Deep Hole Etching Simulation for Advanced NAND Flash Memory



The NAND Flash memory cell has been refined to reduce the bit cost, but the limit of its miniaturization has been reached due to the high electric field problem and the difficulty of lithography. On that account, three-dimensional stack cell structures have been adopted to achieve mass storage devices [1-3]. It has already been reported that the fabrication of 256Gbit NAND Flash memory with 48 stacked layers started on August in 2015 [4, 5]. For the fabrication of the stack structures, it is necessary to realize etching of deep holes. For examples, if using 30nm design rules and one layer thickness is 40nm, its depth becomes 1.92um. If the holes diameter is 100 nm, its aspect ratio becomes 19.2. Then, in the next generation, the 512 Gbit flash memory cell will need the deep hole with the aspect ratio of 38.4 for 3.84um-depth. For investigating more suitable process conditions or optimum etched topography, accurate three-dimensional etching simulation is required, but it takes a very long time to simulate this deep hole etching accurately if using usual simulation methods like the Monte-Carlo method, because the aspect ratio of this deep hole is very large and therefore, the flux calculation effort of enhancing ions and neutral radical species is enourmous for a reactive enhanced ion etching (RIE) model.

We have demonstrated the deep hole etching simulation with practical calculation times even for 3D, using the multi-dimensional process simulator Victory Process, which extensively and efficiently uses parallel processing. In this article, we show its simulation result with the ion enhanced chemical etching model and a good performance scaling of the parallel processing.


Model for the deep hole etching

Victory Process offersseveral etching models within its default open etching model library, from which we selected the Ion Enhanced Chemical Etching (IECE) model. As shown in the Figure 1, the IECE model assumes that the plasma consists of two types of species.

Figure 1. Concept of the ion enhanced chemical etching (IECE) model (x is the average number of B atoms in the ABx molecule).


One is neutrals, which are uncharged thermal particles that chemically react with the surface.

  • The other is ions, which are charged accelerated non-reacting particles that facilitate reactions of the surface material with the neutrals by removing reactions by-products from the surface, exposing it for chemical reactions.

Here, the final etch rate is written down as a function of the flux of neutrals and ions.

R = (Rnetural*fneutral + Rion*fion)*θss

It is assumed that R is the etch rate of the substrate, fneutral is the partial neutral flux , fion is the partial ion flux, Rneutral is the neutral related etching rate, Rion is the ion related etching rate, and θss is the surface coverage of molecules of substrate atoms and the neutral atoms in the steady state.

θss = (jn*S0/b)/(jn*S0/b + β(Ei)*ji +dbyfull covered)

Here, it is assumed that jn is the local flux of the neutral atoms toward the surface, ji is the local flux of the ion atoms toward the surface, S0 is the sticking coefficient of the neutral atoms on the clean substrate surface, b is the average number of the neutral atoms consumed by the substrate atoms, β(Ei) is the ion sputtering efficiency that depends on the ion energy, and dbyfull covered is the maximum desorption rate that corresponds to the full covered surface by the molecules of the neutral atoms and the substrate atoms.

The IECE model can be applied to any type of ion enhanced chemical etching as long as the enhancement is predominantly due to ions cleaning the substrate surface by removing the reaction by-products. In case of using the IECE model for 3D deep hole etching simulations, the most difficult problem is that the effort to calculate the neutral flux and the ion flux is enormous. In order to optimize simulation time, we have made a simple and high speed method for the calculation of the neutral flux based on the method of Kokkoris et al. [6]. Then, regarding the ion flux, we efficiently use parallel processing to keep the simulation time within practical limits


Results and Discussion

At first, regarding the neutral flux, the dependence on the sticking coefficient is shown in Figures 2 (a) and (b). Figure2 (a) is for a trench (2D like geometry) of width/depth=1um/4um , and Figure 2 (b) is for a circular hole of diameter/depth=1um/4um. Those results agree with those in the paper of Kokkoris et al. [6] very well. Having this method in place we can apply it also to large aspect ratio holes as shown in Figure 3. There, the neutral flux density for a deep hole with diameter/depth=0.1um/5um is presented. The calculation of any of these curves only takesone second. The above results demonstrate that the neutral flux can be calculated with high speed. Then, those curves are represented as a simpler function, and these function can be implemented as a C-model function in the open etching model library of Victory Process.

(a) for the trench of

(b) For the hole of
Figures 2. Dependence of the neutral flux density on the sticking coefficient.


Figure 3. Flux density on the deep hole of diameter/depth=0.1um/5um


Next, we show the performance of the parallel processing for a simulation of a half hole etching using the IECE model in Figure 4. This result was obtained on Dell PowerEdge R820 (E5-4650, 32core, 128GB). The calculation times with 10, 20 and 30 threads are about 4, 7.5 and 10 times faster than that of one thread, respectively, The parallel processing is only applied to the ion flux calculation, and you can see a good performance comparable to the ideal performance curve.

Figure 4. Performance of the parallel processing.


Next, in order to investigate the dependence on the mesh resolution, the simple 3D etching simulation topography of a hole (diameter=0.1um, depth=3um) was simulated with the resolution=0.02um, 0.015um and 0.005um and the results were compared. Figure 5 shows a 3D view of the half hole etching simulation result with the resolution=0.015um. In Figures 6, which shows 2D cross-sections, the various simulation results are compared at various depth positions of the hole. The resolutions of 0.005um, 0.02um and 0.015um correspond to the red, green and blue lines, respectively. The etching topographies near Z=0.0um, 1.0um, 2.7um and the bottom are shown in Figures 6 (a), (b), (c) and (d), respectively. The green line of resolution=0.02 um has some discrepancies near Z=0.0um and the bottom with the red line of resolution=0.005um, but the blue line of resolution=0.015um agrees well with the red line of resolution=0.005um. We used resolution=0.015um for etching simulations of multiple deep holes.

Figure 5. A simulation result for the half hole etching with depth=3um and diameter=0.1um in 3D view.


Figures 6. Dependence on the resolution.


Finally, we performed etching simulations of 4 and 5 holes with diameter/depth=0.1/4um using 10 threads on the server: Xeon x5690 6(HT12)*2, 12 threads, 140GB. Those simulation results are shown in Figure 7 and Figure 8. The left image (a) in those two figures shows the 3D solid view, while the right image (b) shows the cross sectional view in the center of the simulation domain in y-direction. The calculations of 4 and 5 holes were finished in the practical times of 5.18 hours and 6.95 hours, respectively.

(a) 3D solid view
(b) 2D XZ cross
sectional view at y=0um
Figure 7. 3D simulation of the 4 holes etching using the IECE model.


(a) 3D solid view
(b) 2D XZ cross
sectional view at y=0um
Figure 8. 3D simulation of the 5 holes etching using the IECE model.




A 3D etching simulator with high speed and high accuracy is required, which can simulate the deep hole etching with the practical calculation time for development and fabrication of advanced NAND Flash memory. We have shown that Victory Process is capable of achieving these requirements.

Regarding the neutral flux, a high speed method was developed based on the method of Kokkoris et al., and then, a very higher speed for 3D was also realized using a simple calibrated C-model function in the open etching model library. Regarding the ion flux, which in this case dominates the calculation effort, we could show that it efficiently makes use of parallel processing. We demonstrated that Victory Process simulates etching of 4 and 5 deep holes with diameter/depth=0.1um/4um using the IECE model in a practical amount of time.



  1. Soon-Moon Jung et al., IEDM Tech. Digest, pp.37-40, 2006.
  2. Erh-Kun Lai et al., IEDM Tech. Digest, pp.41-44, 2006.
  3. Megumi Ishiduki et al., IEDM Tech. Digest, pp.625-628, 2009.
  6. George Kokkoris et al., J. Vac. Sci. Technology, pp. 2008-2020, A 24(6), Nov/Dec 2006