Self-Consistent $GW$ calculations for semiconductors and insulators

At a Glance

Metadata	Details
Publication Date	2018-08-23
Journal	arXiv (Cornell University)
Authors	Manuel Grumet, Peitao Liu, Merzuk Kaltak, Jiří Klimeš, Georg Kresse
Citations	29
Analysis	Full AI Review Included

Technical Documentation & Analysis: Fully Self-Consistent GW Calculations in Diamond

This document analyzes the research paper “Beyond the quasiparticle approximation: Fully self-consistent GW calculations” to provide technical specifications and align 6CCVD’s advanced MPCVD diamond capabilities with the requirements for replicating and extending this fundamental research in solid-state physics.

Executive Summary

The analyzed research validates a highly accurate computational methodology for determining the intrinsic electronic properties of wide-bandgap materials, directly supporting the need for high-purity Single Crystal Diamond (SCD) in advanced applications.

Core Methodology: Validation of fully self-consistent GW (scGW) calculations within the Projector-Augmented Wave (PAW) framework for determining Quasiparticle (QP) energies and fundamental band gaps.
Critical Technical Achievement: Successful implementation of a novel extrapolation scheme (“head correction”) to manage the singularity of the Coulomb kernel, ensuring accurate results even with reasonable k-point sets.
Material Focus: Diamond (C) serves as the primary validation case, establishing crucial reference values for its intrinsic electronic structure.
Key Result: The converged scGW band gap for diamond is calculated at 6.41 eV, significantly higher than single-shot G₀W₀ results (5.69 eV), highlighting the necessity of self-consistency for accurate theoretical modeling.
Convergence Requirements: Achieving convergence required rigorous inclusion of finite basis-set corrections and k-point corrections, demonstrating the extreme sensitivity of QP energies to computational parameters.
6CCVD Value Proposition: The theoretical accuracy achieved in this work necessitates the use of ultra-high purity, low-defect Single Crystal Diamond (SCD) from 6CCVD to experimentally realize and validate these intrinsic electronic properties.

Technical Specifications

The following hard data points were extracted from the scGW calculations, focusing on diamond (C) and other relevant wide-bandgap materials (BN, SiC).

Parameter	Value	Unit	Context
Primary Material Validated	Diamond (C)	N/A	Prototypical semiconductor/insulator
Crystal Structure (C)	Diamond	N/A	Table I
Lattice Constant (C)	3.56	Å	Table I
Plane-Wave Energy Cutoff (C)	741.69	eV	E^cut_PW for C
K-Point Grid Density	6 x 6 x 6	N/A	Used for converged scGW results
scGW Iterations	5	N/A	Sufficient for convergence within 0.01 eV
QP Energy Convergence	0.01	eV	Required precision for convergence
Converged scGW Band Gap (C)	6.41	eV	With basis-set and k-point corrections (Table IV)
G₀W₀ Band Gap (C)	5.69	eV	Single-shot calculation (Table V)
scGW Band Gap (BN)	7.67	eV	Boron Nitride (Table IV)
scGW Band Gap (SiC)	3.29	eV	Silicon Carbide (Table IV)

Key Methodologies

The scGW implementation required stringent computational controls and correction schemes to achieve converged quasiparticle energies.

Computational Framework: Calculations were performed using the Vienna Ab initio Simulation Package (VASP) utilizing approximately norm-conserving GW Projector-Augmented Wave (PAW) potentials.
Self-Consistency Loop (scGW): Full self-consistency was achieved by iteratively solving the Dyson equation for the Green’s function (G) and the screened interaction (W). A minimum of five iterations was required to achieve QP energy convergence < 0.01 eV.
Head Correction Implementation: A critical extrapolation scheme was used to overcome the singularity of the bare Coulomb interaction in the long-wavelength limit (q → 0). This involved a linear least-square fit of finite q data extrapolated to q = 0, shown to be crucial for fast convergence.
Basis-Set Correction: A basis-set correction scheme was applied by fitting results obtained at increased plane-wave cutoffs (up to 1.587x default E^cut_PW) as a linear function of 1/N_PW, then extrapolated to 1/N_PW = 0.
K-Point Correction: Errors introduced by finite k-point sampling were corrected by performing additional calculations using a 4 x 4 x 4 k-point mesh and assuming the error behaves as 1/N_k.

6CCVD Solutions & Capabilities

The rigorous theoretical modeling presented in this paper underscores the necessity of using the highest quality, most precisely engineered diamond materials for experimental validation and device fabrication. 6CCVD provides the necessary foundation for realizing devices based on these intrinsic electronic properties.

Applicable Materials

To replicate or extend this research, which focuses on the intrinsic electronic structure of diamond, the following 6CCVD materials are required:

Optical Grade Single Crystal Diamond (SCD): Essential for studying the intrinsic 6.41 eV band gap and deep valence states (Γ_vBmin). Our SCD is Type IIa, grown via MPCVD, ensuring extremely low nitrogen concentration (< 1 ppm) and minimal lattice defects, which is critical for matching theoretical intrinsic properties.
Polycrystalline Diamond (PCD): For scaling up high-power electronic devices based on these wide bandgap principles, 6CCVD offers large-area PCD plates up to 125mm in diameter.
Boron-Doped Diamond (BDD): While the paper focuses on intrinsic insulators, BDD is the material of choice for high-performance electrochemical and p-type semiconductor applications, offering tunable conductivity and high chemical stability.

Customization Potential

The precision required for fundamental electronic studies demands highly controlled material specifications. 6CCVD offers comprehensive customization capabilities:

Research Requirement	6CCVD Customization Service	Specification Range
Precise Thickness Control	Custom SCD/PCD Growth	SCD: 0.1 µm to 500 µm (films); Substrates: up to 10 mm
Ultra-Smooth Surfaces	Precision Polishing	SCD: Ra < 1 nm; Inch-size PCD: Ra < 5 nm
Advanced Device Integration	Custom Metalization	In-house deposition of Au, Pt, Pd, Ti, W, and Cu for ohmic contacts or gate structures.
Unique Dimensions	Custom Laser Cutting & Shaping	Plates/wafers up to 125 mm (PCD) and custom shapes for SCD.

Engineering Support

The complexity of scGW calculations, particularly concerning deep states and convergence, mirrors the complexity of selecting the optimal diamond material for high-performance applications.

Material Selection for Wide Bandgap Projects: 6CCVD’s in-house PhD team specializes in correlating MPCVD growth parameters with resulting electronic and optical properties. We can assist researchers in selecting the ideal SCD or PCD grade for similar electronic structure and high-power electronics projects.
Defect Engineering: Understanding the theoretical band structure is the first step. We provide consultation on how specific doping (e.g., Boron) or defect control (e.g., NV centers) can be used to modify the electronic structure for specific device goals, such as quantum sensing or high-frequency operation.

Call to Action

The theoretical reference values established in this paper provide the foundation for the next generation of diamond-based electronic and quantum devices. Ensure your experimental materials meet the intrinsic purity standards required by these advanced calculations.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. We ship globally (DDU default, DDP available).

View Original Abstract

We present quasiparticle (QP) energies from fully self-consistent $GW$ (sc$GW$) calculations for a set of prototypical semiconductors and insulators within the framework of the projector-augmented wave methodology. To obtain converged results, both finite basis-set corrections and $k$-point corrections are included, and a simple procedure is suggested to deal with the singularity of the Coulomb kernel in the long-wavelength limit, the so called head correction. It is shown that the inclusion of the head corrections in the sc$GW$ calculations is critical to obtain accurate QP energies with a reasonable $k$-point set. We first validate our implementation by presenting detailed results for the selected case of diamond, and then we discuss the converged QP energies, in particular the band gaps, for the entire set of gapped compounds and compare them to single-shot $G_0W_0$, QP self-consistent $GW$, and previously available sc$GW$ results as well as experimental results.

Tech Support

Original Source

DOI: None