🔬 materials science

Universal model of the growth of III-V tetrahedral semiconductors on polar surfaces: pyramids and glue atoms. VI. Surface diffusion on a nonmetal-terminated surface

This study utilizes ab initio calculations to demonstrate that surface diffusion of nonmetal adatoms on polar III-V semiconductor surfaces proceeds via a stable pyramidal rotation mechanism, resulting in macroscopically large diffusion lengths that ensure all adatoms reach step edges.

Original authors: Pawel Strak, Stanisław Krukowski

Published 2026-11-03

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CC BY 4.0

Original authors: Pawel Strak, Stanisław Krukowski

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

To build the next generation of electronic and optical devices, from the lasers in fiber-optic networks to the tiny transistors powering artificial intelligence, scientists must grow semiconductor crystals with atomic precision. These materials, known as III-V compounds, are made by combining elements from two specific groups of the periodic table. The challenge lies in controlling how atoms land and stick together on a growing surface. If the atoms arrive and wander aimlessly, or if they detach before finding their proper place, the final crystal will be riddled with defects that ruin its performance. The ideal growth process involves atoms landing on a flat terrace, wandering just enough to find the edge of a step, and then locking into the crystal structure. Whether this happens depends on two competing forces: how easily an atom can move across the surface, and how strongly it wants to stay attached versus flying off into the air. Understanding this delicate balance is essential for creating the flawless layers needed for modern technology.

In a recent study, researchers Paweł Strak and Stanisław Krukowski from the Institute of High Pressure Physics in Warsaw investigated exactly how these atoms behave on the surface of four important semiconductors: gallium nitride, gallium phosphide, gallium arsenide, and gallium antimonide. They focused on a specific type of surface where the top layer is made of the non-metal element, such as nitrogen or phosphorus, sitting on a bed of gallium atoms. Using powerful computer simulations based on the laws of quantum mechanics, the team tracked how small groups of atoms move across these surfaces. They discovered that the atoms do not wander individually. Instead, they form stable, three-dimensional structures that look like tiny pyramids. Each pyramid consists of three gallium atoms forming a triangular base, with a single non-metal atom sitting on top. These pyramids act as single units, moving together across the surface rather than breaking apart.

The researchers simulated the journey of these pyramids as they hop from one spot to another. They found that the movement happens through a pivoting motion. Imagine the pyramid as a rigid object; as it moves, one of the three gallium atoms at the base stays firmly planted in place, acting as a pivot point. The other two gallium atoms rotate around this fixed point, swinging the entire structure, including the non-metal atom on top, into a new, empty spot on the surface. This process allows the pyramid to travel across the crystal without falling apart. The energy required to perform this hop varies depending on the material. For gallium nitride, the barrier to move is very low, requiring only about 0.2 electron volts of energy, which means these structures are highly mobile even at moderate temperatures. For the other materials—gallium phosphide, gallium arsenide, and gallium antimonide—the barrier is higher, ranging between 0.5 and 0.6 electron volts. While this makes them move slightly slower, it is still low enough to allow them to travel significant distances across the surface.

A critical question for crystal growth is whether these structures will stay on the surface long enough to reach the edge, or if they will break apart and evaporate back into the vapor. The team calculated the energy needed to pull the non-metal atom off the top of the pyramid. They found that breaking the pyramid apart to release a single atom requires a massive amount of energy, roughly 5 electron volts, which is far too high for the atoms to overcome under normal growth conditions. Even if the atoms were to leave as a pair or a molecule, the energy required remains high, particularly for nitrogen, where the barrier is still around 1 electron volt. This high stability means that once a pyramid forms, it is extremely unlikely to disintegrate before it reaches a step edge.

The results indicate that the surface diffusion length—the average distance a structure travels before it either gets stuck or flies away—is enormous. In practical terms, this means that virtually every pyramid that lands on the surface will successfully make its way to the edge of a step and incorporate into the growing crystal. The atoms do not get lost in the middle of the flat surface; they are efficiently guided to the steps where they can build the next layer of the material. This finding confirms that the growth of these semiconductors on non-metal-terminated surfaces is governed by the movement of these stable pyramidal units. The study provides a clear picture of the microscopic mechanics behind the formation of high-quality semiconductor layers, showing that the atoms organize themselves into resilient, mobile structures that ensure the crystal grows smoothly and without defects.

Technical Summary: Universal Model of III-V Tetrahedral Semiconductor Growth (VI): Surface Diffusion on Nonmetal-Terminated Surfaces

Problem Statement
The growth of high-quality III-V semiconductor structures for electronic and optoelectronic applications (e.g., laser diodes, LEDs, FETs) requires atomic-precision control, particularly in the step-flow growth mode. In this mode, growth units must diffuse across surface terraces to steps before detaching. A critical gap exists in understanding the fundamental diffusion mechanisms on nonmetal-terminated polar surfaces of III-V compounds. While previous studies in this series identified stable surface configurations as triangular-based pyramids (three Ga adatoms at the base with a nonmetal adatom on top), the specific pathways, energy barriers, and mobility of these structures during surface diffusion remained to be quantified. This paper addresses the simulation of surface diffusion for these pyramid structures and single Ga adatoms on nonmetal-terminated surfaces of GaN, GaP, GaAs, and GaSb.

Methodology
The study employs ab initio density functional theory (DFT) calculations using the SIESTA package. The simulations utilize the Born-Oppenheimer approximation and the Nudged Elastic Band (NEB) method to determine minimum-energy pathways (MEP) and saddle points between equilibrium sites.

System Models: Slabs representing wurtzite GaN(0001̅) and zinc blende GaP(1̅1̅1̅), GaAs(1̅1̅1̅), and GaSb(1̅1̅1̅) surfaces were constructed. These were terminated with fractional charge hydrogen pseudoatoms.
Coverage: Simulations focused on highly Ga-covered surfaces ( $\theta_{Ga} \approx 15/16$ ), featuring a first layer of Ga adatoms and a second layer containing a single nonmetal (NM) adatom forming a pyramid.
Analysis: The study calculates energy barriers for diffusion jumps ( $\Delta E_{diff}$ ) and desorption ( $\Delta E_{des}$ ). Electronic structure analysis, including Projected Density of States (PDOS) and Crystal Orbital Hamilton Population (COHP), was performed to understand bonding interactions during the migration process.

Key Results

Diffusion Mechanism:
Surface diffusion proceeds via the motion of the entire NM-Ga pyramid rather than individual adatoms. The mechanism involves a "pivot" rotation where one basal Ga adatom remains immobile, attached to the underlying NM surface atoms, while the other two basal Ga adatoms rotate around it to occupy new, originally empty sites. The pyramid remains geometrically intact throughout the jump, exhibiting only minor deformation.
Diffusion Energy Barriers ( $\Delta E_{diff}$ ):
The energy barriers for the migration of these pyramids vary by material:
- GaN: 0.198. The barrier is low, indicating high mobility at typical growth temperatures.
- GaP: 0.642.
- GaAs: 0.581.
- GaSb: 0.628.
  The barriers for GaP, GaAs, and GaSb are significantly higher than for GaN, suggesting somewhat limited mobility compared to GaN, though still sufficient for step-flow growth.
Desorption Energy Barriers ( $\Delta E_{des}$ ):
The energy required to detach the NM adatom from the pyramid is high for all materials when considering the atomic state.
- Molecular Desorption: When considering molecular desorption (formation of $N_2$ $N_{2}$ , $P_2$ $P_{2}$ , $As_2$ $A s_{2}$ ), the barriers decrease significantly due to the high dissociation energy of the molecules.
  - Nitrogen (GaN): The barrier decreases significantly.
  - Phosphorus (GaP) and Arsenic (GaAs): The barrier decreases significantly.
  - Antimony (GaSb): Not determined (atomic form assumed dominant).
Surface Diffusion Length ( $l_{sur}$ ):
Using the calculated barriers and typical Molecular Beam Epitaxy (MBE) growth temperatures, the surface diffusion lengths were calculated. Both atomic and molecular diffusion lengths are found to be macroscopically large, ranging from thousands of kilometers to tens of thousands of kilometers. Specifically, the calculated atomic diffusion lengths are approximately $1.375 \times 10^6$ m for GaN, $6.324 \times 10^6$ m for GaP, $6.891 \times 10^3$ m for GaAs, and $8.910 \times 10^7$ m for GaSb. This indicates that the flux of nonmetal adatoms effectively reaches the crystal steps before detaching.

Significance and Claims
The paper establishes that the fundamental unit of surface diffusion on nonmetal-terminated III-V surfaces is the stable NM-Ga pyramid. The primary contribution is the quantification of the energy landscape governing the rotation-based diffusion of these pyramids.

The authors claim that because the diffusion barriers are relatively low (especially for GaN) and the desorption barriers are high, the surface diffusion length is sufficiently large to ensure that all attached nonmetal adatoms arrive at the steps. This supports the viability of step-flow growth for these materials. The study concludes that the attachment of these pyramids to steps and the subsequent incorporation into the crystal lattice are complex processes that will be detailed in the subsequent paper (VII) of this series. The current work provides the necessary diffusion parameters to model the pre-step dynamics of III-V semiconductor growth.

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