Subsurface space charge and surface charge in AgBr microspheres

In contrast to previous studies on AgBr thin films, results are presented here on the effects of ionic space-charge layers in AgBr microcrystals. The method of calculating the space-charge potential is discussed for spheres 0.02 to 2.0 μm in diameter. Using spherical polar coordinates, minimization of the total free energy, and solution of Poisson's equation yield the potential and defect concentration profiles. The potential difference between the surface and the interior of the sphere, i.e., the force which repels electrons away from and drives holes toward the surface, increases with level of divalent-cation impurity and with increasing particle size. From the potential profile within a particle, the total concentration (defects/cm 3 ) of excess positive charge within the sphere and the balancing negative surface charge (defects/cm 2 ) can be calculated. The total concentration of interstitials and impurities is greater than the vacancy concentration. The concentration of interstitials decreases with increasing particle size, in agreement with the measured ionic conductivity. The surface charge increases with dopant level for any particular particle size and increases with size in the presence of dopants.