Self Formation of Porous Silicon Structure: Primary Microscopic Mechanism of Pore Separation

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1 Solid State Phenomena Vols (2004) pp (2004) Trans Tech Publications, Switzerland Journal doi: / Citation (to be inserted by the publisher) Copyright by Trans Tech Publications Self Formation of Porous Silicon Structure: Primary Microscopic Mechanism of Pore Separation M.E. Kompan 1, A.E. Gorodetski 2, I.L. Tarasova 2 1 Ioffe Physicotekhnical Institute RAS, Politehnicheskaia 26, S.-Petersburg, Russia kompan@mail.ioffe.ru 2 Institute of the Problems of Machinery Engineering RAS, Bol shoi 69 S.-Petersburg, Russia gae@mail.ipme.ru Keywords: porous silicon, electrochemistry, charge carriers, spatial scaling. Abstract. A microscopic mechanism of the self-formation of a dense pore system in the porous silicon is proposed. According to it, the process of porous silicon self-formation is dictated by the laws of dynamics for a charge carriers system. The proposed mechanism is proved by the results of computer simulation. The values of inter-pore separation distance in p-type based porous material and anodization current threshold density are evaluated; the dependence of an inter-pore separation distance on the carriers concentration, close to n -1/2, is predicted. Introduction Self formation is a fairly wide phenomenon. But till recently, techniques almost did not use self formation; most of technical goods were produced by so called direct manufacturing. Nowadays semiconductor electronics and optoelectronics tend to minimize the size of elements up to nanometer scale. At the same time the ability of modern technology to direct formation the spatial details is limited only by tenths of micron. Processes of self formation give the unique ability to obtain such element as nanotubes, clusters, nanocrystals, quantum dots, the elements, that will be the fundamental for future information technology. This direction in technology promises a lot, but for successful usage of self-formation as a technology stage in production, it demands essential understanding of physical and chemical processes, that lie in the basis of self formation process. Porous silicon is special material, self-formed from usual crystal silicon typically in process of so called anodization. During last decade, it was investigated in numerous laboratories. It was shown, that unusual properties of this material are the result of it s structure. Depending on the type of starting material and conditions of the anodization process, various forms of porous silicon with different structure and properties were obtained. The sponge-like or wire-like silicon can be mentioned. The size of elements in porous silicon vary from nanometers to several microns. But till present time, the mechanism, responsible for the self-formation of structure and for the spatial scale of the elements, was unknown. Porous Silicon Formation Processes and Hypotheses Typically porous silicon is obtained in process of etching of positively biased crystalline silicon in hydrofluoric acid solutions (anodization). This process was first described by Terner [1]. Also, there exist some other methods of preparation of this material. It was shown in [1] and it is well known since, that starting stage of porous silicon formation is the localization of an electronic hole at the one of silicon atoms at a surface. Various considerations and models of the por-si structure formation were formulated, concerning different aspects and conditions of the anodization process. For example, it was thoroughly argued in [2], that positive bias of silicon during etching leads to concentrating of current and then to channel narrowing; it was believed, that it was a critical mechanism of the pore system formation. But it does not explain formation of the multypore system. It is well known, that current pinch leads All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, (ID: , Pennsylvania State University, University Park, United States of America-12/06/14,21:17:03)

2 182 Self-Formation Theory and Applications 2 Title of Publication (to be inserted by the publisher) to S-like current instability; which results in voltage drop and makes breakdown or pinch formation in other sites of surface impossible. In our paper [3] we have shown, that structure of newly formatted porous silicon mainly reproduces the structure of already existed porous silicon layers. This our result is in good agreement with experimental observation of Turner [1]. So, the key to understanding the porous silicon self-formation is in understanding an initial stage of formation of multypore system on a plane surface of silicon crystal. Only recently there appeared attempts to explain the initial stage of pore self-formation. Among the existing starting ideas it should be mentioned the idea of instability of the flat surface profile during the etching process. This approach has been developed in [4]. In this paper the surface tension of silicon together with the hole transport in semiconductor and the ion transport in acide were taken into account. But the conclusion in [4] was that the model is not able to explain the nanometer-size pore self-formation in p-type silicon. So, at the beginning of this work it was known what are the chemical processes during anodization, and also it was clear the role of holes (positive charge carriers), but it was totally unclear why instead of concentrating (according to [2]), or instead of random etching (as usual) one can obtain multypore system over initial surface. Pore Separation Mechanism In this paper we intend to suggest an idea of mechanism, that can provide formation of a dense pore system, with pore separation up to several nanometers. On the basis of this mechanism it is also possible to make some testable predictions. The idea of the mechanism is connected to our explanation of another non-clear phenomenon the dependence of the pore structure scale on the carrier concentration in initial bulk p-type silicon. The last model is available in electronic prepublication [5]. As we understand now, two problems mentioned above are the two sides of the same phenomenon, based on fundamental properties of the mobile charge carriers subsystem. Main problem for the standart theory of chemical etching is to explain why the surface around the vacancy on the surface stay unetched. Normally the atoms, neighbor to vacancy, have less links to crystalline lattice and thus should be etched first. In porous silicon areas around vacancies stays unetched and this forms the multypore structure. So, the main problem is to understand the microscopic mechanism of inter-vacancy passivation. We suggest the following. It is well known, that the initial stage of silicon etching is the localization of a hole at some atom on a surface, e.g. like in [1]. (Note, that p-type silicon has it s own concentration of holes, and positive bias of silicon is necessary only to help the holes to overcome the potential barrier in the depletion layer near the surface). If the surface is initially smooth, a hole will be localized at some arbitrary atom, and this will initiate the chain of chemical reactions, resulting in removal of the atom from the surface. In it s turn, the creation of an empty atom position at surface (vacancy) will make the sites over the surface non equivalent. The atoms, very neighbors to vacancy, will have one less bound to silicon lattice, so the probability to be etched for these neighbors will increase (this may lead to the well-known running steps mode of surface etching). But one should take into account also, that disappearance of an atom from the surface makes some changes in electronic subsystem of silicon, too. (Simply together with the atom removal an electronic hole must disappear from the crystal). As far as the hole is necessary for the beginning of etching, the probability to be etched for the atoms around the just etched position will be decreased for some period. After some period the local hole concentration will recover due to diffusion of carriers. The mentioned local hole removal is anyway a perturbation in the mobile charge carrier subsystem. The size (avarage) of this temporal holeless area and the time of it s existence are the

3 Solid State Phenomena Vols Title of Publication (to be inserted by the publisher) 3 same for any perturbation, that can occur in any mobile charge carrier system. They are well known Debye length (R D ) and Maxwell time ( M ); those quantities can be defined through the parameters of material: (R D ) 2 = kt/(e 2 n ), (1) M = (2) where: n concentration of carriers, kt temperature in energy units, e unit charge, and dielectric susceptibility and resistivity of material. Irrespectively to the parameter of materials, local temporal memory to hole removal will cause a temporal decrease of a probability for next etching act in the area around the just appeared vacancy. Fig. 1. Illustration to mechanism of pore separation. Upper part of figure acid solution, lower part presents silicon crystalline lattice. Silicon atoms schematically shown on a plane as a squares, so they have four nearest neighbors, as the real Si atoms in crystal. Area of a bulk silicon, covered by slash lines p-type silicon with the positive charge carriers (holes). Fluor anion in acid solution are shown as a circles of another size. The H + cations, molecules of solvents and solvation shells around ions are not shown. The areas around vacancies are not covered with slashes. It illustrate temporal absence of the holes in slash-free area. The holes from this area were taken away in previous acts of etching (illustrated in left part of solution). The etching can no occur in hole-free area, but can occur outside of this region(right part of figure). This leads to separation of positions of initial vacancies on a surface, and thus to separation of pores. We can use the parameters of bulk silicon and evaluate the spatial scale of this separation. The correlation distance (L R D ) between pores, according to (1), must depend on carrier concentration as n 1/2. For a concentration value cm -3 and T = 300 K one obtains L 4 nm, that suites very well to known values. The (n 1/2 ) dependence on concentration also is in the qualitative accordance to known experimental facts. Though, there can be deviations from this dependence due to influence of a depletion layer. Essential feature of a new mechanism is it s temporal character of depletion. The region with decreased probability of etching has a limited time of existence. If, for example, the etching is not intensive, the time interval between subsequent removals of atoms will be large. As a result, the

4 184 Self-Formation Theory and Applications 4 Title of Publication (to be inserted by the publisher) interval before etching acts in the neighborhood of an appeared vacancy can become more, than Maxwell time M. Under these conditions, our mechanism will be ineffective. Let us calculate the estimation value for etching rate, necessary for our mechanism. It should be noted, that our estimation considers a very initial stage of etching. At later stages, according to Turner observation [1] and to our model [3] and experience [6], the current does not directly dictate etching rate. At the very initial stage we can take that the number of etched atoms is approximately equal to number of holes, injected from positive bias. Going from this simplification, we can write relation for threshold of anodization current density (j a ), that is able to provide pore separation: j a e/ (R D ) 2 M. (3) The formula (3) shows the density of current, that give a hole per Maxwell time interval through fragment of surface with area (R D ) 2, so the current, enough for acts of etching to be correlated. Taking for M value seconds, we obtain for j a quiet reasonable value a/cm -2. And once more: as the proposed mechanism is of probabilistic character, most probably the estimated value of j a does not correspond to an abrupt threshold. We can only point out, that at lower current densities the correlation between acts of atoms removal become weaker and finally will disappear. So, the account of intrinsic properties of the mobile holes system gives a clear and natural explanation, how the pore distribution originates in p-type based por-si. The model allows to evaluate the pore separation distance and anodization current density. The obtained values appear to be in a fair accordance with the empirically known ones. Computer simulation proves that the proposed mechanism can lead to effective inter-pore separation. The details of simulation will be published elsewhere. Summary A new microscopic mechanism, lying in a basis of self-formation of the multypore structure for porous silicon, was proposed. The mechanism originates from the mobile charge carrier dynamics, so it is of a very general validity. Based on the model, the n -1/2 dependence of the pore separation distance on the p-type carrier concentration was forecasted. The obtained numerical values of the inter-pore distance and anodization current density are in good accordance with the empirically known values. The ability of mechanism to provide the regular relief of surface is proved by computer simulation. References [1] D.R. Terner: J. Electrochem. Soc. Vol. 105 (1958), p [2] M.I.J. Beale, J.D. Benjamin, M.J. Uren, N.G. Chew, A.G. Cullis: J. of Crystall Growth Vol. 72 (1985), p [3] M.E. Kompan, I.Yu. Shabanov: FTP (Semiconductors) Vol. 29 (1995), p (in Russian). [4] A. Valance: Phys. Rev. B Vol. 52 (1995), p [5] M.E. Kompan, I.Yu. Senichenkov, I.Yu. Shabanov, J. Salonen: [6] M.E. Kompan, I.Yu. Shabanov: FTT Vol. 36 (1994), p. 125 (in Russian).

5 Self-Formation Theory and Applications / Self Formation of Porous Silicon Structure: Primary Microscopic Mechanism of Pore Separation / DOI References [2] M.I.J. Beale, J.D. Benjamin, M.J. Uren, N.G. Chew, A.G. Cullis: J. of Crystall Growth Vol. 72 (1985), p doi: /