The distribution of potential in the space charge region of a semiconductor results in a change in the electron energy levels with distance from the interface. This is usually described as 'bending of the energy bands'. Thus the bands are bent, upwards if σ > 0 and downwards if σ < 0, where σ is the free charge density. When σ = 0 the condition of flat bands is met, provided no surface states are present.
Source:
PAC, 1986, 58, 437. 'Interphases in systems of conducting phases (Recommendations 1985)' on page 443 (https://doi.org/10.1351/pac198658030437)