In contrast to the Gerischer model for pure chemical etching, for a electrochemical etching, charge exchange between the semiconductor and the electrolyte is taking place at the interface. Electrochemical etching can be divided in two distinct processes:
Electroless etching is usually called electrochemical oxidation without an external potential. In order to perform such kind of etching, strong oxidizing species are required. These species should be able to inject holes into the valence band of the semiconductor. Injection of holes in semiconductors is not so evident, due to the fact that there are no holes in the electrolyte. However, "injection of holes" is another way of saying "electron extraction" from the semiconductor. Hole injection is more commonly used in electrochemical etching of semiconductors, due to the fact that dissolution is always associated with the presence of holes at the interface. Therefore, in order to make it more evident that holes are generated during the extraction of electrons, the process is usually called "hole injection".
Extraction of electrons by the species in electrolyte is called substrate oxidation. The most effective oxidizing species are the ones with high positive standard electrode potential. However, for effective extraction of electrons and thus etching of the semiconductor, the electronic energy distribution function of the oxidizing species in the electrolyte must overlap with the valence band of the semiconductor.
An illustration of this process is presented in Figure 3.3. The redox couple Ce4+/Ce3+ can be strong oxidizing species for GaP, GaAs as well as for InP. On the other hand, Fe3+/Fe2+ is strong oxidizing only for GaAs, whereas all the other considered redox couples can not be used in electroless processes for any of the III-V compounds involved.
Figure 3.3: Position of the energy bands of GaP, GaAs and InP with respect to standard redox potentials of some redox couples, measured relative to a standard calomel electrode in acid solution, pH=0 .
However, hole injection is not enough for etching of semiconductors. The mechanism of semiconductor dissolution has two reactions:
If one of these steps does not take place, the dissolution will not occur. Thus, for stopping electroless dissolution it is enough to suppress the first step and as a result the second one, i.e., actual dissolution, will not take place as well. For example, in spite of the fact that Ce4+/Ce3+ is a strong oxidizing agent for InP, electroless etching of InP in Ce4+/Ce3+ containing solutions does not occur. This can be explained taking into account that the surface of InP is always covered with a native oxide. The native oxide consists mainly of In2O3, which is a wide band gap semiconductor with Eg(In2O3)=3.5 eV. The concentration of phosphorus is reduced in the native oxide of InP due to its high vapor pressure. Assuming that the conduction band of InP crystal and the conduction band of the In2O3 oxide are nearly on the same level, the valence band of In2O3 will be nearly 2 eV lower that the valence band of InP. Consequently, Ce4+/Ce3+ is not a strong oxidizing agent for In2O3 (no holes can be injected) as it is for InP itself. Thus, the native oxide acts as a protective layer for the bulk InP against electroless etching and hinders the hole injection process (first step) into the valence band of InP.
Extraction of electrons from the semiconductor by strong oxidizing species from the electrolyte is not the only approach to increase the amount of holes at the a semiconductor-electrolyte interface. This can be done also by applying an external potential to the semiconductor-electrolyte interface. Two main cases have to be distinguished:
In what follows we will be interested only in anodic processes due to the fact that they promote the dissolution of the substrate. It is clear that formation of holes at the surface induces the emergence of dangling bonds. Similarly to electroless etching, a certain number of dangling bonds will react with nucleophilic species (such as OH-) from the electrolyte before being saturated by the electrons from the semiconductor. If all bonds of an atom from the solid will be replaced by bonds with nucleophilic molecules, a new chemical compound will form (atom of the solid + nucleophilic molecules) at the interface. The new compound has no or less direct chemical connection to the solid. If this compound is soluble in the etching medium, then it can dissolve chemically and thus the surface of the sample will be free and ready for the next interaction with nucleophilic species from the solution. This way, the electrode is called to be etched anodically .
Otherwise, i.e. if the newly formed compound is not soluble in the used solution medium, a thin "oxide" layer is formed on the surface of the electrode, which will hinder the electrochemical attack to proceed. For this reason, the electrolytes suitable for electrochemical etching contain two main components:
The second component is not a problem for III-V compounds, due to the fact that nearly all oxides of III-Vs are easily dissolved in any acidic solution. This is not the case for Si, for example. In this case the oxide formed at the interface, i.e. SiO2, can be dissolved only by hydrofluoric acid (HF). There is no other acid that can dissolve the Si oxide.
Thus, for III-V compounds the first component is much more important. In general, for n-type semiconductors the holes necessary for anodic etching can be generated by avalanche breakdown mechanism, i.e. applying a sufficiently high positive potential to the electrode. Or, alternatively, by illuminating the semiconductor with photons possessing energies larger than the semiconductor electronic band gap.
Front and Back Side Illumination
Two arrangements for hole generation via illumination exist:
With front side illumination, the SEI is illuminated directly by a light source and holes are generated closely to where they are consumed, i.e. at the illuminated surface. Uniform illumination leads to a uniform hole generation, which usually results in a uniform dissolution of the semiconductor (the so-called electropolishing process). Therefore, FSI is typically used only during the nucleation process of pores, whereas during the pore growth process illumination is switched off. Sometimes, however different types of pores may be formed using front side illumination during the pore growth process [41, 42, 43].
Figure 3.4: A schematic overview of an electrochemical setup with front side illumination. The pores cannot grow too deep into the substrate due to the fact that the holes are generated not only at the tips of the pores but overall on the surface.
When the so-called 'backside illumination' is used , the back side of the wafer, i.e. relative to the side where anodization takes place, is illuminated. Consequently the holes are generated far away from the region where the chemical reaction takes place, i.e. at the front side surface. Therefore, the holes have to diffuse from the back to the front side of the wafer in order to participate in the reaction. In this case, pore formation will be favored because the holes coming from the back side will be focused mainly at the tips of the pores, and not between the pores. Thus, the dissolution of the pores walls will be more or less avoided. However, in order to have an effective back side illumination process, the diffusion length of the holes must be high enough to allow at least some of the back side generated holes to reach the SEI. Back side illumination is extensively used for pore formation processes in n-type Si, which has diffusion lengths for holes in the range of some hundreds of micrometers. The effectiveness of BSI in Si is in the range of 30 %. This means that only 30 % of the generated holes at the back side will reach the front side and participate in the dissolution process.
Unfortunately, back side illumination is not applicable for III-V compounds. These compounds have limited diffusion lengths for holes and electrons, i.e. in the range of some tens of nanometers, which is much too small for typical wafers with thicknesses of about 500 µm. On the one hand, the small diffusion length in III-V compounds is due to their direct band gap, on the other hand the quality of III-V compounds is not so high as the quality of Si, thus the defects present in single crystalline III-V compounds can decrease the diffusion length considerably.
As it was already mentioned, applying a positive potential to a semiconductor will cause the positive charge carriers to drift towards the SEI. For n-type samples in the dark, the number of holes (anodic current) reaching the SEI will be small due to the fact that holes in n-type semiconductors are minority carriers. Dark in this regard means that no back or front side illumination is used.
However, the anodic current remains low only in a small range of applied potentials. Depending on the doping and defect density on the surface of the sample, at a certain potential a steep current increase is usually observed. This high anodic current passing through the semiconductor-electrolyte interface is supposed to be related to avalanche processes produced in the space charge region.
At high voltages, avalanche breakdown can be initiated by a small number of electrons (Figure 3.5, process 1) tunneling from the valence to the conduction band. If the field strength (inside the SCR) is strong enough, the tunneled electrons can gain such a high energy that on their path from the SEI towards the bulk, they will generate new electron-hole pairs as a result of multiple collisions with the atoms.
It should be noted, that the oxidation intermediates (R in Figure 3.5) produced by the initial tunneling process (process 1, Figure 3.5) can be regarded as surface states with an energy level above the valence band edge, i.e. within the band gap. These intermediates are highly reactive and can be oxidized again by injecting an electron into the conduction band by thermal excitations (process 3, Figure 3.5) or also by tunneling (process 2, Figure 3.5).
Figure 3.5: The band diagram of the semiconductor-electrolyte interface explaining the breakdown mechanism by applying a positive voltage on the sample. 1) direct electron tunneling from the valence to the conduction band; 2) tunneling of a second electron into the conduction band; 3) exiting an electron into the conduction band as a result of thermal fluctuations.
Usually, a localized avalanche mechanism is assumed to start at surface defects, scratches, dislocations etc. New electron-hole pairs are generated as soon as breakdown starts and thus etching around the defect will occur. The etching process induces new surface defects, e.g. pits, and the avalanche breakdown can occur at lower externally applied potentials as before . Thus the presence of defects influences the avalanche breakdown and consequently the anodic current.
The holes generated by the avalanche mechanism will drift towards the SEI and, as explained earlier, the semiconductor will dissolve. It is generally accepted that in order to dissolve a III-V couple, for example one unit of Ga-As, six holes are necessary according to the following formula:
The holes will generate six incomplete bonds which can be saturated by the species from the electrolyte (Figure 3.5). However, if one assumes that the GaAs substrate does not dissolve in pairs but atom by atom, then eight holes will be required to dissolve a Ga-As unit, i.e. four holes for each atom. This fact was observed experimentally as well . Thus, depending on the etching conditions, six or eight holes are needed for dissolving a Ga-As pair of atoms.
It is important to note that avalanche breakdown in III-Vs is not so evident for electrolytes with neutral pH values. In such solutions the III-V oxides are not so easily dissolved as in acidic electrolytes. In this case any initial avalanche event localized at defects will be immediately followed by the formation of oxide which is slowly or not dissolved at all. Due to the fact that the oxide has a high resistance, a significant part of the applied potential will be lost on the oxide, thus decreasing the avalanche effectiveness in the semiconductor and after some time the generation of holes by avalanche will quench. The oxide formation at such a defect will stop as well until the already formed oxide will be dissolved and a new avalanche process will start again.
Note that in real situations the local avalanche breakdown can also stop after a short period of time in any kind of electrolytes, not only in neutral pH solutions. The electrolyte and/or the semiconductor can hinder the avalanche breakthrough by diffusion losses or nonlinear ohmic effects.
The Field Strength of a Curved Surface
Since the dissolution starts at defects, the immediate result will be the formation of a small crater in the substrate. Because the whole surface of the crater is full of surface defects it can be expected that the dissolution rate will be equal along all directions oriented perpendicularly to the surface of the crater. However, this is not always the case and the dissolution usually takes place only at the sharp tips of the crater. Two reasons for this behavior can be identified:
Crystallographic features have been discussed already in subchapter 3.2.1 - Anisotropy of III-V Compounds. In what follows we will discuss how the curvature of the surface influences the electrical field distribution within the space charge region, namely increasing it locally. An increased electric field leads to an increased number of generated holes, and thus to higher dissolution rates at curved surfaces, providing that enough reducing species are present in the electrolyte and the reaction products are easily dissolved and transported away from the surfaces.
For an interface with a spherical shape (Figure 3.6) the Poisson equation can be written as follows:
where ε0 is the permittivity of vacuum, ε is the dielectric constant of the substrate, ξ(r) is the electric field, ρ(r) is the charge density in the space charge layer equal to -qNd for r0 < r < rd , Nd is the ionized donor density, q is the elementary electric charge, r0 is the radius of the curvature of the interface, rd-r0 is the width of the space charge layer. Using the boundary conditions and the depletion approximation , the relation between the potential, the electric field, the width of the space charge layer, and the radius of curvature can be obtained as follows :
Figure 3.6: a) A schematic SEI of spherical shape with r0 representing the radius of curvature and xd the width of the space charge region ; b) Dependence of the electric field strength on the radius of curvature. The plot was done for x=0, a doping level of N=1018 cm-3, a SCR width of 50 nm and an ε=12. For example the breakdown field for InP is of about 5×107 V/m. Thus, for a radius of curvature of 60 nm the electric filed is too small for breakdown. On the other hand, for a radius of curvature smaller than 30 nm the electric field approaches the critical breakdown voltage.
assuming r=x+r0. The plot of the electrical field strength, as a function of the radius of curvature, according to Eq. 30, is presented in Figure 3.6b. As one can see, the field strength of a curved surface increases considerably when the radius of the curvature is close to, or smaller than the width of the space charge layer of a flat surface. This means that the electric field at sharp tips of the crater must be strongly increased as compared to the walls of the crater where the radius of curvature is nearly infinite (see Figure 3.7).
Figure 3.7: A schematic representation of a pore and the field distribution at tip and pore walls.