Physic Labs

Condensed matter physics

Band theory and semiconductors

Explore the electron energy spectrum in a crystal: vary the gap opening and Fermi level to distinguish metals, semiconductors, and insulators. Verify the role of the band gap EgE_g in conduction.

Advanced

Equipment

  • 3D model of graphene's Dirac cone (panel 1)
  • Gap-opening and Fermi-level sliders
  • Panel 2 band structure with Model-parameter and Time sliders

Procedure

  1. Observe the Dirac cone with no gap

    In panel 1, set «Gap opening» = 0: the two bands touch at the Dirac point and electrons have zero effective mass — graphene's signature. Sweep «Fermi level» to see occupied states shift while states remain available for conduction.

  2. Open the band gap

    Step up «Gap opening»: the bands separate and a gap EgE_g opens at the Dirac point. Put «Fermi level» inside the gap: no nearby states remain for electrons to hop into — the system turns from semimetal into semiconductor/insulator.

  3. Read the band spectrum in panel 2

    Use «Model parameter» to change the bandwidth and watch the E(k) curves; press «Pause» to read levels. Compare Fermi inside a band (metal: conducts well) with inside a wide gap (insulator) — a semiconductor is a narrow gap ~1 eV that temperature can let electrons cross.

  4. Predict conduction from configuration

    For each (gap, Fermi-level) pair you choose, predict metal/semiconductor/insulator before observing, then explain the result via the position of EFE_F relative to EgE_g. Extension: n-doping adds electrons, pushing EFE_F near the conduction band — mimic it by sliding the Fermi level.

Simulation

Experiment history

Band theory grew from the question of why materials conduct so differently. Felix Bloch applied the young quantum mechanics to electrons in a crystal's periodic potential (1928): Bloch waves ψk=eikxuk(x)\psi_k=e^{ikx}u_k(x) yield a spectrum split into bands — the idea Alan Wilson used in 1931 to distinguish metals, semiconductors, and insulators. The model became practical once controlled doping enabled the transistor (Bell Labs, 1947) and the semiconductor industry. A recent surprise: Geim and Novoselov isolated one-atom-thick graphene in 2004, whose bands meet at a Dirac point with effectively massless electrons — Nobel 2010 — opening the era of Dirac and then topological materials.

Related physicists

Paul DiracMax BornFelix BlochAndre Konstantinovich GeimKonstantin Sergeevich Novoselov

Related library topics

Band theory and semiconductors