Filling pattern

Although this filling pattern conveys a lot of information, it is bulky. A shorthand method for giving the same information has been developed—the electronic configuration. 

The chart below shows electron configurations and partial orbital diagrams for the 18 elements of period 4. You would expect the filling pattern shown for potassium (Z = 19) through vanadium (Z = 23). However, an unexpected deviation from the pattern occurs with chromium (Z = 24). The same thing happens with copper (Z = 29). All other configurations for period 4 conform to the aufbau principle. 

A key benefit of accurate CMP models that needs emphasis is the capability to optimize layout design before polishing. Post-CMP ILD thickness variation is a serious concern from both functionality and reliability concerns. An effective method of minimizing this effect is the use of dummy fill patterns that lead to a more equitable pattern density distribution across the chip. Evaluation of such schemes before actual product implementation has become a major use of CMP modeling [53]. Dummy fill is also being investigated for front-end processes where shallow trench isolation CMP suffers from substantial pattern dependencies. 

B. Stine, D. Boning, J. Chung, L. Camilletti, F. Kruppa, E. Equi, W. Loh, S. Prasad, M. Muthukrishnan, D. Towery, M. Berman, and A. Kapoor, The Physical and Electrical Effects of Metal Fill Pattern Practices for Oxide Chemical Mechanical Polishing Processes, IEEE Ti ans. Electr. Dev., Feb 1998. 

Logic suggests that an electron will occupy the lowest energy level available, and electrons will successively fill these levels as they are added to an atom or molecule. "Quantum mechanics" restricts all orbitals to a maximum of two electrons (these two have opposite "spins" and do not strongly repel one another), and hence a filling process occurs. The filling pattern for the sodium atom (sodium is atomic number 11 - therefore there will be 11 electrons in the neutral atom) is shown in Figure 2.7). 

Again, our first concern must be to see how many ways there are in which the translation vectors can be related to one another (relative lengths, angles between them) to give distinct, space-filling patterns of equivalent points. We have seen (Section 11.2) that in 2D there were only 5 distinct lattices. We shall now see that in 3D there are 14. These are often designated eponymously as the Bravais lattices and are shown in Figure 11.11, in the form of one unit cell of each. 

Since the influence of walls on the U and V flow components disappears upon the separation of the order of 8 from a solid wall, inaccuracy of the scheme cannot have an essential influence on the flow rate calculations. Equations (4.32) may have an explicit solution within some limited time interval when the flow from a point runner is still radial, while the flow front is circular. This filling pattern is realized up to the moment when the radius of a free boundary R(t) will become equal to B/2 (see Fig. 11). Such a filling regime we shall refer to as the first stage of filling the formulae of 4.2 with some minor corrections (for details see 36)) are applicable to this stage the corrections arise mainly due to the fact that the radial flow occurs in... 

The filling of the 3d subshell generally proceeds according to Hund s rule (Section 5.12) with one electron adding to each of the five 3d orbitals before a second electron adds to any one of them. There are just two exceptions to the expected regular filling pattern, chromium and copper ... 

Experimental investigations of filling a thin rectangular mold with a reactive mixture showed that disturbances in stable flow are possible. Three filling patterns, depending on the injection rate, can occur stable, unstable, and transient. 

The optimum time step in a FEM-CVA simulation is the one that fills exactly one new control volume. Once the fill factors are updated, the simulation proceeds to solve for a new pressure and flow field, which is repeated until all fill factors are 1. While the FEM-CVA scheme does not know exactly, where the flow front lies, one can recover flow front information in post-processing quite accurately. One very common technique is for the simulation program to record the time when a node is half full, / = 0.5. This operation is performed when the nodal fill factors are updated if the node has fk <0.5 and fk+1 >0.5 then the time at which the fill factor was 0.5 is found by interpolating between tk and tk+l. These half-times are then treated as nodal data and the flow front or filling pattern at any time is drawn as a contour of the corresponding half-times, or isochronous curves. 

Figure 9.30 Comparison between experimental and FEM-CVA predicted filling patterns. [18].

Figure 9.36 presents a comparison of the experimental and numerical filling pattern. As can be seen, the agreement is excellent. It must be pointed out that the solution was dependent of the heat transfer coefficient between the mold wall and the flowing polymer... 

Figure 2 Experimental arrangement for measurements of the Fe nuclear resonance at the Advanced Photon Source (APS). In the standard fill pattern, electron bunches with a duration of 100 ps are separated by 153 ns. X-ray pulses are generated when alternating magnetic fields in the undulator accelerate these electron bunches. The spectral bandwidth of the X-rays is reduced to 1 eV by the heat-load monochromator and to 1 meV by the high-resolution monochromator. At the sample, the flux of the beam is about 10 photons/s. APD indicates the avalanche photodiode used to detect emitted X-rays. The lower right inset illustrates that counting is enabled only for times weU-separated from the X-ray pulse, so that only delayed photon emission resulting from decay of the nuclear excited state contributes to the experimental signal...

Stine B, Boning D, Chung J, Camiletti L, Equi E, Prasad S, Loh W, Kapoor A. The role of dummy fill patterning practices on intra-die ILD thickness variation in CMP processes. VLSI Multilevel Interconnect Conference Santa Clara, CA 1996. p 421-423. 

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