Scanning Tunneling Spectroscopy: Mapping the Local Density of States

Sample Site

Tip Controls

Bias voltage V +0.50 V

Tip–sample gap d 6.0 Å

Temperature T 77 K

Live Readouts

Current I(V)

0.00 nA

dI/dV (∝ LDOS)

0.00

Band gap

—

κ (decay rate)

1.03 Å¹

dI/dV Spectrum

−2 V0 V+2 V

How it works

In constant-current STM imaging the tip's height traces surface topography. In scanning tunneling spectroscopy (STS) the tip instead parks over one spot and the bias voltage V is swept while current I(V) is recorded. In the Tersoff–Hamann approximation, the differential conductance is directly proportional to the sample's local density of electronic states (LDOS) at the tip position:

dI/dV(V) ∝ ρ_sample(E_F + eV)
I(V) = ∫₀^eV ρ(ε) T(ε,d) dε
T ∝ exp(−2κd),  κ = √(2mφ)/ħ ≈ 0.51√φ[eV] Å¹

Metal — a roughly constant LDOS near the Fermi level, so dI/dV is flat: there's always a state available to tunnel into or out of, at any bias.
Semiconductor — no states exist inside the band gap, so dI/dV drops to zero over a finite voltage window and only rises once V reaches the conduction- or valence-band edge. The width of that dead zone is the band gap, read directly off the spectrum.
Molecule — discrete molecular orbitals (HOMO below E_F, LUMO above) show up as sharp resonance peaks in dI/dV at the bias where the tip's electrons line up energetically with that orbital.
Temperature smears every feature by thermal broadening (~k_BT): sharp gap edges and orbital peaks blur out as T rises, exactly as in a real cryogenic STM losing resolution when warmed up.
Gap d only rescales the overall current magnitude through the exponential transmission factor — it does not change the spectral shape, since T(ε,d) is treated as roughly energy-independent over this bias range.

Real STS is how physicists measure semiconductor band gaps, map molecular orbitals atom-by-atom, and detect superconducting gaps — all from one number, dI/dV, recorded with the tip motionless.

Metal site Semiconductor site Molecule site STM tip

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.