Porous Silicon - Electrochemistry of Silicon and Its Oxide - page 413

has also been adopted by many groups to explain the many phenomena observed on
PS such as current conduction and luminescence. 75,624,1156,1160
The quantum confinement model reasonably explains the formation of crystal-
lites of a few nanometers in size. However, it does not provide an explanation of what
determines pore diameter. If quantum confinement, which is not related to doping type
and concentration, were to occur, it should also occur on all types of silicon substrates.
However, quantum size PS is not found in many types of PS, e.g., the PS formed on
n -Si in the dark.
Surface Curvature Model. Based on the observation that the bottoms of pores
are always curved, Zhang 8 in the early 1990s proposed a surface curvature model for
the formation of PS on n -Si. It was postulated that the rate of reactions can be greatly
increased on a curved surface because the surface curvature on the order of the width
of the space charge layer or smaller reduces the effective width of the space charge
layer and therefore greatly increases the interface tunneling current. Furthermore,
Zhang recognized the variation of radius of curvature from the tip to the wall and
pointed out its importance in determining the distributions of reactions (Si dissolution
and oxide formation) and current density on the pore bottom. The dimension of pores
and pore walls are determined by these distributions.
The model was considered to also be applicable for the PS formed on other types
of silicon substrates. As a generalization, Zhang stated that it is the sensitivity of the
semiconductor interface reactions to the curvature of the interface that enhances the
preferential dissolution and leads to the formation of pores. For p -Si and heavily doped
n -Si which have much thinner space charge layers than does n -Si, the radius of curva-
ture must be small to affect the width of the space charge layer and, as a result, much