Atomic Layer Deposition (ALD) Gas DeliveryDue to its superior conformal properties and sub-nanometer thickness control, ALD technology has become a core technology for advanced semiconductor manufacturing, optical coating, and new energy devices. However, as device feature sizes shrink to below 3nm, high aspect ratio (HAR) structures (such as 3D NAND channel vias and DRAM capacitor vias) pose a severe challenge to precursor transport. This paper starts from the basic flow regimes of fluid mechanics, deeply analyzes the transport mechanisms of precursor molecules under viscous flow, molecular flow, and transitional flow, and explores the influence of the transport process on surface saturated adsorption kinetics. Based on this, this paper proposes a multi-scale transport model based on partitioned coupling, which combines the continuous flow of the macroscopic gas path system with the rarefied gas dynamics within the microstructure, providing a theoretical basis for the uniformity optimization of the ALD process.

1 Introduction

The core of ALD (Alternating Layer Deposition) lies in the alternating pulse delivery of gaseous precursors into the reaction chamber, and the realization of monolayer growth through self-limiting chemical reactions between precursor molecules and active sites on the substrate surface. Ideally, given a sufficiently long pulse duration, the entire substrate surface (including the interior of deep pores) can achieve saturated adsorption. However, in practical processes, as the aspect ratio (AR, typically >50:1) increases, the transport of precursor molecules from the chamber bulk to the bottom of the pores is no longer unimpeded.

These transport restrictions lead to a key problem:Transport-constrained heterogeneous depositionWhen precursor molecules enter narrow structures, they are consumed by collisions with the walls or by surface adsorption, resulting in an effective dose at the bottom of the pore being much lower than at the opening, thus triggering a "pinch-off effect." To solve this problem, it is necessary to have a deep understanding of the transport physics mechanisms under different flow regimes and to establish multi-scale models that can span from the meter scale (gas channels) to the nanoscale (reaction surfaces).

2. Flow regime classification and its physical characteristics

In ALD gas transport, the criteria for determining the flow regime are:Knudsen number(Knudsen number, $Kn$), defined as the mean free path of gas molecules ($\lambda$) and feature size ($d$The ratio of (e.g., pipe diameter or orifice width):$Kn=\lambda /d$.

2.1 Viscous Flow ($Kn<0.01$）

In the main gas line, mass flow controller (MFC), and large chamber areas, the gas is in a viscous flow (continuous flow) state due to the high pressure (typically >100 Pa) and large characteristic dimensions.

• transport mechanismIn this environment, intermolecular collisions dominate, and the gas is considered a continuous medium. The flow follows the Navier-Stokes equations and is primarily driven by pressure gradients.

• 特点In viscous flow, the precursor transport rate is fast, gas molecules exhibit collective behavior, and the flow resistance is relatively small.

2.2 Molecular flow ($Kn>1$）

When gas enters the interior of a high aspect ratio structure (e.g., pore size < 50 nm) or the chamber is under low pressure (< 0.1 Pa), the mean free path of the molecules is greater than the structural size, and the gas enters a molecular flow state.

• transport mechanismMolecular-wall collisions far outnumber molecular-molecular collisions. In this case, transport is no longer driven by pressure gradients, but rather by...Concentration gradientOrMolecular thermal motionThe decision is made. Each molecule moves independently, following the cosine law (Knudsen diffusion).

• 特点The gas phase mass transfer resistance is greatly increased, and precursor molecules need to undergo multiple reflections to enter the bottom of the deep hole.

2.3 Transitional Flow ($0.01\le Kn\le 1$）

In the middle stages of the ALD pulse (such as at the inlet of the through-hole from the main chamber), the flow is often in a transitional state. Molecular collisions are as important as wall collisions in this region; it serves as a bridge between viscous flow and molecular flow, and is also the most difficult region to model accurately.

In high aspect ratio ALD processesMolecular flow and transition flowIt is the main physical bottleneck limiting deposition rate and uniformity.

 

3. The influence of transport mechanisms on surface saturated adsorption kinetics

Surface saturated adsorption kinetics are usually usedLangmuir adsorption modelThe adsorption rate is described as depending on the precursor partial pressure and surface vacancy concentration. However, in HAR structures, the macroscopic Langmuir model needs to be coupled with microscopic transport equations.

3.1 Gradient effect caused by reactant consumption

In the bulk of the chamber dominated by viscous flow, the precursor concentration is uniform. However, when the gas enters the interior of the HAR structure (molecular flow or transition flow), the transport process competes with the surface reaction process.

Let the hole depth be$L$, radius is$R$In the micro-element of the hole $dz$ Precursor flux $J(z)$ The reduction is equal to the adsorption and consumption by the sidewall:

dJ(z)dz=−2R⋅S⋅F(z)dzdJ(z) =-R2 ⋅S⋅F(z)

among them $S$ This is the adhesion coefficient.$F(z)$ For surface flux.

Under molecular flux conditions, flux $J$ Follows the concentration gradientFick's First LawHowever, the diffusion coefficient is the Knudsen diffusion coefficient. DkDk :

Dk=23R8RTπMDk =32 RπM8RT

among them $R$ Where is the radius of the hole.$M$ In terms of molar mass. For high aspect ratio structures, the effective diffusion time is... τ∝L2/DkταL2/Dk This means that as the pore depth increases, the time it takes for the precursor to reach the bottom increases quadratically.

3.2 Modulation effect of adhesion coefficient

Adhesion coefficient $S$ It is a key parameter connecting transport and adsorption. If the precursor has a high adhesion coefficient (such as...) $S>0.1$The molecules are adsorbed upon the first collision. In molecular flux, this means that precursor molecules near the pore opening are rapidly consumed, creating a "masking effect" that causes the precursor flux within the pore to decay exponentially.

Conversely, if the precursor has a low adhesion coefficient (e.g. $S<0.01$Molecules need to undergo multiple reflections at the wall surface to be adsorbed. These multiple reflections increase the probability of molecules entering deep pores and improve aspect ratio tolerance. Therefore,Precursor molecular designUsing precursors with larger molecular weights or lower adhesion coefficients is an important means of improving the conformability of high aspect ratio ALDs.

3.3 Transient saturation behavior

In industrial applications with short pulse durations, the transport mechanism determines...Saturation characteristic timeIn the viscous flow region, the saturation time is limited by the response speed of the mass flow controller and the cavity volume; in the molecular flow region, the saturation time is limited by the mean residence time of the molecules.

For HAR structures, surface saturation does not occur simultaneously. Typically, the pore opening saturates first, followed by the saturation front moving towards the pore bottom. If the pulse duration is shorter than the transport characteristic time at the pore bottom, undersaturated deposition at the pore bottom will occur. This kinetic process can be understood through…diffusion-reaction equationNumerical solutions using the Diffusion-Reaction Equation reveal a three-dimensional process window of "dose-aspect ratio-saturation time".

 

4. Establishment of a multi-scale transport model

due toALD gas conveying equipmentThis involves cross-scale problems ranging from macroscopic (meter-scale) to nanoscopic (angstrom-scale), and single-scale models cannot accurately predict process results. We need to establish a...Multiscale coupling modelIt connects macroscopic gas paths, chamber fluid dynamics, and microscopic intrapore transport.

4.1 Scale Division and Interface Definition

The model is usually divided into three scales:

1. Macroscopic scale (gas path and main pipe)The dimensions range from 0.1 m to 10 m. This includes gas cylinders, valves, mass flow controllers, and transmission pipelines. The pressure in this area is relatively high (typically 1-10 Torr), and the flow pattern is viscous.$Kn<0.01$Modeling usesLumped parameter modelOrOne-dimensional compressible flowThe main focus is on the propagation speed of pressure fluctuations and the sharpness of the pulse leading edge.

2. Mesoscopic scale (reaction chamber and wafer surface)The dimensions are 1 mm to 0.5 m. Gas flow within the chamber may involve viscous or transitional flow. This is used...Computational Fluid DynamicsHowever, this requires combining slip boundary conditions or directly simulating the Monte Carlo method. The key is to obtain the area above the wafer surface (or HAR aperture).Incident flux boundary conditions.

3. Microscale (internal structure with high aspect ratio)The scale is 1 nm to 100 μm. The flow regime is molecular flow or transition flow. At this scale, the continuous medium assumption fails, and alternative methods must be adopted.Knudsen diffusion modelOrMonte Carlo (MC) Simulation.

4.2 Coupling Strategies: Partition Sequential Coupling and Iterative Coupling

The core of building a multi-scale model lies inBoundary condition transfer.

Step 1: Macroscopic Transport Simulation
First, establish the gas path network model of the ALD device. Input the precursor vapor pressure, carrier gas flow rate, and valve timing. Calculate the instantaneous gas flux entering the reaction chamber by solving the mass and momentum conservation equations. Qin(t)Qin (t)The output is the pressure at the chamber inlet. Pchamber(t)Pchamber (t) It is composed of gases.

Step 2: Chamber fluid simulation (mesoscopic)
The flow field within the chamber is simulated using CFD software (such as ANSYS Fluent or COMSOL). For low-pressure ALDs (e.g., below 1 Torr), a rarefied gas model (such as slip flow or DSMC) needs to be enabled. This step extracts the flow field from the wafer surface (especially the chip area).Precursor flux distribution Jwafer(x,y,t)Jwafer (x,y,t) and the pressure at the orifice Pmouth(t)Pmouth (t).

Step 3: Transport Simulation within the Microstructure (Crucial)
orifice pressure PmouthPmouth  As the entry boundary condition for the microscopic model. At the microscale, for structures with an aspect ratio less than 100:1, it is usually adopted...One-dimensional diffusion-reaction equation(Coupled Knudsen diffusion) for rapid engineering calculations.

However, for ultra-high aspect ratios (>100:1) or complex geometries (such as curved ducts), it is necessary to adopt...Particle method,Such as:

• Direct simulation of Monte Carlo (DSMC)Directly solving the Boltzmann equation can accurately simulate the collisions and trajectories of molecules within the structure, but the computational cost is enormous.

• Test Particle Monte Carlo (TPMC)Ignoring intermolecular collisions and considering only molecular-wall collisions, this method is suitable for pure molecular flow regions. The incident flux at the bottom of the aperture is statistically analyzed by tracking the trajectories of a large number of particles. JbottomJbottom  And cumulative adsorption amount.

Step 4: Coupling and Closing the Loop
The adsorption rate or transmission probability calculated by the microscopic model has a feedback effect on the mesoscopic model. For example, if a large amount of precursor is consumed at the aperture, the boundary layer of the wafer surface in the mesoscopic model needs to be recalibrated. Therefore, it is common to use...Iterative couplingFirst, assume uniform adsorption and calculate the orifice flux; then, based on the microscopic simulation results, correct the local consumption rate and rerun the chamber CFD until convergence.

4.3 Model Validation and Parameter Calibration

Multiscale models must be calibrated experimentally. This is typically done using...Through-silicon vias or high aspect ratio test structuresAfter ALD deposition, the film thickness distribution was measured using scanning electron microscopy (SEM) or transmission electron microscopy (TEM). The measured thickness distribution was then...Step coverage(Step Coverage, defined as the ratio of hole bottom thickness to hole opening thickness) is compared with model predictions to infer the actual process conditions.Effective adhesion coefficient.

Studies have shown that, due to surface temperature inhomogeneity or steric hindrance effects of surface ligands, the effective adhesion coefficient of precursors is often lower than that measured on laboratory single-crystal surfaces. Therefore, the model must incorporate an empirical correction factor to match industrial realities.

 

5. Conclusion and Outlook

This article systematically elaborates onALD gas transportThe study of the physical nature of viscous flow, molecular flow, and transition flow during transport reveals that within high aspect ratio structures, the transport mechanism directly determines the saturation kinetics of the ALD process by controlling the competitive relationship between the arrival rate of precursor molecules and the surface adsorption reaction.

To accurately describe the complex process from the gas path header to the bottom of the nanopore, establishing a multi-scale transport model is essential. This model, by coupling macroscopic gas path networks, mesoscopic chamber fluid dynamics, and microscopic rarefied gas dynamics, can effectively predict process windows and provide a theoretical basis for precursor chemical design, chamber structure optimization, and pulse timing setting.

As device architectures evolve towards three-dimensional stacking and atomic-scale precision manufacturing, future ALD transport models will face even higher accuracy requirements. The challenges mainly focus on the following two aspects:

1. Transient effectMost current models assume a steady or quasi-steady state, but the actual ALD pulse duration is extremely short (milliseconds), and the transient propagation effect of pressure fluctuations cannot be ignored.

2. Strong coupling between chemical reactions and transportCurrent models often simplify chemical reactions to linear adhesion coefficients, but in reality, changes in the coverage of surface ligands dynamically alter the adhesion coefficient, forming a real-time "transport-reaction" feedback loop.

Future research needs to combine in-situ characterization techniques (such as the combination of quartz crystal microbalance (QCM) and RGA mass spectrometry) with machine learning-accelerated molecular dynamics to build digital twin models, so as to realize the leap from "trial and error" to "predictive manufacturing" in ALD process.

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