Degree of polarization of luminescence from GaAs and InP as a function of strain: a theoretical investigation

Daniel T. Cassidy; Daniel T. Cassidy; Jean-Pierre Landesman; Jean-Pierre Landesman

doi:10.1364/AO.394624

Applied Optics
Vol. 59,
Issue 18,
pp. 5506-5520
(2020)
•https://doi.org/10.1364/AO.394624

Degree of polarization of luminescence from GaAs and InP as a function of strain: a theoretical investigation

Daniel T. Cassidy and Jean-Pierre Landesman

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Daniel T. Cassidy and Jean-Pierre Landesman, "Degree of polarization of luminescence from GaAs and InP as a function of strain: a theoretical investigation," Appl. Opt. 59, 5506-5520 (2020)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Check for updates

Related Topics
Table of Contents Category
- Instrumentation and Measurements
Optics & Photonics Topics
?

The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: April 7, 2020
- Revised Manuscript: May 13, 2020
- Manuscript Accepted: May 13, 2020
- Published: June 16, 2020

Abstract

Experimentally, it is known that the degree of polarization (DOP) of luminescence is a sensitive function of strain in III–V materials. It has been assumed that DOP = $-{K_e} ({e_1} - {e_2})$ and that the rotated degree of polarization = $2 {K_e} {e_6}$, where ${K_e}$ is a positive calibration constant, ${e_1}$ and ${e_2}$ are the normal components of strain along perpendicular “1” and “2” directions, and ${e_6} = {e_{12}}$ is the tensor shear strain. ${K_e}$ has been measured experimentally for GaAs and InP. In this paper, the results of a simple analytic determination of expressions for DOP as a function of strain are presented. Given the wide ranges reported for the strain deformation potentials $b$ and $d$, it is not possible to give definitive and meaningful numerical values for expressions for DOP and ${K_e}$. However, the sensitivity of DOP to strain suggests that it might be possible to design simple experiments to provide accurate values for the deformation potentials. The $b$ and $d$ deformation potentials might not be independent. For the results presented here and in the limit of isotropic material, an isotropic result for the DOP is found if $d = \sqrt 3 b$.

Full Article | PDF Article

More Like This

Degree of polarization of photoluminescence from facets of InP as a function of strain: some experimental evidence

Daniel T. Cassidy and Samuel K. K. Lam
Appl. Opt. 60(16) 4502-4510 (2021)

Degree of polarization of luminescence from InP under SiN stripes: fits to FEM simulations

Daniel T. Cassidy and and Jean-Pierre Landesman
Opt. Continuum 2(6) 1505-1522 (2023)

Strain mapping by measurement of the degree of polarization of photoluminescence

Daniel T. Cassidy, S. K. K. Lam, B. Lakshmi, and Douglas M. Bruce
Appl. Opt. 43(9) 1811-1818 (2004)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (2)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (73)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Parameter	Symbol	Value	Unit	Remarks
Electron mass	$m_{o}$	$9.10938356 \times 10^{- 31}$	kg
Electron charge	$q$	$1.6021766208 \times 10^{- 19}$	C
Planck’s constant	$h$	$6.62607004 \times 10^{- 34}$	$J \cdot s$
$ℏ$	$ℏ$	$1.0545718 \times 10^{- 34}$	$J \cdot s$
Boltzmann constant	$k_{B}$	$8.617333262 \times 10^{- 5}$	$eV \cdot K^{- 1}$
$k_{B} T$	$k_{B} T$	25.68	meV	$T = 298 K$

Parameter	Symbol	GaAs	InP	Unit	Remarks
Luttinger parameter	$γ_{1}$	6.98	5.08
Luttinger parameter	$γ_{2}$	2.06	1.60
Luttinger parameter	$γ_{3}$	2.93	2.10
Modified Luttinger parameter	$γ_{1 m}$	0.73	0.11		$T = 298 K$
Modified Luttinger parameter	$γ_{2 m}$	$- 1.06$	$- 0.88$		$T = 298 K$
Modified Luttinger parameter	$γ_{3 m}$	$- 0.19$	$- 0.38$		$T = 298 K$
Bandgap	$E_{g}$	1.519	1.4236	eV	$T = 0 K$
Bandgap	$E_{g}$	1.423	1.354	eV	$T = 298 K$
Conduction band coupling	$A_{p}$	$- 14.7$	–	eVÅ $^{2}$
Matrix element	$E_{p}$	28.8	20.7	eV
Matrix element	$P_{o}^{2}$	3.795	3.217	${eV}^{2}$	$P_{o}^{2} = E_{p} / 2$
Spin-orbit splitting	$Δ_{s o}$	0.341	0.108	eV
Conduction band	$m_{c}$	0.067	0.0795	$m_{o}$	$T = 0 K$
Conduction band	$m_{c}$	0.0635	0.075^a	$m_{o}$	$T = 298 K$
Heavy hole	$m_{H H}$	0.35	0.53	$m_{o}$	$T = 298 K$
Light hole	$m_{L H}$	0.083	0.12	$m_{o}$	$T = 298 K$
$E_{g}$ deformation potential	$a$	$- 8.33$	$- 6.6$	eV	$a = a_{c} + a_{v}$
Valence band deformation potential	$a_{v}$	$- 1.16$	$- 0.6$	eV
Deformation potential	$b$	$- {2.0}_{- 1.9}^{+ 0.34}$	$- {2.0}_{- 0.0}^{+ 1.0}$	eV	Note wide range
Shear deformation potential	$d$	$- {4.8}_{- 1.2}^{+ 2.1}$	$- {5.0}_{- 0.0}^{+ 0.8}$	eV	Note range
Stiffness	$c_{11}$	118.0	102.2	GPa	Crystal coordinate
Stiffness	$c_{12}$	53.5	57.3	GPa	Crystal coordinate
Stiffness	$c_{44}$	59.0	44.2	GPa	Crystal coordinate
Stiffness	$c_{11}^{'}, c_{22}^{'}$	144.75	123.95	GPa	{110} Facet
Stiffness	$c_{33}^{'}$	118.0	102.2	GPa	{110} Facet
Stiffness	$c_{12}^{'}$	26.750	35.55	GPa	{110} Facet
Stiffness	$c_{13}^{'}, c_{23}^{'}$	53.5	57.3	GPa	{110} Facet
Stiffness	$c_{44}^{'}, c_{55}^{'}$	59.0	44.2	GPa	{110} Facet
Stiffness	$c_{66}^{'}$	32.250	24.450	GPa	{110} Facet

Parameter	Symbol	Value	Unit	Remarks
Electron mass	$m_{o}$	$9.10938356 \times 10^{- 31}$	kg
Electron charge	$q$	$1.6021766208 \times 10^{- 19}$	C
Planck’s constant	$h$	$6.62607004 \times 10^{- 34}$	$J \cdot s$
$ℏ$	$ℏ$	$1.0545718 \times 10^{- 34}$	$J \cdot s$
Boltzmann constant	$k_{B}$	$8.617333262 \times 10^{- 5}$	$eV \cdot K^{- 1}$
$k_{B} T$	$k_{B} T$	25.68	meV	$T = 298 K$

Parameter	Symbol	GaAs	InP	Unit	Remarks
Luttinger parameter	$γ_{1}$	6.98	5.08
Luttinger parameter	$γ_{2}$	2.06	1.60
Luttinger parameter	$γ_{3}$	2.93	2.10
Modified Luttinger parameter	$γ_{1 m}$	0.73	0.11		$T = 298 K$
Modified Luttinger parameter	$γ_{2 m}$	$- 1.06$	$- 0.88$		$T = 298 K$
Modified Luttinger parameter	$γ_{3 m}$	$- 0.19$	$- 0.38$		$T = 298 K$
Bandgap	$E_{g}$	1.519	1.4236	eV	$T = 0 K$
Bandgap	$E_{g}$	1.423	1.354	eV	$T = 298 K$
Conduction band coupling	$A_{p}$	$- 14.7$	–	eVÅ $^{2}$
Matrix element	$E_{p}$	28.8	20.7	eV
Matrix element	$P_{o}^{2}$	3.795	3.217	${eV}^{2}$	$P_{o}^{2} = E_{p} / 2$
Spin-orbit splitting	$Δ_{s o}$	0.341	0.108	eV
Conduction band	$m_{c}$	0.067	0.0795	$m_{o}$	$T = 0 K$
Conduction band	$m_{c}$	0.0635	0.075^a	$m_{o}$	$T = 298 K$
Heavy hole	$m_{H H}$	0.35	0.53	$m_{o}$	$T = 298 K$
Light hole	$m_{L H}$	0.083	0.12	$m_{o}$	$T = 298 K$
$E_{g}$ deformation potential	$a$	$- 8.33$	$- 6.6$	eV	$a = a_{c} + a_{v}$
Valence band deformation potential	$a_{v}$	$- 1.16$	$- 0.6$	eV
Deformation potential	$b$	$- {2.0}_{- 1.9}^{+ 0.34}$	$- {2.0}_{- 0.0}^{+ 1.0}$	eV	Note wide range
Shear deformation potential	$d$	$- {4.8}_{- 1.2}^{+ 2.1}$	$- {5.0}_{- 0.0}^{+ 0.8}$	eV	Note range
Stiffness	$c_{11}$	118.0	102.2	GPa	Crystal coordinate
Stiffness	$c_{12}$	53.5	57.3	GPa	Crystal coordinate
Stiffness	$c_{44}$	59.0	44.2	GPa	Crystal coordinate
Stiffness	$c_{11}^{'}, c_{22}^{'}$	144.75	123.95	GPa	{110} Facet
Stiffness	$c_{33}^{'}$	118.0	102.2	GPa	{110} Facet
Stiffness	$c_{12}^{'}$	26.750	35.55	GPa	{110} Facet
Stiffness	$c_{13}^{'}, c_{23}^{'}$	53.5	57.3	GPa	{110} Facet
Stiffness	$c_{44}^{'}, c_{55}^{'}$	59.0	44.2	GPa	{110} Facet
Stiffness	$c_{66}^{'}$	32.250	24.450	GPa	{110} Facet

Abstract

Cited By

Tables (2)

Equations (73)

Applied Optics