ONE CRYSTAL. EVERY ELECTRON HAS A ROLE.
Inside a semiconductor
Warm it. Replace an atom. Apply voltage. Follow what the electrons actually do.
THE SAME STRUCTURE, DIFFERENT CONDITIONS
The silicon crystal
How a hole is filled
Same event · enlarged bond statesChoose P-type + current to follow an electron filling a neighboring vacancy.
Slow-motion teaching view of valence-band transport. Dots mark electron states; the transfer path is schematic. Amber rings mark missing electrons.
Two shared electrons occupy each covalent bond. A hole is an empty electron state.
Where is the electron’s energy?
Same electron · a second viewBound electrons occupy the valence band. Free electrons occupy the conduction band. Vertical position here means energy, not height in the crystal.
What changed?
Drawn sample counts · representative scaleMore detail Physics, equations & model notes
How to read this model
Each line is a covalent bond with two shared outer electrons. Inner-shell electrons are omitted. This straight grid is a 2D teaching diagram of silicon’s 3D tetrahedral bonding.
Hole hopping shows how electron transfers displace a vacancy. It is a simplified representation of valence-band transport. At the edges, contacts can supply or collect electrons.
Colored circles around P or B stay at their lattice sites: P⁺ donated an electron; B⁻ captured one. A neutral donor keeps its extra electron nearby.
Physical measurements
Bulk values are equilibrium estimates. The drawn sample approaches its representative population through individual events; its particle counts are not densities.
Materials & energy bands
Silicon and germanium each have four valence electrons for bonding. At room temperature, their approximate gaps are 1.12 eV and 0.67 eV. Gallium arsenide is a III–V compound with an approximate 1.42 eV gap. This interactive lattice specifically models silicon.
Conductors have partially filled bands or overlapping bands; insulators have a large gap; semiconductors have a smaller gap that permits thermally excited carriers. One electron-volt is 1.602 × 10⁻¹⁹ joules.
Majority carriers & Fermi level
In intrinsic material, n = p = nᵢ. Donor doping makes electrons the majority carriers; acceptor doping makes holes the majority carriers. The opposite carrier type remains present as a minority population.
The Fermi level describes equilibrium occupation, not an electron’s trajectory. It shifts toward the conduction band for N-type and toward the valence band for P-type. At low temperature, dopants can remain neutral (freeze-out); at sufficiently high temperature, intrinsic generation can dominate.
Equations behind the experiment
np = nᵢ²
n − p = Nᴅ⁺ − Nₐ⁻
E = V / L
Jₙ = qnμₙE · Jₚ = qpμₚE
I = (Jₙ + Jₚ)A
For silicon at 300 K: Eɢ = 1.12 eV and nᵢ ≈ 1.5 × 10¹⁰ cm⁻³. Temperature and doping affect both carrier populations and mobility.
Diffusion is driven by a concentration gradient: Jₙ = qDₙ dn/dx and Jₚ = −qDₚ dp/dx. The main experiment here uses a uniform sample and illustrates drift.
Assumptions & accessibility
Energy-band transitions are teaching animations between allowed states, not stable states inside the forbidden gap. Freeze-out uses a smooth approximation. The classical carrier model and fixed 1.12 eV gap are approximate, especially at very low temperature or high doping.
Concentration is logarithmically mapped to at most six visible dopants of each type. Temperature adds up to seven representative thermal pairs. Decreasing dopant count prepares a new neutral sample; increasing it retains existing carriers.