Crystallographically oriented pores

The morphology of porous layers obtained during the anodization of semiconductors is
one of the main characteristics which must be investigated in details before any other properties are considered.

3.3.1 Crystallographically oriented pores

The morphology of porous layers obtained during the anodization of semiconductors is one of the main characteristics which must be investigated in details before any other properties are considered. The morphology determines the main properties of the resulting porous structure. By morphology of porous structures it is meant the form of pores as individual units and the architecture of porous layers as a whole. The form of pores is characterized by shape, size and direction of growth. The pore morphologies are studied usually by using modern optical and electron microscope techniques.

However, even using advanced electron microscopes it is not easy to determine the exact 3D architecture of porous layers. There are two possibilities to investigate the porous samples, i.e. from the top and in cross section. Note that it is difficult to investigate all kinds of cross section planes. Fortunately, it is relatively easy to obtain cross sections along the cleavage planes. Due to the persisting danger to destroy the porous layer or to introduce artifacts in the morphology, mechanical polishing is not always suited to obtain different cross section planes.

Nucleation and growth of <a href=crystallographically oriented pores on (100)-oriented GaAs" />

Figure 3.10: Nucleation and growth of crystallographically oriented pores in (100)-oriented GaAs, (n=1017 cm-3), anodized at j=4 mA/cm2 in 5 % HCl; a) Plane view. The stretching of the pyramid-like cavity takes place until {111}A planes have been reached. The high aspect ration of the cavity (length/width) is confirming the difference in dissolution rates of {111}B and {111}A planes. After that the pores begin to grow along <111B> directions. b,c) (011) cross section view; d) (01-1) cross section view. The difference between the two cross sections is evident: (011) is mainly exposing the channels of the pores, whereas (01-1) is exposing the triangular shape of the pores.

Typical top and cross section views of pores obtained in (100) n-GaAs are presented in Figure 3.10. As it can be observed, these macropores are totally different from the usual macropores inherent to Si (see Figures 1.5 and 1.7). The macropores obtained in (100) Si are round and grow perpendicular to the surface of (100) samples, i.e. along (100) direction. This difference is a result of the anisotropy of III-V compounds as discussed in section 3.2.1. Namely, the difference in dissolution rate between {111A} and {111B} facets strongly influences the shape and the direction of pore growth. The experiments done for very short anodization times (1-2 seconds) and current densities between 20 and 50 mA/cm2 show that the first step of pore nucleation leads to the formation of pyramid-like pits exposing four planes, which are catalogued to be {111} planes. Such pyramids are observed also at nucleation of pores on (100) Si. However, in III-Vs, from four {111} planes of the pyramid, two are {111}A and the other two are {111}B planes. A schematic overview of such a pyramid is shown in Figure 3.11.

From the dissolution point of view, a pyramid exposing two types of crystallographic planes is not as stable, as it would be in the case if it would expose only {111}A planes. Therefore, as the etching process goes on, the system will try to reach a situation when the exposed planes will be only {111}A planes. Thus, the pyramid will change its shape exploiting the difference in the dissolution rates of the two types of {111} planes. The initial pyramid begins to stretch along the directions marked with X in Figure 3.11b. Simultaneously the B-planes rotate around the Z axis (Figure 3.11b) until an A-type plane is reached, which is more stable. The resulted cavity (or pit) exposes only A-type planes.

Interestingly, the resulted cavity has two sharp tips oriented along <111>B directions (Figure 3.11c). The <111>B directions point from B to A planes along the shortest distance between them, i.e. from the most unstable (B = As or P) to most stable (A = Ga or In) planes (see Figure 3.1).

Due to the small radius of curvature it is expected that at the tips of the cavity the electric field strength is much higher as compared to flat surfaces. Thus, electron-hole pairs are more easily generated at the two tips and consequently the dissolution will be favored there as well. This way, as a result of dissolution the tips of the pits will start to move along <111>B directions - generating the pores. In order to distinguish the pores growing along definite crystallographic directions from other types of pores which will be discussed in the next chapters, let us call them crystallographically oriented pores (CO) or simply crysto pores.

The pores formed according to the simple mechanism proposed above have triangular shapes. The crystallographic planes defining the triangular shape of the pores and simultaneously being the walls of the pores can be calculated relatively easily. Let us consider a [11-1] direction, i.e. a B-type direction. The pores growing along this direction will expose at their tips the following crystallographic planes: (11-1), (1-1-1) and (-1-1-1). The intersection of each of these planes with the plane perpendicular to the growth direction of the pore, i.e. (11-1), will result in a triangle having its sides on the pore walls. The sides of the triangle can be found by taking the cross product between the normal vectors to the planes participating in intersection. Thus, we have to calculate the following cross products a(1,1,-1) x b1(1,-1,-1), a(1,1,-1) x b2(1,-1,1) and a(1,1,-1) x b3(-1,-1,-1). The results are as follows:

Equation 35(33)

Equation 35(34)

Equation 35(35)

A schematic representation of the nucleation of crystallographically oriented pores in  III-V compounds.

Figure 3.11: A schematic representation of the nucleation of crystallographically oriented pores in III-V compounds. The dissolution process starts at defects and proceeds until stable (against dissolution) crystallographic planes are reached, i.e. {111}A. As in the case of Si, in III-V compounds {111} planes are the most stable against chemical attack. a) A pyramid-like pit is formed at the beginning of the etching process, exposing four {111} planes. However, in III-V compounds the four exposed {111} planes are not equivalent from the chemical/electrochemical point of view. The so-called {111}A planes are more stable against dissolution as compared to the so-called {111}B planes; b) The dissolution process continues only along the directions perpendicular to the {111}B planes. This process will continue until all four planes of the cavity will be equally stable, i.e. {111}A. c) This cavity exposes only {111}A planes. The pores start to grow into the substrates along <111>B directions. d) The resulted pore walls are {112} rather than {111}A planes.

Now we know the vectors defining the sides of the triangle and additionally know that the triangle will form the pore walls if it is moved along the [11-1] direction. By taking the cross product between each side of the triangle and the direction of movement, the normal vector to the planes of the pore walls will be obtained:

Equation 36(36)

Equation 37(37)

Equation 38(38)

We are interested only in the direction of the normal vectors, therefore it can be written that n1, n2 and n3 have the coordinates (-1,2,1), (-2,1,-1), (1,1,2) respectively.

It was found that the pore walls of a pore oriented along 11-1 direction are defined by three planes from the {112} set of crystallographic planes. In a similar way the planes of the pore walls for the 1-11 oriented pores can be obtained. SEM pictures showing the triangular shapes of the pores and the corresponding pore walls taken from (100) n-GaAs are presented in Figure 3.10c and d.

The formation of triangular pores introduces a second anisotropy of the electrochemical etching, besides the preferred directions of pore growth along <111>B directions, and establishes {112} planes as particularly stable against dissolution. In the framework of the current burst model, these anisotropy features can be explained assuming that:

  • Direct dissolution is dominant over the dissolution via oxide formation. This is understandable if we take into account that the oxides of III-Vs are very unstable in acidic solutions and also that the experiments were done at relatively low current density, i.e. the rate of oxide formation is very low and can be even more easily dissolved.
  • The passivation has a very high selectivity between different crystallographic planes, i.e. {111} and {112} planes are much easier passivated as compared to {100} or {110} planes.

As mentioned above, by passivation it is meant the neutralization of surface states. With many surface states, the Fermi level of the semiconductor is "pinned" and the bands can not move up or down. Therefore, the major potential drop occurs over the Helmholtz layer of the electrolyte, thus favoring the electrochemical dissolution reaction. On the other hand, with neutralized surface states the space charge region in the semiconductor 'consumes' most of the applied potential and thus the rate of the electrochemical dissolution reaction decreases significantly. This means that a good passivated surface will be more stable against dissolution as compared with a less passivated one.

The angle between the two {111}B directions can be easily calculated. In this case it is enough to take the scalar product of the vectors determining the two {111}B directions. In strict crystallographic notations the two directions are [11-1] and [1-11]. As a result the angle is:

Equation 39(39)

Equation 40(40)

The nucleation cavity and the pores growing from it are easily recognizable also on the SEM pictures presented in Figure 3.11a and b. The measured angle between the two pores in Figure 3.11b is 109o. These results confirm the nucleation model presented in Figure 3.11.

The nucleation model described above makes an additional restriction, namely that the pores can grow only along <111>B directions and not along <111>B ones. This means that for a (100) oriented sample there are only two different directions along which the pores could grow, i.e. (11-1) and (1-11). Therefore, all the pores should grow within, or in other words parallel to {011} planes and not within {01-1} planes. The two planes, {011} and {01-1}, are perpendicular to the (100) surface of the sample and to each other.

Nevertheless, the careful analysis of the SEM micrographs (see e.g. Figure 3.10c) shows a number of triangular voids within the {011} planes (see the dashed arrows). Thus, the experiment shows that pores can grow also within {01-1} plane and perpendicular to the {011} plane, not only vice versa as the model predicts.

The same behavior was observed in (100) n-InP. The pores obtained in InP are shown in Figure 3.12. In this case, the number of triangles observed on the (011) cleavage plane is even higher as compared to GaAs. Thus, the formation of triangular-prism like pores is a common characteristic of GaAs and InP.

3.3.1  Crystallographically oriented pores

Figure 3.12: (011) cross-section SEM picture taken from a (100) oriented n- InP sample, n=1017 cm-3

, anodized at j = 5 mA/cm2 in 5 % HCl. The triangular voids growing perpendicular to the cleavage plane are more numerous as in the case of GaAs. Thus, the branching of downward growing pores is easier than in GaAs.

Two assumptions can explain the experimental results for pores growing within {01-1} planes:

  • These pores grow downwards, i.e. into the substrate, along <111>A directions, however with a lower probability, therefore the number of such triangles is relatively small;
  • The pores grow upwards, i.e. along <111>B direction. Therefore these pores have to start as branches of <111>A pores which grow into the depth of the substrate.

Up to now no experimental results exist which could unambiguously prove that <111>A pores can grow. However, there is clear evidence, obtained with (111) oriented samples, in the favor of the second assumption. (111) oriented samples have an important particularity. One side of the sample is terminated by Ga atoms, whereas the other side is terminated by As atoms. Therefore, the two sides are called (111)A and (111)B respectively. The results for (111) n-GaAs and n-InP oriented samples anodized from both sides, i.e. A and B, are presented in Figure 3.13.

(111)-oriented samples anodized at low current densities

Figure 3.13: (111)-oriented samples anodized at low current densities j=4 mA/cm2 in 5% HCl aqueous electrolyte solution; a) n- GaAs, n=1017 cm-3. The pores grow perpendicular to the (111)B surface; b) (111)B, n- InP, n=1018 cm-3 anodized in the same conditions as (111)B-oriented n- GaAs in figure a). The pores on (111)B-oriented n- InP also grow perpendicularly to the surface of the sample. However, the pores in InP have a lot of branches as compared to GaAs. In InP, the nucleation of pores in HCl solutions is much easier, therefore the branches can also nucleate more easily. c) Beside the pores growing perpendicularly to the surface, e.g. [1-11], they also grow along [11-1] direction, pointing towards the surface of the sample. d,e) A direct comparison between (111)B and (111)A anodized samples. In the first case the pores grow perpendicular to the surface, whereas in the second case they form an angle of 70.5o with the normal to the surface. This is a demonstration that the pores do not grow along <111>A directions.

From the micrographs it is obvious that the pores starting from the (111)B side grow perpendicularly to the surface of the samples (see Figure 3.13a and c for GaAs and Figure 3.13b for InP). On the other hand, from the (111)A surfaces the pores are inclined at an angle of 70.5o relative to the normal of the anodized surface (Figure 3.13e). This is actually the angle between an A-type surface and a B-type direction.

Thus, there is no doubt that on both (100) and (111)-oriented substrates the pores at low current densities grow only along <111>B directions and the triangles observed in Figures 3.12 and 3.13 are also pores growing along <111>B directions, however, growing towards the surface and not into the depth of the substrate.

Pores growing towards the surface of the sample can be observed on both (100) and (111)B oriented samples. Upward growing pores are usually observed near the O-ring of the electrochemical cell, or within regions with a bad pore nucleation. In Figure 3.13c the [1-11] direction is pointing downwards the substrate (perpendicular), whereas the 111» direction is pointing upwards. This means that, as in the case of (100) oriented samples, the upward growing pores nucleate somewhere under the surface of the sample as branches of the main pores and grow upwards until the surface of the sample is reached. In Section 3.3.3 we will show that such upwards growing pores lead to the formation of the so-called domains of crystallographically oriented pores in n-GaAs and n-InP.

Another important feature of the pores growing along <111>B is their intersection. The importance of pore intersection is interesting due to the fact that <111>B oriented pores nucleated from a (100)-oriented surface can form a 3D structure. Figure 3.10a illustrates an example of the intersection of two pores oriented along [1-11] and [11-1] directions (see also the inset). Somewhat surprisingly, the intersection has no influence on the pore shape, size, and the direction of subsequent propagation.

It is worth to to note that the crossing of pores is somehow unexpected because according to some existing models [28, 48], the formation of pores in n-type semiconductors is a self-adjusted process controlled by the distribution of the electric field at the semiconductor-electrolyte interface. The pores may branch and form porous domains but both individual pores and domains should be separated by walls with characteristic dimensions of twice the thickness of the surface depletion layer and cannot intersect [56]. The inability of pores to grow after they meet was explained by Erne et al assuming that the pore wall between the two pores becomes too thin, i.e. smaller than twice the space charge region, and thus cannot longer support a field perpendicular to the surface which is sufficiently high for anodic hole generation (avalanche mechanism), therefore the pore growth must stop [28].

Schematic representation for intersection of <a href=crystallographically oriented pores." />

Figure 3.14: Schematic representation for intersection of crystallographically oriented pores.

However, the experiments show that this is not true for crystallographically oriented pores [51]. The crysto pores will always intersect if the pores will meet each other with their tips (see Figure 3.14, case A), and will not intersect if a tip of a pore will try to penetrate another pore far away from the its tip. This is caused by the fact that the pore tips are very badly passivated and the space charge region at the tips is very small. Consequently, the electric field inside the space charge region is always high enough in order to support dissolution.

On the other hand, if a tip of a pore is running into a pore wall of another pore (Figure 3.14, case B), the intersection will be less probable. A pore wall is very well passivated and has a much larger space charge region which is more difficult to penetrate.

As we will see below, the situation is different for the Current-line Oriented Pores. The current-line oriented pores cannot intersect even if they will meet each other with their tips. This hints to the fact that the passivation of the pore tips in the case of Current-line Oriented Pores is more effective, i.e. have a larger SCR at tips, than in the case of crystallographically oriented pores.

The intersection of crysto pores demonstrates that this may be a suitable tool for the production of 3D micro- and nanostructured III-V compounds, e.g., for photonic crystals applications. Nevertheless, in addition to pore interconnection a three-dimensional photonic pore crystal requires a very high level of uniformity [57]. Since the dissolution is stimulated by defects [58, 59] and/or illumination [60], it is expected that a predefined nucleation and thus a controlled intersection of the pores can be provided by conventional lithography followed by a conventional chemical treatment to generate small pits (defects), or by proper front side illumination of the sample at the beginning of the anodization.

In order to study if the <111>B oriented pores are characteristic to other III-V compounds or they are restricted only to n-GaAs and n-InP, similar experiments have been performed on (100)-oriented n-GaP samples. The results are presented in Figure 3.15. As it can be observed the angle between the pores equals 109o, which is a confirmation of the fact that also in the case of (100)-oriented n-GaP the pores are oriented along <111>B directions.

(100)-oriented n- GaP

Figure 3.15: (100)-oriented n- GaP, n=1017 cm-3, anodized at j=4 mA/cm2 in 5% H2SO4 aqueous electrolyte solution; The angle between the pores equals 109o. Thus, the pores are crystallographically oriented along <111B> directions.

Note that in n-GaP no triangles within the (011) cleavage plane are observed. This is related to the branching probability of downward growing pores. Comparing three materials in this regard, one can conclude that in GaP branching is practically absent, whereas in GaAs and InP is much higher.

Some differences are observed when analyzing the pore sizes. In GaP the transverse sizes of pores are smaller than in n-InP and n-GaAs under the same doping levels and etching conditions. At the doping level of n=1017 cm-3 and low anodic current densities, the transverse size of <111>B oriented pores in GaAs is in the range of 1 Ám, in InP it is in the range of 300 - 500 nm, whereas in GaP the pores are in the range of 100-200 nm.

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