculate the calculated τ s So ρ = ε 0 ε r / τ s The resistivity ρ is calculated using the following relation:

[0079] Here, the resistivity calculation unit 83 calculates the dielectric relaxation time τ s The method of calculating the periodic digital data E n The real component P obtained by performing a fast Fourier transform or a discrete Fourier transform on (n=1,2,3,...,N) n , the imaginary component Q n , amplitude component S n =[P n 2 +Q n 2 ] 1 / 2 , phase component U n =arctan(Q n / P n ) are the angular frequencies ω n For each (n=1,2,3,...,N), equations (10), (11), (12) and (13) are satisfied, and a simultaneous equation consisting of N equations is obtained for each component. Then, V in n (ω n ), G(ω n ), F(ω n If the angular frequency dependence of τ can be ignored or is previously measured and known, then equations (10), (11) and (12) can be expressed as s , γ and C aThe equation (13) is a simultaneous equation with unknowns, τ s The resistivity calculation unit 83 calculates τ using these continuity equations. s The resistivity calculation unit 83 calculates γ in relation to the geometric dimension d s and d a and the relative dielectric constant ε of the object to be measured r Calculate from C a Let A and d be the geometric dimensions. a and the dielectric constant in vacuum ε 0 The resistivity calculation unit 83 calculates the resistivity from the periodic digital data E n The real component P obtained by performing a fast Fourier transform or a discrete Fourier transform on (n=1,2,3,...,N) n , the imaginary component Q n , amplitude component S n =[P n 2 +Q n 2 ] 1 / 2 , phase component U n =arctan(Q n / P n ) is the angular frequency ω n For each τ, we set τ so that all of equations (10), (11), (12), or (13) are satisfied. s may be calculated.

[0080] The resistivity calculation unit 83 calculates |V n (ω n )| and the amplitude component S obtained by Fourier transform n From this, the dielectric relaxation time τ s Calculate |V n (ω n )| depends on the parameter τ s , γ, C a Including |V n (ω n )| to |V n (ω n :τ s, γ,C a The resistivity calculation unit 83 calculates the resistivity of each angular frequency ω n |V inn (ω n :τ s ,γ,C a )| and S n The average of the squared differences between 2 We use the error function

[0081]

number

[0082] The resistivity calculation unit 83 calculates the variance s 2 The parameter τ for which is the maximum likelihood estimate s , γ, C a Here, the resistivity calculation unit 83 calculates the parameter τ using a nonlinear least squares method such as the Gauss-Newton method or the Levenberg-Marquardt method, which is an iterative method. s , γ, C a When calculating approximately using the least squares method, |V n (ω n )| or the amplitude component S n If there are outliers or abnormal values ​​in , the likelihood of the approximation may be extremely low. Therefore, the parameters γ and C a For the measurement, the geometric dimensions measured in advance and the relative dielectric constant ε r and the parameters γ and C in the least squares method a It is preferable to limit the search range for the value of τ. s So ρ = ε 0 ε r / τ s The resistivity ρ is calculated using the following relation:

[0083] As described above, according to the resistivity measurement system of this embodiment, the capacitance probe unit 20, the substrate W and the substrate support 31 are arranged vertically from top to bottom in the following order: conductor (probe electrode 21)-insulator (gap G)-semi-insulator (substrate W)-conductor (substrate support 31), and the capacitance probe unit 20 does not contact the substrate W. This prevents problems such as damage or destruction of the substrate W and the effects of electrical instability at the contact portion with the substrate W. This allows the resistivity and resistivity distribution of the substrate W to be measured nondestructively, accurately and stably.

[0084] Furthermore, according to the resistivity measurement system of this embodiment, the protected electrode 23 of the capacitance probe portion 20 is at ground potential and the probe electrode 21 is connected to the terminal a' of the current-voltage conversion portion 50, so that the probe electrode 21 is at a pseudo-ground potential, and the electric field distribution between the capacitance probe portion 20 and the substrate support 31 becomes non-uniform at the outer periphery of the protected electrode 23 of the capacitance probe portion 20 due to the end face effect. However, the electric field distribution becomes uniform at the probe electrode 21 portion, i.e., the target area measured by the capacitance probe portion 20, and is not affected by undesirable currents such as leakage currents flowing from the protected electrode 23 to the probe electrode 21. This improves the measurement accuracy of the resistivity.

[0085] Furthermore, according to the resistivity measurement system of this embodiment, the current-voltage conversion unit 50 and the analog-to-digital conversion unit 60 are operated in synchronization with the set period of the voltage generated by the voltage generation unit 40, so that the electrical noise components during measurement can be reduced by adding up the digital data for each set period, thereby suppressing the variation in the measured resistivity value caused by electrical noise during measurement.

[0086] Furthermore, according to the resistivity measurement system of the present embodiment, the digital data obtained at a time interval ΔT (=T / N) that is 1 / N of the set period T of the voltage generated by the voltage generating unit 40 is Fourier-transformed to obtain the angular frequency ω nIt is possible to instantly calculate the real and imaginary components in (=2πn / T, n=0,1,2,...,N), as well as the amplitude and phase components from the real and imaginary components. Therefore, the frequency dependence of the real, imaginary, amplitude and phase components can be obtained quickly all at once, eliminating the effects of undesirable current generation such as DC drift occurring in the substrate W. This makes it possible to perform resistivity measurement quickly and with high accuracy.

[0087] Furthermore, according to the resistivity measurement system of the present embodiment, the real component G(ω n ) and the imaginary component F(ω n ) are calculated in advance, it is possible to easily correct the real and imaginary components obtained by Fourier transform of the digital data obtained at a time interval ΔT (=T / N) that is 1 / N of the set period T of the voltage generated by the voltage generating unit 40. Therefore, it is possible to eliminate the influence of the frequency dependency of the gain and phase of the current-voltage converting unit 50, enabling highly accurate resistivity measurement.

[0088] Furthermore, according to the resistivity measurement system of this embodiment, the digital data measured by placing the capacitance probe unit 20 close to the substrate support 31 without placing the substrate W on the substrate support 31 is Fourier-transformed to obtain the real component G(ω n ) and the imaginary component F(ω n ) is calculated. For this purpose, the real component G(ω n ) and the imaginary component F(ω n ) can be calculated relatively easily.

[0089] Furthermore, in the resistivity measurement system according to the present embodiment, the waveform of the voltage generated by the voltage generating unit 40 is a sawtooth wave, a square wave, or a triangular wave with a set period T. As a result, when the voltage waveform is expanded into a Fourier series, the angular frequency ω n (=2πn / T, n=0, 1, 2, . . . , N). That is, the voltage generating unit 40 generates a voltage having a fundamental angular frequency ω 1 From ultra-high angular frequency ω ∞Since a voltage having a waveform expressed as a sum of sine waves or cosine waves up to 10000000000000 is applied, the processing speed for calculating the resistivity can be increased.

[0090] Furthermore, according to the resistivity measuring system of the present embodiment, the set period T of the voltage generated by the voltage generating unit 40 is set to be equal to or shorter than the dielectric relaxation time τ s This results in a dielectric relaxation time τ s The dielectric relaxation frequency ω is the reciprocal of s is the fundamental angular frequency ω 1 From ultra-high angular frequency ω M Therefore, the resistivity can be calculated with high accuracy from the frequency dependence of at least one of the real component, the imaginary component, the amplitude component, and the phase component after the Fourier transform of the voltage generated by the voltage generating unit 40.

[0091] Furthermore, according to the resistivity measurement system of this embodiment, the capacitance probe part 20 can be moved relatively to the substrate support 31 in a state where a gap G is formed between the capacitance probe part 20 and the substrate W. This allows the resistivity to be measured at multiple positions on the substrate W at high speed and with high accuracy without damaging the substrate W, and therefore the resistivity distribution can be measured at high speed and with high accuracy.

[0092] Although the embodiment of the present invention has been described above, the present invention is not limited to the configuration of the above-mentioned embodiment. For example, the resistivity calculation unit 83 calculates Re[V n (ω n )] and the imaginary component Im[V n (ω n )] and the real component P obtained by Fourier transform n and the imaginary component Q n From this, the dielectric relaxation time τ s Hereinafter, Re[V n (ω n )] and Im[V n (ω n )] into τ s , γ, C aWith parameters, Re[V n (ω n :τ s, γ,C a )] and Im[V n (ω n :τ s, γ,C a Specifically, the resistivity calculation unit 83 calculates each angular frequency ω n In Re[V n (ω n :τ s, γ,C a )] and P n and the mean squared difference between Im[V n (ω n :τ s, γ,C a )] and Q n The variance s is the sum of the weighted average of the squared differences between 2 Alternatively, an error function expressing the following may be used.

[0093]

number

[0094] Here, the weighting coefficients of the real component and the imaginary component are w and v, respectively. The resistivity calculation unit 83 calculates the variance s 2 The parameter τ for which is the maximum likelihood estimate s , γ, C a is calculated by the least squares method.

[0095] In addition, the resistivity calculation unit 83 calculates the resistivity φ given by the above-mentioned equation (13). n (ω n ) and the phase component U obtained by Fourier transform n From this, the dielectric relaxation time τ s Hereinafter, φ n (ω n ) and τ s、 φ with γ as a parameter n (ωn ) to φ n (ω n :τ s, Specifically, the resistivity calculation unit 83 calculates each angular frequency ω n In n (ω n :τ s, γ) and U n The average of the squared differences between 2 Alternatively, an error function expressing the following may be used.

[0096]

number

[0097] The resistivity calculation unit 83 calculates the variance s 2 The parameter τ for which is the maximum likelihood estimate s , γ is calculated by the least squares method. Here, the variance s 2 Unlike the above equation (15) or (16), the parameter C a Therefore, the resistivity calculation unit 83 calculates the parameter τ s, γ can be calculated more quickly.

[0098] The present invention allows various embodiments and modifications without departing from the broad spirit and scope of the present invention. The above-described embodiments are for the purpose of explaining the present invention and do not limit the scope of the present invention. That is, the scope of the present invention is indicated by the claims, not the embodiments. Various modifications made within the scope of the claims and within the scope of the meaning of the invention equivalent thereto are considered to be within the scope of the present invention. [Industrial Applicability]

[0099] The present invention is suitable as a resistivity measurement system for measuring the resistivity and resistivity distribution of a semi-insulating semiconductor substrate. [Explanation of symbols]

[0100] 20: capacitance probe section, 21: probe electrode, 22: insulator section, 23: protective electrode, 24: probe surface, 30: substrate, 31: substrate support, 32: insulating support, 40: voltage generating section, 41: waveform memory, 42: digital / analog conversion circuit, 43: power amplifier circuit, 50: current / voltage conversion section, 51: feedback passive element, 52: operational amplifier, 60: analog / digital conversion section, 61: sampling / hold circuit, 62: analog Log / digital conversion circuit, 70: Fourier transform section, 81: pre-processing section, 82: amplitude / phase calculation section, 83: resistivity calculation section, 90: movement mechanism, 91: X-axis stage, 91a, 92a: moving table, 92: Y-axis stage, 93: Z-axis stage, 95: control section, 96: X-axis driver, 97: Y-axis driver, 98: Z-axis driver, 100: PC, a, a', b, b', c, c', g: terminals, G: gap, VP1: virtual plane

Claims

1. A conductive substrate support for supporting the object to be measured; a capacitive probe portion having a columnar probe electrode, a cylindrical protective electrode disposed so as to surround the probe electrode, and a cylindrical insulator portion interposed between the probe electrode and the protective electrode, wherein an end of the probe electrode on the side of the substrate support and an end of the protective electrode on the side of the substrate support are disposed on the same imaginary plane; a voltage generating unit that generates, between the protective electrode and the substrate support, a voltage having a periodic waveform with a preset period, with the protective electrode at a ground potential; a current-voltage converter that converts into a voltage a current flowing into the probe electrode when the voltage generating unit applies a voltage having the periodic waveform between the protective electrode and the substrate support and the probe electrode is maintained at a pseudo-ground potential while the capacitance probe unit is brought close to the object to be measured that is supported by the substrate support and a gap is formed between the object and the capacitance probe unit; an analog / digital conversion unit that samples the analog voltage output from the current / voltage conversion unit in synchronization with the set period and at a time interval of 1 / N of the set period to convert the analog voltage into digital data; a Fourier transform unit that performs a Fourier transform on the digital data from the analog / digital conversion unit; an amplitude / phase calculation unit that calculates an amplitude component and a phase component from the real component and the imaginary component obtained by the Fourier transform; and a resistivity calculation unit that calculates a resistivity based on frequency dependence of at least one of the real component, the imaginary component, the amplitude component, and the phase component. Resistivity measurement system.

2. The resistivity calculation unit calculates the resistivity based on a frequency dependency of at least one of the real component, the imaginary component, the amplitude component, and the phase component based on a frequency transfer function of the current-voltage conversion unit that is set in advance. The resistivity measurement system of claim 1 .

3. the frequency transfer function is found based on a real component and an imaginary component obtained by Fourier transforming digital data output by the analog / digital conversion unit when a voltage having the periodic waveform is applied between the substrate support and the protected electrode in a state in which the object to be measured is not supported by the substrate support. The resistivity measurement system of claim 2 .

4. The periodic waveform is a sawtooth wave that fluctuates at the set period. The resistivity measurement system according to any one of claims 1 to 3.

5. The periodic waveform is a square wave that fluctuates at the set period. The resistivity measurement system according to any one of claims 1 to 3.

6. The periodic waveform is a triangular wave that fluctuates at the set period. The resistivity measurement system according to any one of claims 1 to 3.

7. the object to be measured is a semi-insulating semiconductor substrate, The set period is longer than the dielectric relaxation time of the object to be measured. The resistivity measurement system according to any one of claims 1 to 6.

8. a moving mechanism for relatively moving the capacitance probe unit and the substrate support; A control unit for controlling the moving mechanism, The control unit controls the moving mechanism so as to measure the resistivity at a plurality of points of the object to be measured. The resistivity measurement system according to any one of claims 1 to 7.

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