N-type macropores in Si

N-type macropores are stright, deep and smooth pores
growing along definite crystallographic directions.

1.2.1 N-type macropores in Si

The basic principles of macropore etching in n-type materials were for the first time described by Föll and Lehmann [7]. They proposed and used the so called backside illumination (BSI). A schematic overview of the BSI principle is presented in Figure 1.6.

Illumination of a semiconductor with photons having energies higher than the electronic band gap of that semiconductor will generate electron-hole pairs. In contrast to the more common front side illumination (FSI), at BSI the holes are generated at the back side of the wafer and not at the front side. This way the holes are free to diffuse through the whole wafer (up to 700 ?m) and eventually being focused preferentially, by the space charge region at the Si/HF interface, at the tips of the pores. If the distance between the pores is equal to the double width of the (surface charge region) SCR, then it will be quite difficult for the holes to penetrate between the pores and this way only a very small number of holes will reach the pore walls.

As a result, preferential dissolution will take place at pore tips (more holes), whereas the pore walls will be more or less protected against dissolution. By this mechanism, called also the "space charge region model", BSI promotes the formation of macropores in n-type substrates. The unbelievable uniformity and "quality" of the electrochemical etched macropores obtained by means of BSI is presented in Figure 1.5. This becomes even more amazing when realizing that one pore has a diameter of 1-2 µm, which is 50 times smaller than a hair.

 Macropores obtained by the Halle group, Germany, in n-types Si by back side illumination.

Figure 1.5: Macropores obtained by the Halle group, Germany, in n-types Si by back side illumination.

The SCR model, however, is valid only for macropore formation in n-type Si and does not work for p-type Si. For p-type Si it predicts the impossibility of macropore formation. The argument is that holes are the majority carriers in p-type substrates and are certainly omnipresent, which consequently will lead to a uniform dissolution even with back side illumination. However, soon after the discovery of macropores in n-Si, macropores have been obtained in p-Si as well. Thus, the SCR model has a limited prediction power and can not be used as a general model for macropore formation in both n- and p-type substrates.

Principles of space charge region model proposed by Föll.

Figure 1.6: Principles of space charge region model proposed by Föll. The holes generated at the back side of the wafer are diffusing towards the front side and are consumed mainly at the pore tips, making possible the formation of macropores in n-type Si.

The most important parameters defining the morphology of macropores are the diameters of the pores, the distance between pores, i.e. pore wall's thickness, and direction of pore growth. Lehmann proposed a simple formula which is relating the diameter of macropores to the current density applied to the sample [8]:

Equation 1(1)

where a is the distance from one pore center to neighbouring pore center, the so called pitch; d is the diameter of the resulted pores; j is the current density applied on the sample and jPSL is the so called PSL current density observed on Si/HF IV curves, see Figure 1.3.

As a mathematical relation Equation 1 allows any ratio between d and a. However, the experiments show that stable pore growth is only possible if d and a have the same order of magnitude as the width of the space charge region formed in the semiconductor at the Si/HF interface. For n-type samples the SCR-model predicted the pore walls thickness dwall to be equal to the double width of the space charge region dSCR.

Equation 2(2)

Equations 1 and 2 give us only a hint how the morphology of the porous structure will look like. However, in order to obtain very smooth pores with large aspect ratios, additional etching parameters have to be correctly adjusted. This includes the HF concentration, the voltage, the temperature, the flow of the electrolyte etc. Changing one parameter without properly readjusting the others will result in the formation of less perfect pores.

It is interesting to note that most of the pore formation models proposed up to now say nothing about the pore directions of growth. According to the SCR model the pores should grow mainly perpendicular to the surface of the samples. Actually this is not the case for normal macropores in Si. Detailed investigations showed that n-macropores in Si grow exclusively in <100> and <113> directions. This fact shows once again that the SCR-model cannot account for all n-macropore features.

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