1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Basic moments of phonon density of states spectra and characteristic phonon temperatures of group IV, III–V, and II–VI materials
Rent:
Rent this article for
USD
10.1063/1.2721749
/content/aip/journal/jap/101/9/10.1063/1.2721749
http://aip.metastore.ingenta.com/content/aip/journal/jap/101/9/10.1063/1.2721749

Figures

Image of FIG. 1.
FIG. 1.

Material-specific constellations of characteristic phonon temperatures for (a) group IV, (b) B-V and Al-V, (c) Ga-V and In-V, and (d) III–VI materials. The magnitudes of average phonon temperatures pertaining to the lower and upper sections of the PDOS spectra, (solid triangles) and (empty triangles), are shown in proportion to their mean values [Eq. (4)] (solid squares). Shown are also, for comparisons with and , the magnitudes of effective phonon temperatures (see Refs. 3–5), (empty squares), which had been detected in previous studies (see Refs. 3–5) from temperature dependences of fundamental energy gaps, and the limiting magnitudes of Debye temperatures [Eq. (7)], (empty circles), respectively.

Image of FIG. 2.
FIG. 2.

Visualization of the roughly monotonic decrease of the magnitudes of total dispersion coefficients [Eq. (6)] (solid squares), with increasing ratio, [Eq. (6)], of the partial average phonon temperatures, and , pertaining to the lower and upper sections of PDOS spectra. The moderate deviations from strict monotonousness are due to more or less different, material-specific magnitudes of the respective partial dispersion coefficients [Eq. (A2)], and , for the lower and upper sections. The lower and upper boundaries [Eq. (A7)] for (represented by solid and dashed curves, respectively) are due to the usual limitations of and applying to almost all materials under study (except CdS). Empty squares are representing the comparable magnitudes of -related dispersion coefficients (see Refs. 3–5), .

Image of FIG. 3.
FIG. 3.

Visualization of the relatively small deviations from unity of the ratios, [Eq. (A8)], of the limiting Debye temperatures, [Eq. (7)], vs average phonon temperatures of the upper (optical) PDOS-sections, . These ratios show a weak, nearly monotonic increase with increasing ratio [Eq. (6)]. The lower and upper boundaries [Eq. (A9)] for ratios (represented by solid and dashed curves, respectively) are due to the same limitations for partial dispersion coefficients, and , as in Fig. 2.

Image of FIG. 4.
FIG. 4.

Theoretical dependences [Eq. (12)], which follow from the quadruplets of values detected from PDOS spectra (see Ref. 12) for Si and Ge (cf. Tables I and II), in comparison with experimental data (see Ref. 6). Very fine fits of the measured heat capacity data follow from least-mean-square fittings on the basis of Eq. (13), in combination with Eq. (12). (The fitted thermodynamic parameter values are listed in Table II.)

Tables

Generic image for table
Table I.

Characteristic phonon energy and temperature parameters of group IV, III–V, and II–VI materials. Listed are the average phonon energies [Eq. (A1)], and , and the respective average phonon temperatures, and {including their ratios, [Eq. (6)]}, for the lower and upper sections of the PDOS spectra under study. For convenience of notations, we have represented the total moments, [Eq. (2)], of orders , 1, 2, and 4, equivalently by respective (th-order) phonon energies [Eq. (3)], , including the respective average phonon temperatures, [Eq. (4)], dispersion coefficients, [Eq. (5)], and limiting magnitudes of Debye temperatures, [Eq. (7)]. For numerical comparisons with parameters obtained by preceding numerical analyses (Refs. 3–5) of the gap shrinkage effect for the materials under study we have also quoted the corresponding effective phonon temperatures, , dispersion coefficients, , and ratios .

Generic image for table
Table II.

Three-oscillator model parameters following for Si and Ge as solutions of the system of coupled Eq. (11) for the material-specific sets of four moment-related (equivalent) phonon energies, (, 1, 2, and 4), that we have detected in Sec. II from corresponding PDOS spectra (see Ref. 12). For the sake of numerical comparisons we have listed also the thermal counterparts of these PDOS-related parameters as following from least-mean-square fittings of the experimental (isobaric) heat capacity data (see Ref. 6), , on the basis of Eqs. (12) and (13). (The fitted parameters are printed in bold).

Loading

Article metrics loading...

/content/aip/journal/jap/101/9/10.1063/1.2721749
2007-05-09
2014-04-19
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Basic moments of phonon density of states spectra and characteristic phonon temperatures of group IV, III–V, and II–VI materials
http://aip.metastore.ingenta.com/content/aip/journal/jap/101/9/10.1063/1.2721749
10.1063/1.2721749
SEARCH_EXPAND_ITEM