Theory of macropore-formation of silicon in hydrofluoric acid
Introduction
In 1990 Lehmann and Föll (J. Electrochem. Soc., 137, 653 (1990)) discovered that very regular arrays of macropores with
extremely large aspect ratios could be obtained in the n-Si/HF system. They explained the formation of these pores on the
base of a so-called "space charge region" model, assumes that the back-side photogenerated current is focused on pore tips
because of the bending of the space charge region around the tip. The model certainly is valid for the formation of macropores
in n-type Si, especially for the regular pore arrays, because based on this model and additional empirical results it
is possible to produce pore structures as desired by Lehmann (J. Electrochem. Soc., 140, 2836 (1993) and V. Lehmann, U. Grüning,
Thin Solid Films, 297, 13-17 (1997)). The model accounts quantitatively for macropore diameters in n-type Si with prestructured
nuclei. 1994 macropores on p-type-silicon were found by Propst and Kohl (J. Electrochem. Soc., 141, 1006 (1994)) by anodic etching
in an HF containing organic electrolyte (hydrofluoric acetonitril).
Scales for macropore formation
There are several length scales that may influence the system dynamics. To name just a few (with very rough numbers):
quantum wire effects (nm scale), avalanche break-through (10 nm scale), space charge region (10 nm - 10 µm), Helmholtz
layer thickness (nm), stability of diffusion (µm - cm). "Perfect" macropores are achieved if the dominating length scales
are similar, complicated morphologies result if they are incompatible.
Figure 1 - Scales for pore formation
We are introducing a intrinsic time constant to the system. This us defined by the local current burst -
the local reaction at the pore tips. In particular, the very long time constant of oxide dissolution is the decisive
factor for the large length scales of macropores.
Figure 2 - Current Burst
Reactions at the pore tip
The important fact is that current-flow is inhomogenious in time and space. Serval chemical and electrochemical reaction are
important for the macropore-formation - schematic shown in the figure.
Figure 3 - Local current flow
The local reactions got different properties - see table below.
Figure 4 - Different reactions
H-Termination
Macropore formation in p- and n-type silicon is an anisotropic process. The anistropic nature can be explained in the current burst model with the
anistropic passivation process of the pore walls. The H-passivation is a kinetic anisotropic process. Correlation in space
is produced by interactions in time which means that the nucleation probability of a current burst depends on what happened
before. Since the nucleation probability is larger for smaller degrees of H-passivation, and H-passivation in turn is minimal
on the {100} sur-faces just after the oxide is removed, there is an automatic coupling of new current bursts to old ones in the
pore regime" (i.e. whenever free Si surface is present) - the interaction in time is an intrinsic feature current burst model.
Figure 5 - Influence of surface orientation
Anisotropic proberties -see Figure x.
Figure 6 - H-Passivation
Current-bursts, nucleation, and stable pore-growth
A first essential feature of the current burst model is that all manifestations of electrode behavior now depend exclusively on when and
where current bursts nucleate. Correlation in space is produced by interactions in time which means that the nucleation prob-ability of a
current burst depends on what happened before. Since the nucleation probability is larger for smaller degrees of H-passivation, and
H-passivation in turn is minimal on the {100} surfaces just after the oxide is removed, there is an automatic coupling of new current
bursts to old ones in the "pore regime" (i.e. whenever free Si surface is present) - the interaction in time is an intrinsic feature of
the model. Whereas this is a necessary ingredient for the clustering of current bursts and thus the appearance of (meso- or macro) pores;
it is not totally sufficient: At low current densities for example, the number of current bursts nucleating per time unit may still be
larger somewhere in a large area having a small nucleation probability, compared to the small area around an "old" current burst having a
large probability, because the number of current bursts nucleating is probability times area. This allows for micropores, otherwise only
macropores would be observed.
Figure 7 - Nucleation and stable pore growth
Publications:
-
Pore Formation Mechanisms for the Si-HF System
J. Carstensen, M. Christophersen, H. Föll, Mat. Sci. Eng. B, 69-70, 23 (2000)
- Self-organized pore formation and open-loop-control in semiconductor etching
J. C. Claussen, J. Carstensen, M. Christophersen, S. Langa, H. Föll, submitted to Chaos as an invited paper (2002)
- A comparison of pores in silicon and pores in III-V compound materials
M. Christophersen, S. Langa, J. Carstensen, I. M. Tiginyanu, H. Föll, Phys. Stat. Sol. (a) - in press (2002)
Back to M. Christophersen's homepage
Last modified: 08/16/02
URL: http://www.marc-christophersen.de