Optical Characterization of Positive Photoresists

		At a Glance
	This article presents an in-depth characterization of the optical properties of a positive g-line photoresist at 632.8 nm from a HeNe laser. The optical properties investigated include absorption and scattering coefficients, total attenuation coefficient, and scattering anisotropy factor.

In recent years, significant advances have been made in the formulation of a number of positive photoresists. Sophisticated photoresists are the backbone of integrated circuit manufacturers because without them today's submicron geometries would have been impossible. Positive photoresist consists of three components: a novolak resin, a photoactive compound (typically a naphthoquinone diazide ester), and a solvent. Occasionally, a dye or other additive is added to improve the latitude of the photolithographic process. These resists must be thermally stable to withstand high-temperature environments such as plasma etching or ion implantation. They must also possess other characteristics that include good adhesion with the underlying film, sufficient photospeed, low particulate level, and high contrast.

Absorption of light by the photoresist is a critical factor to consider when setting up a photolithographic process. The standard Beer's law of exponential decay can be used to calculate the attenuation of light intensity at any wavelength within the photoresist.^1-3 Owing to the complex nature of positive photoresist, it is imperative that absorption and scattering be considered when evaluating optical properties of photoresists. Unfortunately, Beer's law cannot separate the attenuation of light intensity by absorption from the actual loss of light by scattering.

Vacuum ultraviolet (VUV) light is routinely employed in the photolithographic process; it is expected that the photoresist will strongly absorb the UV light, while absorption of the longer visible light is negligible. Therefore, in this paper, we present an in-depth characterization of optical properties of a positive g-line photoresist at 632.8 nm from a HeNe laser. The optical properties investigated include absorption and scattering coefficients, total attenuation coefficient, and scattering anisotropy factor. The information on these optical properties can be obtained from the solution of the Chandrasekhar's radiative transport equation describing the rate of change in the intensity of a narrow incident light beam as a function of the optical properties of the medium involved.⁴ This is a difficult problem to solve analytically for any turbid media such as positive photoresist. Nevertheless, by assuming homogeneity and regular geometry of the medium, an estimate of light intensity distribution can be obtained by solving the radiative transport equation:

where I(r,s) is the intensity per unit solid angle at target location r in the direction s (s is the directional unit vector), µa and µs are the absorption coefficient and scattering coefficient, respectively, of the medium, p(s,s') is the phase function representing scattering contribution from the direction s' to s, and W' is the solid angle.

The first term on the right hand side of Eq. 1 represents the loss in I(r,s) per unit length in direction s due to absorption and scattering. The second term denotes the gain in I(r,s) per unit length in direction s due to scattering from other scattered light I(r,s')dW'(i.e., light intensity confined in the elemental solid angle dW') from direction s'. The functional form of the phase function in turbid media is usually unknown. In many practical applications, however, the following Henyey-Greenstein formula provides a good approximation of the phase function, and is therefore used in all calculations of the Inverse Adding Doubling (IAD) method employed in the present study:

where v is cosine of the angle between s and s'. The Henyey-Greenstein phase function depends only on the scattering anisotropy factor g, which is defined as the mean cosine of the scattering angle:

The value of g ranges from -1 for complete backward scattering to 0 for the absolute isotropic scattering to 1 for the complete forward scattering.

Although the radiative transport theory gives a more adequate description of the distribution of photon intensity in the turbid medium than does any other model, the general analytical solution is not known yet. Approximate solutions are only available for such restricted conditions as uniform irradiation, or when either absorption or scattering strongly dominates. Although the general solution is not available, it has been possible in recent years to obtain elaborate computational solution of the transport equation.

To solve Eq. 1, knowledge of absorption and scattering coefficients, and scattering phase factor (or scattering anisotropy factor), is needed. Therefore, appropriate experimental methods are necessary to measure these optical parameters. As an example, although a single measurement of the total transmission through a sample of known thickness provides an attenuation coefficient for the Lambert-Beer law of exponential decay, it is impossible to separate the loss due to absorption from the loss due to scattering. This problem, to some extent, had been resolved by the one-dimensional, two-flux Kubelka-Munk model,⁵ which has been widely used to determine the absorption and scattering coefficients of turbid media, provided the scattering is significantly dominant over the absorption.

In the past, researchers have applied the diffusion approximation to the transport equation to study turbid media.^6-9 Most notably, following the Kubelka-Munk model and diffusion approximation, an excellent experimental method has been described by van Gemert et al for determining the absorption and scattering coefficients and scattering anisotropy factor.^10,11 Unfortunately, the diffusion approximation, coupled with the Kubelka-Munk method, is valid only when the absorption coefficient is negligibly small compared to the scattering coefficient of the turbid medium under investigation.

The absorption coefficient of the positive photoresist is more than three times higher than the scattering coefficient at the wavelength of our interest and cannot be ignored. Therefore, in our study, the IAD method has been employed to determine both the absorption and the scattering coefficients.

In recent years, the IAD method¹² and Monte Carlo simulation technique^13-15 have been successfully used to obtain information on such fundamental optical properties as absorption and scattering coefficients, and scattering anisotropy factor of turbid media. These methods provide by far the most accurate estimates of optical properties of any other models previously used. Two dimensionless quantities used in the entire process of IAD are albedo, a, and optical depth, t, which are defined as

a = µ_s / (µ_s + µ_a) and t = t(µ_s + µ_a) (4)

where t is the physical thickness of the sample and measured in cm.

The measured values of the total diffuse reflectance and transmittance, using an integrating sphere, and unscattered collimated transmittance, have been applied to the IAD method to determine the absorption and scattering coefficients, and scattering anisotropy factor of the positive photoresist sample.

Employing this method, these optical properties are obtained by repeatedly solving the radiative transport Eq. 1 until the solution matches the measured values of the diffuse reflectance and the diffuse transmittance, and the collimated transmittance.

Materials and methods

The positive g-line photoresist used in this study was HPR 506, supplied by Arch Chemicals Inc. (Norwalk, Conn.). This compound consists of ethyl lactate (the solvent), novolak resin, and naphthoquinone diazide esters. According to the material safety data sheet supplied by Arch Chemicals, the percentage range of the ethyl lactate is 61-90%, the percentage range of novolak resin is 10-29%, and the percentage range of the naphthoquinone diazide esters is 1-11%. Preparation of the photoresist sample for the optical measurements involved fixing an o-ring with a diameter of 1 in. between two glass slides; the o-ring acts as a reservoir to retain the liquid sample. The photoresist mixture was then transferred with a pipette into the reservoir for investigation. The sample thickness in this case is the thickness between the glass slides and was measured to be 0.186 cm.

Measuring absorption spectra

The room-temperature absorption spectrum of the positive photoresist sample was measured in the visible range using a Cary-14 spectrophotometer upgraded by OLIS. Before taking the absorption spectrum on this sample, a base line was set to correct the measured spectrum due to Fresnell reflection losses of about 5% and any marginal wavelength-dependent scattering that might occur. The absorption spectrum was corrected for those losses by subtracting the base line from the measured data. The beam dimension of the light in the Cary-14 spectrophotometer was ~4 × 8 mm.

Measuring index of refraction

1. In the experimental setup for the measurement of index of refraction, a small-angle prism was used so the optical path length would be small enough to avoid excessive scattering.

The index of refraction of the positive photoresist was measured by the method of minimum deviation using a hollow quartz prism. The equilateral, hollow prism was made of 1 × 2 cm quartz slides obtained from NSG Precision Cell Inc. (Farmingdale, N.Y.). This method was chosen for its simplicity and accuracy.^16,17 Figure 1 shows the schematic of the experimental setup for the measurement of index of refraction. A small-angle prism was used so that the optical path length would be small enough to avoid excessive scattering. The prism was firmly attached at the center of a goniometer table. Initially, with no sample in the hollow prism, the collimated laser beam passed through the prism, and the position of the spot on the white screen from the center of the table was marked. Once the prism was filled with the photoresist sample, the collimated laser beam was allowed to pass through the prism. The prism was then rotated so that the angle of incidence was varied and the point at which the refracted beam spot on the screen changed the direction was identified for the angle of minimum deviation dm. In this position, the collimated laser beam was passing symmetrically through the prism, and the angle of total deviation of the emergent beam was minimum. The angle of minimum deviation dm was obtained from the geometry of the experimental arrangement: dm= tan^-1 (Y/X). The method of minimum deviation to determine the index of refraction n, which is based on Snell's law, provides the following expression for n:

where A is the prism angle. The index of refraction measurement was repeated three times on the photoresist sample.

Measurement of anisotropy

Using an independent experimental technique, the scattering anisotropy factor, g, of the photoresist can also be obtained from the measurements of scattered light intensities (I) at various scattering angles (Q ) using a goniometer table. The scattering anisotropy factor, g, is given by the average cosine of the scattering angle Q according to the following expression:

where the sums are over all values, i, of the scattering angles and intensities. The scattering anisotropy factor obtained by this measurement was compared with that from the IAD method.

2. The experimental setup for the measurement of scattering anisotropy used a 632.8 nm laser beam to irradiate the photoresist sample placed at the center of a circular goniometer table, and a photomultiplier tube (PMT) detector mounted at the edge of the table to detect scattered light.

The scattering anisotropy factor was determined by irradiating the photoresist sample placed at the center of a circular goniometer table with a 632.8 nm laser beam and using a PMT detector mounted at the edge of the table to detect scattered light (Fig. 2). The sample holder was affixed to the center of the goniometer table. The laser beam was aligned at a 90° angle with respect to the glass plates containing the sample, and the PMT was attached to an adjustable pointer that could be rotated around the table to measure the scattered intensities at different angles. The scattered light intensity was measured between 0° and 180° at an increment of 1° from 0° to 10° of scattering angle, and an increment of 5° above 10° of scattering angle.

Reflectance and transmittance

The total diffuse reflectance and transmittance measurements were taken using a single integrating sphere (Oriel model 71400). The photoresist sample was placed in a specially designed holder mounted to one of the ports of the integrating sphere. The sample holder was fabricated in the University of Texas at San Antonio Engineering Machine Shop. The light source used for these measurements was a HeNe laser, model 125A from Spectra-Physics Inc. (Mountain View, Calif.). The average output power of the laser was 50 mW, the beam diameter at 1/e² was 2 mm, and the beam divergence was 0.70 mrad at 632.8 nm.

3. The experimental setup used to measure the total diffuse transmittance (T d ) and diffuse reflectance (R d ) used an integrating sphere. The laser was directed into the entrance port A of the integrating sphere, whose exit port is either open or capped with a reflective surface identical to that of the interior surface of the integrating sphere or the sample depending on the measurement taken.

The schematic of the experimental setup employed to measure the total diffuse reflectance and total diffuse transmittance is shown in Figure 3. The laser was directed into the entrance port A of the integrating sphere, whose exit port is either open or capped with a reflective surface identical to that of the interior surface of the integrating sphere or the sample depending on the measurement taken. The diameter of the sphere was 6 in. and each port had a diameter of 1 in. Light leaving the sample was reflected multiple times off the inner surfaces of the sphere. A reflecting baffle within the sphere shielded the PMT from direct emission from the sample. Port A was equipped with a variable aperture so that the beam diameter could be appropriately controlled. The reflected and transmitted light intensities were detected by a PMT (Oriel, model 7068) attached to the measuring port. The PMT was powered by a high-voltage power supply (Bertan, model 215). Signal from the PMT was sent to a digital multimeter (Emco, DMR-2322). The measured light intensities were then utilized to determine the total diffuse reflectance Rd and total diffuse transmittance Td by the following expressions:

and

where Xr is the intensity detected by the PMT with the sample at B, Xt is the intensity detected by the PMT with the sample at A and Z is the intensity detected by the PMT with no sample at A and a reflective surface at B, and Y is the correction factor measured by the PMT with no sample at A and no reflective surface at B.

Collimated transmittance

The unscattered collimated transmittance Tc was measured to determine the total attenuation coefficient. The collimated laser beam intensities were measured by placing the integrating sphere about 3 m from the sample so that the photons scattered off the sample would be prevented from entering the small aperture (about 3 mm in diameter) at the entrance port A. The sample was placed at 90° with respect tothe incident laser beam.

The collimated transmittance Tc was calculated by the relation:

where Xc is the collimated light intensity and Zc is the incident light intensity.

From the Beer-Lambert Law, the total attenuation coefficient can be determined from the following expression:

where t is the physical thickness of the sample.

The IAD method

We have used the IAD method, originally developed by Scott Prahl of the Oregon Medical Laser Center (Portland),¹² to determine the optical properties of biological materials. To solve the radiative transport equation, the IAD algorithm must be supplied with experimentally determined values for the total diffuse reflectance (Rd), total diffuse transmittance (Td) and total collimated transmittance (Tc). The IAD algorithm iteratively chooses values for the dimensionless quantities: albedo, a, and the optical depth, t, defined in Eq. 4 and then adjusts the value of the scattering anisotropy factor, g, until it matches the experimental values of Rd, Td and Tc. The computed values for the albedo, a, and optical depth, t, are then used to calculate the absorption and scattering coefficients, µa and µs, respectively.

Monte Carlo simulation

The accuracy of our measurements of the total diffuse reflectance (Rd) and total diffuse transmittance (Td), employed in the IAD method to determine the absorption and scattering coefficients, was verified by the Monte Carlo (MC) simulation technique. The MC simulation uses the stochastic model to simulate light interaction in turbid media. The values for µa and µs calculated by the IAD method, along with the experimentally determined values for the index of refraction n and scattering anisotropy factor, g, are used to compute values for Rd and Td. Fifteen simulations were run and the results were averaged. These values were then compared for accuracy with the experimentally determined values for Rd and Td and are given in Table 1. A detailed theoretical description of the MC model is given in Jacques and Wang.¹⁵

Table 1. R_d, T_d, T_c, a, t, µ_a, µ_s, µ_t for Positive g-line Photoresist at 632.8 nm

Experimental			IAD
Rd	Td	Tc	a	t	µa	µs	µt
0.003	0.726	0.636	0.225	0.287	1.20	0.350	1.55

 

Results and discussion

The room-temperature absorption spectrum taken on the positive g-line photoresist sample between 575 and 700 nm on the Cary-14 is shown in Figure 4. The spectrum clearly shows that the absorbance of the photoresist sample is extremely high below 600 nm into the UV region, while it is significantly small above 625 nm. Using Beer's exponential decay law, the absorption coefficient at 632.8 nm was determined to be 2.62 cm^-1. This value is comparable with the total attenuation coefficient of 2.43 cm^-1 obtained from the measurement of the collimated transmittance, Tc (Eq. 10).

4. This shows the room-temperature absorption spectrum of a positive g-line photoresist. The spectrum clearly shows that the absorbance of the photoresist sample is extremely high below 600 nm into the UV region, and significantly small above 625 nm.

The index of refraction of the positive photoresist sample was measured using the hollow quartz prism and a HeNe laser and found to be 1.64. This measurement was repeated three times, and the values of index of refraction agreed to within 2%. This value of refractive index was used in all subsequent calculations.

The total diffuse reflectance and diffuse transmittance were measured on the positive photoresist sample using 632.8 nm light from a HeNe laser. These measurements were repeated three times and the data were found to be in excellent agreement. These values along with the measured value of the index of refraction of the photoresist sample were input into the IAD program to obtain the values of the absorption and scattering coefficients, and the scattering anisotropy factor. These values are tabulated in Table 2.

 Table 2. R_d and T_d for Positive g-line Photoresist at 632.8 nm (g=0.95)

Experimental		Monte Carlo
Rd	Td	Rd	Td
0.003	0.726	0.001	0.797

The total attenuation coefficient obtained from the IAD method was found to be 1.55 cm^-1, which is significantly smaller than what is obtained by either the collimated transmittance or the Cary-14 spectrophotometer. This discrepancy can be attributed to the fact that the IAD algorithm employed in this study is very sensitive to the measured reflectance data, which was very small and found to be only 0.003.

Although the photoresist mixture has a complex molecular structure, the scattering coefficient was found to be much smaller than the absorption coefficient at the HeNe laser wavelength of 632.8 nm for the positive g-line photoresist investigated. The scattering anisotropy factor was determined to be about 0.95 by both the IAD method and scattering experiment. It therefore indicates that the scattering is mostly forward scattering. It is also imperative to include the photon diffusion coefficient of the photoresist medium, which can be determined by the following formula¹⁸:

D = c/3(µ_s' + µ_a) (11)

where c is the speed of light and µ_s' is the reduced (transport) scattering coefficient defined by µ_s' = (1-g)µ_s, which is calculated to be 0.0175 cm^-1. The value of the photon diffusion coefficient is 2.72 × 10¹⁰ cm²/sec. The transport mean free path (penetration depth) of a photon in the photoresist sample investigated can be defined as l_t = (µs' + µa)^-1, and is found to be 0.8214 cm.

Finally, the measured values of the total diffuse reflectance and diffuse transmittance were verified by the Monte Carlo simulation technique. These values are given in Table 2. The experimental and Monte Carlo values for the diffuse transmittance were in good agreement, while the values for the diffuse reflectance varied greatly. This discrepancy can be attributed to the significantly low intensity of the diffuse reflected light; the reflectance measurements appeared to be very sensitive and susceptible to the experimental errors, thereby leading to the large variation between the measured Rd and that obtained by the MC method.

The values of the optical properties reported in this paper can be of significant importance to the semiconductor industry. The optical properties are critically important for photoresist manufacturers and process engineers in order for them to be able to characterize and model photolithographic processes. More importantly, absorption and scattering of laser light from a HeNe laser by a photoresist are important parameters to consider with respect to target recognition on a stepper. This is because most steppers in IC fabrication facilities use a HeNe laser light source for target recognition and alignment of semiconductor wafers.

* Currently a senior process engineer at Advanced Micro Devices (Austin, Texas)
** Currently a graduate student in mechanical engineering at the University of Texas (Austin)

Dhiraj K. Sardar is a professor of physics at the University of Texas. He has more than 20 years of research experience in laser materials, and has supervised a large number of student research projects involving characterization of optical and laser properties of various solid-state laser materials. He has a Ph.D. from Oklahoma State University (Stillwater).
Phone: 1-210-458-5748
E-mail: dsardar@utsa.edu

Michael L. Mayo received a B.S. in physics from the University of Texas at San Antonio, and he is now a graduate student in physics at the University of Texas at Arlington. He has done experimental research in laser and semiconductor materials for more than three years.

Anthony Sayka received an M.B.A. and a B.S. in physics from the University of Texas, and is currently a senior process engineer at Advanced Micro Devices (Austin, Texas). He has 14 years of experience in the semiconductor industry, including engineering positions with VLSI Technology Inc., Micron Technology Inc., and NCR Corp. He also has a B.S. in chemistry from the University of Colorado at Colorado Springs.
E-mail: anthony.sayka@amd.com

Raylon M. Yow received a B.S. in mechanical engineering from the University of Texas at San Antonio, and is currently a graduate student in mechanical engineering at the University of Texas at Austin. He has four years of research experience in laser materials.

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Acknowledgement

The authors would like to thank Arch Chemicals for supplying us with the positive g-line photoresist used in this study and also Advanced Micro Devices (AMD, Austin, Texas) for its support of this project.

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