JP4915502B2 - Resist pattern simulation method - Google Patents

Description

  The present invention relates to a resist pattern shape simulation method used for manufacturing a semiconductor integrated circuit device or the like.

  In the field of electron beam lithography, when estimating the resist shape after development, it is common to perform an electron beam scattering simulation to obtain the energy accumulation distribution in the resist, and then calculate the development profile by replacing the accumulated energy with the development speed. Is.

  A representative example of electron beam scattering simulation is the Monte Carlo method. This simulates electron scattering and energy loss using random numbers, and it is assumed that the energy lost by the electron beam is given to the resist and the base substrate in the locus. In the simulation using the Monte Carlo method, the energy accumulation distribution function (EID function) to the peripheral region is calculated from one point of the electron scattering calculation, and the energy is calculated by superimposing this over the desired pattern region. There are a method for calculating the accumulation distribution and a method (direct Monte Carlo method) for irradiating an electron beam to a desired pattern region and calculating the energy accumulation distribution for the scattering state of all the electrons. The energy accumulation distribution in the resist thus obtained is substituted into a development model such as the Mack model and converted into a development speed. From the three-dimensional distribution of the development speed in the resist thus obtained, development calculation such as string method and cell removal method is performed to predict the developed pattern.

  In general, in a method using a development model, it is difficult for the pattern shape to reflect the actual shape, and in order to improve this, a complicated development model has been proposed. However, a complicated development model has a problem that not only the calculation becomes enormous, but also the parameters related to the reaction increase, and it is difficult to reproduce the resist shape.

To solve the problem of developing model calculation, predict the shape after development using the developing speed experimentally calculated using the light interference effect when converting the energy accumulation distribution obtained by simulation to the developing speed There is a method (see Patent Document 1).
This is because the resist after electron beam irradiation is immersed in the developer, and the resist film thickness change in the irradiated area is reflected by the reflected light from the resist layer surface and the boundary surface between the developed resist layer and the undeveloped resist layer inside. By measuring the intensity of interference light with light, the development time is calculated by obtaining the change in film thickness time of the undeveloped resist.
JP 2003-37050 A

  However, with conventional development speed measurement methods using interference light, depending on the type of resist, the light used for measurement may be absorbed or transmitted, so there are some that cannot be measured accurately. When the thickness is small, the change in the interference light intensity itself is small, and the accuracy at the time of developing speed conversion deteriorates. Further, in the development speed measurement using interference light, the waveform of the interference light is disturbed and accurate measurement cannot be performed when it is dissolved non-uniformly during development or when the resist swells during development. For this reason, there has been a problem that fine behavior in the development process cannot be detected, such as development speed that varies depending on the resist dissolution depth, resist swelling, and the presence of a residual resist layer remaining on the substrate interface.

  Furthermore, with the miniaturization of semiconductor processing technology, it is necessary to form a fine pattern with a thin resist, and there is a problem that a fine shape must be reproduced for simulation as well.

  The present invention has been made in view of such circumstances, and an object thereof is to provide a simulation method capable of predicting a resist pattern shape after development in more detail regardless of the type of electron beam resist.

To solve the above problems, the present onset bright calculates the energy storage distribution to the peripheral region from the irradiation electron scattering calculations one point, this superimposed calculated over a desired pattern region, and calculates the energy accumulated distribution Or irradiating a desired pattern region with an electron beam, calculating the energy accumulation distribution by calculating all the scattering states of each electron, and converting the calculated energy accumulation distribution into a development speed distribution; and developed calculated based on the development rate distribution, and a step of estimating the resist pattern shape, I resist pattern simulation method der to simulate post-development shape of the resist layer, developing the energy storage distribution In dose conversion conditions where the resist film thickness increases in the process of converting to velocity distribution, the relationship between resist film pressure and development time The developing speed r (t, D) under the above-mentioned film thickness increasing dose condition is calculated based on the film thickness increasing rate with the image time change, and the calculated developing speed r (t, D) corresponds to the energy accumulation amount. In the step of converting to the developing speed R (t, D) and estimating the resist pattern shape, development calculation based on the developing speed distribution is performed using the converted developing speed R (t, D). Further, in the step of converting the energy accumulation distribution into the development speed distribution, the development under the film thickness reduction dose condition is based on the relationship between the resist dissolution depth and the development time in the dose condition in which the resist film thickness decreases. A speed r ′ (t, D) is calculated, and the calculated development speed r ′ (t, D) is converted into a development speed R ′ (t, D) corresponding to the energy accumulation amount, and the pattern shape of the resist is changed. In the estimation process, before Converted development rate R '(t, D) and performing a development calculations based on the development rate distribution using the.

  According to the resist pattern simulation method of the present invention, the resist shape change with respect to the development time can be reproduced in detail in the resist development simulation, and the swelling behavior of the resist can be reflected. Therefore, it is possible to perform simulation with higher accuracy at two points of time change and shape than the conventional method.

In the resist pattern simulation method according to the embodiment of the present invention, an energy accumulation distribution in a peripheral region is calculated from a single irradiation electron scattering calculation, and this is superimposed on a desired pattern region to calculate an energy accumulation distribution. Or irradiating an electron beam to a desired pattern region, calculating the energy accumulation distribution by calculating all the scattering states of each electron, and converting the calculated energy accumulation distribution into a development speed distribution. and developed calculated based on the development rate distribution, and a step of estimating the resist pattern shape, a resist pattern simulation method for simulating the development after the shape of the resist layer, developing speed of said energy storage distribution In the process of converting to the distribution, the resist condition is increased under dose conditions where the resist film thickness increases. From the relationship between the film pressure and the development time, the development speed r (t, D) under the film thickness increase dose condition is calculated based on the film thickness increase rate accompanying the development time change, and the calculated development speed r ( (t, D) is converted into a developing speed R (t, D) corresponding to an energy storage amount, and the resist pattern shape is estimated using the converted developing speed R (t, D) in the step of estimating the resist pattern shape. Based on the relationship between the resist dissolution depth and the development time under the dose condition in which the resist film thickness is reduced in the step of performing development calculation based on the development speed distribution and further converting the energy accumulation distribution to the development speed distribution. The developing speed r ′ (t, D) under the film thickness reducing dose condition is calculated, and the developing speed r ′ (t, D) corresponding to the energy storage amount is calculated. Convert the resist pattern into In the step of estimating Jo, the converted development rate R '(t, D) is obtained so as to perform development calculations based on the development rate distribution using the.
That is, a development rate table determined from two parameters of an electron beam irradiation amount (hereinafter referred to as “dose”) and a resist dissolution depth is calculated by experiment. By converting the energy accumulation distribution of the resist layer obtained by simulation using this table into the developing speed, a simulation result with higher accuracy than the conventional method is provided.
FIG. 1 is a flowchart showing an outline of a resist pattern simulation method according to this embodiment.

  In the present embodiment, film thickness measurement using a quartz crystal microbalance (hereinafter referred to as QCM) is used as a method for calculating the developing speed with high accuracy. FIG. 2 is a schematic diagram showing the principle of film thickness measurement using this QCM. A disk is cut out from a single crystal of quartz, and a resist layer 3 is formed on the piezoelectric element (hereinafter referred to as a crystal resonator) 4 having electrodes formed thereon as a substrate. Reference numeral 1 denotes a connection wiring between the crystal resonator 4 and the resonance circuit, and reference numeral 2 denotes a resonator fixing jig. The crystal unit 4 has a specific resonance frequency, and when the resist layer 3 is formed on the surface, the resonance frequency is shifted to the low frequency side according to the type of resist layer, the difference in film thickness, and the like. When the crystal resonator 4 on which the resist layer 3 is formed is uniformly irradiated with an electron beam and then immersed in the developer 5, the resist film thickness changes during development, which appears as a change in resonance frequency.

  Calculation is performed from the relationship between the obtained development time and the resonance frequency, and the relationship between the resist film thickness and the development time is obtained. By performing the same measurement while changing the dose and obtaining the development speed in the resist dissolution depth direction corresponding to each dose, the relationship between the two parameters of dose and resist dissolution depth and the development speed can be obtained. Furthermore, in this embodiment, when the resist is swollen and the film thickness is increased, the resist swelling behavior is reflected by defining the developing speed as a negative value.

In addition, electron beam scattering simulation is performed when a uniform electron beam is irradiated to a resist layer separately formed on a crystal resonator, and a relationship between dose and accumulated energy is obtained. Using this relationship, the development speed in the resist dissolution depth direction with respect to the dose is converted into the development speed in the resist dissolution depth direction corresponding to the energy accumulation distribution.
The conversion table for calculating the resist development speed from the two parameters of the energy accumulation distribution and the resist dissolution depth is obtained by the above steps. By applying this conversion table to the three-dimensional energy accumulation distribution of a resist layer that has been subjected to desired patterning with an electron beam, a resist development simulation is performed.

  As this embodiment, a simulation of a pattern shape was performed when electron beam patterning was performed on a substrate in which a chemically amplified negative resist layer was formed on a photomask original (mask blank). The incident energy of the electron beam was 50 kV, the resist film thickness was 250 nm, and the resist pattern was an isolated line with a line width of 100 nm.

First, a plurality of samples in which the resist layer 3 having the above resist type and film thickness conditions is formed on the crystal resonator 4 for film thickness change measurement using the QCM method are prepared. After forming a uniform electron beam irradiation region with a different dose in each quartz crystal resonator 4 in a region equal to or higher than the frequency measurement region, the resonance frequency is monitored while the irradiated sample is immersed in the developer 5. From the change of the resonance frequency obtained in this way with the development time, the change in the thickness of the resist layer 3 on the crystal unit 4 is calculated for each dose.
FIG. 3 is an explanatory diagram showing the relationship between the development time and the resist film thickness obtained by the QCM method measurement.

As shown in FIG. 3, it can be seen that the film thickness of the resist irradiated at 2 uC / cm 2, which is an underdose condition, does not decrease linearly, and the development speed is not constant in the depth direction. Further, it can be seen that the resist film thickness after development increases conversely as the development time advances under the condition of the dose threshold value (≦ 9 uC / cm 2). This is presumed that the resist swells. Based on the measurement results obtained above, the development speed is calculated by dividing the conditions for each dose with respect to the conflicting behavior of the resist.
(1) Under the dose condition in which the resist film thickness increases in the development process, the film thickness increase rate with the development time change t is calculated from FIG. 3, and this is set as the development speed r (t, D) [nm / sec]. .
(2) For the dose condition in which the resist film thickness is reduced in the development process, the development speed r ′ (t, D) [nm / sec] is calculated by differentiating the result of FIG. 3 with respect to time. Further, with this as the vertical axis, the dissolution depth z [nm] from the initial film thickness of the resist at that time is taken as the horizontal axis, and the development speed r ′ (z, D) [nm / sec] with respect to the resist dissolution depth is obtained. Ask.
FIG. 4 is an explanatory diagram showing the relationship between the resist dissolution depth obtained by the QCM method measurement and the development speed.
As can be seen from FIG. 4, even at a dose of 2 uC / cm 2 where the resist dissolves, the developing speed becomes zero about 30 nm before the resist dissolves and reaches the bottom surface. This tends to be recognized as the cause of insufficient electron beam irradiation. According to electron beam scattering simulation, the 50 kV electron beam penetrates the resist layer almost linearly due to its energy level, and the energy reaches the bottom of the resist. The result that is accumulated. Therefore, it is presumed that there are other factors (baking, acid generation, diffusion process, etc.) that the development speed differs in the depth direction.

  Further, an electron beam scattering simulation is performed when a uniform electron beam is irradiated using the resist layer formed on the crystal resonator as a model, and the relationship between dose D (uC / cm2) and energy storage amount E [J / m3]. Ask for. Using this relationship, r (t, D) and r ′ (z, D) are converted into development speeds R (t, D) and R ′ (z, E) corresponding to the energy accumulation amount.

Development calculation was carried out using the development rate determined from the distribution of the energy storage amount thus obtained and the resist dissolution depth, and a resist pattern shape by simulation was obtained.
FIG. 5 is an explanatory view showing the cross-sectional shape of the resist pattern obtained by the simulation. FIG. 5 shows the result of development calculation using a development speed table determined from two parameters of dose and resist dissolution depth by experiment. FIG. 5 shows a shape in which the side surface portion of the resist projects laterally, and reflects the swelling behavior of the resist. Further, since the developing speed becomes slow near the bottom surface of the resist, the bottom shape is strongly reflected in the resist shape.
As a comparison, FIG. 6 shows a development calculation result in the case where the average value of the development speed for a constant energy accumulation distribution is used regardless of the resist dissolution depth and the increase in film thickness due to swelling behavior is not taken into consideration.
FIG. 6 is an explanatory view showing a cross-sectional shape of a resist pattern obtained by a conventional simulation method.

  As described above, according to the present embodiment, a development rate table determined from two parameters of dose and resist dissolution depth is calculated by experiment, and the energy of the resist layer obtained by simulation using this table is calculated. By converting the accumulated distribution into the development speed, there is an effect that it is possible to realize a development simulation that can obtain a shape close to the resist pattern after actual development with higher accuracy than the conventional method.

It is a flowchart which shows the outline of the procedure of the resist pattern simulation method by embodiment of this invention. It is a schematic diagram which shows the principle of the film thickness measurement using QCM in the resist pattern simulation method by embodiment of this invention. It is explanatory drawing showing the relationship between the development time obtained by the QCM method measurement in the resist pattern simulation method by embodiment of this invention, and a resist film thickness. It is explanatory drawing showing the relationship between the resist melt | dissolution depth obtained by the QCM method measurement in the resist pattern simulation method by embodiment of this invention, and development speed. It is explanatory drawing which shows the cross-sectional shape of the resist pattern calculated | required by the simulation in the resist pattern simulation method by embodiment of this invention. It is explanatory drawing which shows the cross-sectional shape of the resist pattern calculated | required with the conventional simulation method.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Crystal oscillator-resonance circuit connection wiring, 2 ... Vibrator fixing jig, 3 ... Resist layer, 4 ... Crystal oscillator, 5 ... Developer.

Claims (1)

Calculate the energy accumulation distribution in the surrounding area from one-point irradiation electron scattering calculation, and calculate the energy accumulation distribution over the desired pattern area, or irradiate the desired pattern area with the electron beam Calculating the energy accumulation distribution by calculating all the scattering states of each electron;
Converting the calculated energy accumulation distribution into a development speed distribution;
The development is performed calculations based on the development rate distribution, and a step of estimating the resist pattern shape, I resist pattern simulation method der to simulate post-development shape of the resist layer,
In the step of converting the energy accumulation distribution into the development speed distribution, in the dose condition in which the resist film thickness increases, the film thickness is based on the film thickness increase rate accompanying the development time change from the relationship between the resist film pressure and the development time. The developing speed r (t, D) under the increased dose condition is calculated, and the calculated developing speed r (t, D) is converted into a developing speed R (t, D) corresponding to the energy accumulation amount, and the resist In the step of estimating the pattern shape, development calculation based on the development speed distribution is performed using the converted development speed R (t, D),
Further, in the step of converting the energy storage distribution into the development speed distribution, the development rate under the film thickness reduction dose condition is based on the relationship between the resist dissolution depth and the development time in the dose condition where the resist film thickness is reduced. r ′ (t, D) is calculated, and the calculated developing speed r ′ (t, D) is converted into a developing speed R ′ (t, D) corresponding to the energy accumulation amount, and the pattern shape of the resist is estimated. A development calculation based on the development speed distribution using the converted development speed R ′ (t, D).
A resist pattern simulation method.

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