Current Burst Model and III-V Compounds

The most fundamental questions about pore formation are why and how do pores grow?

3.2.5 Current Burst Model and III-V Compounds

The most fundamental questions about pore formation are why and how do pores grow? Different models, most of them developed only for Si, have been proposed, trying to answer these questions. The current burst model (CBM) is one of them. In contrast to other models, CBM assumes that the processes which take place at nanometer scale during the dissolution, i.e. at nearly atomic level, are similar for all semiconductors, whereas the macroscopic behavior of different electrodes is determined by the interaction (in space and time) of these nanometer events. This allows the current burst model to have a high prediction power for different semiconductors.

The first phenomenon explained by the CBM was the current/voltage oscillations observed during the electropolishing of Si [9, 10, 11]. The CBM predicted oscillations also for the pore formation regime. Indeed, recently oscillations in the pore formation regime have been observed experimentally, first in III-Vs [51] and later in Si [52].

The general assumptions of the CBM are the following:

  • A mechanism for a local oscillator is required. These local oscillators are called 'current bursts';
  • A synchronization mechanism (between current bursts) must exist in order to see macroscopic electrode oscillations;
  • A desynchronization mechanism is required as well, otherwise electrodes would either oscillate strongly or not at all.

A current burst is assumed to be composed of four main steps: direct dissolution, oxide formation, oxide dissolution and surface passivation (see Figure 3.9). The repetition of these steps in time will result in a local ON/OFF oscillatory behavior of the current. These implies that charges are mainly flowing through a current burst during direct dissolution and oxide formation (ON), whereas no or little charge is flowing (OFF) during oxide dissolution and passivation.

The synchronization between the current burst is due to oxide overlapping of neighboring current bursts, i.e. the surrounding current bursts will contribute with their oxide bumps to the oxide bump of a newly nucleated current burst. This way, its stopping point is already much closer to the stopping point of the surrounding current bursts, because it has to produce less oxide as if it would have been alone, i.e.,without neighbors.

For a realistic model, a desynchronization mechanism is necessary as well. Once a current burst starts, the current density is locally increased, leading to increased ohmic and diffusion losses, which locally reduces the potential across the oxide layer. This reduces the electric field strength in the neighborhood of an active current burst, and therefore reduces also the probability for nucleation of a new current burst next to an active current burst [9]. This process can be regarded as desynchronization.

Due to the fact that the nucleation of current burst is a stochastic process, it may happen that the oxide of an old current burst is completely dissolved but there are no new current bursts nucleated meanwhile on the same place. In such a case the passivation process of the surface will start. The nucleation probability will depend on how strongly the new surface was passivated by different species from the solution, i.e. the higher the passivation the lower the probability that a current burst will nucleate on this surface. The passivation of the surface in time is called "aging".

Since the nucleation probability is larger for smaller degrees of passivation, and passivation in turn is minimum just after the oxide is removed, there is an intrinsic coupling of new current bursts to old ones. This will result in clusters of current bursts, and one possible consequence will be the formation of pores.

Sequence of events in a  current burst

Figure 3.9: Sequence of events in a current burst: Charge transfer for direct dissolution is followed by oxidation; these are fast processes. The dissolution of the oxide is slow for Si and fast for III-Vs and so is the H-passivation and OH-passivation. Sometime and somewhere - depending on the external system parameters and the microscopic conditions - a new current burst nucleates.

Passivation in this context means the removal of mid-gap states. In III-V compounds the dissolution process is divided in several reaction steps. After the first reaction step, a high density of mid-gap states is generated [37]. If these mid-gap states are easily passivated by the species in solution, then the next reaction steps cannot occur and dissolution will stop. In other words, the probability for current burst nucleation will decrease if passivation will increase.

In most cases, in Si as well as in III-V compounds, {111} surfaces passivate faster that {100} surfaces and thus they are relatively more stable against dissolution [53, 54]. However, in III-V compounds there is a difference in passivation even within the {111} set. Namely, {111}A (Ga or In terminated surfaces) are passivated easier than {111}B (As or P terminated surfaces). This feature has a great influence on the porous morphologies obtained in these materials (see the nucleation mechanism described in section 3.3.1). In particular, there is a strong tendency to nucleate new current bursts on {100} rather than on {111} Si, and on {100} or {111}B rather than on {111}A in III-V's (see Figure 3.9). It is assumed that the surface is passivated by hydrogen in the case of Si, and by OH- or Cl- in the case of III-V compounds [55].

Each stage of a current burst, i.e. direct dissolution, oxide formation, oxide dissolution and passivation, consumes charges and time. For Si, the ratio between the oxide-dissolution time (long) and charge-transfer-time (short) is much higher than for III-V compounds. This is mainly caused by the short dissolution time of III-V oxides. Mathematically this can be described as follows:

Equation 31(31)

The long time constant for oxide dissolution in Si is the decisive factor for the large scale difference of macropores in Si (1-5 Ám) and III-Vs (

100-200 nm). Thus, the size (and morphology) of pores is given by the dominating length scales in a particular system.

Combining all charge and time consuming processes, it is possible to write an average current density for one current burst iCB:

Equation 32(32)

where Qdir.-diss. is the charge consumed during the direct dissolution process; Qox.-form. - charge consumed for oxide formation; tch.-tr. - time required for charge transfer (both Qdir.-diss. and Qox.-form. ); tox.-diss. - time required for oxide dissolution; tpass. - time left for passivation before a new current burst starts on the same place.

The shape and growth velocity of the pores depend on the processes which dominate the current of a burst: direct dissolution or dissolution via oxide formation.

The direct dissolution part of a current burst has the following properties:

  • The valence of dissolution is higher as compared with dissolution via oxide formation;
  • Strong preference for nucleation on {100} and {111}B surfaces;
  • Preferred reaction at high field strength (including carrier generation by avalanche effects, always true for III-V's);
  • Depends on passivation kinetics;
  • If dominant, produces 'dendritic pores' (or 'break-through pores', 'fractal pores', octahedron pores, tetrahedron pores, etc.).

On the other hand, the oxidation part of a current burst has the following properties:

  • It is a rather isotropic process;
  • It is driven by electrochemistry, i.e. by the potential at the interface;
  • Preferred reaction at high potentials and surplus of holes if sufficient O- is available;
  • If dominant compared to direct dissolution, it produces 'macropores' with not very pronounced directionality.

Macropores are formed if the direct dissolution part and the oxidizing part of a current burst are balanced within some limits depending on the system. If the system looses this balance, e.g. the supply of holes (or reactants) decreases, a critical point may be reached where the pore morphology changes suddenly. A relevant example is the switch from crystallographically oriented to Current-line Oriented Pores in InP and GaP (see Chapter 3.3.2 - Current-line Oriented Pores).

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