Module 2 · after Hemmi et al., 2025

Semiconductor characterization

The calculations of the “Results” section of the MgAl₂O₄ paper, applied to your own measurements: optical gap, flat band, point of zero charge, band positions and impedance.

The “Example” datasets are generated to reproduce the published results (gap 2.88 eV, flat band 0.53 V…): the raw data of the papers is not published. Only the point of zero charge uses points read from figure 3 (approximate).

Spectrum (λ in nm, then value) The second column is Transition

Linear range from (eV) to (eV)

hν = 1240/λ ; F(R) = (1 − R)²/(2R). Eg is the intersection of the fitted line with the hν axis (eq. 2 of the paper).

Measurements (E in V, then value) The second column is

Linear range from (V) to (V)

Relative permittivity εAdapt to the material Reference

1/C² = 2/(ε·ε₀·e·N_D)·(E − E_fb) (eq. 5 of the 2021 paper). Positive slope: n-type; negative: p-type.

Initial pH, then final pH

pH drift method (KNO₃ 10⁻² M, 48 h). pH_PZC is the intersection of the curve pH_final = f(pH_initial) with the bisector. Below it, the surface is positively charged.

Starting point

Gap Eg (eV) E_CB (V vs NHE)

E_VB = E_CB + Eg (electrochemical scale). For an n-type semiconductor, E_CB is often taken close to E_fb (converted to NHE): to be confirmed for your method.

Reference redox couples (V vs NHE, pH 0 — editable)

O₂/O₂•⁻ •OH/H₂O

Z′ and −Z″ (Ω·cm²), one line per frequency Semicircle points: from no. to no.

Circle fitted on the chosen semicircle: R_s = high-frequency intercept, R = diameter on the real axis. A centre below the axis indicates a constant phase element (CPE), as in the paper.