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Phenomenological Single-Particle
Modeling of Reactive Transport
in Semiconductor Processing

Chapter 4 Modeling of Thermal Atomic Layer Processing

From the many existing thin-film processing techniques, a certain class of methods has recently garnered increased attention: Thermal atomic layer processing (ALP) [129]. These methods are defined by their use of self-limiting — that is, a reaction which stops occurring after saturating the available surface sites — and thermodynamically favored surface-chemical behavior to achieve a very high degree of control of film quality and conformality. Such self-limiting reactions can be employed to enable controllable film growth, in what is called thermal atomic layer deposition (ALD) [142], or to precisely remove material through atomic layer etching (ALE) [143].

Due to its isotropic nature, thermal ALP is a key technology for three-dimensional (3D) integration [143], since it enables control over the materials at the sidewalls of high aspect ratio (AR) structures. To support the further development of these methods and to understand the impact of the processing conditions on the 3D structures, accurate modeling is required. Since the processes involve uncharged thus isotropically reflecting species, and the structures typically have high AR, thermal ALP is a great candidate for Knudsen diffusion-type modeling. In addition, these processes are commonly limited by a single reactant, therefore, single-particle models can be applied where the particle represents said chemical species. However, unlike the equations derived in Chapter 3, the constant sticking probability approximation cannot be used. As the methods themselves exploit self-limiting surface reactions, the models must include a more complete description of Langmuir surface kinetics including the coverage-dependent sticking coefficient \(\beta (\Theta )\) presented in Section 2.2.

Own contributions: An integration of the aforementioned reactive transport model with level-set (LS) based topography simulation as well as its application are presented. This model is calibrated to reported experiments in order to derive physically meaningful insight from its parameters. Lastly, the model is applied to investigate non-idealities in a potential platform for 3D integration of novel memories. This work has been partially published at the SISPAD 2022 conference [144] and in a follow-up journal article currently under review [145].

4.1 Thermal Atomic Layer Deposition and

ALP is a class of processing techniques which is defined by its high degree of authority over quality aspects of the processed structure [129]. The two main subcategories within ALP are the growth and etching procedures, respectively named ALD [142] and ALE [143]. The defining aspect of ALP techniques is that they divide the growth or etch reaction into at least two self-limiting reaction steps. Since each reaction is individually self-limiting and the surface evolution only occurs from the combination of reactions, excellent control over the conformality and thickness can be achieved. Similar self-limiting behavior is observed in the aluminum oxidation in Josephson junctions [29].

What defines thermal ALP in particular is that the involved reactions are thermodynamically favored by the reactor pressure and temperature [143, 146]. In contrast, plasma-assisted methods include an external electric field to generate neutral and ion species with differing chemical properties. In directional ALE, one of the reaction steps involves accelerated ions which modify the surface through their kinetic energy instead of a chemical reaction [129]. Plasma-assisted ALD instead takes advantage of highly chemically reactive but unstable neutral species which would otherwise not be possible in the same reactor temperature [147].

One crucial advantage of thermal ALP is that these techniques a higher degree of conformality in comparison to other processing methods such as conventional chemical vapor deposition (CVD) [110]. Conformality is the ability to uniformly modify a surface with a high degree of independence from the AR, so that the entire structure is grown or etched at the same rate. This is necessary for high AR structures such as dynamic random-access memory (DRAM) capacitors [148] or 3D NAND memory channel holes [149].

Should a given reactor setup and involved chemistry yield an ideal self-limiting reaction, then perfect conformality is in principle always achievable by adapting the reactor pulse time \(t_p\) until saturation is reached. Having determined the required \(t_p\), the process is then determined straightforwardly by two parameters. The first parameter for ALD is the growth per cycle (GPC), or, equivalently, the etch per cycle (EPC) for ALE. These parameters are regularly measured and are usually fixed by the reactor and chemical setup [129]. Since they are in essence fixed, control over final grown or etched thickness is achieved by the second parameter: The number of cycles \(N_\mathrm {cycles}\).

In practice, however, this ideal behavior is not always observed for two main motives [110]. Firstly, the chemical reactions might not be perfectly self-limiting, thus an increase in \(t_p\) might not necessarily lead to saturation. Also, the reactant transport might be severely constricted, leading to regions where there is insufficient supply, i.e., the processing regime is transport-controlled. These two phenomena, namely chemical reactions and transport, are intrinsically linked and must be jointly considered in a reactive transport model, as first discussed in Chapter 2.

Before moving into describing the developed reactive transport model, it is important to briefly review the involved chemical reactions. The ALD of aluminum oxide (Al2O3) from water (H2O) and trimethylaluminum (TMA), or Al(CH3)3, has emerged as a model system [142, 146]. Although this process has found application in DRAM [148], more importantly it has become the paradigmatic system for ALD due to its near-ideal surface chemistry. An idealization of this process is illustrated in Fig. 4.1, showing an initial OH-terminated surface which reacts with the TMA pulse. This reaction is illustrated as being ideally self-limiting and irreversible, so the TMA does not interact with a methyl-terminated surface and does not desorb as the reactor is purged. Similarly, the H2O reacts irreversibly with the methyl-terminated surface only.

This idealized process can be represented by the following chemical reactions [142]:

\begin{align} \label {eq::ald_tma} \mathrm {AlOH^*}+\mathrm {Al(CH_3)_3} &\rightarrow \mathrm {AlOAl(CH_3)_2^*} + \mathrm {CH_4}\text {, and} \\ \label {eq::ald_h2o} \mathrm {AlCH_3^*}+ \mathrm {H_2O} &\rightarrow \mathrm {AlOH^*} + \mathrm {CH_4}, \end{align} where the superscript \(^*\) indicates a surface species. Although Eqs. (4.1) and (4.2) are useful for a cursory understanding of the processes, in reality there is still uncertainty about the details of the surface reactions including the involved stoichiometric factors [150].

For ALE, the involved chemistries are considerably more complex. It is substantially more challenging to find thermodynamically favored reactions which have as a product a volatilized surface species [143]. Usually, one of the reaction steps in fact deposits on the surface, changing its chemical composition. Then, the following reactions undergo a complex chemical process leading to a volatile etch product. There are a plethora of proposed methods to achieve this complex feat [143]. Similarly to ALD, Al2O3 can be used as the basis for an illustrative ALE process.


Figure 4.1: Illustration of ALD of Al2O3 from TMA and H2O. Adapted from Cremers et al., Appl. Phys. Rev. 6, (2019) p. 021302. [110], © The Authors, licensed under the CC BY 4.0 License, https://creativecommons.org/licenses/by/4.0/.

Lee and George [151] propose the thermal ALE of Al2O3 from fluorination and ligand-exchange using tin(ii) acetylacetonate (Sn(acac)2) and hydrogen fluoride (HF). As an initial conditioning step, HF gas is introduced, converting the top layer of Al2O3 to aluminum fluoride (AlF3). The ALE cycle then properly begins with the introduction of Sn(acac)2 which then causes the following ligand-exchange

\begin{align} \label {eq::ale_snacac2} \mathrm {Al_2O_3}|2\mathrm {AlF_3^*}+6\mathrm {Sn(acac)_2} \rightarrow \mathrm {Al_2O_3}|x\mathrm {SnF(acac)^*} + 2\mathrm {Al(acac)_3} +(6-x)\mathrm {SnF(acac)}\, , \end{align} where the \(|\) indicate a different surface species over a certain substrate and \(x\) is a temperature-dependent stoichiometric factor. The second ALE reaction is obtained by re-introducing HF which volatilizes any remaining tin-based compounds and again converts the top layer to AlF3:

\begin{align} \label {eq::ale_hf} \mathrm {Al_2O_3}|x\mathrm {SnF(acac)^*} + 6\mathrm {HF} \rightarrow 2\mathrm {AlF_3^*} + x\mathrm {SnF(acac)} + \mathrm {H_2O} \end{align}

In summary, thermal ALP processes involve rich and complex chemical behavior. This complexity has only been briefly explored as this is an active field of research. For example, super-cycle combinations of ALD and ALE can be used to enable area-selective deposition (ASD) by exploiting differences in nucleation delays for each underlying material [152]. Nonetheless, all crucial chemical phenomena occur at the surface, thus a phenomenological approach, such as the first-order Langmuir surface kinetics introduced in Section 2.2, can provide valuable insight.