Phonon spectra of porous GaP structures

One of the main characteristics of the porous structures is their extremely large surface.
In this connection surface-related vibrations should be much more pronounced as compared with bulk materials.

4.4 Phonon spectra of porous GaP structures

One of the main characteristics of the porous structures is their extremely large surface. In this connection surface-related vibrations should be much more pronounced as compared with bulk materials. Here we will describe the first observation of surface-related vibrations in porous semiconductors, namely in porous GaP. Interestingly, no analogous phonon modes have been found in extensively studied porous Si. Note that the surface-related vibrations observed in GaP was interpreted in terms of the so called Fröhlich modes, which should occur in small structures of heteropolar semiconductors in the region between the transversal (TO) and the longitudional (LO) modes. A suitable way to study the Fröhlich vibrational modes is the Raman technique. For basic principles of Raman measurements see Appendix 4.


Figure 4.27, curve 1 illustrates the micro-Raman spectrum from a bulk n-GaP crystal. Curves 2 and 3 were obtained from the samples anodized at current densities of 5 and 15 mA/cm2. The as-grown crystal exhibits only one Raman band centered at 404 cm-1, which corresponds to the Brillouin-zone-center LO phonon. The q = 0 TO phonon is forbidden in (100) geometry and therefore it is absent in the bulk GaP spectrum. The anodization process leads to a small downward frequency shift and broadening by 15 to 20 % of the LO-phonon band accompanied by a significant Raman signal intensification (up to 5–6 times). A complete breakdown of the polarization selection rules is reflected in Figure 4.27 by the appearance of a strong TO-phonon band. Like the LO phonon, the TO phonon also exhibits a downward frequency shift with increasing the anodization current.


Unpolarized micro-Raman spectra of bulk GaP and porous layers.

Figure 4.27: Unpolarized micro-Raman spectra of bulk GaP and porous layers. The curves are normalized to the intensity of the LO peak.


Another important feature caused by anodic etching is the emergence of a Raman peak positioned in the frequency gap between the TO and LO phonons. As seen from Figure 4.27, this peak appears as a well-defined shoulder on the low-energy side of the LO band. According to the results of a spectral deconvolution (Figure 4.28), the peak under consideration broadens and shifts to lower frequencies with increasing anodization current density corresponding to decreasing GaP concentration. The maximum of the peak corresponds to 398 cm-1 for j=5 mA/cm2 and to 394.3 cm-1 for j=15 mA/cm2.



Deconvolution of micro-Raman spectra of porous GaP layers prepared at different anodization current densities.

Figure 4.28: Deconvolution of micro-Raman spectra of porous GaP layers prepared at different anodization current densities.


It is important to note that the micro-Raman spectra are the same when taken from different areas of the porous layers prepared at current densities of 5 and 15 mA/cm2. Only samples subjected to dissolution at j=40 mA/cm2 were found to exhibit rather different spectra when scanned by the laser beam (Figure 4.29). Apart from that, the broad Raman band in the region 80 to 200 cm-1, inherent to amorphous GaP [104] was not observed in the porous layers studied. This proves the crystallinity of GaP skeleton remaining after dissolution.


Since the GaP skeleton consists of nanometer-size structures, a reduced thermal conductivity may be expected for porous layers in comparison with the bulk material leading to a temperature enhancement with increasing excitation power. In order to throw light upon this matter, the micro-Raman spectra have been measured at different powers of the exciting laser beam. A Raman signal intensification occurs with increasing the excitation power. No changes in the frequency position and full width at half maximum of Raman peaks were observed at P<2 mW. At the same time a pronounced broadening and low-frequency shift of Raman bands occur in porous layers with a further increase of the excitation power (Figure 4.30). For the purpose of comparison Figure 4.30 presents the dependence of the Raman peak position upon the excitation power for both the as-grown crystals and porous layers fabricated at j=15 mA/cm2.


The local temperature in porous GaP layers under laser-beam excitation can be estimated using the value of the temperature shift gradient for optical phonon frequencies in GaP [105]. ForP=15 mW it equals about 160 Co. Taking into account the nearly symmetric shape of the LO-phonon bands (Figure 4.29), Tiginyanu et al proposed the surface-related mode to be a Froölich mode as first observed by Raman measurements in GaP microcrystals [106]. The effective dielectric constant of a system of column-like oriented pores in GaP can be calculated by using the so called one-pole approximation [107]:


Equation 55

where

Equation 56

Equation 57

and

Equation 58


Here c denotes the GaP concentration, ε1=1 and ε22(ω) are the dielectric functions of bulk GaP in the phonon region. From the poles and zeros of εeff(ω) one can deduce an unchanged (compared with the bulk value) TO phonon, a downward shift of the LO phonon with decreasing c and a Fröhlich mode (degenerate at c~0 and c~1) which splits into TO-like and LO-like surface-related modes for c not equal 0 or 1 as in the case of spherical microcrystals and voids [108].


Micro-Raman spectra from especially selected regions of a porous GaP

Figure 4.29: Micro-Raman spectra from especially selected regions of a porous GaP layer prepared at a current density of 60mA/cm2


In Figure 4.31 the measured spectra are compared with calculations assuming c=0.91 and c=0.75. A column size distribution was taken into account by a Gaussian distribution of the GaP concentration centered at these c values with a standard deviation of 0.1.


Dependence of micro-Raman spectra upon the power P of the exciting laser beam.

Figure 4.30: Dependence of micro-Raman spectra upon the power P of the exciting laser beam. The porous layer was prepared at a current density of 15mA/cm2. The inset shows the shift of the LO band position of the porous layer in comparison with that of bulk n-GaP.


Because the porous GaP is not ideally columnlike shaped, calculations for spheres are enclosed in Figure 4.31 too. The good agreement between the experimental and theoretical results supports the interpretation of the surface-related mode as a Fröhlich mode. The observed frequency shift of the bulk TO phonon, however, cannot be obtained on the basis of an effective-medium approach taking into account only ε2(ω,k=0). This shift may be due to additional confinement effect [109] and/or internal strain.


In conclusion, the surface-related Raman band observed in porous GaP in the gap between the bulk optical phonons was found to shift to lower frequencies and to broaden with increasing anodic current. Taking into account the results of a Raman line-shape analysis based on the effective dielectric function of a composite, the surface-related vibrational mode is interpreted as a Fröhlich mode. A reduced thermal conductivity was evidenced for porous GaP layers as well.


Comparison of a) experimental spectra with theoretical curves obtained in a b) column and c) sphere approximation.

Figure 4.31: Comparison of a) experimental spectra with theoretical curves obtained in a b) column and c) sphere approximation.



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