2.5.1 Space Charge Layer in Semiconductors

2.5.1 Space Charge Layer in Semiconductors

In the following we will have a look in more detail on the semiconductor-electrolyte junction (SEJ), or in other words semiconductor-electrolyte interface (SEI).The behaviour of this interface is of paramount importance for all electrochemical processes.

A schematic representation of the energy diagram of the semiconductor-electrolyte junction.

Figure 2.10: A schematic representation of the energy diagram of the semiconductor-electrolyte junction.

Let us discuss first the contact between a non-degenerated n-type semiconductor and an electrolyte. Assuming that the redox level, Eredox, of the electrolyte solution is lower than the Fermi energy EF in the semiconductor, e.g., the electrolyte contains strong oxidizing species, it is obvious that the electrons will pass across the SEI from the semiconductor into solution until the equilibrium will be reached (EF=Eredox). The electron transfer from the semiconductor into solution will cause the bands (valence and conduction) to move relatively to the Fermi level, i.e. to bend upwards. This situation is presented in Figure 2.10. Note that the Fermi level still remains within the band gap of the semiconductor.

The region of the semiconductor in the vicinity of the SEI contains less electrons than the bulk of the semiconductor. This depleted region, similarly to Schottky barrier and p-n junction, is called ‘space charge region’ (SCR). However, this is only one example of space charge regions. In the general case, a SCR can consist of charged immobile donors or acceptors, or by mobile electrons or holes from the conduction and valence bands respectively. Consequently, three main types of SCR layers for a n-type semiconductor can be distinguished:

  • Depletion layer – immobile and uncompensated dopant ions;
  • Accumulation layer – mobile electrons;
  • Inversion layer – mobile holes.

The three kinds of space charge layers are presented in Figure 2.11. From the electrochemical point of view, they are important when an external voltage is applied to the semiconductor-electrolyte interface. Namely, they determine if the voltage drops entirely on the semiconductor, in the electrolyte, or it is distributed along both.

Types of charged layers in n-type semiconductors.

Figure 2.11: Types of charged layers in n-type semiconductors. a) Depletion layer. b) Inversion layer. c) Accumulation layer.

The main parameters of a SCR layer are the following:

  • The distribution of the electric field E inside SCR. The so-called breakdown mechanism responsible for the hole generation during the electrochemical etching of III-V semiconductors is mainly determined by the electric field E in the SCR;
  • The width W of the SCR. During pore formation 2W is supposed to be the minimum width of the pore walls.

Both these parameters are decisive during pore formation in semiconductors. If a depletion region is considered, then the charge density in the SCR layer is equal to q x Nd, where Nd is the doping concentration in the semiconductor. Therefore, the electrical field inside this region is determined from the Gauss equation

Equation 23(23)

where ε is the dielectric permitivity of the semiconductor, E is the electric field, and q is the magnitude of the elementary charge.

The width of the space-charge region (W) is related to the potential drop j across the interface according to the following formula:

Equation 24(24)

It is not difficult to see that the Eq. 24 for a semiconductor-electrolyte interface is similar to Eq. 6 for a Schottky contact. Both equations say that by decreasing the donor concentration the width of the SCR will increase. Anticipating the results, one can say that this is why the distance between pores in low doped samples is bigger than in high doped ones.



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