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Phenomenological Single-Particle
Modeling of Reactive Transport
in Semiconductor Processing

4.5 Atomic Layer Processing for Novel 3D
Memory Technologies

One key technology which can be unlocked by the continuing development of thermal ALP is the 3D integration of novel memories [143]. The ongoing success of 3D NAND flash memory demonstrates that it is possible to create a charge storage structure — whether a charge trap or a floating gate — in a vertical 3D stack without relying on planar technology [105]. This stacking has enormously increased the density of memory technology, therefore, similar ideas can be applied to novel memory technologies such as resistive random-access memory (ReRAM) [166]. To enable the patterning of these sophisticated material stacks at the sidewalls of a high AR structure, conformality in thermal ALP will have to be taken to its limits. Topography modeling can be an invaluable tool in this development by providing insight into the reactive transport issues limiting conformality, as well as enabling the investigation and simulation of devices with realistic shapes.

To aid the development of new 3D memory technologies, Fischer et al. from Lam Research have developed a 3D NAND-like test structure and used it to investigate thermal ALD and ALE [149]. These structures are oxide-nitride (ON) stacks with either 76 or 98 ON pairs, to a maximum height of \(\SI {4}{\micro \meter }\) or \(\SI {5}{\micro \meter }\) respectively. After the ON deposition, a cylindrical hole is etched using RIE [26]. This hole is then used as the basis for the thermal ALP experiments. Afterward, the samples are cleaved and subsequently imaged with transmission electron micrography (TEM).

The material chosen to be investigated on the test structure is hafnium oxide (HfO2) which is a promising material for novel memory technologies [166]. It was deposited using thermal ALD from H2O and an undisclosed hafnium-based reactant [149], achieving a \(\mathrm {SC}\) of \(85\,\%\). To simulate the reported thickness profile, the hafnium reactant is taken to be the limiting species and is assumed to be tetrakis(ethylmethylamino)hafnium (TEMAH), with the necessary parameters taken from [167]. The calibrated parameters are shown in Tab. 4.3, and the simulated geometry is compared to the experimental data in Fig. 4.11.

Having demonstrated ALD of the investigated HfO2, the next step in the development of thermal ALP is the establishment of an etching method. Fischer et al. propose thermal ALE of HfO2 from dimethylaluminum chloride (DMAC) and HF [149], following a similar ligand-exchange reaction to that from Eqs. (4.3) and (4.4). They thoroughly investigate the necessary DMAC dosing by exploring two different reactors: Low-pressure and high-pressure. Several reactor conditions were investigated, extracting an EPC profile from TEM measurements for each experiment.

\(\Gamma _\mathrm {ev}\) (\(\si {\meter ^{-2}\second ^{-1}}\)) \(\beta _0\)
\(3.5 \cdot 10^{22}\) \(7.0 \cdot 10^{-3}\)
Table 4.3: Calibrated model parameters for ALD of HfO2 for the hafnium step to experimental data from Fischer et al. [149].


Figure 4.11: Comparison of simulated topography using parameters from Tab. 4.3 to ALD of HfO2 in a 3D NAND-like test structure reported by Fischer et al. [149].

The low-pressure reactor experiments were performed at \(\SI {250}{\celsius }\) and had no background gas for a process pressure of \(\SI {30}{\milli \torr }\) for both the DMAC and the HF steps. Two HF dose configurations were investigated by varying the pulse time: A low dose of \(\SI {5}{\second }\) and a high dose of \(\SI {30}{\second }\). The DMAC dose was varied by changing its pulse time between \(\SI {5}{\second }\) and \(\SI {90}{\second }\).

The high-pressure experiments performed etching at \(\SI {350}{\celsius }\) using N2 as a carrier gas for a total process pressure of \(\SI {1}{\torr }\). The DMAC partial pressure was kept as \(\SI {48}{\milli \torr }\), thus its dose was varied by changing the pulse time between \(\SI {3}{\second }\) and \(\SI {90}{\second }\). Two sets of experiments varying the HF dose were also performed. The low HF dose was achieved with a partial pressure of \(\SI {150}{\milli \torr }\) for a pulse time of \(\SI {2}{\second }\). The high HF dose had a partial pressure of \(\SI {400}{\milli \torr }\) for \(\SI {60}{\second }\). It was observed by the authors of the original publication that there is a decline in EPC for comparatively lower DMAC doses. They conclude that a substantially large dose is necessary to enable thermal ALE.

Nonetheless, reactive transport modeling can be used to further characterize and fine-tune this process. This is achieved by applying the model described in Section 4.2 assuming the DMAC is the limiting reactant. It has been reported that the HF dose has only a very slight impact in the EPC profile [149], therefore, it is reasonable to assume that the process is DMAC-limited. The effects of HF are captured by a global reduction in the maximum EPC which is extracted from each experiment. The simulated EPC profiles are obtained by dividing the etch depth at each \(z\) position by \(N_\mathrm {cycles}=20\) and are shown in Fig. 4.12 in comparison to experimental data from Fischer et al. [149]. The calibrated parameters are in Tab. 4.4, including \(s_0\).

Given the complex fluorination and ligand-exchange chemical process, \(s_0\) cannot be calculated using the "billiard ball" approximation from Eq. (4.7). Instead, it is taken as an additional model parameter. For the high-pressure reactor, the flow is clearly not in the molecular flow regime. Thus, the Bosanquet interpolation formula is used with \(d_\mathrm {N_2} = \SI {374}{\pico \meter }\) [109] and the DMAC radius estimated from its liquid density to be \(d_\mathrm {DMAC} = \SI {748}{\pico \meter }\).


Figure 4.12: Comparison of simulated ALE using parameters from Tab. 4.4 to DMAC-limited ALE of HfO2 in a 3D NAND-like test structure reported by Fischer et al. [149]. Both a low-pressure (\(\SI {30}{\milli \torr })\) and a high-pressure (\(\SI {1}{\torr }\)) reactor conditions are simulated, including different doses of HF and DMAC.
Reactor condition \(\Gamma _\mathrm {ev}\) (\(\si {\meter ^{-2}\second ^{-1}}\)) \(\beta _0\) \(s_0\) (\(\si {\meter ^{-2}}\))
Low pressure, \(\SI {250}{\celsius }\) \(2.5 \cdot 10^{17}\) \(6.0 \cdot 10^{-4}\) \(7.0 \cdot 10^{-21}\)
High pressure, \(\SI {350}{\celsius }\) \(1.0 \cdot 10^{18}\) \(5.0 \cdot 10^{-3}\)
Table 4.4: Calibrated model parameters for DMAC-limited ALE of HfO2 to experimental data from Fischer et al. [149].

Due to the comparatively higher noise of TEM data in comparison to the optical profilometry reported in Section 4.4, the calibrated simulations in Fig. 4.12 demonstrate only qualitative agreement. Nonetheless, the parameters reported in Tab. 4.4 already enable a preliminary analysis. They enable a first estimation of \(\beta _0\) for DMAC which has not been hitherto reported. Additionally, the increase in \(\beta _0\) with increasing temperature is an indication of Arrhenius-like behavior similar to Fig. 4.6. However, further experimental studies with a more detailed description of the temperature range are required to substantiate this hypothesis. Surprisingly, unlike the analysis in Section 4.4.1, the evaporation flux also appears to increase with temperature, an unexpected behavior which warrants further investigation.

Even though the obtained results are qualitative in nature, they already show a path for the investigation of device performance. The entire 3D NAND-like stack from [149] has been simulated using Silvaco’s Victory Process [55], shown in Fig. 4.13. Both the ON deposition and the RIE are assumed to be ideal and are thus geometrically modeled. The thermal ALP of HfO2 is modeled with the presented reactive transport model implemented in the Open Model Library. For the ALD step, the parameters from Tab. 4.3 are used. From the multiple reported thermal ALE conditions, the low-pressure, high HF dose, and the \(\SI {12}{\second }\) DMAC dose are assumed with parameters from Tab. 4.4. The simulation shows a clear tapering of the HfO2 film thickness. Although the test structure itself is not a physically operable device, this simulation shows a path for optimization of device performance. Device engineers can, for example, use this tapering information to obtain realistic insights into the novel memory performance in the presence of non-ideal thermal ALP.


Figure 4.13: Cross-section of simulated thermal ALP of HfO2 inside 3D NAND-like test structure [149] showing different film thickness at three different regions of the full stack (top, middle, and bottom).