Self-organized single-crystalline porous structures

The uniformity of porous semiconductor structure is a must if these
structures are intended to be used as photonic band gap materials.

3.5.2 Self-organized single-crystalline porous structures

The uniformity of porous semiconductor structure is "a must" if these structures are intended to be used as photonic band gap materials. The standard way of obtaining highly ordered porous structures in semiconductors is by means of lithography, i.e. by defining a pre-patterned surface and then anodizing it. Pre-patterning in this context means that the wafer is covered bz a thin layer of photoresist and by a suitable mask a periodic arrays of small windows are developed in the resist, which will serve as nucleation points for the pores in a subsequent anodization step. This method is extensively used in Si for obtaining uniform 2D porous structures [64].

However, there are particular cases when uniform porous structures can be obtained without prestructuring, e.g. by self-organization. Taking into account that pore ordering in a self-organization process is strongly dependent on the anodization conditions, for the purpose of optimization it is important to study the degree of ordering in a self-arranged porous structure.

It is well known that diffraction patterns (DP), e.g. X-ray, TEM etc., provide a way for studying the structure and uniformity of atomic crystals. Investigating the DP of different materials it is possible to distinguish between perfect, amorphous, textured etc. structures. In fact, a diffraction patterns is nothing else but the image of a crystal in its reciprocal space, i.e. the Direct Fourier Transform (DFT) of the crystal. Using the Inverse Fourier Transform (IFT) it is possible to reconstruct the image of the crystal from its DP.

It is not always necessary, however, to use hardware methods like TEM or X-ray in order to generate DPs. DPs of porous structures can be generated numerically, for example by taking DFTs from top-view SEM images. Thus, a DP can be obtained by calculating the direct 2D Fourier Transform from the pixel-arrays of SEM pictures. The way how the DP will look like, i.e. rings, spots etc., will characterize self-organized arrangement of pores. More details about the 2D Fourier Transform are discussed in Appendix 3.

Long Range Ordering of Pores Obtained by Self Organization in InP

As already emphasized several times, the most effective mechanism for hole generation in III-V compounds is junction breakdown or 'break through'. Two types of break through pores have been reported in n-InP up to now: crystallographically oriented pores and Current-line Oriented Pores (see Chapter 3.2). In order to understand the self-organization mechanism of pores on large areas, it is noteworthy to mention once again the etching conditions for the two types of pores.

crystallographically oriented pores are obtained at low voltage/current densities. Like most break through pores, they possess a very high level of anisotropy. As indicated by the name, crystallographically oriented pores grow along a definite crystallographic direction, i.e.<111>B. They have triangular-prism like shapes exposing three {112} planes [51, 62].

Hexagonal arrangement of Current-line Oriented Pores after the nucleation layer has been removed.

Figure 3.32: Hexagonal arrangement of Current-line Oriented Pores after the nucleation layer has been removed. a) Potentiostatic control. The inset shows a nearly perfect pore domain. b) galvanostatic control. The difference in pore diameters in a and b is caused by the doping level: n=1018 cm-3 and n=1016 cm-3 respectively. Please note in b the modulation of the diameters of the pores (galvanostatic control).

The second type of breakthrough pores, the Current-line Oriented Pores, grow only at relatively high current densities and do not have preferential crystallographic directions of growth, i.e. they grow always perpendicularly to the equipotential lines of the electric field inside the sample, independent of sample orientation. Depending on the etching conditions, sometimes they can also exhibit slightly triangular-prism like shapes (see Figure 3.34b), but normally the shape tends to be round.

The Current-line Oriented Pores possess a lot of interesting properties and sometimes not without the help of crysto pores. An important feature of the curro pores is that they self-arrange locally in a hexagonal closed packed lattice. Local self arrangement means that domains of nearly perfectly arranged pores can easily be distinguished. Such kind of domains with a hexagonal arrangement of pores are presented in Figure 3.32a, where the inset shows a higher magnification of a nearly perfect domain.

It is to be noted that the current-line oriented pores obtained under high constant current densities (galvanostatic experiments) differ from those obtained under potentiostatic conditions. As it has already mentioned in Chapter 3.4, the pores obtained galvanostatically show strongly modulated diameters and external voltage oscillations [51]. On the other hand, potentiostatically grown pores, at optimized etching conditions, expose smooth pore walls and no sudden change in pore diameters (Figure 3.33a) or externally measured current oscillations (Figure 3.33b) are observed. As one can see from Figure 3.33b, the current in a potentiostatic experiment decreases exponentially in time in a nearly perfect way. In spite of these differences, in potentiostatic as well as in galvanostatic experiments, the pores self-arrange locally in a hexagonal lattice (see Figure 3.32a and b).

However, the curro pores do not start growing in a hexagonal lattice immediately on the surface of the sample. The hexagonal arrangement will be always preceded (at least in HCl aqueous electrolytes) by a nucleation layer (NL). The NL layer is also porous and is made of crysto pores. A SEM micrograph illustrating the NL layer followed by a stable curro pore growth layer is presented in Figure 3.33a. The width of the nucleation layer is normally up to several microns and depends on the electrolyte concentration and voltage/current applied to the sample. It increases slightly by increasing the electrolyte concentration and by decreasing the voltage/current.

The nucleation layer

Figure 3.33: a) The nucleation layer, i.e. crystallographically oriented pores, is followed by the layer of stable pore growth, i.e. Current-line Oriented Pores; b) In a potentiostatic experiment the externally measured current decreases exponentially and no oscillations are observed. The exponential current decrease is due to diffusion limitations.

In order to study the Current-line Oriented Pores and their arrangement into the depth of the sample, the NL should be removed. The NL layer can be removed chemically or mechanically. For example, in Figure 3.32 the NL was removed mechanically. In this example the domains of Current-line Oriented Pores are totally uncorelated i.e. each domain is more or less arbitrarily oriented with respect to its neighbors. Thus, one can assume that the entire porous array forms a 2D "polycrystalline"-porous structure. As was already mentioned, a suitable method for proving this assumption is the 2D DFT using Fast Fourier Transform (FFT) analysis.

For FFT analysis a large area of the porous array should be chosen. Figure 3.34a presents a SEM picture taken immediately from the surface of the anodized sample, whereas the inset shows the frequency domain pattern, i.e. the diffraction pattern, generated by 2D FFT analysis. It is obvious that the frequency domain pattern is a highly diffuse spot, which undoubtedly is a characteristic of a highly random arrangement of nucleated pores.

However, the DP changes if the FFT is taken from the top of a current-line oriented layer (see for example Figure 3.34b) after the nucleation layer has been removed. In this case, the frequency domain pattern is a diffuse ring. Interestingly, the ring exposes slight variations in intensity along its perimeter. Namely, six regions with a slightly higher intensity can be distinguished. This means that there are six directions along which the pores are arranged more preferentially, i.e. the pores tend to expose a long-range six fold symmetry.

3.5.1  Self-organized single-crystalline porous structures

Figure 3.34: (100) n-InP, n=1018 cm-3 anodized in 5% HCl at different voltages. SEM picture taken from: a) the surface of the anodized sample and the corresponding 2D FFT image (inset). The FFT image is a highly diffuse spot, i.e. the nucleated pores are randomly distributed; b) sample anodized at U = 5 V, i.e. lower than the optimized voltage. The corresponding 2D FFT image which is composed of a diffuse ring exposing six slightly higher in intensity spots, i.e. a tendency to a long-range six fold symmetry; c) sample anodized at an optimized voltage of U = 7 V. The six fold symmetry is easily obserbed in the FFT image (inset), i.e. instead of diffuse rings this time spots along definite directions are present. This is a clear indication that the structure has a long range order, i.e. is a single crystalline structure but with a high density of defects; d) sample anodized at U = 8 V, i.e. above the optimized voltage U = 7 V. The long range order is destroyed again, i.e. the FFT image is a diffuse ring which is a characteristic of amorphous structures.

Thus, from Figure 3.34b follows that the Current-line Oriented Pores have a significant improvement in their arrangement as compared to crystallographically oriented pores nucleated immediately on the surface of the sample. The self-arrangement of the Current-line Oriented Pores can be further improved by optimizing the etching conditions. Figure 3.34c shows a top view SEM picture taken from a sample anodized under optimized conditions. The FFT pattern, taken from a larger area of the presented picture, shows evident spots exhibiting clearly a six-fold symmetry of a closed packed structure. The presence of spots instead of rings in the frequency domain pattern undoubtedly proves the long-range order, or in other words proves that the structure tends to be "single crystalline". In spite of the fact that the monocrystalline porous structure is still not perfect, i.e. it possesses a large number of defects which make the spots to be more or less diffuse, this is the first self-arranged long-range ordered 2D porous structure ever reported in the literature (see Figure 3.34 d and Figure 3.35 for larger views).

The anodization conditions must be carefully optimized in order to obtain the long-range order. The optimized conditions mainly depend on the electrolyte concentration, substrate doping level and the anodization voltage. For example, for (100) InP, n=1018 cm-3 and 5 % HCl aqueous electrolytes the long-range order is obtained at approximately U=6 V. Amazingly, at anodization voltages higher that the optimum the long-range order disappears. More than that, the intensity of the ring in the DP is uniformly distributed along its perimeter. Thus, at voltages higher than the optimum the tendency to long-range order disappears completely.

Large area a) top and b) cross section view taken from a self-arranged monocrystalline  porous array

Figure 3.35: Large area a) top and b) cross section view taken from a self-arranged single crystalline porous array.

The arrangement of the pores in a long range order is a self organized process, therefore there should be internal 'forces' which guide the system to this state. In order to find a hint concerning the internal 'forces' responsible for the long-range order, it is important to compare in more details the samples with and without long-range ordering of pores. Figure 3.36 shows SEM pictures in cross section taken from samples with long range order (Figure 3.36a) and without (Figure 3.36b). The most evident difference between Figure 3.36a and b is that in Figure 3.36a the nucleation layer is quite thick, whereas in Figure 3.36b the nucleation layer is practically absent. Thus, one of the 'forces' leading to a monocrystalline self-arrangement of pores could be the nucleation layer. Indeed, the nucleation layer can have a strong influence on the whole porous structure if it is taken into account that the nucleation layer consists of crystallographically oriented pores, i.e. the crystallographic nature of the NL can determine somehow the global ordering of curro pores.

3.5.1  Self-organized single-crystalline porous structures

Figure 3.36: (100) oriented n- InP, n=1018 cm-3, 5% HCl solutions a) at U = 6V the nucleation layer is prominent; b) at U = 9V no significant nucleation layer is present;

A Model for Long Range Order

As mentioned in Chapter 3.2, crystallographically oriented pores have a very high tendency to branch [62, 56]. They can branch and grow upwards towards the surface of the sample, forming the so-called domains of crystallographically oriented pores. Such kinds of domains were discussed for GaAs in Chapter 3.2 and were observed in InP as well in a mixture of HCl and HF solution. An example of crysto pore domains obtained in InP is presented in Figure 3.37. The similarity between the crysto domains shown for (100) InP in Figure 3.37 and those shown for (100) GaAs in Figure 3.21 is evident.

It should be noted that the surface of InP samples anodized in 5 % HCl (without HF) aqueous electrolyte is not covered by domains like that presented in Figure 3.37. However, if such domains exist in a solution of HCl+HF, it is hard to believe that the absence of HF could suppress totally the formation of domains. It is more probable that HF only 'helps' the upward growing branches to reach the surface of the sample, i.e. increases the number of upward growing branches and thus the probability that more of them will succeed to reach the surface.

The number of upward growing branches can be increased by increasing the degree of passivation of the pore tips, thus forcing the system to use all the possibilities to carry the current, i.e. generating more upward growing pores. Thus, it is highly probable that crysto domains can form also in HCl aqueous solutions without HF, but the upward growing pores of a domain do not succeed to reach the surface of the sample. It can be assumed that the nucleation layer is composed of small crysto domains, aligned along certain crystallographic planes, i.e. {011} planes. A schematic representation of a domain for (100) and (111) oriented samples, is presented in Figure 3.38.

Consequently, the Current-line Oriented Pores, which grow as a prolongation of the crystallographically oriented pores, will also form a domain with the orientation determined by the a priori developed crysto domain. It is clear that the size of the crysto and thus also of the curro domain will depend on the thickness of the nucleation layer. The thicker the nucleation layer the larger will be the domains and vice versa.

3.5.1  Self-organized single-crystalline porous structures

Figure 3.37: (100) oriented n- InP, n=10e18 cm-3, 5% HCl+HF solutions a) a high magnification of a crysto domain in InP; b) An overview of crysto domains in InP;

Thus, due to the high number of nucleation points at the surface of the sample a corresponding number of crysto domains and thus curro domains will be formed. All these domains will have one and the same orientation determined by the crystallographic orientation of the sample.

The 2D long-range ordering of Current-line Oriented Pores in InP results from an interplay of two independent phenomena:

  • The overlap of the space charge regions of neighboring pores induces a next neighbor repulsing force, leading to a medium range ordering and locally closed packed pore array;
  • The nucleation layer of crystallographically oriented pores induces a global orientation for all domains of Current-line Oriented Pores.

Schematic representation of the nucleation layer in (100) and (111) oriented samples.

Figure 3.38: Schematic representation of the nucleation layer in (100) and (111) oriented samples. a) (100) samples. From one nucleus two pores begin to grow. These primary pores begin to branch. The branches can be oriented into the substrate or towards the surface of the sample. The entire set of branches form a domain with one and the same nucleation ancestor on the surface. These crysto pores are aligned within {011} planes. Consequently, the curro pores which nucleate at the tips of the crysto pores from one and the same crysto domain will also form a domain with the same characteristics, i.e. the curro pores will be situated within {011} planes. Thereby, all curro pore domains will be oriented along <011> directions leading to a long-range order; b) The same schematic representation for (111)B oriented samples. In this case only one primary pore is found (perpendicular to the surface). Therefore, the domains are smaller if compared with (100) samples. As a result the long-range ordering will be more difficult to achieve.

If one of these two factors is not sufficiently strong, then no long-range order can be obtained. For example, if the anodization voltage is too low, the space charge region of the pores will be also smaller, i.e. the pores will not interact sufficiently strong with each other in order generate a local closed packed structure. This insufficient interaction at lower voltages is proved also by the triangular shapes of the curro pores (see Figure 3.34b). On the other hand, if the voltage is too high the thickness of the nucleation layer decreases, i.e. the domain size decreases, and as a result the disorder in the structure increases (see Figure 3.34d). This is actually what was observed experimentally: there is an optimum voltage assuring long-range ordering of pores.

Inducing Periodicity in the Z Direction

The Current-line Oriented Pores can form a two dimensional (X, Y directions) periodical structure, however the Z direction is still non-periodic. The self-induced diameter and voltage oscillations observed in InP (see Figure 3.40b and c) as well as the sharp transition from Current-line Oriented Pores to crystallographically oriented pores can be used to induce periodicity in the third dimension as well (see Figure 3.40a).

Cross-sectional  SEM micrograph of a  porous n- InP Bragg-like structure with spatially modulated porosity.

Figure 3.39: Cross-sectional SEM micrograph of a porous n- InP Bragg-like structure with spatially modulated porosity. The current was periodically switched from I=600 mA/cm2 (duration t1=0.1 min) to I=0 mA/cm2 (duration t2=0.5 min).

In order to change the degree of porosity as a function of depth and thus to make the structure periodic in the Z direction, the anodic etching was periodically switched on and off, e.g. from I=600 mA/cm2 (duration t1=0.1 min) to I=0 mA/cm2 (duration t2=0.5 min) and vice-versa. It is obvious that etching occurs only during the first 0.1 min of the cycle, while in the last 0.5 min no dissolution is possible since no current is flowing.

Current line oriented pores in a (100) sample in the upper part, and crystallographically oriented pores

Figure 3.40: a) Current line oriented pores in a (100) sample in the upper part, and crystallographically oriented pores branched in two <111>B directions in the lower part; b) Self- induced synchronized diameter oscillations of Current-line Oriented Pores in a InP sample; c) Example of well developed voltage oscillations always observed together with synchronized diameter oscillations.

The general finding is that an interruption of the etching process for 0.5 min is enough for the system 'to loose its memory', i.e. to start the pore etching with a new nucleation layer. When the current is switched on again, a new nucleation phase is required, i.e. a new nucleation layer with crysto pores emerges before the formation of curro pores. Note that this fact is not understandable in any static pore formation model where the equilibrium structure, once reached, should be maintained under all conditions. This observation, however, fits into the general scheme of the current burst model, because in the current-free phase the pore tips become passivated and the self-ordering process of current bursts has to start again.

Thus, periodically pulsing, the current leads to concomitant switches from crysto pores to curro pores and vice versa. The result is a stack of porous layers with different porosities and consequently different effective refractive indexes. Such structures are called Bragg-like structures (Figure 3.39).

Anticipating the events, at this point it is important to mention that the difference in porosity between the layers of the structure is also confirmed by cathodoluminescence (CL) measurements (see Chapter 4, Figure 4.10). SEM and CL images have been taken from the same cleavage of a Bragg-like structure. As can be seen from Figure 4.10b, the CL proves to be spatially modulated. The CL intensity from nucleation layers is higher than that from the curro pores layers. Taking into account that the CL intensity from bulk InP is higher than that from a porous layer, it can be concluded that a porous layer with a higher CL has a lower porosity (more similar to the bulk) than the one with a lower CL intensity. Different porosities means also different refractive indices. Porous layers with crysto pores have higher effective refractive indices than those formed by curro pores.

Voltage oscillations obtained during the anodization

Figure 3.41: Voltage oscillations obtained during the anodization of (100) n- InP, n=1018 cm-3, in 5% HCl at different external modulation frequencies of the current density. The current density was modulated around j=100 mA/cm2 with an amplitude of 5 mA/cm2. The resulting voltage oscillations are as follows: a) without external modulations of the current (f = 0 Hz); b) obtained at f = 250 mHz; c) obtained at f = 550 mHz; d) obtained at f = 750 mHz.

A second option for inducing a periodicity in the Z direction is to modulate periodically the pore diameters. The modulation of pore diameters can be done by modulating external current. This method was extensively investigated in n-Si. It was found that is quite difficult to modulated the pore diameters, mainly because the system often reacts to the external changes in a strongly nonlinear fashion. In other words, the profile is not necessarily found in the variation of the pore diameter d with depth Z .

Induced pore diameter modulaiton

Figure 3.42: (100) n- InP, n=1018 cm-3, in 5% HCl, j=100 mA/cm2 with an amplitude of 5 mA/cm2, f = 550 mHz. a) The pore diameter modulation is not uniform, i.e. the distance between two modulations decreases as the pores grow into the substrate; b) A higher magnification taken from a.

This is not surprising, considering that in all materials investigated so far it has been found that pore growing systems have intrinsic time-constants. A measure for the internal time-constant of the InP/HCl electrolyte system is the oscillation frequency of the self-induced voltage oscillations observed in the galvanostatic regime.

How the self-induced oscillations interact with the external changes is shown in Figure 3.41, where the behaviour of voltage oscillations at different externally induced current frequencies is shown. As one can see, the amplitude of oscillations is maximal at approximately 550 mHz (Figure 3.41c), whereas at lower or higher external frequencies (Figure 3.41b and d) the amplitude decreases compared with that in Figure 3.41a where no induced oscillations were applied. Thus, the frequency of 550 mHz can be considered to be a resonant frequency and it is directly related to an intrinsic time constant of our system. It should be noted, however, that due to diffusion effects the intrinsic constant of the system changes in time while the pores grow into the substrate, i.e. internal oscillation frequency decreases (see section 3.4.2). As a result, by modulating externally the current with a constant frequency will result in a nonuniformly modulated structure in the Z direction, see Figure 3.42.

However, by adjusting continuously the external frequency as the pores grow into the substrate it was possible to obtain for the first time a completely self-organized 2D crystal with uniformly modulated pores in the Z direction (2.5D) as shown in Figure 3.43.

A collage of the first 2.5D single pore crystal obtained by self-organization.

Figure 3.43: A collage of the first 2.5D single pore crystal obtained by self-organization.

Considering that the pores are arranged as a single (but defective) crystal in the XY-plane with a lattice constant between 50 nm and 1 mm, this is the most cost-effective approach to a large 2D photonic pore crystal far below 1 mm range obtained so far. With proper external stabilization of the pore arrangement and tight control of the growth conditions including external current modulations, perfect 2.5D crystals with a periodicity in the Z direction appear to be possible.

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