Estimation of the Heat Capacity of Some Semiconductor Compounds Using n-Dimensional Debye Functions

Abstract

In the present study, a simple and efficient expression for the accurate and quick calculation of the specific heat capacity of semiconductor compounds is presented on the basis of n-dimensional Debye functions using binomial coefficients. As will be seen, the present formulation yields compact, closed-form expressions which enable the straightforward calculation of the heat capacity of solids for arbitrary temperature values. As an example of the application, the calculation is performed for the specific heat capacity of semiconductor compounds. The calculated results have been compared with those reported in the literature and are found to be in good agreement with those of other studies.

Analytic approximation of the Debye function

“…As one can see in figure 4(b) and table 1, the maximum absolute values of the relative deviations |δC V LM | m (for x > 0) decrease monotonically with increasing L from 1 to 2 and with increasing M from 0 to 4. Moreover, using equation (13) gives a higher relative deviation than using equation (9). In the best case for L = 2 and M = 4, the maximum absolute value of the relative deviation |δC V LM | m in the region x > 0 is approximately 0.0009 using equation (9).…”

“…Note that the relative deviation of the third derivative K ′′′ (x) from the reference D ′′′ (x) grows at x → 0 in inverse proportion to x. The ratios of the isochoric heat capacity C V (x) to its value in the high-temperature limit (x → 0), C h = 3R/ν, from equation 9with the approximation derivative K ′′ 10 (x) and from equation (13) with the approximation function K 10 (x) are shown in figure 4 in comparison with the reference dependence C V (x)/C h that is obtained using equation 9with the reference D ′′ (x).…”

“…where the cases A = LM and P correspond to the approximation functions K LM (21) and D P [47]; the last two columns correspond to the use of equations (9) and (13), respectively. In the best case for L = 2, the maximum absolute values of the relative deviations for x > 0 are approximately 0.0007 for K 24 (x), 0.001 for K ′ 24 (x), 0.002 for K ′′ 24 (x) and 0.04 for K ′′′ 24 (x).…”

“…The ratios of the isochoric heat capacity C V (x)/C h from equation (9) with the approximation derivatives K ′′ 2M (x) and from equation (13) with the approximation functions K 2M (x) are shown in figure 4. One can see that, for L = 2 and M = 0 and 1, as well as for L = 1, these ratios are easily distinguishable from the reference dependence C V (x)/C h in figure 4(a).…”

“…One can see that, for L = 2 and M = 0 and 1, as well as for L = 1, these ratios are easily distinguishable from the reference dependence C V (x)/C h in figure 4(a). For L = 2 and M = 2, the dependence C V (x)/C h can be distinguished in the case of the use of equation (13) with the approximation function K 22 (x). The dependences C V (x)/C h for the remaining cases of L = 2 and M = 2, 3 and 4 almost coincide with the corresponding reference dependence in figure 4(a).…”