Dispersion, attenuation, and bandgap of in-plane coupled Bloch waves in piezoelectric semiconductor phononic crystal with PN junction

doi:10.1007/s10483-025-3252-7

Abstract

Abstract:

In this paper, the dispersion, attenuation, and bandgap characteristics of in-plane coupled Bloch waves in one-dimensional piezoelectric semiconductor (PSC) phononic crystals are investigated, emphasizing the influence of positive-negative (PN) junctions. Unlike piezoelectric phononic crystals, the coupled Bloch waves in PSC phononic crystals are attenuated due to their semiconductor properties, and thus the solution of Bloch waves becomes more complicated. The transfer matrix of the phononic crystal unit cell is obtained using the state transfer equation. By applying the Bloch theorem for periodic structures, the dispersion relation of the coupled Bloch waves is derived, and the dispersion, attenuation, and bandgap are obtained in the complex wave number domain. It is found that the influence of the PN junction cannot be neglected. Moreover, the effects of the PN junction under different apparent wave numbers and steady-state carrier concentrations are provided. This indicates the feasibility of adjusting the propagation characteristics of Bloch waves through the regulation of the PN heterojunction.

Key words: piezoelectric semiconductor (PSC), phononic crystal, positive-negative (PN) junction, dispersion and attenuation, carrier field, transfer matrix

2010 MSC Number:

O472

Zibo WEI, Peijun WEI, Chunyu XU, Xiao GUO. Dispersion, attenuation, and bandgap of in-plane coupled Bloch waves in piezoelectric semiconductor phononic crystal with PN junction. Applied Mathematics and Mechanics (English Edition), 2025, 46(5): 813-830.

TrendMD

Figures/Tables 9

Fig. 1

Fig. 2

Table 1

The physical constants of N-ZnO and P-GaN[31-32]"

Material	$c 11$ /GPa	$c 33$ /GPa	$c 13$ /GPa	$c 44$ /GPa	$e 31$ / $(C ⋅ m − 2)$
N-ZnO	209.7	210.9	105.1	42.47	$− 0.57$
P-GaN	298.4	289.2	142.5	23.1	$− 0.52$
Material	$e 33$ / $(C ⋅ m − 2)$	$e 15$ / $(C ⋅ m − 2)$	$ρ$ / $(kg ⋅ m − 3)$	$d 11 p (d 33 p)$ / $(cm 2 ⋅ s − 1)$	$d 11 n (d 33 n)$ / $(cm 2 ⋅ s − 1)$
N-ZnO	1.32	$− 0.48$	5 680	0.020 8	2.6
P-GaN	0.61	$− 0.61$	6 070	9.1	26
Material	$μ 11 p (μ 33 p)$ / $(cm 2 ⋅ V − 1 ⋅ s − 1)$	$μ 11 n (μ 33 n)$ / $(cm 2 ⋅ V − 1 ⋅ s − 1)$	$ε 31$ / $(C ⋅ V − 1 ⋅ m − 1)$	$ε 33$ / $(C ⋅ V − 1 ⋅ m − 1)$	$q$ /C
N-ZnO	0.8	100	$7.61 × 10 − 11$	$8.85 × 10 − 11$	$1.602 × 10 − 19$
P-GaN	350	1 000	$8.45 × 10 − 11$	$9.39 × 10 − 11$	$1.602 × 10 − 19$

Table 1

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

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