Pores in n-Type InP: A Model System for Electrochemical Pore Etching
- Malte Leisner^{1}Email author,
- Jürgen Carstensen^{1} and
- Helmut Föll^{1}
DOI: 10.1007/s11671-010-9624-z
© The Author(s) 2010
Received: 15 April 2010
Accepted: 28 April 2010
Published: 14 May 2010
Abstract
The growth mechanism of currentline-oriented pores in n-type InP has been studied by Fast-Fourier-Transform Impedance Spectroscopy (FFT IS) applied in situ during pore etching and by theoretical calculations. Several pore growth parameters could thus be extracted in situ that are otherwise not obtainable. These include the space-charge-region (SCR) width, the SCR potential, the capacitance at the pore tips, and the avalanche breakdown field strength. It could be demonstrated that the system adjusts itself in such a way that the potential across the space-charge-region at the pore tips is kept constant within a certain bandwidth of the applied potential. This provides for a constant field strength at the pore tips, ensuring that avalanche breakdown occurs, generating the necessary holes for the electrochemical dissolution of InP.
Keywords
Porous semiconductors InP Impedance spectroscopyIntroduction
Porous semiconductors have been envisioned for the use in a broad range of applications, and substantial R&D efforts have been made in this direction [1–7]. In the majority of the proposed applications, the detailed morphology of the porous structure is decisive for the functioning of the application. Morphology parameters like pore diameter and shape, pore wall thickness and roughness, or pore density have to be established with often a rather high precision, i.e. for optical applications [4, 8]. To meet precise specifications, a thorough understanding of the pore formation mechanism is needed but not yet established for any pore system, including the thoroughly investigated porous Si. For deeper insights into general pore etching mechanisms, InP can be considered as a model semiconductor, which allows easier systematic investigations than, e.g., Si because only two kinds of pores seem to exist, which are quite different in their general behavior. Changing external parameters like the etching current density or the potential can easily control the respective pore formation modes. Both pore growth modes seem to embody the simplest case of electrochemical pore etching, where only one main electrochemical reaction occurs, in contrast to systems like Si, where always several reactions occur, making the system harder to analyze.
Figure 1b shows a typical example of curro pores in (100) n-type InP [11, 12]. The pores have a circular cross-section and semispherical pore tips. They grow in direction of the current flow, i.e. usually perpendicular to the sample surface, independent of the crystal orientation.
The growth mechanism of crysto pores has already been studied by FFT Impedance Spectroscopy and could be successfully modeled by a stochastic model of the “current burst” type [13], which has been implemented into a Monte-Carlo simulation [14, 15]. This work will focus on the growth mechanism behind the currentline pores, expanding the work presented in [16]. Results of the in situ FFT impedance spectroscopy [17] will be analyzed.
Experimental Procedure
All pores have been etched into single-crystalline n-type InP wafers. The orientation was (100), and three different doping concentrations N _{D} have been used: 1·10^{17}, 8·10^{17}, and 3·10^{18} cm^{−3}. The sample size was A = 0.25 cm^{2}. The samples have been etched in an electrochemical double cell, the basic set-up is described in detail in [18]. 6 wt% HCl aq. has been used as electrolyte. All experiments have been conducted at T = 20°C under constant etching potential. The dc potential used was in the range of 6–8 V for N _{D} = 1·10^{17} cm^{−3}, 4–7 V for N _{D} = 8·10^{17} cm^{−3}, and 2–4 V for N _{D} = 3·10^{18} cm^{−3}. In these potential ranges “good quality” pores can be obtained, i.e. pores with straight and smooth pore walls, growing perpendicular to the surface. In the beginning of the experiments, a high-potential pulse has been applied for 1 s to guarantee a homogeneous nucleation of the pores. Typical etching times were between 5 and 70 min, resulting in pore depths up to 500 μm, i.e. aspect ratios of >1,000.
During all experiments, FFT impedance spectra (FFT IS) [17, 19] were recorded every 1.5 s. The measurement signal contained 28 frequencies between 30 Hz and 20 kHz. The spectra obtained were fitted to a model, which allowed on-line extraction of the model parameters.
Results
where Z(ω) is the model impedance, R _{S} is a serial resistance, R _{1}, R _{2}, and R _{3} are transfer resistances, C _{1} and C _{3} are capacitances, and τ _{2} is a time constant. The measurement frequencies are indicated in the graphs. It can be seen that Eq. 1 is able to fit the data for all three doping concentrations very well, even though the absolute numbers on the axes are quite different between the experiments. It should be mentioned that the fit is just as good to the 500–2,800 FFT IS obtained through one etching experiment after the short nucleation phase (<1 min), lending credibility to the model used. The amount of data generated will easily exceed the page limitation of any publication, in what follows we will therefore focus on some selected aspects of the model that yield the deepest insights into the pore etching mechanisms.
Discussion
Pore wall thickness d _{wall} as measured from Fig. 2 is in good agreement with twice the value of the SCR width d _{SCR}, which has been calculated for * planar geometry and ** semispherical geometry
N _{D}/cm^{−3} | d _{wall}/nm measured | 2 d _{SCR}/nm* calculated | 2 d _{SCR}/nm** calculated |
---|---|---|---|
1·10^{17} | 148 | 230 | 168 |
8·10^{17} | 94 | 62 | 55 |
3·10^{18} | 27 | 22 | 21 |
Potential drop in the SCR, U _{SCR}, and field strength at the pore tips E _{calc}, as calculated from the FFT IS data
N _{D}/cm^{−3} | U _{SCR}/mV | E _{calc} Vcm^{−1} | E _{m} Vcm^{−1} |
---|---|---|---|
1·10^{17} | 956 | 350.000 | 648.000 |
8·10^{17} | 553 | 470.000 | 840.000 |
3·10^{18} | 272 | 540.000 | 991.000 |
This last finding supports the fact that the part of the impedance described by R _{2} and τ _{2} is the avalanche breakdown mechanism, indeed. This interpretation is also capable of explaining the negative (differential) impedance, i.e. the “inductive” loop, which is always present.
All things considered, the results strongly support the validity of the model expressed in Eq. 1 and the interpretation of parameters extracted.
We believe that the third process represents the diffuse layer inside the pores, where R _{3} and C _{3} describe the respective resistance and capacitance. This claim has not yet been supported by theoretical calculations, but might yield further insights in the near future.
Conclusion
It has been demonstrated that currentline pore growth in InP is governed by a constant potential U _{SCR} in the SCR, which keeps the field strength required for avalanche breakdown constant (since the pore tip shape does not change). This mechanism is present at all three investigated doping concentrations N _{D}, for which hexagonally close packed pore structures with different pore wall thicknesses, but constant pore diameter have been observed. It was possible to extract several important parameters for the etching process in situ, which are otherwise not obtainable. These include the SCR width, the SCR potential, the capacitance at the pore tips, and the avalanche breakdown field strength.
Declarations
Open Access
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Authors’ Affiliations
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