Coulomb gap in a doped semiconductor near the metal-insulator transition: Tunneling experiment and scaling ansatz

Electron tunneling experiments are used to probe Coulomb correlation effects in the single-particle density of states (DOS) of boron-doped silicon crystals near the critical density n_c of the metal-insulator transition (MIT). At low energies (ε<0.5 meV), a DOS measurement distinguishes between insulating and metallic samples with densities 10 to 15 % on either side of n_c. However, at higher energies (1meV<ε<50 meV) the DOS of both insulators and metals show a common behavior, increasing with energy as ε^m where m is roughly 0.5. The observed characteristics of the DOS can be understood using a classical treatment of Coulomb interactions combined with a phenomenological scaling ansatz to describe the length-scale dependence of the dielectric constant as the MIT is approached from the insulating side.