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 | Institute of Applied Physics, N. I. Lobachevsky State University of Nizhny Novgorod |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”This research paper investigates the failure to achieve high hole mobility via delocalization in existing metallic boron delta (δ)-doped diamond layers and proposes the necessary parameters for success using numerical modeling.
- Core Problem Identified: Previous models failed to account for the valence band edge energy shift (Pearson-Bardin effect) caused by high concentrations of ionized boron atoms. This shift significantly deepens the potential well, leading to much stronger hole confinement (localization) than anticipated, thus suppressing mobility enhancement through delocalization.
- Delocalization Failure: Modeling a typical 2 nm metallic δ-layer (NB = 5 x 1020 cm-3) showed only ~7% of holes delocalized outside the layer, confirming strong confinement and explaining the low experimentally measured mobility (~3.6 cm2/(V·s)).
- Optimized Parameters: To achieve significant delocalization-induced mobility increase, the δ-layer must meet strict criteria: Boron concentration (NB) must be greater than 5 x 1020 cm-3 (to ensure metallic conductivity), layer thickness must be less than or equal to 0.5 nm, and the compensation ratio must be less than 42%.
- Predicted Mobility Gain: For an optimized 0.5 nm layer (uncompensated), the calculated mobility is 58 cm2/(V·s). This represents a factor of ~2 increase compared to uniformly doped diamond with the same boron concentration (~30 cm2/(V·s)).
- Technological Feasibility: The required ultra-thin, weakly compensated metallic δ-layers have not yet been experimentally realized but are considered achievable with modern nanotechnology.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Boron Concentration (IMT Threshold) | > 5 x 1020 | cm-3 | Required for Insulator-Metal Transition (metallic conductivity) |
| Optimized δ-Layer Thickness | ≤ 0.5 | nm | Required for significant hole delocalization |
| Maximum Compensation Ratio (K) | < 42 | % | Required to preserve delocalization effect |
| Calculated Mobility (Optimized 0.5 nm, K=0) | 58 | cm2/(V·s) | Predicted maximum mobility via delocalization |
| Calculated Mobility (2 nm, K=0) | 33 | cm2/(V·s) | Mobility comparable to uniformly doped diamond |
| Experimental Mobility (Previous Metal Layers) | 3.6 ± 0.85 | cm2/(V·s) | Measured mobility in existing metallic δ-layers [14] |
| Hole Delocalization (Optimized 0.5 nm) | ~47 | % | Percentage of holes located outside the δ-layer |
| Hole Delocalization (2 nm thickness) | ~7 | % | Percentage of holes located outside the δ-layer (strong confinement) |
| Valence Band Edge Shift (NB=5x1020 cm-3) | ~0.6 | eV | Deepening of potential well due to ionized boron |
| Boron Ionization Energy (Isolated Atom) | ~370 | meV | Shallowest known acceptor impurity in diamond |
| Heavy Hole Effective Mass | 0.588 | me | Used in simulation (me = free electron mass) |
| Light Hole Effective Mass | 0.303 | me | Used in simulation |
Key Methodologies
Section titled “Key Methodologies”The study relied on numerical simulation using Mean Field Theory in the Hartree approximation to solve the coupled Schrödinger and Poisson equations self-consistently.
- Interface Approximation: δ-doped layers were modeled assuming infinitely sharp interface boundaries, an approximation justified by high experimental doping sharpness (order of 1 nm decade-1).
- Doping Profile: Simulations used a metallic boron concentration (NB = 5 x 1020 cm-3) within the δ-layer, embedded in weakly (unintentionally) doped diamond (NB = 1015 cm-3).
- Physical Correction Implementation: The dependence of the valence band edge energy on the concentration of ionized boron atoms was included using the Pearson-Bardin formula (aNB-1/3) to accurately model the potential well depth.
- Quantum Modeling: Three doubly spin-degenerate hole subzones were included: heavy holes, light holes, and spin-orbitally split holes (with a 6 meV splitting energy).
- Delocalization Quantification: The degree of hole penetration was calculated as the ratio of the number of valence band holes located outside the δ-layer to the total number of holes supplied by the δ-layer.
- Mobility Calculation: Hole mobility was calculated based solely on scattering on ionized impurity atoms, incorporating hole degeneracy and the Lindhard screening approximation, primarily focusing on uncompensated (K=0) scenarios.
Commercial Applications
Section titled “Commercial Applications”The successful realization of ultra-high mobility δ-doped diamond layers is critical for advancing diamond-based semiconductor technology in several high-performance sectors.
- High-Frequency Field-Effect Transistors (FETs): The primary application, enabling faster switching speeds and higher operating frequencies than conventional silicon or GaAs devices.
- High-Power and High-Temperature Electronics: Diamond’s superior thermal conductivity and wide bandgap allow devices to operate reliably under extreme conditions (high voltage, high current, high temperature).
- Advanced Nanodevices: Utilizing the precise control offered by ultra-thin δ-doping (≤ 0.5 nm) for novel quantum and classical electronic structures.
- Integrated Diamond Circuits: Providing highly conductive, localized channels necessary for complex monolithic microwave integrated circuits (MMICs) based on diamond.
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.