Effects of crystallinity of silicon channels formed by two metal-induced lateral crystallization methods on the cell current distribution in NAND-type 3D flash memory

The grain maps examined in this study were experimentally obtained using the Automated Crystal Orientation Mapping (ACOM) tool in transmission electron microscopy (TEM). ⁸⁾ The ACOM-TEM analysis was performed on a sample thinned using a focused ion beam technique to evaluate the crystallinity of the Si channel in the memory hole. These maps were color-coded to represent individual crystal grains, with colored boundaries indicating grain boundaries.

2.2.1. Conventional polycrystalline Si channel

First, cell dielectric films were deposited in a memory hole (MH) and an amorphous Si (a-Si) layer was deposited on these films. After macaroni dielectric formation, ^9,10) the a-Si layer was crystallized by annealing, as shown in Fig. 1(a).

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2.2.2. Single-MILC channel

2.2.3. Regional MILC channel

Figure 2 shows the grain maps obtained experimentally using ACOM-TEM. Figure 2(a) shows the grain map of the conventional poly-Si channel crystallized by annealing only; this figure panel shows many small grains of size less than 0.2 μm. Figure 2(b) shows the grain map of a single MILC channel. The entire channel in one MH was single-crystallized by NiSi₂ nuclei that migrated through the channel from the top to the bottom of the memory hole. Figure 2(c) shows a grain map of the regional MILC channel. Many large crystals of size 0.2 μm or more are observed because many single crystallizations occur simultaneously from each NiSi₂ nucleus in the MH.

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Ideally, the whole Si channel in the MH should be single crystallized by single-MILC methods, but in practice, a single MILC is obstructed by the SPC nuclei generated in the amorphous phase, as shown in Fig. 3. MILC ceases when the NiSi₂ that migrates from the top of the MH encounters the SPC nuclei. Therefore, unintended SPC nuclei hinder MILC and act as "MILC stoppers." The entire region between the SPC nuclei and MH bottom is not single-crystallized; instead, it comprises various lengths of residual a-Si. To reveal the impact of the a-Si regions on the cell current distribution, the occurrence of residual a-Si regions was modeled based on the MILC stopper density, which is equivalent to the SPC density. The probability density of the residual a-Si length was calculated, as shown in Fig. 4, where H, L, s, and C_s are the MH height [μm], residual a-Si length [μm], average stopper density [pcs/μm], and normalization constant of a single MILC, respectively.

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When the stoppers are randomly distributed along the MH height H [μm] with a mean density s [pcs/μm], the probability that no stopper exists along the MILC length M [μm] is expressed by Eq. (1).

$$\begin{eqnarray}&&{\left(1-\frac{M}{H}\right)}^{H\cdot s}\end{eqnarray} \tag{ 1 }$$

Now, considering the limit at which H reaches infinity, Eq. (1) can be transformed as follows:

$$\begin{eqnarray}&&\begin{array}{l}\mathop{\mathrm{lim}}\limits_{H\to {\rm{\infty }}}{\left(1-\frac{M}{H}\right)}^{H\cdot s}\\ \,=\mathop{\mathrm{lim}}\limits_{H\to {\rm{\infty }}}{\left(1-\frac{1}{H/M}\right)}^{\left(-\frac{H}{M}\right)\cdot \left(-s\cdot M\right)}={e}^{-s\cdot M}\end{array}\end{eqnarray} \tag{ 2 }$$

Equation (2) denotes the probability that there is no stopper at length M in an MH of any height, i.e., the probability that an MILC channel of length M exists. This formula is a common exponential function that is also used in yield calculations. ^25–27)

Furthermore, by replacing M in Eq. (2) with (H − L), as shown in Fig. 4(a), the equation indicates the probability of the existence of residual a-Si of length L. Thus, the probability density of the residual a-Si length can be expressed as shown in Eq. (3) using Eq. (2), stopper density s, and normalization constant C_s .

$$\begin{eqnarray}&&{C}_{{\rm{s}}}\cdot s\cdot {e}^{-s\cdot \left(H-L\right)}\end{eqnarray} \tag{ 3 }$$

If the stopper density is sufficiently low, the probability density of the residual a-Si length is constant in a single MILC, as shown in Fig. 4(b), because a-Si remains below the point where SPC is present.

Through the device fabrication process after MILC, the residual a-Si region was transformed into a high-resistance poly-Si region, ²⁸⁾ as shown in Fig. 5. Hence, the channel resistance is a series connection of the low-resistance MILC (R_MILC) and high-resistance poly-Si (R_poly-Si) which degrades the cell current of the 3D flash memory. Because the length of the residual poly-Si is directly correlated with the resistance, the product of the probability density and residual poly-Si length directly represents the impact on the cell current. Figure 6 shows the calculated result of the impact factor for the cell current (I_cell). The impact factor for I_cell is proportional to the poly-Si length because the probability density is independent of the poly-Si length. The resistance of poly-Si is proportional to its length.

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The regional MILC was also hindered by the SPC nuclei. Because the MILC occurs at multiple locations simultaneously, residual a-Si exists in regions where no NiSi₂ nuclei exist between the SPC nuclei, as shown in Fig. 7. Therefore, in the case of regional MILC, it is necessary to consider not only the stopper density but also the NiSi₂ density when calculating the probability density of the residual a-Si length. The probability density of the residual a-Si length was calculated, as shown in Fig. 8, where H, L, s, n, and C_r are the MH height [μm], residual a-Si length [μm], average stopper density [pcs/μm], average initial NiSi₂ density [pcs/μm], and normalization constant of the regional MILC, respectively.

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When NiSi₂ is randomly distributed in the MH with mean density n, the probability that no NiSi₂ is present in length L is expressed as shown in Eq. (4) using unit length dL.

$$\begin{eqnarray}&&{\left(1-n\cdot {dL}\right)}^{L/dL}\end{eqnarray} \tag{ 4 }$$

Considering the limit, where dL is zero, Eq. (4) can be transformed as follows:

$$\begin{eqnarray*}&&\mathop{\mathrm{lim}}\limits_{{dh}\to 0}{\left(1-n\cdot {dh}\right)}^{L/{dh}}\,\end{eqnarray*}$$

$$\begin{eqnarray}&&=\mathop{\mathrm{lim}}\limits_{1/(n\cdot {dh})\to {\rm{\infty }}}{\left(1-\frac{1}{1/\left(n\cdot {dh}\right)}\right)}^{\left[-1/\left(n\cdot {dh}\right)\right]\cdot \left(n\cdot L\right)}={e}^{-n\cdot L}\end{eqnarray} \tag{ 5 }$$

Equation (5) indicates the probability of the absence of NiSi₂ within a specific length L, i.e., the probability of residual a-Si of length L. Thus, the probability density of the residual a-Si length can be expressed as shown in Eq. (6) using Eq. (5), stopper density s, and normalization constant C_r.

$$\begin{eqnarray}&&{C}_{{\rm{r}}}\cdot {s}^{2}\cdot {e}^{-n\cdot L}\end{eqnarray} \tag{ 6 }$$

If the NiSi₂ density is sufficiently high, the probability density of the residual a-Si length steadily decreases in the regional MILC, as shown in Fig. 8(b). Residual a-Si is less likely to remain longer in regional MILC than in single MILC, resulting in shorter a-Si regions because regional MILC occurs at multiple locations simultaneously.

The calculated result of the impact factor for I_cell is shown in Fig. 9. Long poly-Si with high resistance occurs less frequently in regional MILC; therefore, the major impact of the regional MILC process on the cell current is observed in short poly-Si regions with low resistance.

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The cell current distribution was calculated based on the simulated crystallinity and channel resistance. The MILC channel resistance and poly-Si region resistance were obtained from experimental data. As shown in Fig. 10, the crystal distribution maps of the single and regional MILC methods for 915 WLs and 2250 MHs were simulated using Eqs. (3) and (6), under the assumption that the stopper and NiSi₂ are randomly distributed in an MH. In the figure, the black blocks indicate poly-Si with a higher resistance, which was obtained by the transformation of residual a-Si after thermal processing. The stopper density "s," which was fitted to the experimental data, was much higher in the case of the regional MILC than in the case of a single MILC. The experimentally obtained channel resistances for the single-MILC and poly-Si channels are shown in Fig. 11. To evaluate the cell-array characteristics, Ni metal was removed by gettering. ^29–32) The I_d –V_g acquired by driving all the WLs at the same voltage was considered to represent a quasi-MOSFET with a long channel. Using this approach, the channel resistance can be separated from the parasitic resistance. Clearly, the resistance of the single-MILC channel was approximately 10 times less than that of the poly-Si channel. The same method was used to measure the channel resistance of the regional MILC. The resistance of the regional MILC channel was approximately six times lower than that of the poly-Si channel.

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Figure 12 shows the results of the calculated cell current distributions for 915 WLs and 2250 MHs. A single MILC had a higher cell current (median) than a regional MILC; however, the former suffers from rapid degradation of the tail of the cell current distribution because of the long-residual a-Si region. The lower tails of the cell current distribution affect the bit error rate.

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Therefore, SPC suppression techniques are required to prevent the formation of long-residual a-Si regions. In contrast, the cell current (median) in regional MILC is lower than that in single MILC; however, in regional MILC, rapid degradation does not occur in the lower tail. Therefore, the regional MILC is more robust against rapid cell current degradation due to the long-residual a-Si regions. The technology used to grow large Si grains is essential for improving the cell current (median).

Figure 13 shows the calculated cell current distribution expected for the single and regional MILCs after the improvement of crystallinity. In a single MILC, the lower tail of the cell current distribution was suppressed by reducing the stopper density. In contrast, in the regional MILC, the cell current (median) is improved by increasing the Si grain size.

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