Basic Theories of Semiconductor Electrochemistry - Electrochemistry of Silicon and Its Oxide - page 27

1.4.3. Limiting Current

The limiting current for an n -type semiconductor electrode under a reverse bias
consists of that from majority carrier current in the conduction band and minority car-
riers in the valence band. The relative contribution of the two currents is a function of
temperature. For silicon at room temperature the limiting current in the dark is domi-
nated by the transport of minority carriers. 699
When the limiting current in the dark is determined by the minority carriers, under
a steady-state condition, in the absence of additional generation in the bulk for n -type
semiconductor the hole concentration and hole diffusion current can be given by the
following equations:

where is the diffusion current, the diffusion coefficient of holes, p the hole con-
centration, the hole concentration at equilibrium, and
boundary conditions

the hole lifetime. Using the
at and p = 0at (boundary between the space
charge layer and bulk) and solving Eqs. (1.71) and (1.72), the limiting (or saturation)
hole current is obtained as

where is the diffusion length.

The limiting current described by Eq. (1.73) is the maximum hole current that
can flow from the semiconductor bulk to the space charge region under a steady-state
condition. It depends on the assumption that bulk thermal generation is the only source
of the minority carriers. In many systems there may be other sources of minority carrier
generation, for example, generation in the space charge region and through the surface
607,717,839 In some cases the measured limiting current can be much larger than the
true limiting current due to current multiplication which generates current via injection
of carriers into the band of majority carriers.

states.

1.4.4. Breakdown

Breakdown of a semiconductor electrode occurs when the limiting current
at reverse bias sharply increases with increasing potential. At breakdown the
electrode loses its “insulating” character and becomes “conductive.” Two types of
breakdown may occur in a semiconductor at high field: Zener breakdown and avalanche
breakdown. 45,964
In Zener breakdown, the field may be so high that it exerts sufficient forces on a
covalently bound electron to free it, which creates two carriers, an electron and a hole,
to conduct the current. In this breakdown process, shown in Fig. 1.17a, an electron
makes the transition, or tunnels, from the valence band to the conduction band without
the interaction of any particles. It is essentially a band-to-band tunneling process. In