Modeling and realization of a multilevel read-only disk

doi:10.1364/OE.14.001199

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Modeling and realization of a multilevel read-only disk

Jie Song, Yi Ni, Duanyi Xu, Longfa Pan, Qicheng Zhang, and Heng Hu »View Author Affiliations

Optics Express, Vol. 14, Issue 3, pp. 1199-1207 (2006)
http://dx.doi.org/10.1364/OE.14.001199

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▸ Article Outline
– Abstract
1. Introduction
2. Reaction process of exposed and developed photoresist
3. Manufacture of ML-RLL read-only disk
4. The readout signal of ML disks
5. Conclusion
– References and links

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Abstract

A model for exposing and developing photoresist using the reaction mechanism of physics and the chemistry of resist is built, and the micropatterns of recording marks on a stamper are calculated. Compared with our experimental results, the deviation of pit width in simulation is less than 8%. When the width of recording marks is varied by modulating laser power during exposure, a multilevel (ML) read-only disk can be achieved as a result of the corresponding readout signal. Experimental results show that an 8-level read-only optical disk can be realized. The model of mastering serves well for the development of novel ML disks in which the integration of conventional run-length deviations technologies can greatly increase recording density.

1. Introduction

The optical disk is a read-only disk that can issue information cheaply and spread switftly. Multilevel (ML) recording technology increases the capacity of optical disks without changing the optical and mechanical units. There have been some kinds of ML optical recording including 3-level run-length-limited (3L-RLL) modulation on phase-change materials [1

A. Shimizu, K. Sakagami, and Y. Kadokawa, “Multi-level recording on phase-change optical discs,” Ricoh Technical Report No. 28, 34–41 (2002).

][2

S. H. Jiang and F. H. Lo, “PRML process of multilevel run-length-limited modulation recording on optical disc,” IEEE Trans. Mag. 41, 1070–1072 (2005). [CrossRef]

][3

S. H. Jiang, J. W. Kuo, C. P. Ma, and F. H. Lo, “Signals from multi-level run-length-limited modulation recordings using partial response maximum likelihood,” Jpn. J. Appl. Phys. 44, 3453–3456 (2005). [CrossRef]

]. Adopting ML technology for use with read-only disks will be beneficial to optical recording if the ML stamper can be manufactured.

For a long time, lithography has been widely regarded as an art or craft. The experienced lithographer with a background of on-the-job training is able to deliver results but not always able to explain how and why, which is far inadequate for the mastering of new kinds of optical disk. In semiconductor manufacturing, simulation of lithography has a long history of 30 years [4

F. H. Dill, “Optical lithography,” IEEE Trans. Electron. Devices ED–22, No. 7, 440–444 (1975). [CrossRef]

] [5

F. H. Dill, A. R. Neureuther, J. A. Tuttle, and E. J. Walker, “Modeling projection printing of positive photoresists,” IEEE Trans. Electron. Devices , ED–22, No. 7, 456–464 (1975). [CrossRef]

] [6

L. F. Thompson, C. G. Willson, and M. J. Bowden, Introduction to Microlithography (Academic, Washington, 1983). [CrossRef]

] [7

C. A. Mack, “PROLITH: A Comprehensive Optical Lithography Model,” in Optical Microlithography IV, Harry L. Stover, ed., Proc. SPIE 538, 207–220 (1985).

]. However, for optical recording, the signal recorded on the photoresist and posterior material must be picked up, modeling the mark on stamper, and the corresponding readout signal will improve technology in the mastering of optical disks.

In this paper, the model of ML mastering and corresponding readout signal is established. We simulate the process of exposing and developing photoresist from the reaction mechanism of physics and the chemistry of resist. When positive photoresist is eradiated by a laser beam with varying power, micropatterns such as the transverse dimensions are varied, which can be used to ML read-only disks due to the different readout signals. Simulation is in agreement with the experimental results, and can help us choose appropriate laser power for mastering. Combined with the RLL technology in traditional optical disks, ML can increase recording capacity greatly. For example, the capacity of a DVD double layer disk with the {2, 10} 8L-RLL modulation can be increased to over 20 GB without any changes on optical or mechanical units.

2. Reaction process of exposed and developed photoresist

2.1 The intensity distribution of the focusing laser

Fig. 1. Coordinate system of incident laser beam.

Figure 1 illustrates the incident laser beam. The exposing system includes a blue semiconductor laser with wavelength of 405 nm and an object lens with a large numerical aperture of 0.90, which must be calculated by the vector diffraction theory. The laser beam emitting from the semiconductor laser can be regarded as plane and circularly-polarized wave when reaching the focusing object lens. The lens converts the incident plane wave into a converging spherical one. The angular aperture on the image side is 2α′. OX, OY, and OZ are Cartesian rectangular axes, respectively, with origin at the focus and with OX and OY in the direction of vibration of the incident electric field, and with OZ along the axis of revolution. (r,θ,ϕ) are spherical polar coordinates, with azimuth ϕ = 0 in the OX direction. In the electromagnetic field, the electric vector and magnetic vector in x-direction of any point P are expressed respectively as:

E_{0} (p, t) = Re [e_{0} (p) \exp (iwt)],

(1)

H_{0} (p, t) = Re [h_{0} (p) \exp (iwt)] .

(2)

In the y-direction, the electrical vector is equal to that in the x-direction in amplitude, but with π/2 difference in the phase angle. The light intensity of point P on the focus plane is expressed as [8

A. Boivin and E. Wol, “Electromagnetic field in the neighborhood of the focus of a coherent beam,” Phys. Rev. 138(6B), 1561–1565 (1965). [CrossRef]

I (v) = 2 C^{2} [2 H_{1}^{2} (0, v) + H_{0}^{2} (0, v) + H_{2}^{2} (0, v)],

(3)

where

v = kρ \sin α'

(4)

in which

k = \frac{2 π}{λ} .

(5)

λ is the exposing wavelength, and ρ is shown in Fig. 1(b).

C = \frac{kf a_{0}}{2} .

(6)

and

H_{0} (0, v) = \int_{0}^{α'} {(\cos θ)}^{\frac{1}{2}} \sin θ (1 + \cos θ) J_{0} (\frac{v \sin θ}{\sin α'}) dθ

H_{2} (0, v) = \int_{0}^{α'} {(\cos θ)}^{\frac{1}{2}} \sin θ (1 - \cos θ) J_{2} (\frac{v \sin θ}{\sin α'}) dθ,

H_{1} (0, v) = \int_{0}^{α'} {(\cos θ)}^{\frac{1}{2}} \sin^{2} θ J_{1} (\frac{v \sin θ}{\sin α'}) dθ .

(7)

Figure 2 demonstrates the distribution of light intensity normalized to that on the focus spot.

Fig. 2. Distribution of normalized light intensity.

2.2 Chemical reaction mechanism of exposed photoresist

The exposing parameters A , B , and C are the keys to describing the exposure-dependent optical properties of the photoresist. A and B, exposure dependent and independent parameters, respectively, describe the absorption constant α(ρ, z, t) according to

α (ρ, z, t) = AM (ρ, z, t) + B,

(8)

where M is the relative amount of photoactive inhibitor present at any position (ρ,z) and time t , during exposing. For optical computation purposes, we prefer to use the complex index of refraction of the photoresist

N = n - ik,

(9)

where n is the real part of the index and k is the extinction coefficient

k = \frac{αλ}{4 π} .

(10)

Combining Eqs. (8), (9), and (10

H. H. Hopkins, “Diffraction theory of laser read-out systems for optical video discs,” J. Opt. Soc. Am. 69(1), 4–24 (1979). [CrossRef]

) gives

N = n - i \frac{λ [AM (ρ, z, t) + B]}{4 π} .

(11)

The complex index of refraction changes as the inhibitor is destroyed by the exposing light with local intensity I . The intensity I changed with the absorption constant α and the optical sensitivity parameter C relates the rate of destruction of inhibitor to the light intensity, as in

\frac{\partial I (ρ, z, t)}{\partial z} = - αI (ρ, z, t)

(12)

\frac{\partial M (ρ, z, t)}{\partial t} = - I (ρ, z, t) M (ρ, z, t) C

(13)

The optical properties of resist vary during exposure as a function of depth into the photoresist and the parameter ρ. Berning [9

P. H. Bernlng, “Theory and calculations of optical thin films,” in Physics of Thin Films, Films, Vol. I, George Hass, ed., (Academic, New York, 1963), pp. 69–121.

] has mathematically subdivided the resist film into sublayers thin enough to be treated as isotropic along the depth direction. In our optical computation, the optical properties of the resist vary along z and ρ directions, as shown in Fig. 1. Sublayer thickness is expressed as δz_j at the radius ρ. The complex reflection r_ρj and transmission t_ρj , terms for each interface, start from the substrate. Figure 3 shows the substrate and its overlying layers and the terms used in the computation.

We can get the absorptivity A_ρj of each resist sublayer. For some radius ρ, the calculation method of A_ρj is extracted by Dill [5

F. H. Dill, A. R. Neureuther, J. A. Tuttle, and E. J. Walker, “Modeling projection printing of positive photoresists,” IEEE Trans. Electron. Devices , ED–22, No. 7, 456–464 (1975). [CrossRef]

]. Thus, the average light intensity can be expressed as

I (ρ, j) = \frac{I_{0} (ρ) A_{ρj}}{α_{ρj} δ z_{j}} .

(14)

The terminal and initial conditions of M and I are expressed as:

I (ρ, 0, t) = I (ρ)

I (ρ, z, 0) = I (ρ) \exp [- (A + B) z],

(15)

M (ρ, 0, t) = \exp [- I (ρ) Ct]

M (ρ, z, 0) = 1 .

(16)

When A_ρj are calculated we combine formulas (13), (14), (15), and (16), and the rate of destruction of inhibitor M (ρ, z,t) can be obtained by repetition with δt and δz chosen properly.

Fig. 3. Diagram of substrate and overlaying layers in computation.

2.3. Calculation of developed photoresist

When exposure is completed, the description of photoresist is a two-dimensional matrix of inhibitor concentration values. Development is modeled as a surface-limited-etching reaction controlled by the local inhibitor concentration [5

F. H. Dill, A. R. Neureuther, J. A. Tuttle, and E. J. Walker, “Modeling projection printing of positive photoresists,” IEEE Trans. Electron. Devices , ED–22, No. 7, 456–464 (1975). [CrossRef]

]. Using the R(M) curve, development rate values can be substituted for the inhibitor concentration values, giving an R(ρ, z) matrix description of the photoresist film for development. We calculate the development time assuming that only the top surface of exposed photoresist cells is developed. When a cell is removed, the newly exposed cells are allowed to start etching. For any point in the photoresist the developing time is

t_{ρj} = \frac{z_{j}}{R_{ρj}} .

(17)

When any development time is given, contours of the resist image can be calculated.

3. Manufacture of ML-RLL read-only disk

For a common optical disk, the EFM or EFM+ modulation information is carried on the length, which is realized by changing the semiconductor laser pulse width when positive photoresist is exposed. Figure 4 shows the edge profile simulation result of an 11T pit recording mark in a DVD, and Table 1 shows the associated parameters.

Fig. 4. Simulation result of an 1 1T pit recording mark.

Table 1. Parameters used in the experiment.

Substrate	SiO₂
Photoresist	Kind	Microposit S1813
	Thickness	130nm
Exposure	Wavelength of laser (λ)	405nm
	Numerical Aperture (NA)	0.9
	The power of laser power	1.3mW
Development	Developer	3:1 D.I. Water: Microposit
		Developer Concentrate
	Temperature	22 deg
	Time	12 sec
Recording speed	3.25m/s

According to the mechanical reaction of photoresist during exposure and development, when we change the light intensity irradiating to the positive photoresist, the recording mark profile calculated by above-described methods can be remarkably different with all the other conditions unchanged, including optical equipment, photoresist parameters, and exposure and development conditions. Figure 5 is the mean width of pits on the stamper versus laser power. The horizontal ordinate is the relative laser power (the ratio of the laser power getting to the photoresist surface to its initial set power emitting from a semiconductor laser diode). Figure 5 indicates that simulation is consistent with the experimental results, with deviation ≤ 8%. However, processes of metallization and electroplating can have a minute effect on the micropatterns of recording marks. Furthermore, the polarization states of a laser beam and purity of photoresist influence the absorption of photoresist. So the lost laser energy is more than expected, which leads to deviation, especially when laser power increased. With the exposure and development model, the production process of both conventional and novel read-only disks can be simulated.

When the stampers fabricated with varying laser power act as injection moldings to stamper disks (novel optical disks), ML read-only disks are manufactured. Figure 6 is the comparison of AFM photos of a conventional DVD and ML DVD.

Fig. 5. Mean width of pit vs. laser power. The curve depicts the simulation results.

Fig. 6. The AFM photographs of a conventional DVD (a) and ML disk modulated by DVD (b).

4. The readout signal of ML disks

When the ML disks are read out, the light intensity reflected from the recorded mark with different profiles is different. Figure 7 shows the experimentally measured mean peak-peak amplitude and the calculated values of a readout signal based on the HH Hopkins diffraction theory [10

H. H. Hopkins, “Diffraction theory of laser read-out systems for optical video discs,” J. Opt. Soc. Am. 69(1), 4–24 (1979). [CrossRef]

], with the conditions same as in Fig. 5 and the lengths of lands and pits are all 11T in a conventional DVD. The simulation curve accords with the experimental results very well, which indicates that our model is suited to simulate the process of exposing and developing photoresist.

Fig. 7. Normalized mean peak-peak amplitude of readout signal vs. recording laser power. The curve depicts the simulation results.

In ML recording, Sigma to Dynamic Range (SDR) has been proposed for the evaluation of recording quality [1

A. Shimizu, K. Sakagami, and Y. Kadokawa, “Multi-level recording on phase-change optical discs,” Ricoh Technical Report No. 28, 34–41 (2002).

]. SDR is the ratio of the mean standard deviation (σ) of a recorded level to the total dynamic range (DR) between minimum and maximum reflectivity, expressed as Eq. (18). Usually the bit error rate (BER) needs to be about 10^-4 before the performance of the error correction that is generally used for optical disks. In order to keep the BER at 10^-4, the SDR is required to satisfy Eq. (19), in which M is the number of levels [11

S. Spielman, B.V. Johnson, G. A. McDermott, M. P. O’Neill, C. Pietrzyk, T. Shafaat, D. K. Warland, and T. Long, “Using pit-depth modulation to increase capacity and data transfer rate in optical discs,” in Optical Data Storage, Proc. SPIE 3109, 11–18 (1997).

SDR = \frac{(\sum σ_{i})}{n \times DR} .

(18)

SDR \leq \frac{1}{6 \times (M - 1)}

(19)

In our experiment, the SDR is estimated to be less than 2.4 %, which indicates that 8-level recording can be achieved from Eq. (19) in a read-only disk by conventional detection of peak value. When we adopt a new detection such as the partial response maximum likelihood (PRML) method, more levels can be achieved [2

S. H. Jiang and F. H. Lo, “PRML process of multilevel run-length-limited modulation recording on optical disc,” IEEE Trans. Mag. 41, 1070–1072 (2005). [CrossRef]

], [12

A. Shimizu, K. Sakagami, Y. Kadokawa, K. Takeuchi, H. Tashiro, and K. Takatsu, “Data detection using pattern recognition for multi-level optical recording,” Jpn. J. Appl. Phys. Part 1 41(3B), 1745–1746 (2002). [CrossRef]

Intersymbol interference (ISI), a description of how the readout signal from a particular recorded mark is affected by the adjacent recorded marks, is an important consideration in ML recording. In ML recording, M profiles of adjacent recorded marks can lead to different influence to the current mark. So ISI is more serious in ML recording than recording on conventional DVD. Fortunately, the PRML detection method, including an appropriate writing strategy, can solve the problem successfully. The model of exposing and developing can aid and accelerate the establishment of strategy.

Our ML read-only storage experiment is carried out using blue laser mastering equipment. The results validate the feasibility of the novel optical storage technology. Next, we will perform research on the method of mastering using shorter wavelength lasers, which has rigorous requirements on recording material, mastering device, and the precision of replication. When a shorter wavelength laser is used in ML read-only disks mastering, the recording marks will be smaller and the capacity of optical storage is expected to be larger.

5. Conclusion

The recording density and transfer rate can be obviously increased by applying ML technology. We have modeled the fabrication process of a ML stamper from the chemical reaction mechanism of positive photoresist, and the simulations are coincident with the experiment results, which facilitates development of ML recording technology. Experiment results indicate that 8-level recording is feasible in a read-only disk, and the capacity is estimated to reach 20GB in {2, 10} 8L-RLL disks. If we use shorter wavelength laser mastering technology, the capacity of ML read-only disks can be greatly improved.

References and links

1.	A. Shimizu, K. Sakagami, and Y. Kadokawa, “Multi-level recording on phase-change optical discs,” Ricoh Technical Report No. 28, 34–41 (2002).
2.	S. H. Jiang and F. H. Lo, “PRML process of multilevel run-length-limited modulation recording on optical disc,” IEEE Trans. Mag. 41, 1070–1072 (2005). [CrossRef]
3.	S. H. Jiang, J. W. Kuo, C. P. Ma, and F. H. Lo, “Signals from multi-level run-length-limited modulation recordings using partial response maximum likelihood,” Jpn. J. Appl. Phys. 44, 3453–3456 (2005). [CrossRef]
4.	F. H. Dill, “Optical lithography,” IEEE Trans. Electron. Devices ED–22, No. 7, 440–444 (1975). [CrossRef]
5.	F. H. Dill, A. R. Neureuther, J. A. Tuttle, and E. J. Walker, “Modeling projection printing of positive photoresists,” IEEE Trans. Electron. Devices , ED–22, No. 7, 456–464 (1975). [CrossRef]
6.	L. F. Thompson, C. G. Willson, and M. J. Bowden, Introduction to Microlithography (Academic, Washington, 1983). [CrossRef]
7.	C. A. Mack, “PROLITH: A Comprehensive Optical Lithography Model,” in Optical Microlithography IV, Harry L. Stover, ed., Proc. SPIE 538, 207–220 (1985).
8.	A. Boivin and E. Wol, “Electromagnetic field in the neighborhood of the focus of a coherent beam,” Phys. Rev. 138(6B), 1561–1565 (1965). [CrossRef]
9.	P. H. Bernlng, “Theory and calculations of optical thin films,” in Physics of Thin Films, Films, Vol. I, George Hass, ed., (Academic, New York, 1963), pp. 69–121.
10.	H. H. Hopkins, “Diffraction theory of laser read-out systems for optical video discs,” J. Opt. Soc. Am. 69(1), 4–24 (1979). [CrossRef]
11.	S. Spielman, B.V. Johnson, G. A. McDermott, M. P. O’Neill, C. Pietrzyk, T. Shafaat, D. K. Warland, and T. Long, “Using pit-depth modulation to increase capacity and data transfer rate in optical discs,” in Optical Data Storage, Proc. SPIE 3109, 11–18 (1997).
12.	A. Shimizu, K. Sakagami, Y. Kadokawa, K. Takeuchi, H. Tashiro, and K. Takatsu, “Data detection using pattern recognition for multi-level optical recording,” Jpn. J. Appl. Phys. Part 1 41(3B), 1745–1746 (2002). [CrossRef]

OCIS Codes
(230.4170) Optical devices : Multilayers
(330.4060) Vision, color, and visual optics : Vision modeling

ToC Category:
Optical Data Storage

History
Original Manuscript: October 19, 2005
Revised Manuscript: December 23, 2005
Manuscript Accepted: January 3, 2006
Published: February 6, 2006

Citation
Jie Song, Yi Ni, Duanyi Xu, Longfa Pan, Qicheng Zhang, and Heng Hu, "Modeling and realization of a multilevel read-only disk," Opt. Express 14, 1199-1207 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-3-1199

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References

A. Shimizu, K. Sakagami, and Y. Kadokawa, "Multi-level recording on phase-change optical discs," Ricoh Technical Report No. 28, 34-41 (2002).
S. H. Jiang and F. H. Lo, "PRML process of multilevel run-length-limited modulation recording on optical disc," IEEE Trans. Mag. 41, 1070-1072 (2005). [CrossRef]
S. H. Jiang, J. W. Kuo, C. P. Ma, and F. H. Lo, "Signals from multi-level run-length-limited modulation recordings using partial response maximum likelihood," Jpn. J. Appl. Phys. 44, 3453-3456 (2005). [CrossRef]
F. H. Dill, "Optical lithography," IEEE Trans. Electron. Devices 22,No. 7, 440-444 (1975). [CrossRef]
F. H. Dill, A. R. Neureuther, J. A. Tuttle, and E. J. Walker, "Modeling projection printing of positive photoresists," IEEE Trans. Electron. Devices, 22, No. 7, 456-464 (1975). [CrossRef]
L. F. Thompson, C. G. Willson, and M. J. Bowden, Introduction to Microlithography (Academic, Washington, 1983). [CrossRef]
C. A. Mack, "PROLITH: A Comprehensive Optical Lithography Model," in Optical Microlithography IV, Harry L. Stover, ed., Proc. SPIE 538, 207-220 (1985).
A. Boivin and E. Wol, "Electromagnetic field in the neighborhood of the focus of a coherent beam," Phys. Rev. 138,1561-1565 (1965). [CrossRef]
P. H. Bernlng, "Theory and calculations of optical thin films," in Physics of Thin Films, Films, Vol. I, George Hass, ed., (Academic, New York, 1963), pp. 69-121.
H. H. Hopkins, "Diffraction theory of laser read-out systems for optical video discs," J. Opt. Soc. Am. 69,4-24 (1979). [CrossRef]
S. Spielman, B.V. Johnson, G. A. McDermott, M. P. O’Neill, C. Pietrzyk, T. Shafaat, D. K. Warland, and T. Long, "Using pit-depth modulation to increase capacity and data transfer rate in optical discs," in Optical Data Storage, Proc. SPIE 3109,11-18 (1997).
A. Shimizu, K. Sakagami, Y. Kadokawa, K. Takeuchi, H. Tashiro, and K. Takatsu, "Data detection using pattern recognition for multi-level optical recording," Jpn. J. Appl. Phys. 41,1745-1746 (2002). [CrossRef]

Boivin, A.
Dill, F. H.
Hopkins, H. H.
Jiang, S. H.
Johnson, B.V.
Kadokawa, Y.
Kuo, J. W.
Lo, F. H.
Long, T.
Ma, C. P.
McDermott, G. A.
Neureuther, A. R.
O’Neill, M. P.
Pietrzyk, C.
Sakagami, K.
Shafaat, T.
Shimizu, A.
Spielman, S.
Takatsu, K.
Takeuchi, K.
Tashiro, H.
Tuttle, J. A.
Walker, E. J.
Warland, D. K.
Wol, E.

IEEE Trans. Electron. Devices

F. H. Dill, "Optical lithography," IEEE Trans. Electron. Devices 22,No. 7, 440-444 (1975). [CrossRef]
F. H. Dill, A. R. Neureuther, J. A. Tuttle, and E. J. Walker, "Modeling projection printing of positive photoresists," IEEE Trans. Electron. Devices, 22, No. 7, 456-464 (1975). [CrossRef]

IEEE Trans. Mag.

S. H. Jiang and F. H. Lo, "PRML process of multilevel run-length-limited modulation recording on optical disc," IEEE Trans. Mag. 41, 1070-1072 (2005). [CrossRef]

J. Opt. Soc. Am.

H. H. Hopkins, "Diffraction theory of laser read-out systems for optical video discs," J. Opt. Soc. Am. 69,4-24 (1979). [CrossRef]

Jpn. J. Appl. Phys.

A. Shimizu, K. Sakagami, Y. Kadokawa, K. Takeuchi, H. Tashiro, and K. Takatsu, "Data detection using pattern recognition for multi-level optical recording," Jpn. J. Appl. Phys. 41,1745-1746 (2002). [CrossRef]
S. H. Jiang, J. W. Kuo, C. P. Ma, and F. H. Lo, "Signals from multi-level run-length-limited modulation recordings using partial response maximum likelihood," Jpn. J. Appl. Phys. 44, 3453-3456 (2005). [CrossRef]

Phys. Rev.

A. Boivin and E. Wol, "Electromagnetic field in the neighborhood of the focus of a coherent beam," Phys. Rev. 138,1561-1565 (1965). [CrossRef]

Proc. SPIE

S. Spielman, B.V. Johnson, G. A. McDermott, M. P. O’Neill, C. Pietrzyk, T. Shafaat, D. K. Warland, and T. Long, "Using pit-depth modulation to increase capacity and data transfer rate in optical discs," in Optical Data Storage, Proc. SPIE 3109,11-18 (1997).

Other

A. Shimizu, K. Sakagami, and Y. Kadokawa, "Multi-level recording on phase-change optical discs," Ricoh Technical Report No. 28, 34-41 (2002).
P. H. Bernlng, "Theory and calculations of optical thin films," in Physics of Thin Films, Films, Vol. I, George Hass, ed., (Academic, New York, 1963), pp. 69-121.
L. F. Thompson, C. G. Willson, and M. J. Bowden, Introduction to Microlithography (Academic, Washington, 1983). [CrossRef]
C. A. Mack, "PROLITH: A Comprehensive Optical Lithography Model," in Optical Microlithography IV, Harry L. Stover, ed., Proc. SPIE 538, 207-220 (1985).

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