Extrinsic Doping in Group IV Hexagonal-Diamond-Type Crystals
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2020-07-07 |
| Journal | The Journal of Physical Chemistry C |
| Authors | Michele Amato, Thanayut Kaewmaraya, Alberto Zobelli |
| Institutions | Centre National de la Recherche Scientifique, Khon Kaen University |
| Citations | 9 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis study uses Density Functional Theory (DFT) to analyze the extrinsic doping stability of Group III (p-type) and Group V (n-type) impurities in hexagonal-diamond (2H) versus cubic-diamond (3C) Group IV crystals (C, Si, Ge).
- P-Type Preference (Group III): Acceptor dopants (B, Al, Ga) exhibit a strong, marked preference for the 2H hexagonal-diamond phase across all host materials (C, Si, Ge).
- Symmetry Driving Force: This preference is driven by the local C3v symmetry of the 2H lattice, which better accommodates the three-fold coordination required by trivalent impurities compared to the Td symmetry of the 3C phase.
- N-Type Stability (Group V): Donor dopants (P, As) show no clear phase preference in Si and Ge hosts. However, n-type doping in Carbon (lonsdaleite) is significantly more stable in the 2H phase than in the 3C phase.
- Dopant Segregation: The calculated negative formation energy differences (ÎE2H-3Cform) for p-type dopants imply a high concentration ratio (up to 105 times higher in 2H), suggesting a strong tendency for dopant segregation at 2H/3C interfaces in heterostructures.
- Structural vs. Electronic Effects: Volume changes at the doping site are nearly identical between 2H and 3C phases; therefore, the observed stability trends are primarily dictated by electronic valence and local symmetry requirements.
- Optimal Doping Conditions: These findings suggest that 2H Group IV polymorphs are ideal hosts for p-type dopants, providing crucial guidance for synthesizing high-quality, extrinsically doped hexagonal nanowires.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| C Lattice Parameter (3C) | 3.56 | A | a3C (Cubic Diamond) |
| C Lattice Parameter (2H) | 2.50, 4.16 | A | a2H, c2H (Hexagonal Lonsdaleite) |
| Si Cohesion Energy (3C) | 5.56 | eV | E3Ccoh |
| Ge Cohesion Energy (2H) | 4.13 | eV | E2Hcoh |
| Atomic Density (Si, Ge) | ~2.38, ~5.05 | g/cm3 | Density difference between 2H and 3C is negligible. |
| B ÎE2H-3Cform (in C) | -0.32 | eV | Strong preference for 2H phase (p-type). |
| P ÎE2H-3Cform (in C) | -0.54 | eV | Strong preference for 2H phase (n-type). |
| As ÎE2H-3Cform (in Ge) | 0.17 | eV | Slight preference for 3C phase (n-type). |
| B Concentration Ratio (in C) | 2.58 x 105 | [C2H]/[C3C] | Equilibrium concentration ratio at KBT (high segregation). |
| P Concentration Ratio (in C) | 1.11 x 109 | [C2H]/[C3C] | Extremely high segregation tendency in Carbon. |
| Dopant Concentration Modeled | 1019 - 1020 | cm-3 | Simulating high-doping regimes observed in experiments. |
| Force Convergence Criteria | 0.01 | eV/A | Geometry optimization standard. |
| Stress Convergence Criteria | 0.1 | GPa | Lattice parameter relaxation standard. |
Key Methodologies
Section titled âKey MethodologiesâThe study utilized first-principles simulations based on Density Functional Theory (DFT) to calculate defect formation energies (Eform) and structural distortions.
- Simulation Codes: Calculations were primarily performed using the SIESTA code (Local Density Approximation, LDA). Additional calculations for Ge (to correct the small band gap) used the VASP code (Generalized Gradient Approximation + U, GGA+U).
- Basis Sets and Potentials: An optimized double-polarized basis set was employed. Core electrons were replaced by norm-conserving Troullier-Martins pseudopotentials.
- Supercell Modeling: Host bulk crystals were modeled using large supercells to minimize spurious interactions between periodic replicas of impurities:
- 3C Phase: 4 x 4 x 4 supercell (512 atoms).
- 2H Phase: 6 x 6 x 3 supercell (432 atoms).
- Convergence Parameters: Atomic coordinates and lattice parameters were relaxed until strict convergence criteria were met: 0.01 eV/A for forces and 0.1 GPa for stress.
- Formation Energy Calculation: The formation energy (Eform) of a neutral substitutional defect was calculated using the Zhang and Nortrup formalism, referencing the bulk ground state total energy per host atom and the energy of the free dopant atoms.
- Ge Electronic Structure Correction: For Ge, GGA+U was applied (U=0.4 eV, J=4 eV) to accurately represent the electronic structure and band gap, confirming the trends observed in the LDA calculations.
- Symmetry Analysis: Local structural deformation was quantified using the synthetic parameter DC3v, which measures the modification of the aspect ratio of the pyramidal site occupied by the dopant.
Commercial Applications
Section titled âCommercial ApplicationsâThe findings provide critical design rules for engineering Group IV semiconductor materials, particularly in the context of nanowire growth and advanced electronic/optoelectronic devices.
- Nanowire Phase Control: The strong preference of p-type dopants (e.g., B) for the 2H phase suggests they can be used as phase-promoting agents during vapor-liquid-solid (VLS) growth, stabilizing the desired hexagonal structure in Si and Ge nanowires.
- Optoelectronic Devices: 2H-Si and 2H-Ge exhibit superior optical properties (e.g., direct band gap in Ge, higher visible absorption in Si). Optimized p-type doping in 2H materials is essential for creating high-performance LEDs, lasers, and photodetectors based on these novel polymorphs.
- Heterostructure Engineering: The predicted strong dopant segregation tendency at 2H/3C interfaces (especially for p-type dopants) must be accounted for when designing axial or radial heterostructures, influencing junction sharpness and electrical performance.
- High-Hardness Electronics: The enhanced stability of n-type dopants (P, As) in 2H-C (lonsdaleite) suggests a pathway for creating conductive, ultra-hard materials, potentially useful in extreme environment electronics or protective coatings.
- Defect Management: Understanding the local symmetry preference (C3v vs. Td) allows engineers to predict and mitigate the formation of unwanted defect complexes or stacking faults that can trap carriers and degrade device efficiency.
View Original Abstract
Over the last few years, group IV hexagonal-diamond type crystals have\nacquired great attention in semiconductor physics thanks to the appearance of\nnovel and very effective growth methods. However, many questions remain\nunaddressed on their extrinsic doping capability and on how it compares to\nthose of diamond-like structures. This point is here investigated through\nnumerical simulations conducted in the framework of the Density Functional\nTheory (DFT). The comparative analysis for group III and V dopant atoms shows\nthat: i) in diamond-type crystals the bulk sites symmetry ($T_d$) is preserved\nby doping while in hexagonal crystals the impurity site moves towards a higher\n($T_d$) or lower ($C_{3v}$) symmetry configuration dependently on the valence\nof the dopant atoms; ii) for Si and Ge, group III impurities can be more easily\nintroduced in the hexagonal-diamond phase, whose local $C_{3v}$ symmetry better\naccommodates the three-fold coordination of the impurity, while n-type\nimpurities do not reveal any marked phase preference; iii) for C, both n and p\ndopants are more stable in the hexagonal-diamond structure than in the the\ncubic one, but this tendency is much more pronounced for n-type impurities.\n