Piezoelectric constant temperature dependence in strained [111]-oriented zinc-blende MQW-SOAs

Horacio Soto-Ortiz; Gerson Torres-Miranda

doi:10.3788/COL202321.092501

Journals >Chinese Optics Letters >Volume 21 >Issue 9 >Page 092501 > Article

Chinese Optics Letters
Vol. 21, Issue 9, 092501 (2023)

Piezoelectric constant temperature dependence in strained [111]-oriented zinc-blende MQW-SOAs

Horacio Soto-Ortiz^* and Gerson Torres-Miranda

Author Affiliations

Applied Physics Division, Center for Scientific Research and Higher Education of Ensenada, Ensenada 22860, Mexico

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DOI: 10.3788/COL202321.092501 Cite this Article Set citation alerts

Horacio Soto-Ortiz, Gerson Torres-Miranda. Piezoelectric constant temperature dependence in strained [111]-oriented zinc-blende MQW-SOAs[J]. Chinese Optics Letters, 2023, 21(9): 092501 Copy Citation Text

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Abstract

Here, we present a study of the effective piezoelectric constant (e_{14_e}) temperature dependence in strained [111]-oriented zinc-blende quantum wells (QWs) embedded within a semiconductor optical amplifier (SOA). We determined e_{14_e} using a method that was insensitive to the segregation phenomenon and to the temperature dependence of the bandgap energy, which required neither fitting parameters nor temperature-dependent expressions for energy and out-of-plane effective masses of electrons and heavy holes. An e_{14_e}

= - 0.0534 \pm 0.0040

C · m^-2 at 23°C was obtained for an SOA with 1.2 nm [111]-oriented strained In_0.687Ga_0.313As/In_0.807Ga_0.193As_0.304P_0.696 QWs. Unlike previously published research, where e_{14_e} magnitude increased as temperature rised, we extracted an e_{14_e} magnitude that decreased as temperature increased.

Keywords

excitons piezoelectric constant pyroelectric effect quantum wells quantum-confined Stark effect semiconductor optical amplifiers zinc-blende

E_{x_{sc, {oc}_{n}}} = E_{g} (T, δ E_{hy}, δ E_{sh}, ϕ_{x_{i}}) + E_{q} - E_{b} + Δ E_{s_{sc, {oc}_{n}}} (T, F_{w_{n}}),

(1)

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F_{w_{n}} (T) \approx \frac{ε_{i}}{ε_{w}} \frac{V_{{bt}_{n}} (T)}{L_{i}} - e_{14_{e}} (T) \frac{L_{i} - m L_{w}}{L_{i}} η_{x y},

(2)

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η_{x y} = \frac{2 \sqrt{3}}{ε_{w} ε_{0}} (\frac{C_{11_{w}} + 2 C_{12_{w}}}{C_{11_{w}} + 2 C_{12_{w}} + 4 C_{44_{w}}}) ε_{s},

(3)

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Δ E_{x_{{os}_{n}}} = Δ E_{s_{{oc}_{n}}} - Δ E_{s_{sc}} = (- {\bar{A}}_{ehh} L_{w}^{4} F_{w_{n}}^{2} + Q_{q} L_{i w s_{n}} F_{w_{n}}) - (- {\bar{A}}_{ehh} L_{w}^{4} F_{w_{sc}}^{2}),

(4)

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e_{14_{e}} = \frac{\frac{ε_{i}}{ε_{w}} V_{{bt}_{1}} (L_{i} L_{w} Q_{q} - {\bar{A}}_{ehh} \frac{ε_{i}}{ε_{w}} L_{w}^{4} V_{{bt}_{1}}) - Δ E_{x_{{os}_{1}}} L_{i}^{2}}{η_{x y} (L_{i} - m L_{w}) (L_{i} L_{w} Q_{q} - 2 {\bar{A}}_{ehh} \frac{ε_{i}}{ε_{w}} L_{w}^{4} V_{{bt}_{1}})} .

(5)

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{\bar{A}}_{ehh} = \frac{[- 2 W_{-} + L_{w} Q_{q} (V_{{bt}_{1}}^{2} - V_{{bt}_{2}}^{2}) ε_{i} / ε_{w}] L_{i}}{4 V_{{bt}_{1}} V_{{bt}_{2}} L_{w}^{4} (V_{{bt}_{1}} - V_{{bt}_{2}}) ε_{i}^{2} / ε_{w}^{2}} - \frac{L_{i} \sqrt{R - 4 V_{{bt}_{1}} V_{{bt}_{2}} L_{i}^{2} Δ E_{x_{{os}_{1}}} Δ E_{x_{{os}_{2}}}}}{2 V_{{bt}_{1}} V_{{bt}_{2}} L_{w}^{4} (V_{{bt}_{1}} - V_{{bt}_{2}}) ε_{i}^{2} / ε_{w}^{2}},

(6)

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R = W_{+}^{2} + L_{w} Q {(V_{{bt}_{1}} - V_{{bt}_{2}})}^{2} (W_{+} + M) ε_{i} / ε_{w},

(7)

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W_{\pm} = L_{i} (Δ E_{x_{{os}_{1}}} V_{{bt}_{2}} \pm Δ E_{x_{{os}_{2}}} V_{{bt}_{1}}),

(8)

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M = [\frac{1}{4} {(V_{{bt}_{1}} - V_{{bt}_{2}})}^{2} - V_{{bt}_{1}} V_{{bt}_{2}}] L_{w} Q_{q} ε_{i} / ε_{w},

(9)

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Horacio Soto-Ortiz, Gerson Torres-Miranda. Piezoelectric constant temperature dependence in strained [111]-oriented zinc-blende MQW-SOAs[J]. Chinese Optics Letters, 2023, 21(9): 092501

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