JPH0820276B2 - Physical quantity measurement method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial field of application] The present invention is to accurately and promptly perform measurement on a measurement target at which a measurement value at an arbitrary measurement point in a physical quantity measurement obtains a measurement value with time change. The present invention relates to a physical quantity measuring method capable of

[Conventional technology]

Conventionally, a measurement method for a measurement object in which a measurement value at an arbitrary measurement point changes with time is mainly the following (a),
(B) It is performed by two methods.

(A) Sweeping of measurement points is performed at a constant speed, the speed is variously changed, the time change of the measurement value at each measurement point is associated with the difference between the measurement results, and the true value of the measurement result is obtained. presume.

(B) The measurement points are discretely selected, waiting measurement results are obtained until the time change of the measurement values ends at each measurement point, and the true value of the measurement results between the discrete measurement points is estimated.

[Problems to be Solved by the Invention]

The problems of each of the above-mentioned conventional techniques (a) and (b) will be described.

(A) Since the measurement points are swept at various speeds, if the sweep speed of the measurement points is different depending on the time change of the measurement value at each measurement point, the measurement result is different. As shown in FIG. 7, when the measured value at a certain measurement point changes over time, the measured value represented at each point in the time locus of the measured value in FIG. This is because it depends on the time to obtain it. Therefore, there is a drawback that the measurement result is estimated by performing sweeping at various speeds, and the measurement result never becomes a true value. Also, if the measurement is performed with a sweep that reciprocates the measurement point, unless the sweep is performed at an extremely slow rate, the measurement results will differ depending on the forward and backward passes, depending on the time change of the measured value. There is also a drawback that an erroneous measurement result such as is obtained.

(B) Accurate measurement values can be obtained in order to obtain measurement values by selecting measurement points discretely and waiting until the time change of the measurement values is completed, but measure values between discrete measurement points. It cannot be obtained, and there is a drawback that the measurement result does not become a true value when the measurement value changes abruptly at such a measurement point.

〔Purpose〕

INDUSTRIAL APPLICABILITY The present invention eliminates the drawbacks of the prior art, and does not depend on the change (dy / dt) in the time (t) of the measured value (y), and the accurate measured result can be promptly obtained without missing the temporal change of the measured value. It provides a measurement method that can be obtained.

[Means for solving the problem]

The time differential amount dy / dt of the measured value y is extracted from the measured value y corresponding to the measured point x based on the time reference value dt, and the sweep speed dx of the measured point x described below is used by using this dy / dt. / dt is determined and, for example, the measurement point x is determined by integrating this dx / dt.

To determine the time differential amount dx / dt, which is the sweep speed of the measurement point x from the time differential value dy / dt of the measurement value y, for example, the measurement result of an XY recorder with the measurement point x and the measurement value y as the coordinate axes. The relation that the speed dL / dt of drawing the line segment L of is constant, that is, (d
L / dt) ² = (dx / dt) ² + (dy / dt) ² = constant. This relationship does not have to be strictly constant, (dx / dt) + (dy / dt) = constant, or (dx / d
t) · (dy / dt) = constant, (dx / dt) U (union), (dy /
dt) = constant, etc. If the relationship between dx / dt and dy / dt is such that dx / dt is small when dy / dt is large, or conversely, dx / dt is large when dy / dt is small. Good. That is, the sweep speed of the measurement point is determined from the relationship that the speed of drawing the line segment of the measurement result is almost constant.

[Action]

In the measurement region where the variation of the measurement value y at the time t is large, the time derivative dy / dt of the measurement value y becomes large, and the speed dL / dt for drawing the measurement result is related (dL / dt) ² = (dx / dt)
^From the relationship of ² + (dy / dt) ² = constant, the speed dx / dt of sweeping the measurement point x becomes small, and as a result, the speed of drawing the line segment of the measurement result becomes constant or almost constant. For example,
Since (dx / dt) ² + (dy / dt) ² = constant, dx / dt becomes small and the sweep of the measurement point x becomes slow. Conversely, the measured value y
In the measurement region in which the change with time is small, dy / dt becomes small, and the sweep speed dx / dt at the measurement point x is increased to perform swept quickly.

[Embodiment 1] FIG. 1 is an example of a recording apparatus to which the measuring method of the present invention is applied, in which a voltage is used as a measuring point which is widely used for product inspection and development of semiconductor devices such as diodes in the semiconductor-related industry. This is an example applied to C-V characteristic measurement in which V and measured value are depletion layer capacitance C.

In the figure, reference numeral 11 is a sample as a measurement object for measuring the C-V characteristic, which is connected to a capacitance meter 12 for measuring the depletion layer capacitance of the sample 11.

A voltmeter 13 applies a bias voltage Vb to the sample 11 via the capacitance meter 12. 14 is a recorder for recording C-V characteristics,
The voltage value is on the horizontal axis and the output of the capacitance meter is on the vertical axis. A time differentiator 15 is connected to the capacitance meter 12 to output the time derivative of the capacitance change obtained by the capacitance meter 12. 16 is a proportional constant setter which outputs a proportional constant k. The 17 calculator is the time derivative of the output capacity of the time differentiator 15 and the proportional constant setting device.
The proportional constant with respect to the output of 16 is input and the calculation by the method of the present invention is performed to output the time differential value of the bias voltage for setting the bias voltage. 18 is a time integrator for determining the bias voltage applied to the sample 11, 19 is an initial value setter for setting the initial value of the bias voltage applied to the sample together with the time integrator 18, 20 is an initial value setter 19 It is connected to the voltage source 13 to control the voltage applied to the sample 11 with an adder that adds the outputs from the time integrator 18. Reference numeral 21 is a measurement start switch, which sets the time integrator output to zero on the (A) side before starting measurement,
This is to activate the time integrator 18 on the side (B) to start the measurement.

Next, the operation of the device will be described. Switch before measurement
21 is set to the side for obtaining voltage (A), the voltage source 3 is applied to the measurement sample 11, and the bias voltage Vb = Vi is applied to the measurement sample 11 only by the value of Vi determined by the initial value setting device 19.
The output C from the capacitance meter 12 becomes stable, and its time differential amount dC / dt
Must be small enough.

In this state, the other parts of the apparatus of this embodiment have the proportional constant setter 16 set to k, and dC / dt is almost zero as described above. In the embodiment, the calculation content is dV / dt = k−dC / dt, so the value of dV / dt = k is output.

The measurement is started by switching the switch 21 to the side (B) that obtains the output of the time integrator 18. As a result, the sum Vb = V + Vi of the output V of the time integrator 18 and the output Vi of the initial value setting device 19 is output from the adder 20, and the voltage is applied to the sample 11 from the voltage source.

The depletion layer capacitance C of the measurement sample changes due to this measurement point voltage Vb, and this change is output as dC / dt by the time integrator 15. When this time change dC / dt is large, the calculator 17
In the calculation dV / dt = k−dC / dt, dV / dt becomes small and the measuring point V is output by the time integrator 18. At this time, the sweep speed of the measuring point V becomes slow.

The time variation of the depletion layer capacitance C is small, and the time variation dC / dt
On the contrary, when is small, dV / dt becomes large and the sweep speed of the measurement point becomes fast. This control is continuously performed until the measurement is completed.

This operation has the following effects. "Deep levels" in the semiconductor crystal that constitutes the sample to be measured
And the charge state due to the thermal excitation of this "deep level", which is a problem in the semiconductor-related industry, differs depending on the nature of the "deep level". In the "deep level", for example, trapped electrons are thermally excited and emitted to the conduction band, and various "deep levels" exist in the region depleted during CV characteristic measurement. , The measurement value C corresponding to the measurement point V is accompanied by various time-dependent changes. According to the measurement in the present embodiment in which the method of the present invention is performed, when the measured value C changes greatly with time, the measurement point V is gently swept, so that a rapid change can be accurately captured, and conversely, the time When the change is small, the measurement point V is swept quickly, so that the measurement time is not wasted.

Measurement results of the method of the present invention ((a) in FIG. 2) and measurement results by the method according to the conventional technique (a) ((b) in FIG. 2)
When compared with (d) to (d), the measurement results obtained by the conventional technique are different according to the sweep speed of the measurement point, and in the order of (b), (c), and (d) in FIG. This shows a defect that the measurement result becomes more different in the forward and return paths as the sweep speed of the bias voltage becomes faster. On the other hand, the measurement results according to the present invention are the same measurement results on the outward and return routes, and accurately capture the inflection point of the CV characteristic curve due to the "deep order".

Example 2 An example in which the method of the present invention is applied to the photocapacitance method will be described.

The photocapacitance method is the most sensitive method for directly measuring the "deep level", which is one of the most important criteria for crystal evaluation of semiconductor materials in the research and development of semiconductor related industries.

The photocapacitance method will be briefly described. A diode is formed with a pn junction or the like using a semiconductor crystal to be evaluated, or monochromatic light is irradiated to the junction of a semiconductor device formed on a crystal substrate using an optical system using a spectroscope or the like. . When the electrons trapped in the “deep level” corresponding to the energy value of this monochromatic light: hν are excited and reach the conduction band and flow away from the junction as carriers, the space charge of the junction changes.

This change in space charge is measured by a capacitance meter as a change in junction capacitance. The energy hν of monochromatic light is swept, the change in the junction capacitance is measured, the optical transition energy value related to the “deep level” is known from the energy value to which the junction capacitance responds, and the “deep level” is determined from the change amount of the capacitance. You can know the value of "rank". In this embodiment, in order to keep the spread of the depletion layer constant, the bias voltage is controlled to keep the junction capacitance constant, the energy hν of monochromatic light is swept, and the bias voltage and light energy thus controlled are measured. Get as a result.

FIG. 3 is a block diagram of an apparatus for explaining an example in which the method of the present invention is applied to the photocapacitance method. Reference numeral 31 in the figure is connected to a capacitance meter 32 for measuring the junction capacitance of a sample to be measured for "deep level" in this device. The capacitance meter 32 is capable of outputting the value of the difference between the junction capacitance that should be kept constant and the set capacitance, and is input to the integrator 33 that integrates this difference, and is connected to the integrator 33 by the integrated value. A bias voltage is applied to the measurement sample 31 from the voltage source 34 via the capacitance meter 32. As a result, a negative feedback loop is formed, and even if the space charge state of the depletion layer of the sample junction changes due to the irradiation of light energy, it is held at a constant junction capacitance.

On the other hand, in order to obtain the bias voltage as a numerical value, a digital voltmeter is connected to the output side of the voltage source 34.
The digitized bias voltage value of the digital voltmeter 35 can be read from the control computer.

Reference numeral 36 denotes a monochromatic light source, for example, a tungsten sphere light source is dispersed by a spectroscope to obtain monochromatic light, and the sample diode is irradiated with the optical system such as a mirror. This monochromatic light source is connected so that the wavelength sweep can be controlled by the control computer 37. 38 is a measurement start point setting device, which sets the wavelength sweep start point and outputs it to the control computer. Reference numeral 39 is a proportional constant device connected to output to the control computer 37. The measurement start point and the constant of proportionality can also be input from the keyboard of the control computer 37 or the like. Reference numeral 40 is an XY plotter that outputs the measurement result from the computer 37 and draws it.

A flowchart executed by the control computer 37 for measuring the photocapacitance in which the measurement point is the energy hν of monochromatic light and the measurement value is the bias voltage Vb according to the method of the present invention will be described.

FIG. 4 is a flow chart. In order to determine the time reference value Δt, this flow starts at 41 at regular time intervals. At 42, the bias voltage Vb is applied to the measurement sample 31 from the voltage source 34 and digitized by the digital voltmeter 35 to control the computer 37.
And the difference ΔVb = Vb′−Vb from the value Vb ′ input last time is obtained as the time differential amount ΔVb / Δt of the measured value. The proportional constant k is input at 43, and the XY plotter according to the method of the present invention is input.
The calculation is performed so that the speed at which 10 draws the measurement result is constant. Therefore, in this example, (dx / dt) ² + (dy / dt) ²
= K (constant). That is, since the calculation is performed for each time reference amount Δt, Δhν = (k− (ΔVb) ² ) ^1/2 is calculated. At 44, add Δhν to the current measurement point hν and hν ′ = h
Let ν + Δhν. (However, at the start of measurement, the value hν ₀ of the measurement start point setting device 38 is set to hν ′. This hν ′ is the value of the next measurement point. With this, the monochromatic light source 36 is controlled to determine the measurement point. At 45, record the measurement result in the XY plotter 40, or store the measurement result if necessary. After the measurement, the measurement result can be drawn on the XY plotter. After that, the flow returns to 41 and is repeated until the measurement is completed. Be done.

Next, the operation of this embodiment will be described. The measurement is started by activating the control computer, and the monochromatic light having the energy value hν from the monochromatic light source 36 is applied to the joint portion of the sample 37 according to the value of hν ₀ input from the measurement start point setter 38. . If a “deep level” that responds to this hν-sized energy is inherent in the crystal that constitutes the sample,
The deviation of the capacitance which is the output of the capacitance meter 32 due to the change of the junction capacitance ΔC
Occurs, and the voltage Vb of the voltmeter 34 changes to cancel it. Flowchart of control computer 37 (4th
If the time variation ΔVb / Δt of Vb is large at 42 in the figure), Δhν is calculated at Δhν = (k−
The light energy value hν ′ = hν + Δhν is reduced to (ΔVb) ² ) ^1/2 and the change Δhν of the monochromatic light energy, which is the process performed in the flowchart 44, is added to the monochromatic light source 36.
Control. Since this action is repeatedly performed within a short time, as a result, the sweep of the light energy performed by the monochromatic light source 36 is delayed. On the contrary, when the “deep level” in response to the light energy hν does not exist in the crystal of the sample 37 and the voltage Vb does not change, ΔVb / Δt becomes zero at 42 in the flowchart of FIG. 4 and Δhν = ( k- (ΔVb) ² )
^1/2 = k ^1/2 , and as a result, the energy sweep of the monochromatic light source 36 becomes faster.

This action produces the following effect. The “deep level” trapping cross section σ is defined as τ = 1 / (σ / Nph) in relation to the time constant τ of excitation by monochromatic light hν and the intensity Nph of monochromatic light, and various “deep levels” The capture cross section σ differs greatly depending on the cause of the “level”, and the time change of the measured value Vb also greatly changes. By using the method of the present embodiment, an accurate measurement result can be promptly obtained despite a large difference in the change over time of the measured value Vb due to the difference in capture cross-section.

FIG. 5 is a measurement result according to the present example in which the method of the present invention is carried out, which accurately captures a sharp change in the applied voltage Vb to the sample with respect to the monochromatic light energy hν. Select the discrete measurement point hν by
FIG. 6, which is the measurement result by the measurement method of waiting until the time change of Vb is completed, clearly shows that the abrupt change of Vb with respect to hν is not captured.

As described above, when the method of the present invention is used, it is possible to accurately know the light energy hν for obtaining the optical transition energy value of “deep level” in the photocapacitance measurement, which greatly contributes to the quality improvement of the semiconductor crystal. be able to.

〔The invention's effect〕

In the physical quantity measurement in the industrial field, measurement values that vary greatly at different measurement points with time change and are difficult to measure are captured from the cause of the "deep level" of the physical phenomenon, which is the measurement target of Example 2, for example. The phenomenon due to the temporal change of the measured value such as the cross-sectional area cannot be accurately grasped, and the cause can be clarified by carrying out the method of the present invention.

In the physical quantity measurement in the industrial field, a measurement value corresponding to an arbitrary measurement point often changes with time, and accurate measurement is difficult and problematic in such measurement.

By using the measurement method of the present invention, the measurement value is delayed in the measurement area with a large change over time in the measurement area, and the measurement point is swept quickly in the area in which the change over time in the measurement value is small. The measurement result is accurate according to the time change.

Moreover, since the time required for measurement is efficient, it has high industrial utility value.

[Brief description of drawings]

FIG. 1 is an example of a recording apparatus to which the measuring method of the present invention is applied,
2 is an example of a measurement result, FIG. 3 is a block diagram of a measurement example for explaining an example in which the method of the present invention is applied to a photocapacitance method, and FIG. 4 is a photocapacitance characteristic to which the method of the present invention is applied. FIG. 5 is a diagram showing a flow chart of a program for measurement, FIG. 5 is a diagram showing measurement results of photocapacitance characteristics obtained by an apparatus to which the method of the present invention is applied, and FIG. , FIG. 7 is a diagram showing a temporal change of the measured value at an arbitrary measuring point. 11, 31 …… Sample as the object to be measured, 12 …… Capacity meter,
13 ... Voltage source, 14 ... Recorder, 15 ... Time integrator, 17 ...
… Computer, 35 …… Digital voltmeter, 36 …… Monochromatic light source, 37 …… Control computer

Claims (1)

[Claims] 1. When recording a measurement result in which a measurement value of an object to be measured with respect to an arbitrary measurement point changes with time, a time differential amount of the measurement value at the arbitrary measurement point is detected, and a new measurement point is detected from the detection result. In order to obtain the above, a method for measuring a physical quantity, characterized by having a process of making a drawing speed of a measurement result constant or almost constant.