**2. Cell library development for character projection equipment**

Standard cell methodology is a quite popular design method to design an ASIC. The standard cell methodology exploits a cell library which is a collection of low-level logic functions, called cells, such as NAND gates, NOR gates, flip-flops, latches and buffers. From a viewpoint of character projection lithography, it is important to project as many cells as possible with character projection lithography.

Cell library development methodologies were studied for character projection lithography (Sugihara et al., 2005, 2006a, 2006c, 2007b, 2008, 2010, Inanami et al., 2000). In this section, we focus on a cell library development methodology for a single-column-cell system (Sugihara et al., 2005, 2006a, 2006c, 2007b).

*Cells*, which are components for IC designs, are ordinarily utilized as the basis of characters. The characters are placed in an array on a CP aperture mask as shown in Fig. 4. It accommodates several hundred characters, which are several-m squares. The number of characters available on a single CP aperture mask is limited to a small one and not all cells in a cell library can be realized on it. For example, if there are four variations for every cell function as shown in Fig. 5, a CP aperture mask accommodates about 100 or less of cell functions at the 90 nm technology. Even if multiple CP aperture masks are utilized for placing all the cells on them, it takes forbiddingly long time to switch CP aperture masks for setting and adjusting. This chapter assumes that a single CP aperture mask is allowed to use for each layer and that the cells off the CP aperture mask are projected with the VSB lithography. It is quite important to select frequently-utilized cells to put on a CP aperture mask because a CP aperture mask is a precious resource to increase the throughput of the system.

Fig. 4. A CP mask

70 Recent Advances in Nanofabrication Techniques and Applications

Inanami et al., 2003; Nakamura et al., 2006; Nakasugi et al., 2003). The system can accommodate 400 characters on a CP aperture mask and any character can be chosen at every EB shot, so that the throughput of the system can be enhanced quite effectively with the CP lithography. The projection system can also project rectangular and triangular shapes with the VSB lithography. Their system is capable of projecting patterns with both the VSB

and CP lithographies.

Fig. 2. Single-column-cell character projection equipment

**All electromagnetic lenses are in type-C. Electron Gun (4x4) Blanking Deflectors Rectangular pertures (4x4) Pre. Mask Deflector CP Aperture Masks (on separated stage) Post Mask Deflectors Round Apertures Major Deflector (100x100 um) Minor Deflector (10x10 um)**

Fig. 3. An Advantest multi-column-cell character projection equipment

Yasuda et al. proposed a multi-column-cell (MCC) system, which can project multiple characters in parallel by equipping it with multiple projection mechanisms called columncells (Yasuda et al., 2004). The motivation to develop the MCC system is to achieve higher

*300mm Wafer*

*Wafer Stage*

Fig. 5. Cell directions

$$\mathbf{x}\_{l} = \begin{cases} \mathbf{1} & \text{if cell object } l \text{ is drawn with the CP,} \\ \mathbf{0} & \text{if cell object } l \text{ is drawn with the VSB.} \end{cases} \tag{2}$$

$$\begin{array}{rcl} \mathsf{S}\_{\mathsf{A}}(\mathsf{x}) & = & \mathsf{EB} \text{ shots with the } \mathsf{CP} + \text{EB shows with the VSB} \\ & = & \sum\_{l=1}^{c} \mathsf{S}\_{\mathsf{CP}\_{l}} r\_{l} \mathsf{x}\_{l} + \sum\_{l=1}^{c} \mathsf{S}\_{\text{VSB}\_{l}} r\_{l} (1 - \mathsf{x}\_{l}) \\ & = & \sum\_{l=1}^{c} (\mathsf{S}\_{\mathsf{CP}\_{l}} - \mathsf{S}\_{\text{VSB}\_{l}}) r\_{l} \mathsf{x}\_{l} + \sum\_{l=1}^{c} \mathsf{S}\_{\text{VSB}\_{l}} r\_{l} . \end{array} \tag{3}$$

$$
\Sigma\_{l=1}^{\mathcal{C}} c\_l \mathfrak{x}\_l \le N\_{\text{char}\prime} \tag{4}
$$

Character Projection Lithography for Application-Specific Integrated Circuits 75

times were insignificant while those of the areas were noticeable, that is about 14% area increase. This is because of the same reasons that the area of Conf. 3 increased. Comparing Conf. 4 with Conf. 3, the differences of their best delay times were insignificant while those of their areas were about 4.2%. Horizontal flipping had some influence on the area increase

There was no great difference among delay times between the four configurations. It was experimentally confirmed that cell directions were not strongly relevant to the increase of delay time. The existence of vertical flipping of cells was relevant to increase of area. This was because gaps between cell areas come to arise and each cell area got to own its own

In this section, a case study is shown for five cases to examine the relation between the number of EB shots and how to select cell objects to place on characters. The five cases are described in Table 2. We developed the cell selection software described in Section 2.1.1 with a commercial mathematical optimization engine, ILOG CPLEX 9.0 (ILOG, 2003). Every

Case 1 Only a basic cell direction is available. The optimal set of cells is exactly

Case 3 The basic and Mirror-Y directions are available. Cell objects to be placed on a CP aperture mask are exactly searched with our cell selection method.

Case 5 The four cell directions are available. Cell objects to be placed on a CP aperture

The specification of the CP equipment for which we assumed is shown in Table 3. Two benchmark circuits were used to examine their numbers of EB shots under the five cases. The description for the benchmark circuits is shown in Table 4. Note that the cell library is

> The maximum width and length of rectangles for VSB 3.5 m The width and length of characters for CP 5 m The number of characters on a CP aperture mask 400

mask are exactly searched with our cell selection method.

from academia and comprises fewer kinds of cells than that from industry.

The basic and Mirror-Y directions are available. It is assumed that the reference count of a direction of a cell function is equal to that of the other direction of the cell function. Each direction is assigned 1/2 of available characters to. This

The four cell directions are available. It is assumed that the reference count of a direction of a cell function is equal to that of the other directions. Each direction is assigned 1/4 of available characters to. This is also after the fashion

searched out by solving an ILP problem instance.

is after the fashion of Inanami's (Inanami, 2000).

as vertical flipping was completely forbidden.

optimization process finished within a second.

of Inanami's (Inanami, 2000)

Table 2. Cell directional variations for experiments

Table 3. Specification of CP/VSB equipment

power and ground lines.

Description

**2.3 Case study** 

Case 2

Case 4


account, the number is 1, otherwise 0. Likewise, the second, third and fourth bits denote the existences of the mirror-X, mirror-Y and mirror-XY directions respectively.

Table 1. Delay times for four cell directional variations

A number in each column denotes the delay time with the least area "N/A" means that the given areas were infeasible to place and route the circuit with the place-and-route tool. For example, the least area and the delay time for the area were obtained as 810 × 808.5 and 7.09 ns respectively in Conf. 1. The least areas in Confs. 1, 2, 3, and 4 were 810 × 808.5, 810 × 808.5, 870 × 858, and 879 × 874.5 respectively. About 14% area increased when the mirror-Y and the mirror-XY were forbidden. Theoretically speaking, delay time decreases under a case in which one can use a larger place-and-route area. Delay time in a column of the table is expected to decrease downward but it did not. This is because the CAD tool is based on approximate algorithm. Comparing the two values of Conf. 2, 6.6% delay time increased while place-and-route area increased.

Conf. 1 is the configuration in which all the four cell directions are available and is supposed to be best with regard to area and delay time among the configurations because its design space includes design space of the other configurations. In other words, any layout based on Confs. 2, 3 or 4 can be realized by Conf. 1. The results which the CAD tool reported does not straightforwardly reflect this supposition because the layouts obtained by the CAD tool are approximate solutions, e.g. the delay time of Conf. 2 (6.97 ns) was shorter than that of Conf. 1 (7.09 ns) as the place-and-route area was 810 × 808.5!

Conf. 2 is the configuration in which the horizontal flippings are removed from Conf. 1. In other words, the mirror-X and mirror-XY directions are not taken into account in Conf. 2. There was no great difference of delay times among Confs. 1 and 2. Horizontal flipping seems not to be so effective to reduce delay time and area.

Conf. 3 is the configuration in which the vertical flippings (mirror-Y and mirror-XY) are removed from Conf. 1. Experimental results show that the vertical flipping of cells had little influence on delay time of the chip and it had some influence on the area. Comparing Conf. 3 with Conf. 1, about 14% area increased. This is because the gaps between cell areas were added by eliminating vertical flipping of cells and each cell area got to own its own power and ground lines.

Conf. 4 is the configuration in which any flipping cells are forbidden and only a basic direction of cells is available. Comparing Conf. 4 with Conf. 1, the differences of the delay times were insignificant while those of the areas were noticeable, that is about 14% area increase. This is because of the same reasons that the area of Conf. 3 increased. Comparing Conf. 4 with Conf. 3, the differences of their best delay times were insignificant while those of their areas were about 4.2%. Horizontal flipping had some influence on the area increase as vertical flipping was completely forbidden.

There was no great difference among delay times between the four configurations. It was experimentally confirmed that cell directions were not strongly relevant to the increase of delay time. The existence of vertical flipping of cells was relevant to increase of area. This was because gaps between cell areas come to arise and each cell area got to own its own power and ground lines.
