JP2003045799A - Laser-annealing apparatus, and manufacturing method of thin-film transistor - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a laser-annealing apparatus, that can manufacture a thin- film transistor where mobility is high over the entire substrate, and at the same time, the characteristics are uniform, and to provide a manufacturing method of the thin-film transistor using the laser annealing apparatus. SOLUTION: When on an amorphous silicon thin film is irradiated with a laser beam pulse on a glass substrate for forming polycrystalline silicon thin film, a laser beam where a strength distribution in a direction in parallel with the advance direction (short axis) of the glass substrate of nearly a trapezoidal form is used, the width of the steepness of a beam profile being sampled from the beam profile of a plurality of continuous pulses, or the coefficients in a linear regression straight line in a plateau region are measured and controlled, thus determining failure in laser beams.

Description

Detailed Description of the Invention

[0001]

TECHNICAL FIELD The present invention relates to a laser annealing apparatus and a method of manufacturing a thin film transistor using the same.

[0002]

2. Description of the Related Art At present, amorphous silicon (a-S) is used.
Insulated gate type thin film transistor (TFT) comprising i)
A liquid crystal display (LCD) using a pixel switch has been mass-produced. However, in order to realize a display having high definition such as high definition and high speed, electric field mobility (μF
E) TF using a-Si as low as 1 cm ² / Vs or less
At T, I lack the ability.

On the other hand, in a TFT using polycrystalline silicon prepared by a laser annealing method in which a-Si is irradiated with an excimer laser, μFE is 100 to 100 in the experimental stage.
The one having a size of about 200 cm ² / Vs has been obtained, and it can be expected that the display has higher definition, higher speed, and higher functions such as integral formation of a drive circuit.

The excimer laser annealing (ELA) method is
In this method, a-Si on a glass substrate is irradiated with an excimer laser to form polycrystalline silicon. In this method, a
The beam size of the excimer laser on the Si surface is, for example, 250 mm in length and 0.4 mm in width. This pulse beam is oscillated at 300 Hz, and the irradiation area of each pulse is gradually moved to a- Convert Si to polycrystalline silicon. Liquid crystal displays manufactured using such a method are collectively called a low temperature polysilicon LCD.

A factor that determines the μFE of a polycrystalline silicon TFT is the grain size of the polycrystalline silicon, which largely depends on the energy density called the fluence of the irradiating laser. That is, as the fluence increases, the grain size of polycrystalline silicon also increases, but the mobility is 1
In order to obtain high-performance polycrystalline silicon of 00 cm ² / Vs or more, a fluence higher than a certain fluence of F1 is required.

However, if the fluence is increased more than F1, the grain size of polycrystalline silicon further increases, but it becomes fine crystal grains at a certain fluence value F2. It becomes impossible to obtain desired TFT characteristics.

The grain size of the polycrystalline silicon can be determined by etching the polycrystalline silicon with a solution called Secco etching solution and observing the grain size with a scanning electron microscope. Using this method, the fluence of the laser is selected in a region where the grain size of polycrystalline silicon is relatively large, that is, between F1 and F2.

Further, the beam profile in the scanning direction has the shape shown in FIG. 1 (a) as shown in Japanese Unexamined Patent Publication No. 2000-111950, and the beam direction in the scanning direction is as shown in FIG. 1 (b). By limiting the profile from the higher profile to the lower profile, a polycrystalline silicon TFT having a desired mobility can be obtained even if the laser oscillation intensity changes to some extent.

[0009]

However, even if the above-mentioned measures are taken, due to the fluctuation of the laser, particles having an abnormal particle diameter are produced, and the particle diameter of polycrystalline silicon is often irregular, resulting in low temperature poly-silicon. This is a big problem in mass-producing silicon LCDs. The dimension of the abnormal grain size region of this polycrystalline silicon is such that the length is close to the length of the laser beam on the substrate and the width is close to the feed pitch of the stage on which the substrate is placed.

Further, when an LCD is manufactured by using polycrystalline silicon containing such a crystal as a pixel transistor, an image having a contrast which is clearly different from that of the surroundings is obtained, resulting in a poor quality liquid crystal panel. Such an LCD panel cannot be sold as a product.

The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a laser annealing apparatus capable of manufacturing a thin film transistor having high mobility and uniform characteristics over the entire surface of a substrate. And

Another object of the present invention is to provide a method of manufacturing a thin film transistor having high mobility and uniform characteristics over the entire surface of the substrate by using the above laser annealing apparatus.

[0013]

In order to solve the above-mentioned problems, a first invention is a laser for converting amorphous silicon into polycrystalline silicon by irradiating a laser beam pulse on the amorphous silicon thin film. Before irradiating the laser beam pulse in the annealing apparatus, in the short-axis beam profile of the substantially trapezoidal laser beam, the level of the upper side is set to 100%, and its level is 5 to 45% and 55 to 9%.
The projected lengths of the left and right side line segments between the two straight lines drawn horizontally at the 5% level are d1 and d, respectively.
When 2 and d2> d1, the value of r = d2 / d1 is sequentially measured for a limited number of k pulses, and 1.0 <r0 <2.5 with respect to the average value r0 of r. , All the r of finite k pulses are compared with the real number p, and the number of times n1 in which r is less than the real number p1 or the number of times n2 in which r is more than the real number p2 is counted, and n1 / k is the real number q1. There is provided a laser annealing apparatus comprising a means for determining a case of the above or a case where n2 / k is a real number q2 or more as a laser beam defect.

The first aspect of the present invention includes the steps of forming an amorphous silicon thin film on a glass substrate, and irradiating the amorphous silicon thin film with a laser beam pulse while moving the glass substrate. In the method of manufacturing a thin film transistor, comprising the step of converting the amorphous silicon into polycrystalline silicon, the level of the upper side is 100% in the short axis beam profile of the substantially trapezoidal laser beam before the laser beam pulse is irradiated. As
When the projection lengths of the left and right side line segments between the two straight lines drawn horizontally at the levels of 5 to 45% and 55 to 95% are set to d1 and d2, respectively, and d2> d1 , The value of r = d2 / d1 is sequentially measured for a limited number of k pulses, and 1.0 <r0 with respect to the average value r0 of r.
In the state of <2.5, all the r of the finite k number of pulses are compared with the real number p, and the number of times n1 in which r is less than the real number p1 or the number of times n2 in which r is more than the real number p2 is counted. , N1 / k is a real number q1 or more, or n2 / k is a real number q2 or more is determined as a laser beam defect.

In the above first invention, the real number p1 is 1
And q1 compared with n1 / k is 0.001 to 0.
It is preferable that the real number is between 1 and the real number p2 is 2, and q2 to be compared with n2 / k is a real number between 0.001 and 0.1. In this case, q1 compared with n1 / k can be 0.01, and q2 compared with n2 / k can be 0.01.

A second aspect of the present invention is a laser annealing apparatus for converting amorphous silicon into polycrystalline silicon by irradiating the amorphous silicon thin film with a laser beam pulse, before irradiating the laser beam pulse. In the short-axis beam profile of the substantially trapezoidal laser beam, with the level of the upper side as 100%, an equation showing a linear regression line of the region of the upper side sandwiched between the positions corresponding to the level of s% between 50% and 99%. y = ax + b is calculated, all a of finite k times of pulses are compared with the real numbers t1 and t2, and the number of times a3 where a is below the real number t1 or the number n4 where a is above the real number t2 is counted, and n3 / A laser annealing apparatus comprising means for determining a case where k is a real number u1 or more or n4 / k is a real number u2 or more as a laser beam defect. To provide.

A second aspect of the invention is to form an amorphous silicon thin film on a glass substrate, and to irradiate the amorphous silicon thin film with a laser beam pulse while moving the glass substrate. In the method of manufacturing a thin film transistor, which comprises the step of converting the amorphous silicon into polycrystalline silicon, the level of the upper side is 100% in the short-axis beam profile of the substantially trapezoidal laser beam before the irradiation with the laser beam pulse. As
An equation y = ax + showing a linear regression line of the upper side region sandwiched at the position corresponding to the s% level between 50% and 99%.
b is calculated, and all a of the finite k number of pulses and the real number t1,
By comparing t2, the number of times a3 where a is below the real number t1 or the number n4 where a is above the real number t2 is counted, and n3 /
Provided is a method for manufacturing a thin film transistor, which is characterized in that a case where k is a real number u1 or more or n4 / k is a real number u2 or more is determined as a defect of a laser beam.

In the second invention, the real number s is 90%, t
1 is 0, t2 is 1.1, and u1 is compared with n3 / k.
Is preferably a real number between 0.001 and 0.1, and u2 compared to n4 / k is a real number between 0.001 and 0.1. In this case, u1 compared with n3 / k is 0.0
It is possible to set u2 to 0.01, which is compared with 1 and n4 / k.

The present invention will be described more specifically below.

In the process of irradiating the amorphous silicon thin film on the glass substrate with excimer laser to form polycrystalline silicon, the moving direction 1 of the substrate 14 shown in FIG.
When 5 is plotted on the horizontal axis and the intensity distribution of the laser beam 16 with which the amorphous silicon thin film on the glass substrate is irradiated is plotted, it has a substantially trapezoidal shape as shown in FIG. Such an intensity distribution can be measured by a device called a CCD profiler for measuring the intensity distribution of a laser beam.

In the present specification, in the intensity distribution of the laser beam shown in FIG. 1A, a substantially flat part including the top is called a plateau, and a part where the hem has a lower strength is called a steepness.

The steepness is on both sides of the intensity distribution, as shown in FIG. It is common to adjust the optical system so that the plateau region intensities are almost equal regardless of the place. However, in order to increase the above-mentioned F2, it is necessary to make the beam intensity on one side slightly higher than that on the opposite side. However, since the emission direction of the laser beam may change at the timing of gas exchange or window exchange, in order to maintain the above-described intensity distribution shape, the intensity profile is sometimes measured with a CCD profiler,
Need to be inspected.

However, in the measurement of a normal CCD profiler, several tens of pulses are overlapped in order to increase the S / N ratio, and as a result, not a true beam profile but an averaged beam profile is used. It cannot be detected. However, it is not the averaged beam that is irradiated on the substrate, but a plurality of beams each having a slightly different shape. Therefore, it is necessary to extract not the averaged beam profile but the characteristics of the individual beam profile to determine whether or not there is a problem with the beam profile.

The present invention is intended to solve the above-mentioned problems of laser annealing by performing unique data processing by using beam profile data. Specifically, continuous data of the ratio of the widths of the inclined regions of the short-axis beam profile called two steepness, or continuous data of the coefficient a of the linear regression equation y = ax + b of the top region (upper side) is managed, This is to judge the defect of the laser beam.

In the profile represented by the normal average value, adjustment is performed by changing the angle of the mirror installed in the optical system so that the ratio of the left and right steepness widths falls within a certain range. However, this only changes the average value of the beam traveling directions and does not align the traveling directions of all the pulses.

The variation in the traveling direction of all the pulses is expressed by the term pointing stability, and if it can be easily measured, the above-mentioned problem of laser annealing can be solved. But in reality, 3
A method for measuring the pointing stability of a laser oscillating at 00 Hz has not been found yet.

In the present invention, the beam profile of a plurality of pulses is sampled to obtain continuous data of the ratio of the width of the steepness of the short-axis beam profile or continuous data of the coefficient a of the linear regression equation y = ax + b in the plateau region. , Based on the finding that it can be used as a substitute for pointing stability.

[0028]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below with reference to the drawings.

(Embodiment 1) X in the first embodiment
A short axis (beam axis in the scanning direction) profile of the eCl excimer laser beam is shown in FIG. Figure 1 (a)
The horizontal axis represents the dimension, and the vertical axis represents the beam intensity at each part.

In FIG. 1A, a line 1 parallel to the horizontal axis
Draw 1, 12 across the steepness. Line 11
Intensity level corresponds to 80% of the apex intensity level and line 12 has an intensity level of 20% of the apex intensity level.
Equivalent to%. The left side of the steepness cut by the lines 11 and 12 is s2, and the right side is s1. If the angles formed by s2 and s1 and the line 12 parallel to the base are θ2 and θ1, respectively, the steepness widths d2 and d1 are d2 =
It is represented by s2cos θ2 and d1 = s1cos θ1.

The laser was oscillated at the same frequency as the actual laser annealing, the beam profile was measured in that state, and the ratio r = d2 / d1 of d1 and d2 was recorded for continuous pulses. The result is shown in FIG. Show. The average value r0 of r
Has been adjusted in advance with a mirror so that is about 1.5. The measurement was performed twice, and the variation was small in the first measurement, but was large in the second measurement.

The lower limit p1 of the ratio r of the steepness width is
It was set to 1.0, and none fell below 1.0 in the first measurement, but fell below five times in the second measurement. Since the measurement parameter is 50, the frequency of occurrence of the second measurement is 0.
It is 1. Since the standard value q of frequency is set to 0.01,
The second measurement does not meet specifications and requires gas exchange there. If the gas does not meet the specifications after several gas changes, the tube itself must be replaced. The increase in fluctuation of the short-axis beam profile is due to the discharge space expanding due to the consumption of the discharge electrode in the tube, so unless the discharge electrode or tube is replaced,
There is no improvement.

In this way, it is possible to properly know the time for gas exchange and the time for tube exchange. In the present embodiment, the upper limit value p2 of the ratio r of the steepness width is set to 2, but it does not exceed 2.

(Embodiment 2) X in the second embodiment
A short axis (beam axis in the scanning direction) profile of the eCl excimer laser beam is shown in FIG. The name of each part is the same as that of the first embodiment. The linear regression equation y = ax + b of the alternate long and short dash line 13 is obtained for the plateau region sandwiched by the height of s = 90% with the intensity level at the top as 100%.

The laser was oscillated at the same frequency as the actual laser annealing, the beam profile was measured in that state, and the value of a in the linear regression equation y = ax + b was recorded by recording for consecutive pulses. The results are shown in FIG. The mirror is adjusted in advance so that the average value r0 of r is about 1.5. The measurement was performed twice, and the a value was always positive in the first measurement, but a negative value was observed in the a value in the second measurement.

The lower limit value t1 of the coefficient a of the linear regression equation was set to 0, and none fell below 0 in the first measurement, but fell below 6 times in the second measurement. Measurement parameter is 5
Since it is 0, the occurrence frequency is n1 / k = 0.12.
Since the standard value of the frequency was set to u = 0.01, the second measurement did not meet the standard, and it was necessary to perform gas exchange there. If the gas does not meet the specifications after several gas changes, the tube itself must be replaced.

In this embodiment, the linear regression equation y = a
Although the upper limit t2 of the value of a in x + b is set to 25,
Nothing exceeded 25.

(Embodiment 3) In this embodiment, a method of forming a TFT array for driving a liquid crystal display will be described. The thin film used was Si on a glass substrate.
Undercoat layer consisting of Nx and SiOx is plasma C
After being formed by the VD method, a-Si having a film thickness of 49 nm is formed by the plasma CVD method. Substrate size is 400
It is mm × 500 mm.

After forming the a-Si film, in an atmosphere of nitrogen, 5
Heat treatment was performed at 00 ° C. for 10 minutes to reduce the hydrogen concentration in the film. Then, the film thickness of a-Si was calculated | required by the spectroscopy ellipso method. As a result, the actual film thickness of a-Si is 49.
It was 5 nm.

Next, the short-axis beam profile was checked by the method shown in the second embodiment, and the frequency at which the coefficient a was less than 0 was determined, and it was n2 / k = 0.001. This value was smaller than the standard u = 0.01, and it was judged that there was no problem, and the substrate was subjected to laser annealing using the excimer laser annealing apparatus shown in FIG.

According to the excimer laser annealing apparatus shown in FIG. 4, the laser pulse from the excimer laser apparatus 41 is applied to the sample placed on the excimer laser annealing stage 44 via the excimer laser annealing optical system. The laser pulse is reflected by the CCD profiler beam introducing mirror 47, and its intensity profile is measured by the CCD profiler 45. Incidentally, reference numeral 42 is an excimer laser control PC for controlling the excimer laser device 41, and reference numeral 46 is a CCD.
CCD profiler control P for controlling the profiler 45
C is shown respectively.

Irradiation size of excimer laser is 250 mm
A linear beam of × 0.4 mm was used, and the fluence on the substrate was set to 350 mJ / cm ² , and the overlap of the irradiated laser pulses was set to 95%. The laser is operated at 300 Hz and the XY stage with the substrate is
It was moved at a moving speed of mm / s.

A thin film transistor was manufactured by photolithography using the polycrystalline silicon film formed by the above laser annealing process, and an active matrix liquid crystal display device was manufactured using the thin film transistor. The obtained active matrix liquid crystal display device is shown in FIG.

The active matrix liquid crystal display device shown in FIG. 5 is constructed as follows. That is, T
A glass substrate 501 having an FT, a color filter 510, and a pixel electrode 511 and a counter glass substrate 514 having a counter electrode 513 are arranged to face each other with a liquid crystal 512 interposed therebetween.

An undercoat layer 502 is formed on the surface of the glass substrate 501, an amorphous silicon layer is formed on the undercoat layer 502, and as described above, it is converted into a polycrystalline silicon layer by laser annealing according to the present invention. .

The polycrystalline silicon layer obtained by this laser annealing constitutes a TFT. That is, by doping the both sides of the semiconductor layer 503 made of polycrystalline silicon with impurities, the polycrystalline silicon source layer 504a
And a polycrystalline silicon drain layer 504b is formed,
A gate electrode 506 is formed on the gate electrode 506 through the gate oxide film 505.
Are formed.

The source / drain electrodes 508 are respectively connected to the source layer 504a and the drain layer 504b through the connection holes formed in the interlayer insulating film 507, the protective film 509 is provided thereon, and the color filter 510 is provided. And a pixel electrode 511 is formed.

As described above, by using the laser annealing method of the present invention, TFTs having excellent characteristics can be mass-produced, so that a high quality liquid crystal display device can be manufactured with a very high yield. done.

[0049]

As described above in detail, according to the present invention, continuous data of the width ratio of the steepness of the short-axis beam profile, or the continuous coefficient a of the linear regression equation y = ax + b in the plateau region. By managing the data and judging the failure of the laser beam, it becomes possible to perform laser annealing using a laser having an optimum intensity distribution at all times, and as a result, the mobility is high on the entire surface of the substrate and the characteristics are uniform.
It was possible to manufacture FT, and it became possible to put into practical use a low-temperature polysilicon liquid crystal display having high performance, which was only in the experimental stage in the past.

[Brief description of drawings]

FIG. 1 is a diagram showing a minor axis profile of a laser beam of the present invention and a substrate moving direction.

FIG. 2 is a characteristic diagram showing a result of recording a steepness ratio in a short-axis profile of a laser beam of each pulse according to the first embodiment of the present invention.

FIG. 3 is a characteristic diagram showing a result of recording a linear regression coefficient a in a short-axis profile of a laser beam of each pulse according to the second embodiment of the present invention.

FIG. 4 is a diagram showing an excimer laser annealing apparatus used in a third embodiment of the present invention.

FIG. 5 is a diagram showing a cross-sectional structure of a polycrystalline silicon active matrix type liquid crystal display obtained by using a laser annealing method according to a third embodiment of the present invention.

[Explanation of symbols]

11 ... A line showing a height of 80% with respect to the top of the laser beam short-axis profile, 12 ... A line showing a height of 20% with respect to the top of the laser beam short-axis profile, 13 ... A laser beam A linear regression line of a region sandwiched by a height of 90% with respect to the apex of the short-axis profile, 14 ... A glass substrate on which amorphous silicon is deposited, 15 ... A traveling direction of the glass substrate, 16 ... On a glass substrate Laser beam, s1 ... Straight line of steepness near the top of the short-axis profile, s2 ... Straight line of steepness far from the top of the short-axis profile, 41 ... Excimer laser device, 42 ... Excimer laser control PC 43 ... Excimer laser annealing optical system, 44 ... Excimer laser annealing stage, 45 ... CCD profiler, 46 ... CCD profiler control PC , 47 ... CCD profiler beam introducing mirror, 501 ... Glass substrate, 502 ... Undercoat layer, 503 ... Polycrystalline silicon, 504a ... Polycrystalline silicon source, 504b ... Polycrystalline silicon drain, 505 ... Gate oxide film, 506 ... Gate electrode , 507 ... Interlayer insulating film, 508 ... Source / drain electrode glass substrate, 509 ... Protective film, 510 ... Color filter, 511 ... Pixel electrode, 512 ... Liquid crystal counter substrate, 513 ... Counter electrode, 514 ... Counter glass substrate.

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Claims (8)

[Claims] 1. A laser annealing apparatus for converting amorphous silicon into polycrystalline silicon by irradiating an amorphous silicon thin film with a laser beam pulse, wherein a substantially trapezoidal shape is formed before the laser beam pulse is irradiated. In the short-axis beam profile of the laser beam, the level of the upper side is 100%, and its level is 5-45% and 55-95%
When the projection lengths of the left and right side line segments between the two straight lines drawn horizontally at the level of are respectively d1 and d2 and d2> d1, finite k number of pulses r = The value of d2 / d1 is sequentially measured, and the average value r of r
In the state where 1.0 <r0 <2.5 with respect to 0,
Comparing all r of finite k pulses and the real number p, r
Is counted below the real number p1 or n2 above the real number p2, and n1 / k is the real number q.
A laser annealing method comprising means for determining a case where it is 1 or more, or a case where n2 / k is a real number q2 or more as a defective laser beam. 2. The real number p1 is 1, q1 to be compared with n1 / k is a real number between 0.001 and 0.1, the real number p2 is 2, and q2 to be compared with n2 / k. Is 0.
The laser annealing apparatus according to claim 1, wherein the laser annealing apparatus is a real number between 001 and 0.1. 3. The laser annealing apparatus according to claim 2, wherein q1 compared with n1 / k is 0.01, and q2 compared with n2 / k is 0.01. 4. A step of forming an amorphous silicon thin film on a glass substrate, and irradiating the amorphous silicon thin film with a laser beam pulse while moving the glass substrate to remove the amorphous silicon thin film. In the method of manufacturing a thin film transistor, which comprises a step of converting into polycrystalline silicon, before irradiating the laser beam pulse, in the short-axis beam profile of the substantially trapezoidal laser beam, the level of the upper side is set to 100%, and the level is 5 to 45 % And 55-95%
When the projection lengths of the left and right side line segments between the two straight lines drawn horizontally at the level of are respectively d1 and d2 and d2> d1, finite k number of pulses r = The value of d2 / d1 is sequentially measured, and the average value r of r
In the state where 1.0 <r0 <2.5 with respect to 0,
Comparing all r of finite k pulses and the real number p, r
Is counted below the real number p1 or n2 above the real number p2, and n1 / k is the real number q.
A method of manufacturing a thin film transistor, characterized in that when it is 1 or more, or when n2 / k is a real number q2 or more, it is determined as a defect of a laser beam. 5. A laser annealing apparatus for converting the amorphous silicon into polycrystalline silicon by irradiating the amorphous silicon thin film with a laser beam pulse, wherein the laser annealing is performed before the irradiation with the laser beam pulse. In the short-axis beam profile of the laser beam, with the level of the upper side as 100%, an equation y = ax + b showing a linear regression line of the region of the upper side sandwiched between positions corresponding to the s% level between 50 and 99%. And all a of finite k pulses are compared with the real numbers t1 and t2, and a is the real number t1.
N3, which is less than n, or n, where a is greater than the real number t2
4 is counted and n3 / k is a real number u1 or more, or n4
A laser annealing apparatus comprising means for determining a case where / k is a real number u2 or more as a laser beam defect. 6. The real number s is 90%, t1 is 0, t2 is 1.1, and u1 compared with n3 / k is a real number between 0.001 and 0.1, and compared with n4 / k. u2 is 0.0
The laser annealing apparatus according to claim 5, wherein the laser annealing apparatus is a real number between 01 and 0.1. 7. The u1 compared with the n3 / k is 0.01,
7. The laser annealing apparatus according to claim 6, wherein u2 compared with the n4 / k is 0.01. 8. A step of forming an amorphous silicon thin film on a glass substrate, and irradiating the amorphous silicon thin film with a laser beam pulse while moving the glass substrate to remove the amorphous silicon thin film. In a method of manufacturing a thin film transistor, which comprises a step of converting into polycrystalline silicon, before irradiating the laser beam pulse, in a short-axis beam profile of a substantially trapezoidal laser beam, the level of the upper side is set to 100%, and the level is 50 to 99. The equation y = ax + b showing the linear regression line of the upper side region sandwiched at the position corresponding to the level of s% between% is obtained, and all a of the finite k number of pulses are compared with the real numbers t1 and t2. And a is a real number t1
N3, which is less than n, or n, where a is greater than the real number t2
4 is counted and n3 / k is a real number u1 or more, or n4
A method for manufacturing a thin-film transistor, wherein a case where / k is a real number u2 or more is determined as a defect of a laser beam.