Scanning Tunneling Spectroscopy: Mapping the Local Density of States

Scan Mode

Sample Lattice

Drag the tip across the lattice. Toggle Edit defects and click an atom to cycle it: clean → acceptor (−0.7 eV) → donor (+0.6 eV) → clean.

Tip Controls

Bias voltage V +0.50 V

Tip–sample gap d 6.0 Å

Setpoint current I₀ 0.40 nA

Temperature T 77 K

Live Readouts

Current I(V)

0.00 nA

dI/dV (∝ LDOS)

0.00

Site under tip

clean

κ (decay rate)

1.03 Å¹

dI/dV Spectrum at Tip

−2 V0 V+2 V

How it works

This is a genuine 2D counterpart of the 3D STM/STS simulator: instead of three preset sites it uses a real square atomic lattice whose local density of states LDOS(x,y,E) you edit yourself by planting defects. Each clean atom contributes a flat, metal-like background LDOS. A defect atom adds a localized electronic resonance centered at its own energy that decays with distance from the defect — exactly how a real adsorbate or dopant perturbs the surrounding LDOS.

LDOS(x,y,E) = 1 + Σ_defects exp(−r²/2ℓ²)·exp(−(E−E_d)²/2σ²)
dI/dV(V) ∝ LDOS(x,y,E_F+eV)
I(V) = ∫₀^eV LDOS(x,y,ε)·T(ε,d) dε,  T ∝ exp(−2κd)

Spectroscopy mode — drag the tip anywhere, sweep the bias, and dI/dV traces the real LDOS(E) at that exact point. Park it over a clean atom for a flat spectrum, over an acceptor defect for a peak below E_F, over a donor defect for a peak above E_F.
Topography mode — the tip auto-rasters the whole lattice in constant-current mode: at every pixel it solves exp(−2κd)·I_rel(x,y,V) = I₀ for the height d that keeps the current fixed. The resulting image is real STM topography — it mixes true geometric corrugation with electronic corrugation, so a defect's LDOS bump shows up as an apparent bump in "height" even though the lattice itself is flat, exactly as it does on a real instrument.
Temperature thermally broadens every LDOS feature by ~k_BT, blurring defect peaks and rounding topography contrast as it rises.

Spectroscopy

Clean atom Acceptor defect (−0.7 eV) Donor defect (+0.6 eV) STM tip

Scanning Tunneling Spectroscopy: Mapping the Local Density of States (2D)