Comprehensive Study on Band-Gap Variations insp3-Bonded Semiconductors - Roles of Electronic States Floating in Internal Space

At a Glance

Metadata	Details
Publication Date	2017-04-07
Journal	Journal of the Physical Society of Japan
Authors	Yu‐ichiro Matsushita, Atsushi Oshiyama
Institutions	The University of Tokyo
Citations	9
Analysis	Full AI Review Included

Technical Documentation and Material Solutions Brief: Band Gap Engineering via Polytype Control in Diamond

Source Analysis: Matsushita, Y., & Oshiyama, A. (2017). Comprehensive study on band-gap variations in sp³-bonded semiconductors: roles of electronic states floating in internal space. arXiv:1701.00235v1.

Executive Summary

This study provides critical theoretical validation, using Density Functional Theory (DFT), for controlling the band gap in sp³-bonded semiconductors, most notably diamond, through precise manipulation of crystal polytypes (e.g., 2H, 3C, 6H).

Floating States Mechanism: The primary cause of band gap variation is identified as “peculiar electron states floating in internal channel space” at the conduction-band minimum (CBM).
Band Gap Dependence: The energy level of these floating states is directly dependent on the interstitial channel length and the local electro-static potential within the crystal structure.
Key Diamond Discovery: Unlike SiC and AlN (which show the smallest band gap in the 3C polytype), diamond exhibits its narrowest calculated band gap (3.406 eV) in the 2H structure, demonstrating potential band gap engineering opportunities specific to elemental semiconductors.
Structural Influence: Band gap narrowing in elemental semiconductors (like diamond) in the 2H structure is attributed to a lower electro-static potential at interstitial sites compared to the 3C structure due to differences in nearest-neighbor coordination.
Advanced Control: The findings underscore the necessity of high-precision MPCVD growth techniques to stabilize and replicate specific, non-native polytypes (e.g., 2H-diamond) for tunable electronic applications.

Technical Specifications

The following parameters summarize the calculated and experimental data relevant to the structural and electronic properties of diamond polytypes analyzed in the paper.

Parameter	Value	Unit	Context
Material Focus	Diamond (C)	N/A	sp³-bonded semiconductor analysis
Calculated E_gap (2H-C)	3.406	eV	Indirect gap, smallest among C polytypes
Calculated E_gap (3C-C)	4.246	eV	Indirect gap (Expt. 5.48 eV)
Calculated E_gap (6H-C)	4.521	eV	Indirect gap
E_gap Variation (2H vs 3C)	0.8	eV	Significant theoretical narrowing for 2H-C
Most Stable Polytype (C)	3C-C	N/A	Lowest calculated total energy difference (ΔE = 0 meV)
Lattice Constant a (2H-C)	2.503	Å	Calculated hexagonal lattice constant
Lattice Constant a (3C-C)	2.514	Å	Calculated hexagonal lattice constant
Floating State Character (2H-C CBM)	0.47	N/A	Residual norm indicating non-atomic orbital character (Fig. 8)

Key Methodologies

The electronic band structure analysis was performed using advanced theoretical techniques focused on high-precision simulation of material properties across different stacking sequences.

Fundamental Theory: Total-energy band-structure calculations were based on the Density Functional Theory (DFT).
Software & Basis Set: Calculations were executed using the plane-wave-basis-set ab initio program package, TAPP.
Approximation Method: Exchange-correlation energy was calculated using the Generalized Gradient Approximations (GGA). (Note: The paper confirms GGA underestimates absolute band gaps by ~50% but accurately models the relative energy difference between polytypes).
Pseudo-potential Generation: Norm-conserving pseudo-potentials (following Troullier and Martins) were used to simulate nuclei and core electrons, with specific core radii defined for C (0.85 Å for 2s/2p).
Focus of Analysis: Analyzing the quantum confinement effect on “floating states” at the Conduction-Band Minimum (CBM) as a function of the internal interstitial channel length, which changes with polytype stacking periodicity.
Structural Optimization: Lattice constants ($a$ and $c/na$) were theoretically determined for geometry-optimized polytypes (2H, 3C, 6H) to ensure accurate band structure mapping.

6CCVD Solutions & Capabilities

This research demonstrates that precise control over crystal stacking sequence (polytype) is a viable path for engineering the electronic band gap of diamond, transitioning it from a large-gap insulator to a smaller-gap semiconductor suitable for advanced UV/power electronics. Replicating or extending this work requires materials grown with exceptional crystallographic fidelity.

Research Requirement	6CCVD Material & Service Solution
Need for Controlled Crystal Structure (2H, 3C, 6H)	Single Crystal Diamond (SCD) Wafers: 6CCVD specializes in MPCVD growth, enabling the high-purity, low-defect material required to stabilize and study specific non-native diamond polytypes (e.g., 2H-C). Custom orientations and highly controlled growth along the (111) direction are available.
Investigating Charge Transfer & Electrostatics	Custom Boron-Doped Diamond (BDD): To extend the floating state analysis to extrinsic materials, 6CCVD provides highly controlled Boron-Doped Diamond (BDD) films and substrates, essential for modulating the Fermi level and channel potential dynamics.
Required Sample Dimensions for Characterization	Custom Dimensions and Thicknesses: We provide wafers up to 125mm (PCD) and custom thicknesses for SCD (0.1µm - 500µm) and substrates (up to 10mm), supporting both thin-film device fabrication and bulk property analysis.
Integration into Electronic Devices	In-House Metalization Services: For researchers needing to study the electronic properties of these polytypes, 6CCVD offers expert metal deposition (Au, Pt, Pd, Ti, W, Cu) services, ensuring reliable ohmic or rectifying contacts necessary for high-frequency or high-power tests.
Surface Quality for Atomic/Orbital Analysis	Ultra-Smooth Polishing (Ra < 1nm): To ensure crystal structure characterization (like EBSD or TEM) and electrical testing are not impacted by surface roughness, our SCD wafers are polished to achieve Ra < 1nm, critical for maintaining surface integrity across atomic layers.
Project Design and Recipe Optimization	Expert Engineering Support: Our in-house PhD material science team offers comprehensive consultation to assist engineers and scientists in selecting the ideal SCD or PCD material specifications necessary to successfully replicate the floating state phenomena and pursue applications like custom band gap engineering.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

We have performed electronic structure calculations to explore the band-gap dependence on polytypes for $sp^3$-bonded semiconducting materials, i.e., SiC, AlN, BN, GaN, Si, and diamond. In this comprehensive study, we have found that band-gap variation depending on polytypes is common in $sp^3$-bonded semiconductors; SiC, AlN, and BN exhibit smallest band gaps in $3C$ structure, whereas diamond does in $2H$ structure. We have also clarified that the microscopic mechanism of the band-gap variations is attributed to peculiar electron states $floating$ in internal channel space at the conduction-band minimum (CBM), and that internal channel length and the electro-static potential in channel affect the energy level of CBM.

Tech Support

Original Source

DOI: https://doi.org/10.7566/jpsj.86.054702

References

1966 - Polymorphism and Polytypismin Crystals
2014 - Fundamentals of Silicon Carbide Technology: Growth, Characterization, Devices, and Applications [Crossref]
1995 - Properties of Silicon Carbide