E3 229 : Principles of Microelectronic Devices

Parameters

Effective Mass (m*):

Global parameter altering quantum dispersion and energy scaling.

Model conventions: ℏ = 1. Energies, lengths, time, and frequencies use dimensionless model units. Unspecified phonon/KP lattice constants are 1; Coupled Wells uses the displayed distance d.

Time (t):

Watch the wavepacket disperse over time.

Initial Width (σ₀):

A narrower initial width spreads faster (Heisenberg uncertainty).

Time (t):

Animates an equal superposition containing every state from 1 through the selected n.

State Index (n, ground = 1):

n = 1 is the ground state with one central antinode.

Well Width (L):

Energy levels scale inversely with L².

Quasi-2D thickness (Lz / L):

Range: 0.15–1.00. Thin wells show isolated 2D subbands; Lz = L is the cubic 3D limit.

State counter

1D:—

2D:—

3D:—

Each row reports energy, exact degeneracy g, and cumulative states N(E).

Well Depth (V₀):

Higher V₀ traps more bound states.

Well Width (w):

Observe the exponential decay in forbidden regions.

Bound States Found: 0

Quantum State (n):

Energy levels scale roughly as (n - 0.25)^(2/3).

Electric Field / Slope (F):

Controls the steepness of the potential V(x) = F·x.

Number of Atoms (N):

Exact interior levels through N=50. Above 50, numerical band edges are joined by a tight-binding cosine interpolation. (Max 5000)

Interatomic Distance (d):

Bring the atoms closer to see the wavefunctions overlap and split.

Well Depth (V₀):

Well Width (w):

Simulates the size of individual atomic orbitals.

Particle Energy (E):

Adjust the energy of the incoming particle.

Barrier Height (V₀):

Classical physics forbids crossing if E < V₀.

Barrier Width (a):

Tunneling probability drops exponentially with width.

Barrier Strength (P):

Controls the gap size between allowed energy bands.

Interatomic Distance (a):

a = 1 is unstrained; compression raises the kinetic-energy scale.

Engineering Strain (ε, %):

Positive values stretch the lattice; negative values compress it.

Elastic Modulus (C):

Sets the slope of the linear stress–strain relation in model units.

Barrier Strength (P):

Controls periodic scattering and the resulting band gaps.

Animation Speed:

Controls the rate of the cyclic tensile–compressive loading.

Time (t):

Shows the time-dependent phase of the selected energy eigenstate.

Quantum State (n):

Energy levels are equally spaced: E = ℏω(n + 1/2)

Angular Frequency (ω):

Controls the steepness of the parabolic potential well.

Number of Atoms (N):

Identical atoms arranged in two-atom unit cells; even values up to 250.

Primary Spring Constant (K₁):

Stiffer bonds raise every vibrational frequency.

Atomic Mass (m):

Every site in the spring model has this same mass.

Alternating Spring Ratio (K₂/K₁):

K₂ = (K₂/K₁)K₁. Unequal alternating bonds open a frequency gap.

Highlighted branch:

Crystal structure:

Selected cubic and tetragonal lattices, plus zinc blende.

Displayed cells in each direction:

Rotate and zoom both direct and reciprocal lattices independently.

Crystal structure:

The first zone is constructed as the reciprocal-lattice Wigner–Seitz cell.

Reciprocal lattice context:

Controls how many neighboring reciprocal points are shown around the zone.