Formation and application of porous silicon

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Abstract

All manifestations of pores in silicon are reviewed and discussed with respect to possible applications. Particular emphasis is put on macropores, which are classified in detail and reviewed in the context of pore formation models. Applications of macro-, meso-, and micropores are discussed separately together with some consideration of specific experimental topics. A brief discussion of a stochastic model of Si electrochemistry that was found useful in guiding experimental design for specific pore formation concludes the paper.

Introduction

The electrochemistry of Si (and of other semiconductors) exhibits a large range of peculiar phenomena, many of which are not well understood at present. The most prominent feature under anodic etching conditions is the formation of pores and “porous silicon” has attracted increasing interest for a wide spectrum of potential applications since the discovery of the unexpected optical properties of microporous Si in 1990 [1], [2]. In this paper, we endeavor to cover applications of porous Si, and since there are several recent papers dealing with properties and applications of microporous Si [3], [4], [5], [6], [7], [8], the focus of this paper will be on everything else, i.e. on mesoporous and macroporous Si.

The parameter space for pore formation is very large and has not been fully explored. As shown in recent papers [9], [10], [11], [12], it is still possible to find new kinds of pores in Si with peculiar features that may be of interest for applications. We will therefore review and classify the many types of pores that have been observed.

The Si–electrolyte contact, however, has more to offer to science and technology than just pore formation. Specific features with potential uses include:

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    ohmic or diode-type contacts with obvious potential for applications [13],

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    interfaces with an extremely low density of interface states and therefore very low values of the surface recombination velocity [14], [15], [16],

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    solar cell like behavior, i.e. photo currents which may increase linearly or non-linearly with the light intensity [17],

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    anodic oxide formation in various modes [18],

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    strong non-linear response to frequencies superimposed on voltages or currents as a relatively new issue [12], [13], [14], [15], [16], [17], [18], [19], [20],

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    very peculiar anisotropies of certain properties, in particular macropore growth [21], [22],

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    self-induced current or voltage oscillations in certain areas of the parameter space for constant external voltage or current, respectively (referred to as potentiostatic or galvanostatic conditions), cf. [23], [24].

All points, except the last two, have found applications (at least in proposals), and it is quite possible that new features will be added to this list in due time. So far, e.g. no self-ordered pore arrays have been observed as reported for Al2O3 [25] or, more to the point, for GaAs [26], [27], GaP [28], [29] or InP [30], [31]—always occurring with self-induced voltage oscillations (cf. Fig. 29). Will we be able to find self-ordered pores in Si, too? Also in connection with voltage oscillations? If not—why not? Nobody knows—and nobody is able to make a convincing prediction. This example serves to highlight our present level of the understanding of pore formation and to emphasize the viewpoint of the authors: pore formation in Si and all the other phenomena listed above (especially oscillations) are closely related.

This is a departure from more conventional approaches that try to model pore formation independently of all the other phenomena. We will therefore include the present status of a general model of the electrochemistry of Si in a final section and apply it to pore formation in Si.

Making porous Si in one of its many manifestations demands specific sets of parameters and some control of the etching process. While some pore morphologies are unique expressions of special parameters, others can be obtained for many, sometimes widely different conditions. With applications in mind, which set of parameters is best suited to the task—including economic considerations? While there are no simple answers at present, some guidelines can be given. The second section therefore attempts to correlate the zoology of macropores in Si and the most important ingredients from the available parameter space.

The third section deals with applications of macropores, the fourth and fifth with mesopores and micropores, respectively. While we try to review all potential applications presently pursued in the scientific/engineering communities together with specific problems, open questions, and emerging applications, it goes without saying that there are certainly some activities in the laboratories that the authors are not aware of—either because we failed to notice them or because they are (totally or partially) kept confidential on purpose. To compensate for this, there are some unpublished results that the authors are aware of and that will be included. In total, we cannot claim completeness in the listing of the application oriented work in this field and not always substantiate certain statements by citations.

There is a large and growing diversity of pores in Si. Typical dimensions from 1 nm to 10 μm and morphologies from sponge-like to perfect-cylindrical are encountered. In what follows we will first define some terms useful for discussing the geometry and morphology as well as the production and application of pores. First, we will distinguish the three major types of electrolytes in use today.

  • •

    Electrolytes derived from the HF–H2O system; called “aqueous electrolytes” and abbreviated with “aqu”. This includes not only all mixtures of HF (commonly 49% p.w.) with water, but also fluorine bearing salts dissolved in H2O (e.g. NH4F), additions of ethanol (C2H4OH) and/or acetic acid (C2HOH), or anything else that serves to reduce surface tension, adjusts the pH-value or the viscosity, or simply helps to get the desired results for unknown reasons. The nominal concentration of F (in any form) may range from 0.001 to 49%. All aqueous electrolytes have in common that a “PSL-peak” (see Fig. 1) is found in the I(V)-characteristics and that they are rather strongly oxidizing, i.e. tend to form SiO2.

  • •

    Electrolytes mixing HF and an organic solvent (always including some water coming from adding HF (49%)). This class will be called “organic electrolytes” (“org” for short). There is a large number of organic solvents that have been used; most prominent, perhaps, is acetonitrile (MeCN), dimethylformamide (DMF), and dimethylsulfoxide (DMSO). While there might be some confusion with HF/ethanol mixtures which we count among the aqu electrolytes as explained above, the meaning is sufficiently clear in practice. Organic electrolytes so far have in common that their I(V)-characteristics do not show a PSL-peak. While it is possible that the PSL-peak is actually there but hidden due to the usually large resistance of the org electrolytes (which means that the series resistance of the system dominates the characteristics), it will be reasoned in Section 2 that this is a decisive feature of most (not necessarily all) org electrolytes and intimately linked to their “oxidizing power” (see later), which can be rather small. In any case, the absence of a PSL-peak gives a clear signal that formation models intimately tied to the current density jPSL at the PSL-peak are limited in their application range.

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    Electrolytes for anodic oxidation (called oxidizing electrolytes; abbreviated “ox”); always without F ions and containing some oxidizing reagent. Most common electrolytes without a HF addition fall into this category and we may classify their “oxidizing power” according to how well they form an oxide on Si. In practical terms, this is easily measured by performing a constant current experiment. Due to the oxide being formed (but not dissolved), the voltage has to rise in order to keep the current constant. In the beginning of such an experiment, the V(t)-curves are always linear and the value of the slope dV/dt will be used as a measure of the “oxidizing power” of the oxidizing electrolytes, Fig. 1d shows some typical characteristics. “Oxidizing power” in the context of this paper is thus a well defined entity and will now be used without quotation marks in the remainder of the paper. Pure ox electrolytes have only limited applications, but may provide a key for the understanding of the electrochemistry of Si.

    There is one more (potentially large group) of electrolytes not covered in this scheme which one might call “mixed electrolytes”. This set contains everything not contained in the sets defined above, but so far not much practical significance has emerged. Examples that can be found in the literature include H3PO4 (by itself an “ox” electrolyte) with a dash of HF [32], absolutely water free org electrolytes [33], or diluted HF with some CrO4 [34]. As the need arises, we will pinpoint these cases by mixing the symbols; the latter electrolyte than is designated (aqu+ox).

    Next, we define some nomenclature regarding pores. According to the IUPAC standard, we must distinguish three categories by looking only at the parameters (average) pore diameter and (average) distance between pores, i.e. at the geometry of the pores.

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    Micropores, with pore diameters and pore distances (from now on subsumed under “geometries”) <10 nm.

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    Mesopores, with geometries in the 10–50 nm region.

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    Macropores with geometries in the >50 nm region.

Note that the geometry of pores does not contain much information about their morphology. This term will be used as the collective identifier for properties like the shape (smooth, branched, facetted, …), orientation, or interaction of pores, that are independent of the geometry.

All three kinds of pores can be obtained under a variety of (sometimes very different) conditions, and with widely differing morphologies. Key parameters are the electrolyte type (aqu, org, ox), the HF concentration, the doping type and level of the Si (n, n+, p, p+), and in some cases the illumination state (back side illumination (bsi), or front side illumination (fsi)). We will use these abbreviations to extend the classification of pores in a self-explaining notation: n-macropores(aqu/bsi) or n-macropores(aqu/fsi) thus are macropores produced in n-Si under backside or frontside illumination using aqueous electrolyte; p-macropores(aqu) or p-macropores(org) denote macropores obtained without illumination in p-type Si with aqueous or organic electrolytes; and n+-macropores(aqu+ox) denotes macropores obtained in heavily doped n-type Si in a mixture of an aqueous electrolyte with the addition of an oxidizing electrolyte, respectively.

It is absolutely essential to adhere to this nomenclature to avoid considerable confusion—the examples chosen demonstrate this point: macropores can be obtained under a variety of very different conditions; Fig. 2 illustrates this. This was a rather unforeseen development since the discovery of smooth cylindrical (“perfect”) n-macropores(aqu/bsi) with large aspect ratios by Lehmann and Föll in 1990 [35]. While this kind of macropores was investigated in some detail, only few investigations dealt with the rest.

The basic IUPAC distinction of pores into micro-, meso-, and macropores is far to coarse and not particularly well suited to unambiguously sort out pores in Si. The term “macropore” usually is associated with smooth cylindrical pores in the 1 μm region, and no such macropores have been observed (so far) in the 50 to 500 nm region to which the term nominally applies. Contrariwise, while n+-, p+-mesopores(aqu) are indeed (mostly) found within their admissible size range of 10–50 nm, it is simply not useful to call pores “macropores” that have a morphology exactly like “proper” mesopores as soon as their diameter exceeds 50 nm. “Break through” pores, e.g. obtained in n-type Si in the dark at large potentials (and in all electrolytes), while very similar in appearance to n+-mesopores(aqu), tend to be a bit larger in diameter and may exceed the 50 nm limit, but still will be called n-mesopores(dark) in this paper.

It should be noted that current research produced “pores” that cannot be adequately described in this system. Examples are the two-dimensional “trenches” and “wings” [22] observed under conditions that also produce p-macropores(org) and n-macropores(org/bsi), respectively, cf. Fig. 6, Fig. 15.

Why do pores form under a wide range of experimental conditions and what determines their geometry and morphology? As stated before, the authors are of the opinion that pore formation cannot be understood by itself, but must be seen in a larger context that includes the other salient features of the Si electrode. A first attempt at such a generalized model, including pore formation, has been proposed by the authors [10], [12], [20]; it attempts to describe all features of Si electrochemistry as the expression of the interaction between stochastically occurring “current bursts” (CB) which are localized in space and time. This model is called the current burst model (CBM) and will be briefly described in Section 7.

It is not necessary to go into details of the various pore formation models in order to obtain some basic understanding of what determines pore parameters. No matter what kind of pores results from some experiment, they always have some characteristic dimensions—average diameter, average distance, spacing between branches—and all these length scales are usually rather well defined. While not many quantitative investigations on characteristic dimensions have been made, it is safe to say that pore formation of any kind (almost) always defines a specific length scale prevalent in the Si—electrolyte system employed that expresses itself in the (average) pore geometry and morphology. Any model thus must ultimately give a reason for the actual scale found in the pores under investigation in order to explain the geometry. Note, however, that the presence of a specific length scale does not necessarily explain pore formation per se.

The most advanced models for pore formation essentially give a reason for pore nucleation and stability and define a characteristic length scale. The most important length scales proposed are as follows.

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    Width of the space charge region (LSCR). This was first proposed by Lehmann and Föll [35] not only as the major parameter governing pore geometry and morphology, but also as the only cause for the actual formation of n-macropores(aqu/bsi). The model has been quantified to some extent [36] and has been used with great success to produce beautiful pore structures for many applications [37], [38]. However, while LSCR and other effects due to the space charge region undoubtedly are very important for pore parameters, it has become obvious that LSCR is not sufficient to explain macropores in general [39], not least because it relies heavily on the presence of a PSL-peak which is not observed for most org electrolytes.

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    Pore tip radius LAV inducing avalanche break down. At high field strengths at pore tips with a sufficiently small radius, avalanche break down necessarily occurs, supplying plenty of carriers to drive the electrochemical reactions—a process often exploited in n-type semiconductors where holes are scarce. While not a new idea [40], Lehmann et al. give a fully quantitative treatment and apply this effect to pore formation in general [41]. However, while avalanche break down will occur under certain conditions, it will be a locally and temporarily self-stopping process if some oxide formation occurs because this will locally decrease the field strength. Seen in this context, LAV will give the smallest dimensions possible for pores obtainable under conditions where it occurs. Smaller pores will simply grow to a diameter just above LAV and avalanche break down only happens “every once in a while and here or there”—stochastically, in other words. In addition, the relative avoidance of avalanche break down will lead to round pore tips having a constant field strength at any point.

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    Diffusion instabilities, well known from the growth of dendritic crystals (e.g. snowflakes) may induce gradients in the hole concentration with a typical dimension LDIF and thus induce or stabilize pores with that dimension. This case was treated in detail by Chazalviel et al. [42], Smith and Collinsbut [43] since LDIF is always tied to the diffusion length or Debye length of the holes, LDIF is too restricted to account for all effects. It appears, however, that LDIF is an important length scale for some p-macropore (org) systems.

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    Quantum wire effects at length scales below LQU ≈ 1 nm that prevent the movement of holes to the Si–electrolyte interface. This effect was invoked to explain the formation of micropores [44]. However, while LQU may define the minimum distance between micropores, it has nothing to say about the diameter of the micropores itself.

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    Another typical length, often overlooked, is the spacing between lithographically defined nuclei, LNU, which is totally independent of the system parameters and thus a truly extrinsic length scale.

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    The CBM finally defines a typical length scale, too, called the correlation length LCO of the interaction between localized current bursts [12], [20]; see Section 7 for details.

All these length scales definitely exist—at least in a subset of the available parameter space—and influence the geometry and morphology of pores. It is, however, not always clear which scales dominate the pore formation process and what will happen when major conflicts of length scales are unavoidable. For example, a clear conflict of scale occurs when the extrinsic length scale LNU is too different from LSC—it is simply not possible to obtain macropores spaced at distances much larger or much smaller than LSC. Another conflict of scales occurs if one tries to produce macropores with diameters much smaller than LAV or LCO—and this is as much a prediction as a (largely unpublished) experimental fact.

It should be realized that there is a large body of experimental results that was never published, especially if the experiments were made with a particular goal in mind that could not be achieved. Etching well-formed macropores in the sub-μm region, e.g. has been tried in several laboratories; but only one success was reported for a 0.5 μm geometry after extensive work (including growing a special Si crystal) [45] while the unsuccessful attempts at even smaller spacings have not been published (including the efforts of the authors). Defined modulations of macropore diameters fall in this category, too.

Section snippets

Macropores in n-silicon obtained in aqueous electrolytes with back side illumination

Since n-macropores(aqu/bsi) are the best known species of macropores, we will consider them in some detail before treating the other kinds. “Perfect” pores with very large aspect ratios have been obtained for this species, and “perfect” means not only smooth pore walls, but also smooth cross-sections (albeit not necessarily circular) and constant diameter with depth.

The n-macropores(aqu/bsi) were first predicted by one of the authors and then found in a suitably designed experiment [35]. The

General remarks

Macropores offer a number of attractive features for many kinds of applications. A listing includes:

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    extremely large aspects ratios (length/diameter) of >600 for diameters in the 1 μm region;

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    defined geometries (arrays) are possible—periodic, periodic with defects, or aperiodic—the only limitation being that the average pore density should be constant;

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    large porosities and thus large volume to surface ratios are possible;

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    large areas can be homogeneously etched due to the supreme homogeneity of Si

Formation and appearances

By IUPAC definition, mesopores are all pores with 10nm<d<50 nm, but, as stated before, this definition is too limited to be of much value. We will therefore use the following list as a working definition of mesopores; it coincides roughly with the geometric definition.

Mesopores are obtained for the following configurations.

  • 1.

    Etching of highly doped Si in aqueous electrolytes always produces n+/p+-mesopores(aqu); Fig. 22a shows an example. No light is required in the case of n+ Si because avalanche

Some general remarks

Micropores and their possible applications have been covered in detail elsewhere [6], [7], [8] and this chapter will be brief accordingly. In particular, we will not cover the luminescent properties of microporous Si or applications that were envisioned and investigated (but never used in production) before the discovery of the luminescent properties of microporous Si, e.g. the “FIPOS” process (short for “full isolation by oxidized porous silicon”), cf. [90].

Generally, groups working with

General

It is not uncommon that beginners in the field have initial problems to obtain homogeneous etching and reproducible results. Some factors that need attention are as follows.

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    The back side contact of the sample may not be ohmic (“ohmic” meaning that the contact resistance shows a linear current voltage relationship and is small). Just putting Si on a metal plate is mostly not good enough, especially for low doped samples. Rubbing liquid In–Ga alloy on the back side, together with some scratching,

General features of the current burst model

A complete model of the electrochemistry of Si should not only be able to explain the bewildering multitudes of pores, but also the current or voltage oscillations and the peculiarities of the I(V) characteristics. It must, moreover, accommodate the many models applicable to pore growth in some way, because those models are not wrong—SCR regions do exist and will focus holes on pore tips, avalanche break-through will occur at high field strength, and diffusion instabilities are real, too, as

Acknowledgements

The authors are indebted V. Lehmann, S. Rönnebeck, F. Müller, S. Langa and I.M. Tiginyanu who supplied some of their pictures for inclusion in this review and were valued partners in many stimulating meetings. Invigorating discussions with R. Wehrspohn, J.-N. Chazalviel and F. Ozanam concerning the electrochemistry of silicon and pore formation are gratefully acknowledged. G. Popkirov and J. Bahr supplied the experimental help and the special equipment for many experiments.

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