Dimensionality and Density of States Explorer
Run MicroSim in Fullscreen
Specification
The full specification below is extracted from
Chapter 5: "Bloch's Theorem, Band Formation, and E-k Diagrams".
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29 | Type: MicroSim
**sim-id:** density-of-states-explorer<br/>
**Library:** p5.js<br/>
**Status:** Specified
**Learning objective:** Students will predict and compare g(E) in 3D, 2D, 1D, and 0D and explain (Understand, L2) how dimensionality reduction improves semiconductor laser performance.
**Canvas size:** 900 × 540 px, responsive.
**Controls:**
- Select dropdown: Dimensionality — "3D (Bulk)", "2D (Quantum Well)", "1D (Quantum Wire)", "0D (Quantum Dot)". Default: "3D".
- Slider: Effective mass \(m^*/m_0\), 0.05–1.0, default 0.067. Label: "m*/m₀:"
- Slider: Confinement dimension L, 1–20 nm, default 10 nm (active when not 3D). Label: "L (nm):"
- Checkbox: "Show gain bandwidth" — overlays schematic optical gain curve width relative to DOS shape.
**Visual layout:**
Left panel (65%): Plot of g(E) vs. E from E_c to E_c + 0.4 eV.
- 3D: smooth √(E-E_c) curve.
- 2D: staircase with equal-height steps at E_n = n²·ħ²π²/(2m*L²).
- 1D: spiky curve with 1/√(E-E_n) peaks at subband edges.
- 0D: vertical arrows at discrete energies E_n.
All normalized to same peak height. Color: 3D=blue, 2D=green, 1D=orange, 0D=red.
Right panel (35%): Card showing dimensionality, g(E) formula, device application, laser threshold comparison (bulk > QW > QD).
**Behavior:** All controls update the plot in real time. On resize: updateCanvasSize() reflows.
**Implementation:** p5.js, single HTML file. Parent canvas to document.querySelector('main').
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