JP2014120021A - Band gap calculation device and band gap calculation program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a band gap calculation device and a band gap calculation program that can calculate a band gap with more accuracy.SOLUTION: The band gap calculation device is configured to: in a range of an input hν value (a range between points P1 and P2), plurally set a calculation range of a predetermined width in a different range by shifting the calculation range thereof at predetermined intervals; while changing a value of the predetermined width, out of each calculation range, identify the calculation range in which a Tauc curve is the closest to a linear line; calculate a liner line L1 extending along the Tauc curve in the identified range; and calculate the hν value at an intersection point P3 of the linear line L1 and a predetermined reference line (a lateral axis or a baseline linear line L2) or P6 thereof as a band gap.

Description

  The present invention relates to a band gap calculation apparatus and a band gap calculation program for calculating a band gap using a Tauc curve.

  The calculation of the band gap (forbidden band width) of a substance is important as a basic measurement in physical physics, and various methods for calculating the band gap have been proposed (for example, see Patent Document 1 below). ). Among them, the method using the Tauc curve is widely used as a method for calculating the band gap.

FIG. 4 is a diagram for explaining a conventional example of a band gap calculation method using a Tauc curve. In the Tauc curve, spectral data is represented with the vertical axis (hνα) ^{(1 / n)} and the horizontal axis hν. Here, h is the Planck constant, ν is the frequency, and α is the extinction coefficient. n is a value determined by the type of transition of the sample. For example, in the case of direct allowable transition, n = 1/2.

  When calculating a band gap using a Tauc curve, instead of obtaining a tangent at the inflection point for the Tauc curve as illustrated in FIG. 4, for example, a least square method within a range set around the inflection point. Use to find the straight line. Specifically, when the operator inputs two points P101 and P102 around the inflection point, a range between the two points P101 and P102 is set as the calculation range R100. Then, a straight line L101 is obtained using the least square method within the set calculation range R100, and an intersection point P103 between the straight line L101 and the horizontal axis is obtained. Thereby, the hν value at the intersection P103 can be calculated as a band gap.

JP-A-5-215699

  However, in the conventional method as described above, since the operator visually inputs the two points P101 and P102 around the inflection point, the set calculation range R100 is not necessarily an appropriate range. If the set calculation range R100 is not appropriate, the straight line L101 obtained using the least square method in the calculation range R100 is a line that is greatly different from the tangent at the inflection point. In this case, the band gap calculated from the hν value at the intersection point P103 between the obtained straight line L101 and the horizontal axis is also a value significantly different from the actual value, and the band gap cannot be calculated with high accuracy. There's a problem.

  Further, when the operator visually inputs the two points P101 and P102 around the inflection point, it is conceivable that the operator inputs the information with sufficient care so that an appropriate calculation range around the inflection point is set. . However, in such a case, there is a problem that the operator cannot easily perform the input operation.

  The present invention has been made in view of the above circumstances, and an object thereof is to provide a band gap calculation device and a band gap calculation program capable of calculating a band gap with higher accuracy. It is another object of the present invention to provide a band gap calculation apparatus and a band gap calculation program that can calculate a band gap with simpler work.

  A band gap calculation apparatus according to the present invention is a band gap calculation apparatus for calculating a band gap using a Tauc curve, and includes an input reception processing unit that receives an input of a range of hν values, and an input hν value. Within a range, a plurality of calculation ranges with a predetermined width are shifted by a predetermined interval to set a plurality of different ranges, and a calculation range in which the Tauc curve is closest to a straight line is specified among the calculation ranges while changing the value of the predetermined width. A range identification processing unit, and a band gap calculation processing unit that calculates a straight line extending along the Tauc curve in the specified calculation range and calculates an hν value at the intersection of the straight line and a predetermined reference line as a band gap. It is characterized by having.

  According to such a configuration, while changing the width of a plurality of calculation ranges that are set by shifting by a predetermined interval within the range of the input hν value, the calculation range in which the Tauc curve is closest to the straight line among the calculation ranges. The straight line extending along the Tauc curve in the specified calculation range can be determined as the straight line closest to the tangent at the inflection point of the Tauc curve. By calculating the hν value at the intersection of the straight line thus obtained and the predetermined reference line as the band gap, the band gap can be calculated with higher accuracy.

  In addition, when inputting the range of hν value, just enter a wider range including the inflection point of the Tauc curve, and automatically change the calculation range within that range, automatically calculating the appropriate value. The band gap can be calculated by specifying the range. Therefore, compared to a configuration in which an appropriate calculation range around the inflection point must be set, the input work is simple, and the band gap can be calculated with a simpler work. .

  The calculation range specifying processing unit may calculate a correlation coefficient in each calculation range and specify a calculation range in which the value of the correlation coefficient is closest to 1.

  According to such a configuration, by using the correlation coefficient in each calculation range, it is possible to accurately specify the calculation range in which the Tauc curve is closest to the straight line in each calculation range. Can be calculated.

  The band gap calculation processing unit may obtain a straight line using a least square method within a specified calculation range, and calculate an hν value at the intersection of the straight line and a predetermined reference line as a band gap. Good.

  According to such a configuration, since the straight line extending along the Tauc curve in the specified calculation range can be accurately obtained by using the least square method, the band gap can be calculated with higher accuracy.

  The calculation range specifying processing unit may change the value of the predetermined width in a stepwise manner until the predetermined width becomes smaller than a predetermined threshold.

  According to such a configuration, since the width of the calculation range becomes too small, it can be prevented that the accuracy in specifying the calculation range in which the Tauc curve is closest to the straight line among the calculation ranges is reduced. The band gap can be calculated with higher accuracy.

  A band gap calculation program according to the present invention is a band gap calculation program for calculating a band gap using a Tauc curve, and includes an input reception processing unit that receives an input of an hν value range, and an input hν value. Within a range, a plurality of calculation ranges with a predetermined width are shifted by a predetermined interval to set a plurality of different ranges, and a calculation range in which the Tauc curve is closest to a straight line is specified among the calculation ranges while changing the value of the predetermined width. Computer as a band gap calculation processing unit that calculates a straight line extending along the Tauc curve in the specified calculation range and a hν value at the intersection of the straight line and a predetermined reference line as a band gap. Is made to function.

  According to the present invention, since the straight line closest to the tangent line at the inflection point of the Tauc curve can be obtained, by calculating the hν value at the intersection of the straight line and a predetermined reference line as a band gap, The band gap can be calculated with higher accuracy. In addition, according to the present invention, the band gap can be calculated by automatically specifying an appropriate calculation range within the range of the input hν value, so that the input work is simple and simpler. The band gap can be calculated with

It is the block diagram which showed the structural example of the band gap calculation apparatus which concerns on one Embodiment of this invention. It is the figure which showed an example of the display screen of a display part when the process by a control part is performed. It is the flowchart which showed an example of the process by the control part at the time of calculating a band gap. It is a figure for demonstrating the prior art example of the calculation method of the band gap using a Tauc curve.

  FIG. 1 is a block diagram showing a configuration example of a band gap calculation apparatus according to an embodiment of the present invention. The band gap calculation device can be configured by a computer, for example, and includes a control unit 1, an operation unit 2, a display unit 3, a storage unit 4, and the like.

  The control unit 1 includes, for example, a CPU (Central Processing Unit), and when the CPU executes a program, for example, the input reception processing unit 11, the calculation range specifying processing unit 12, the band gap calculation processing unit 13, and the baseline It functions as various functional units such as the processing unit 14.

  The operation unit 2 includes, for example, a keyboard or a mouse, and an operator can perform an input operation by operating the operation unit 2. The display unit 3 can be configured by a liquid crystal display, for example, and can display the result of processing by the control unit 1 on the display unit 3. The storage unit 4 can be configured by, for example, a hard disk, a RAM (Random Access Memory), a ROM (Read Only Memory), and the like.

  FIG. 2 is a diagram illustrating an example of a display screen of the display unit 3 when processing by the control unit 1 is performed. In this example, a graph display area 31, an input area 32, a band gap display area 33, and the like are displayed on the display unit 3. Below, the aspect at the time of calculating a band gap is demonstrated concretely, referring FIG.1 and FIG.2.

  The band gap calculation apparatus according to this embodiment is for calculating a band gap using a Tauc curve, and a Tauc curve is displayed in the graph display area 31 based on input data. As the Tauc curve data, for example, spectrum data such as a transmission spectrum or a reflection spectrum obtained by measurement with a spectrophotometer can be employed.

In the Tauc curve, spectral data is represented with the vertical axis (hνα) ^{(1 / n)} and the horizontal axis hν. This is to utilize the fact that the following relational expression holds.
(Hνα) ^{(1 / n)} = A (hν−E _g )
Here, h is the Planck constant, ν is the frequency, α is the extinction coefficient, A is the proportionality constant, and E _g is the band gap. n is a value determined by the type of transition of the sample. For example, n = 1/2 for direct allowable transition, n = 3/2 for direct forbidden transition, n = 2 for indirect allowable transition, indirect forbidden In the case of transition, n = 3.

  The input area 32 is an area for inputting a fitting range, and includes, for example, a tangential input area 321, a baseline input area 322, and a K value input area 323. For example, by operating the mouse of the operation unit 2, the worker can input any numerical value using the keyboard after specifying one of the areas 321 to 323.

  For example, two hν values (unit: eV), which is the horizontal axis of the Tauc curve, can be input to the tangential input area 321, and thereby, a range of hν values having two hν values as start points and end points can be set. Can be entered. However, the present invention is not limited to the configuration in which the hν value is directly input to the tangential input area 321. For example, an operation for designating a point on the Tauc curve displayed in the graph display area 31 corresponds to the point. The configuration may be such that the hν value can be input to the tangential input area 321.

  In the baseline input area 322, for example, it is possible to select whether or not to use a base line when calculating a band gap. When the base line is selected, two hν values are input. By doing so, it is possible to input a range of hν values starting from these two hν values. For example, an arbitrary natural number can be input to the K value input area 323.

  The input reception processing unit 11 of the control unit 1 performs processing for receiving input by an operator using the operation unit 2, such as data input to the input area 32, for example. For example, when two hν values are input to the tangential input area 321, the input acceptance processing unit 11 accepts an input of a range of hν values starting from these two hν values. In this example, on the Tauc curve displayed in the graph display area 31, points P1 and P2 corresponding to the two hν values input in the tangential input area 321 are displayed.

  In this embodiment, by performing predetermined processing within the range of the hν value input to the tangential input area 321, a straight line closest to the tangent at the inflection point in the Tauc curve is obtained, and the band is based on the straight line. The gap can be calculated. For this purpose, first, the calculation range specifying processing unit 12 of the control unit 1 sets a plurality of calculation ranges having a predetermined width W by shifting the predetermined width W by a predetermined interval within the range of the input hν value. The processing for specifying the calculation range in which the Tauc curve is closest to the straight line is performed among the calculation ranges.

  In the present embodiment, in order to specify the calculation range in which the Tauc curve is closest to the straight line in the calculation range specifying processing unit 12, the correlation coefficient R in each calculation range is calculated, and the value of the correlation coefficient R is the largest. A calculation range close to 1 is specified. For example, the calculation range specifying processing unit 12 changes the value of the predetermined width W to a smaller value stepwise until the predetermined width W becomes smaller than a predetermined threshold.

Specifically, the predetermined width W can be expressed as W = W ₀ -mp. W ₀ is the range of the input hv value, when hv value at the point P1 as in the example of FIG. 2 is 1.25, hv value at point P2 is inputted and 1.35, _{W 0} = 1.35-1.25 = 0.1. Further, p is the predetermined interval (pitch) when the calculation range of the predetermined width W is shifted, and is set to a predetermined value. m is an arbitrary integer, and the value of the predetermined width W can be changed by changing the value of m.

  However, the predetermined interval is not limited to a configuration that is set to a predetermined value, and may be a configuration that can be set to an arbitrary value, for example, or a value similar to the predetermined width W. It is possible to adopt a configuration that can change the above.

FIG. 3 is a flowchart illustrating an example of processing by the control unit 1 when calculating the band gap. In the following, as in the example of FIG. 2, the hν value at the point P1 is input as hν ₁ = 1.25 and the hν value at the point P2 is input as hν ₂ = 1.35 in the tangential input region 321, and the K value input region As an example of the case where K = 4 is input in H.323, the processing by the control unit 1 when calculating the band gap will be described with reference to FIG.

At this time, the value of _{W 0} is a street 0.1 above. The value of p is set in advance to 0.01 eV, for example. The threshold value can be set to W ₀ /K=0.025 using, for example, the K value input to the K value input area 323. However, it is not limited to these numerical values.

When the input to the input region 32 is completed (Yes in step S101), first, (step _S102) by the m = 0, as _{W = W 0 -mp = W 0} = 0.1, (hν 1 ~hν 1 + W ₀ ) is set. That is, one calculation range of (1.25 to 1.35) is set, and the correlation coefficient R in this calculation range is calculated (step S103). At this time, since the value W of 0.1 is larger than the threshold value W ₀ /K=0.025 (No in step S104), by setting m = 1, the value of the predetermined width W is stepped. To a small value (step S105).

When m = 1, W = W ₀ −mp = W ₀ −p = 0.09, and (hν _{1 to} hν ₁ + W ₀ −p) and (hν ₁ + p to hν ₁ + W ₀ ) Set the range. That is, two calculation ranges (1.25 to 1.34) and (1.26 to 1.35) are set, and the correlation coefficient R in these calculation ranges is calculated (step S103). At this time, since 0.09 which is the value of W is larger than the threshold value W ₀ /K=0.025 (No in step S104), the value of the predetermined width W is changed by setting m = 2. To a small value (step S105).

When m = 2, W = W ₀ −mp = W ₀ −2p = 0.08, and (hν _{1 to} hν ₁ + W ₀ −2p) and (hν ₁ + p to hν ₁ + W ₀ −p ) and to set the range of _{(hν 1 + 2p~hν 1 + W} 0). That is, three calculation ranges of (1.25 to 1.33), (1.26 to 1.34), and (1.27 to 1.35) are set, and a correlation coefficient R in these calculation ranges is set. Calculate (step S103). At this time, 0.08 which is the value of W is larger than the threshold value W ₀ /K=0.025 (No in step S104), so by setting m = 3, the value of the predetermined width W is changed in steps. To a small value (step S105).

If it is the m = 3 _{is, W = W 0 -mp = W} 0 as _{-3p = 0.07, (hν 1 ~hν} 1 + W 0 -3p) and _{(hν 1 + p~hν 1 + W} 0 -2p ) and (to set _{hν 1 + 2p~hν 1 + W 0} -p) and the range of _{(hν 1 + 3p~hν 1 + W} 0). That is, four calculation ranges of (1.25 to 1.32), (1.26 to 1.33), (1.27 to 1.34), and (1.28 to 1.35) are set, The correlation coefficient R in these calculation ranges is calculated (step S103). At this time, since 0.07 which is the value of W is larger than the threshold value W ₀ /K=0.025 (No in step S104), by setting m = 4, the value of the predetermined width W is stepped. To a small value (step S105).

In this way, until the predetermined width W becomes smaller than the threshold value W ₀ / K (until Yes in step S104), the value of the predetermined width W is gradually changed to a smaller value, and all the calculated phases are The calculation range corresponding to the correlation coefficient R closest to 1 among the relation numbers R is specified (step S106). Since the process for calculating the correlation coefficient R is a known technique, a detailed description thereof will be omitted. The points P1 and P2 displayed in the graph display area 31 may be updated to positions representing the start point and end point of the specified calculation range.

  Thereafter, the band gap calculation processing unit 13 of the control unit 1 obtains a straight line L1 extending along the Tauc curve in the specified calculation range, and calculates the hν value at the intersection of the straight line L1 and a predetermined reference line as the band gap. Calculate as More specifically, the straight line L1 is obtained using the least square method within the specified calculation range (step S107). Since the process for obtaining the straight line L1 using the least square method is a known technique, a detailed description thereof will be omitted. The obtained straight line L1 is displayed with the Tauc curve in the graph display area 31, for example.

  At this time, if it is selected in the baseline input area 322 in FIG. 2 that the base line is not used when calculating the band gap (No in step S108), it is shown in the graph display area 31 in FIG. As described above, the hν value at the intersection point P3 between the obtained straight line L1 and the horizontal axis is calculated as a band gap (step S109). The calculated band gap is stored in the storage unit 4, and the value of the band gap is displayed in the band gap display area 33 of the display unit 3.

  On the other hand, in the baseline input area 322 of FIG. 2, when it is selected that the base line is used when calculating the band gap, and two hν values are input to the baseline input area 322 (step S108). Yes), the input acceptance processing unit 11 accepts an input of a range of hν values starting from these two hν values. In this example, on the Tauc curve displayed in the graph display area 31, points P4 and P5 corresponding to the two hν values input to the baseline input area 322 are displayed.

  Then, the baseline processing unit 14 of the control unit 1 obtains the straight line L2 using the least square method in the range between the two points P4 and P5, whereby the baseline is approximated as a straight line (baseline straight line) L2. . In this case, the hν value at the intersection P6 between the straight line L1 and the baseline straight line L2 previously obtained by the band gap calculation processing unit 13 of the control unit 1 is calculated as the band gap (step S110). The calculated band gap is stored in the storage unit 4, and the value of the band gap is displayed in the band gap display area 33 of the display unit 3. However, the configuration is not limited to such a configuration, and the baseline straight line L2 can be obtained by the same processing as that for obtaining the straight line L1 described above.

  As described above, in the present embodiment, while changing the width W of a plurality of calculation ranges that are shifted by a predetermined interval (pitch p) within the range of the input hν value, the Tauc curve in each calculation range is changed. The calculation range closest to the straight line is specified, and the straight line L1 extending along the Tauc curve in the specified calculation range can be obtained as the straight line L1 closest to the tangent at the inflection point of the Tauc curve. By calculating the hν value at the intersection P3 or P6 between the straight line L1 thus determined and a predetermined reference line (horizontal axis or baseline straight line L2) as the band gap, the band gap can be calculated more accurately. can do.

  In addition, when inputting the range of hν value, it is possible to input a wide range including the inflection point of the Tauc curve. The band gap can be calculated by specifying the calculation range. Therefore, compared to a configuration in which an appropriate calculation range around the inflection point must be set, the input work is simple, and the band gap can be calculated with a simpler work. .

  In the present embodiment, the calculation range specifying processing unit 12 can accurately specify the calculation range in which the Tauc curve is closest to the straight line among the calculation ranges by using the correlation coefficient R in each calculation range. In addition, the band gap calculation processing unit 13 can accurately determine the straight line L1 extending along the Tauc curve in the specified calculation range by using the least square method. Therefore, the band gap can be calculated with higher accuracy.

Furthermore, in the present embodiment, the calculation range specifying processing unit 12 changes the value of the predetermined width W to a small value stepwise until the predetermined width W becomes smaller than the predetermined threshold value W ₀ / K. As a result, the width W of the calculation range becomes too small, and it is possible to prevent the accuracy when the calculation range where the Tauc curve is closest to the straight line from each calculation range can be prevented. The gap can be calculated.

  In the above embodiment, the configuration in which the calculation range identification processing unit 12 identifies the calculation range in which the Tauc curve is closest to the straight line by using the correlation coefficient R in each calculation range has been described. However, the present invention is not limited to such a configuration, and the calculation range can be specified in any other manner.

  In the above embodiment, the configuration in which the band gap calculation processing unit 13 obtains the straight line L1 extending along the Tauc curve in the specified calculation range by using the least square method has been described. However, the present invention is not limited to this configuration, and the straight line L1 can be obtained in any other manner.

  The band gap calculation device according to the present invention may be configured individually, or may be configured integrally with various devices such as an analysis device.

  It is also possible to provide a program (band gap calculation program) for causing a computer to function as the band gap calculation device as described above. In this case, the program may be provided in a state stored in a storage medium, or may be configured such that the program itself is provided.

DESCRIPTION OF SYMBOLS 1 Control part 2 Operation part 3 Display part 4 Storage part 11 Input reception process part 12 Calculation range specification process part 13 Band gap calculation process part 14 Baseline process part 31 Graph display area 32 Input area 33 Band gap display area 321 Input for tangent Area 322 Baseline input area 323 K value input area

Claims (5)

A band gap calculation device for calculating a band gap using a Tauc curve,
an input reception processing unit that receives an input of a range of hν values;
Within a range of input hν values, a plurality of calculation ranges with a predetermined width are shifted by a predetermined interval to set a plurality of different ranges, and the Tauc curve is closest to a straight line in each calculation range while changing the value of the predetermined width. A calculation range specifying processing unit for specifying a calculation range;
A band gap calculation processing unit that calculates a straight line extending along the Tauc curve in the specified calculation range and calculates an hν value at the intersection of the straight line and a predetermined reference line as a band gap; Band gap calculation device.   The band gap calculation device according to claim 1, wherein the calculation range specification processing unit calculates a correlation coefficient in each calculation range and specifies a calculation range in which the value of the correlation coefficient is closest to 1. .   The band gap calculation processing unit calculates a straight line using a least square method within a specified calculation range, and calculates an hν value at an intersection between the straight line and a predetermined reference line as a band gap. The band gap calculation apparatus according to claim 1 or 2.   The said calculation range specific process part changes the value of the said predetermined width to a small value in steps until the said predetermined width becomes smaller than a predetermined threshold value. Band gap calculation device. A band gap calculation program for calculating a band gap using a Tauc curve,
an input reception processing unit that receives an input of a range of hν values;
Within a range of input hν values, a plurality of calculation ranges with a predetermined width are shifted by a predetermined interval to set a plurality of different ranges, and the Tauc curve is closest to a straight line in each calculation range while changing the value of the predetermined width. A calculation range specifying processing unit for specifying a calculation range;
A straight line extending along a Tauc curve in the specified calculation range is obtained, and the computer functions as a band gap calculation processing unit that calculates an hν value at the intersection of the straight line and a predetermined reference line as a band gap. A band gap calculation program.

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