Helmholtz and Gouy Layers in Electrolyte Solutions

When a semiconductor is brought into contact with an electrolyte solution,
besides the space charge region in the semiconductor, additional charged layers
are present on the electrolyte side: Helmholtz and Gouy Layers.

2.5.2 Helmholtz and Gouy Layers in Electrolyte Solutions

When a semiconductor is brought into contact with an electrolyte solution, besides the space charge region in the semiconductor, additional charged layers are present on the electrolyte side. As in the case of a metal-electrolyte interface, two different charged double layers can be distinguished in the electrolyte as well. They are the Helmholtz and the Gouy layers. In Figure 2.12 all three charged layers are present, including the SCR layer in the semiconductor.

The three double layers at the semiconductor-electrolyte interface

Figure 2.12: The three double layers at the semiconductor-electrolyte interface on the example of aqueous solution of NaCl; Space charge region of a semiconductor dipped into a solution is a function of the doping level of the semiconductor and surface states. The number of surface states, and thus the SCR, will be affected by their interaction with the ions in solution. An additional influence on the SCR will have the external voltage applied on the SEI. The width of the SCR can be in the range of 1000 , and consequently has a relatively small capacity; The Helmholtz double layer (HL) is considered to be formed by two planar sheets of charges. One is due to the ions in solution adsorbed at the surface of the solid (OH- in our case), the other is due to the ions of opposite sign (Na+) attracted by adsorbed ions. The HL can be in the range of 3-5 . Therefore its capacity is higher as compared with the capacity of the SCR; Gouy layer (GL) describes a region in the solution near the electrode within which there is a space charge due to an excess of free ions of one sign. The ions attracted to the outer HL do not suffice to compensate all the charges from the electrode surface, and the residual electric field directed normal to the surface results in a charged Gouy layer.

The Helmholtz layer is in general composed of adsorbed water species (H+ and OH-) at the surface of the semiconductor, followed by a layer of solvated electrolyte ions. The water species form the so-called inner Helmholtz layer, while the solvated ions form the external Helmholtz layer. The two Helmholtz layers can be considered to form a planar capacitor. The charge density within the Helmholtz planes is in the range of NA=1015 ions per square centimeter. This is a very high value as compared with the immobile donor/acceptor ions within the space charge region of the semiconductor (ND=1012 cm-2).

Between the inner and outer Helmholtz layers there is a voltage drop VH which is called the Helmholtz double layer voltage (Figure 2.13). In usual electrolytes, one of the two (H+ or OH-) water species are dominating the inner Helmholtz layer, depending on the pH value of the solution. When the number of adsorbed H+ and OH- species is equal, then the effective charge on the surface is zero. In this case the voltage drop across the Helmholtz layer VH will be zero

2.4.2  Helmholtz and Gouy Layers in Electrolyte Solutions

Figure 2.13: A schematic energy band diagram of a solution in contact with a semiconductor where the most important layers at the semiconductor-electrolyte interface are shown: the Helmholtz layer and the space charge layer.

It is important to mention that the Helmholtz potential can depend on the applied external potential. However, the dependence is negligible when the SCR capacity is much smaller than the capacity of the Helmholtz double layer. This is true when the SCR is a depletion layer (Nadsorbed >> ND). For n-type semiconductors this is the case at moderate positive external voltages applied to the semiconductor. In this case nearly all externally applied potential will drop in the SCR, and will not influence the Helmholtz potential.

On the other hand, VH will not be independent of the externally applied potential when the capacity of the SCR will be comparable with the Helmholtz capacity. This is true when an accumulation or inverted space charge layer in the semiconductor is formed, e.g., at negative or very high positive external voltages. In this case the semiconductor behaves like a metal and nearly all externally applied potential drops across the Helmholtz layer.

Usually the adsorbed charge on the surface of the semiconductor (e.g., OH- in Figure 2.12) cannot be compensated by the attracted ions (e.g., Na+), therefore a region with Na+ as majority is formed outside the Helmholtz layer. This region is called the Gouy layer. The Gouy layer is usually not so important unless very low concentrated electrolytes are used. Thus, the applied potential is considered to be distributed between the SCR and Helmholtz layer, depending on what kind of SCR is formed in the semiconductor.

From the electrochemical point of view, semiconductor electrodes in contact with electrolyte solutions behave very different in comparison to metal ones [19]. The semiconductors can be considered unique materials not only for their capabilities of practical use but also for providing rapid improvement in the basic understanding of the main subject of electrochemistry, i.e. the charge transfer through the electrode-electrolyte interface. This is based on some characteristic properties of semiconductors when they come in contact with electrolytes.

The first feature is that the energies of conduction and valence band at the interface are fixed, i.e. they move only slightly relative to the energy levels of the ions in the electrolyte, since most of the applied potential drops on the semiconductor. This means that if the band edges are favorable for electron transfer to or from a redox couple, the transfer will occur independently of the applied voltage. Certainly this is true only if the surface is clean and no oxides are present, which can hinder the charge transfer.

The second special feature of semiconductor electrodes in redox reactions is the possibility to control the band (valence or conduction) in which the reacting carrier will be transferred. These unique properties of semiconductor electrodes allow one to measure the characteristics of ions in solutions and to define the steps of an electrochemical reaction in more details as compared to metal electrodes.

Thus, the semiconductors allow for a better understanding and control of the processes that play a major role in modern IC technology [23, 24] and also allow the prediction of new features which may be used for fabrication of novel semiconductor structures.

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