High hole mobility in boron delta-doped layers in diamond - why it is not achieved as yet and how it can be achieved
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2022-01-01 |
| Journal | Физика и техника полупроводников |
| Authors | V. A. Kukushkin |
| Institutions | N. I. Lobachevsky State University of Nizhny Novgorod, Institute of Applied Physics |
| Analysis | Full AI Review Included |
Technical Analysis and Documentation: High Hole Mobility in Boron Delta-Doped Diamond
Section titled “Technical Analysis and Documentation: High Hole Mobility in Boron Delta-Doped Diamond”Reference: Kukushkin, V.A. (2022). High hole mobility in boron delta-doped layers in diamond: why it is not achieved as yet and how it can be achieved. Semiconductors, 56(10), 742-747.
Executive Summary
Section titled “Executive Summary”This paper provides critical theoretical insight into achieving high hole mobility in Boron Delta-Doped (BDD) diamond nanostructures, a key requirement for high-frequency field-effect transistors (FETs). 6CCVD is uniquely positioned to supply the necessary ultra-precise materials.
- Challenge Identified: Existing metallic $\delta$-doped layers (thickness $\sim$ 2 nm) exhibit low hole mobility ($\sim$ 3.6 cm2/(V $\cdot$ s)) due to strong hole confinement caused by the valence band edge shift (0.6 eV correction) induced by ionized boron atoms.
- Solution Proposed: Significant delocalization and mobility increase can be achieved only if the metallic $\delta$-layer thickness is reduced to $\le$ 0.5 nm.
- Material Requirement: The boron concentration ($N_{B}$) must exceed the Insulator-Metal Transition (IMT) threshold, $N_{B} > 5 \cdot 10^{20}$ cm-3, ensuring metallic conductivity.
- Compensation Control: The degree of compensation must be strictly controlled to < 42% to prevent the potential well from deepening and suppressing delocalization.
- Predicted Performance: Optimized 0.5 nm layers are predicted to yield hole mobility up to 58 cm2/(V $\cdot$ s), a two-fold increase over uniformly doped diamond at the same concentration.
- 6CCVD Value: 6CCVD specializes in high-purity MPCVD diamond substrates and advanced Boron-Doped Diamond (BDD) growth, enabling the precise nanometer-scale doping control required for these next-generation nanostructures.
Technical Specifications
Section titled “Technical Specifications”The following critical parameters were extracted from the numerical modeling and experimental comparisons detailed in the research.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Critical Boron Concentration ($N_{B}$) | > 5 $\cdot$ 1020 | cm-3 | Required threshold for Insulator-Metal Phase Transition (IMT) at room temperature. |
| Optimal $\delta$-Layer Thickness | $\le$ 0.5 | nm | Required for significant hole delocalization and mobility enhancement. |
| Maximum Compensation Ratio | < 42 | % | Required to maintain shallow potential well and preserve delocalization effect. |
| Predicted Hole Mobility (0.5 nm, uncompensated) | 58 | cm2/(V $\cdot$ s) | Calculated mobility for optimized $\delta$-layer, 2x higher than uniform doping. |
| Experimental Hole Mobility (2 nm, metallic) | 3.6 $\pm$ 0.85 | cm2/(V $\cdot$ s) | Measured mobility in existing metal $\delta$-layers (low due to confinement). |
| Hole Delocalization (0.5 nm layer) | 47 | % | Calculated percentage of holes located outside the $\delta$-doped layer. |
| Valence Band Edge Correction (2 nm layer) | $\sim$ 0.6 | eV | Significant deepening of the potential well due to ionized boron atoms. |
| Ionization Energy of Boron | $\sim$ 370 | meV | For isolated boron atoms in diamond. |
| Interface Sharpness (Experimental Basis) | $\le$ 1 | nm decade-1 | Required sharpness of the doping profile for accurate modeling. |
Key Methodologies
Section titled “Key Methodologies”The research relies on advanced numerical modeling confirmed by comparison with existing experimental data to determine the optimal physical parameters for high-mobility BDD $\delta$-layers.
- Numerical Simulation: Metallic $\delta$-doped layers in CVD diamond were modeled using a self-consistent solution of the Schrödinger and Poisson equations (Hartree approximation).
- Valence Band Correction: The model incorporated the Pearson-Bardin formula correction, accounting for the dependence of the valence band edge energy on the concentration of ionized boron atoms ($N_{B}^{-}$). This correction was crucial for accurately modeling the potential well depth.
- Interface Approximation: The $\delta$-doped layers were assumed to have infinitely sharp interface boundaries, an approximation justified by experimentally achieved doping sharpness (on the order of or smaller than 1 nm decade-1).
- Hole Subzones: Three doubly spin-degenerate hole subzones were included in the calculation: heavy holes (effective mass 0.588$m_{e}$), light holes (effective mass 0.303$m_{e}$), and spin-orbitally split holes (effective mass 0.394$m_{e}$).
- Mobility Calculation: Hole mobility was calculated considering only the contribution of scattering on ionized impurity atoms, using formulas that account for hole degeneracy and the Lindhard screening effect.
6CCVD Solutions & Capabilities
Section titled “6CCVD Solutions & Capabilities”6CCVD provides the foundational MPCVD materials and precision engineering services necessary to realize the ultra-thin, highly conductive BDD nanostructures proposed in this research. Achieving the critical $\le 0.5$ nm thickness and high $N_{B}$ requires state-of-the-art CVD control, which is a core competency of 6CCVD.
Applicable Materials
Section titled “Applicable Materials”To replicate or extend this research, engineers require materials that combine high purity with extreme doping precision:
- Substrate Material: Optical Grade Single Crystal Diamond (SCD) or High-Purity Polycrystalline Diamond (PCD). These materials serve as the weakly (unintentionally) doped surrounding medium (required $N_{B} \sim 10^{15}$ cm-3). 6CCVD offers SCD up to 10x10 mm and PCD plates up to 125 mm diameter.
- Active Layer Material: Heavy Boron-Doped Diamond (BDD). 6CCVD can achieve the required metallic concentration ($N_{B} > 5 \cdot 10^{20}$ cm-3) necessary for IMT.
Customization Potential for Nanostructure Fabrication
Section titled “Customization Potential for Nanostructure Fabrication”The success of high-mobility $\delta$-layers hinges on nanometer-scale control, a capability 6CCVD supports through advanced processing:
| Research Requirement | 6CCVD Capability | Technical Advantage |
|---|---|---|
| Ultra-Thin Doping Profile | SCD/PCD thickness control from 0.1 µm to 500 µm. | While the $\delta$-layer is $\le 0.5$ nm, 6CCVD’s precision CVD allows for the necessary sharp, controlled BDD growth interfaces required (approximated at $\le 1$ nm decade-1). |
| High-Quality Substrates | SCD and large-area PCD wafers (up to 125 mm). | Provides the high-purity, low-defect foundation critical for minimizing compensation and maximizing hole mobility. |
| Surface Preparation | Polishing capability: Ra < 1 nm (SCD), Ra < 5 nm (Inch-size PCD). | Essential for subsequent nanolithography and ensuring high-quality interface growth for the $\delta$-layer. |
| Device Integration | Custom Metalization Services (Au, Pt, Pd, Ti, W, Cu). | Although not the focus of the paper, high-frequency FETs require ohmic contacts. 6CCVD offers in-house deposition of multi-layer stacks for device integration. |
Engineering Support
Section titled “Engineering Support”The theoretical findings confirm that achieving high hole mobility in diamond FETs is an engineering challenge requiring precise material synthesis. 6CCVD’s in-house PhD team specializes in optimizing MPCVD growth recipes to control doping profiles, compensation ratios, and interface sharpness. We offer consultation services to assist researchers and engineers in designing material stacks for similar High-Frequency Field-Effect Transistor (FET) projects based on BDD nanostructures.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
The required parameters of nanometer boron delta-doped layers in diamond for achieving high conductivity and hole mobility are calculated. The boron concentration in such layers has to be sufficient to achieve the insulator—metal phase transition, i. e. metallic conductivity. Then, it is demonstrated that taking into account valence band edge energy shift due to the presence of ionized boron atoms leads to the significant deepening of the potential well formed by the delta-doped layer for holes. It results in much stronger hole confinement than it was expected before. Thus, it is predicted that a significant delocalization-induced increase of hole mobility can be achieved if metallic boron delta-doped layer thickness is of order and smaller than 0.5 nm and compensation ratio does not exceed 42%. Keywords: delta-doped layers, nanostructures, diamond films chemically deposited from the vapor phase, hole mobility, insulator-metal phase transition.