## Abstract

A dynamic model of mastering for multilevel run-length limited read-only disc is built, and corresponding experiments on DVD are done to validate it. Results show that this model consists with real mastering process. Using the model, a preliminary write strategy for 4-level run-length limited read-only disc is calculated out. The readout signals of the disc optimizing by write strategy are very close to desired.

©2007 Optical Society of America

## 1. Introduction

Multilevel run-length-limited (ML-RLL) technology on read-only disc can increase the capacity of optical disc without changing the optical and mechanical units.[1] But the marks on the disc are very different from the conventional optical disc, so shaping the accurate multilevel patterns is the key point of the ML-RLL technology. The write strategy of ML-RLL read-only optical disc is much more complex than conventional optical disc. Both the recording power and pulse are adjusted during mastering, in contrast the recording power is not changed in conventional optical disc.

A good model of mastering for ML-RLL read-only disc can be very helpful in calculating the write strategy and reduce the computation work. Several models of mastering have been developed. [2, 3] But these models are all static and too complex to use. In this paper, a simple and dynamic model of mastering is described.

Using this model, a preliminary write strategy for a 4-level run-length limited read-only disc is given. In our multilevel read-only disc system, because of the difficulty of making conjoint multilevel pits, every two pits must be divided by a land, and this restriction is realized by a special coding method[4]. Experiments show good results on the consistency between the real and simulated data.

## 2. Mastering model

#### 2.1 Focusing laser

In optical disc mastering process, the exposure light source is a short wavelength laser which is focused into a converging beam by a high numerical aperture object lens, as Fig. 1(a).

In this paper we assume that the polarization state of the laser is linear and the optical system is aplanatic. So the lens converts the incident plane wave into a spherical one. Here, it is convenient to introduce polar coordinates (*ρ,φ*) to describe the focal plane, see Fig. 1(b),
since the optical system is revolution. *ρ* is in the xy-plane, and when the azimuth *φ* = 0, *ρ* is in the ox direction. The distribution of the energy density on the focal plane (z = 0) is given by [5]:

where

and

Here *f* is the focal length of the lens, *l*
_{0} is the amplitude factor, *λ* is the wavelength of
the incident laser, α is the angular semi-aperture and *J _{n}* is the Bessel function of the first kind
and order n.

The coordinate transformation equations between the rectangular coordinates and polar coordinates are expressed as:

Figure 2(a) shows the 3D view of normalized light intensity on the focal plane, and Fig. 2(b) gives out the cross sections distributions through the center when the laser power is changed.

#### 2.2 Exposure process

In IC-lithography a model proposed by Dill et al.[6], is widely used for the description of the exposure process. This model is based on the assumption that the conversion of the photo active compound (PAC) depends on the exposure energy. In this model the conversion of the PAC at any position in the photoresist layer is described by:

where I(x, y, z, t) is the exposure intensity, M(x, y, z, t) is the PAC concentration relative to the initial concentration (for unexposed photoresist M=1.0, for fully exposed photoresist M=0.0) and C is the conversion efficiency. In optical disc mastering process the If C is a constant this equation reduces to:

where *E*(*x*,*y*,*z*) = ∫^{t}_{0} *I* (*x*,*y*,*z*,*τ*)d*τ* is the exposure dose and *M*(*x*,*y*,*z*,0) ≡ 1 .

#### 2.3 Development

Several models have been proposed for the description of the development process by Kim et al[7], Trefonas et al.[8] and Hirai et al.[9] Local development rate of non-absorbing photoresist can be calculated according to these models. The Trefonas model and Hirai model are similar, except Hirai model includes an extra term for the development rate of unexposed photoresist. But in optical disc mastering process, the development rate of exposed photoresist is chose nearly a thousand times of unexposed photoresist, in order to obtain very sharp profile. [2] Thus the Trefonas model is accurate enough and more convenient for the mastering process. The local development rate is given by:

where R is the development rate, h is the dissolved photoresist film thickness, R_{0} is the development rate of fully exposed photoresist and q is the contrast of the photoresist.

#### 2.4 Dynamic mastering model

Instead of splitting the process into an exposure and a development part, we combined the exposure model and development model and deduced a whole mastering model.

$$=\frac{I{\left(x,y\right)}^{*}P\left(x\right)}{v}\phantom{\rule{1.0em}{0ex}}$$

where

According to J. Pasman’s analysis, the absorption effects of the photoresist can be neglected, because of the absorption coefficient and the layer thickness in the mastering process are both very small. [10] Also, standing waves are negligible because the refractive index of the glass substrate is rather close to the value for positive photoresist. [2] Basing on above investigation, we can assume that the conversion of the PAC in mastering process is independent of the depth into the photoresist layer. Thus from equation (6) and (7), the depth of any point on the photoresist surface after development is given by:

where h(x, y) is the depth of dissolved film thickness, T is the development time, and the exposure dose E(x, y) can be calculated from the equation(8).

## 3. DVD experiment

The experiments is carried on a commercial DVD mastering system AM200 manufactured by a Dutch company ODME. Some key parameters during the mastering process are shown in Table 1.

First, the standard DVD disc is made to prove the model is correct and accurate enough. Before mastering, the optimum recording power should be chose according to the asymmetry of the readout signals. If the recording power is suitable, then the continuous 3T pits and 3T lands like Fig. 3(a), and have nearly equal length. Figure 3(b) shows the calculated result which is very close to the real data.

In Fig. 4, model calculations are given for pits with different lengths (3T to 11T). The 3T, 4T and 5T pits have smaller depth than others. In DVD, usually the coat thickness is no more than 130nm, so this difference will not affect the actual patterns. But in multilevel disc, the middle levels’ depths are smaller than coat thickness, so this effect must be treated carefully.

## 4. Adjusting write strategy using dynamic mastering model.

The reason we developed this dynamic mastering model is to help calculate the write strategy for multilevel read-only disc. Because adjusting the recording power and recording pulse both have complicated effects on readout signals, and only according to RF signal is difficult to make an accurate decision on how to change the write strategy. We must know what changes have been done to the marks on the disc.

First, based on readout signals, the recording power for each level is determined roughly. Figure 5 shows the readout signals of a 4-level read-only disc without optimizing photoresist thickness, write strategy and other parameters. The recording power for each level is P_{0}, 0.7P_{0} and 0.6P_{0}, where P_{0} is the normal DVD recording power.

From Fig. 6 we can see that when the recording power is changed, the pits’ width, length, depth, angles of the pit walls all will change.

In order to compensate the pits length and depth for middle level pits and the short T pits, the recording powers and recording pulses need to be adjusted. Table 2 gives a preliminary write strategy for multilevel pits.

Generally, level 1pits are recorded with 0.5 T pulse width added at both the beginning and ending for each T, level 2 pits are recorded with 0.33 T added, and level 3 pits are recorded with no T added. But for short T pits, such as 3T, 4T and 5T, their depths are insufficient, so they not only need to be compensated by adding the recording pulses but also by increasing recording powers. Figure 7 shows the cross sections in the tangential direction through the center of the pits after optimizing by the write strategy above.

The write strategy is applied on the AM200 DVD mastering system. Patterns are recorded regularly with the sequences of 3T1P, 11TL, 3T2P, 11TL, 3T3P, 11TL, 4T1P, 11TL, 4T2P… 11T1P, 11TL, 11T2P, 11TL, 11T3P, 11TL, and repeat incessantly, 11TL indicates an 11T land.

In our multilevel read-only disc system, PRML is used in signal detection[11]. And the PRML detector is designed using a linear optical disc readout model. So the agreement between simulated signals and actual readout signals is used as a criterion to evaluate the write strategy. From Fig. 8, we can see that it is very similar between the actual data and simulated data.

## 5. Conclusion

In this paper a dynamic mastering model of optical disc is described and experiments prove that this model can represent the recorded patterns acceptably with a very low cost calculation by converting the computations into a convolution. Based on this mastering model, a preliminary write strategy for multilevel read-only disc is determined by adjusting recording powers and recording pulses. Finally, the agreement between the actual and theoretical signals shows that the adjusting of the write strategy is in a right direction.

## Acknowledgments

This work is supported by National Natural Science Foundation of China (Grant No. 60677036).

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