Correlation between transport, dielectric, and optical properties of oxidized and nonoxidized porous silicon

Using the correlation between transport, dielectric relaxation phenomena, and the state of oxidation of porous silicon, we have found that there are two major transport routes in the porous silicon medium. The first route of conduction via the disordered tissue that surrounds the silicon nanocrystals dominates for nonoxidized porous silicon and gradually disappears during the first stage of oxidation, where the disordered tissue is oxidized. The second route of tunneling and hopping in between the nanocrystals persists up to the second stage of oxidation where the nanocrystals are oxidized. This dual transport route model is consistent with the presence of two Meyer-Neldel rules and two power-law ac conductivities at mid and high temperatures. In addition, we have found that dc conduction is limited by narrow geometrical constrictions along the transport path that give rise to a Coulomb blockade type activation process. At lower temperatures the transport is characterized by a Cole-Cole relaxation associated with thermally activated intercrystallites hopping due to the shorter distances needed to walk by the carriers. Finally, for oxidized porous silicon we have found a new relaxation mechanism of interfacial polarization that is characterized by long relaxation times at high temperatures.

Figure 1

(Color online) Room temperature PL spectra of the reference (R) and the oxidized PS samples.

Figure 2

The dependence of (a) the PL peak photon energy and (b) the integrated PL on the time of oxidation. The point R is related to the reference PS sample. The vertical dashed lines show the splitting into two stages of oxidation where the PL peak energy and the integrated PL are essentially constant during the first stage.

Figure 3

Infrared absorption spectra of the reference PS (R) and the PS samples that were oxidized for 10 and $150\mathrm{s}$. The arrows indicate the vibrational modes used to obtain Fig. 4 while the dashed lines represent Gaussian fitting of these modes.

Figure 4

The integrated IR absorption versus oxidation time for the various vibrational modes shown in Fig. 3. The empty symbols stand for the $\mathrm{Si}\text{−}\mathrm{O}\text{−}\mathrm{Si}$ modes of vibration while the full symbols stand for the $\mathrm{Si}\text{−}\mathrm{OH}$ mode of vibration. Similar to Fig. 2, the vertical dashed lines represent a separation into two stages of oxidation.

Figure 5

(Color online) Three-dimensional plots of the imaginary part (top) and the real part (bottom) of the complex dielectric function versus frequency and temperature for (left) nonoxidized PS (sample R); PS samples that were oxidized for $30\mathrm{s}$ (middle) and $150\mathrm{s}$ (right), respectively.

Figure 6

The amplitude of the Cole-Cole relaxation process [see Eq. (1)] versus temperature for various oxidized PS samples. The solid line represents the exponential dependency of the amplitude on temperature, which is essentially independent on the time of oxidation.

Figure 7

Arrhenius Plot (semilog scale versus the inverse temperature) of the low temperature, Cole-Cole relaxation times of oxidized PS samples.

Figure 8

Semilogarithmic plot of the CC relaxation time prefactors ${\tau }_0$ versus the corresponding activation energies for a variety of oxidized and nonoxidized PS samples. The arrow indicates the direction of oxidation. The solid line represents the best fit to the data into Eq. (7). The inset schematically shows the model used to derive this equation.

Figure 9

Frequency dependence of the imaginary part of the complex dielectric function $\left({\epsilon }^{″}\right)$ at $373\mathrm{K}$ for oxidized and nonoxidized (sample R) PS samples. The solid lines represent the best fit of the data to Eq. (2) while the dashed lines represent a separate plot of the LF and the HF Jonscher terms for each sample.

Figure 10

(a) The ratio between the high-frequency (HF) and the low-frequency (LF) Jonscher amplitudes; (b) the LF Jonscher exponent, and (c) the HF Jonscher exponent versus temperatures for the reference and for oxidized PS samples.

Figure 11

Arrhenius plot of the dc-conductivity versus the inverse temperature for nonoxidized and oxidized PS samples. The solid lines represent fitting of the experimental data to a simple thermally activated process; see text.

Figure 12

Hilbert transform of the (measured) real part of the complex dielectric function at $523\mathrm{K}$ for oxidized PS samples. Notice that the data do not include the contribution of the dc conductivity. The solid lines represent the best fit to the Cole-Davidson expression (4).

Figure 13

The CD relaxation times versus the inverse temperature.

Figure 14

The experimental values of the dc-conductivity prefactors $(∎)$ and the corresponding activation energies $(엯)$ versus the oxidation time. The dashed lines represent the second MNR for all oxidized PS samples (including sample $t0$) while the notation R stands for the reference PS with a conductivity prefactor that is three orders of magnitude larger (first MNR).

Figure 15

(Color online) Schematic illustration and summary of the various transport channels in PS. The dashed line represents transport routes in the disordered tissue including dc conduction via narrow constrictions (first MNR) and anomalous ac conduction (LF process). The bold dash line represents transport channels associated with hopping in between the nc’s. The red open circles stand for geometrical constrictions along the transport path for both cases.