NSM Archive - Gallium Indium Arsenide Phosphide (GaInAsP)

GaInAsP - Gallium Indium Arsenide Phosphide

Band structure and carrier concentration

Basic Parameters
Band structure
Intrinsic carrier concentration
Lasing wavelength
Effective Density of States in the Conduction and Valence Band
Temperature Dependences
Dependences on Hydrostatic Pressure
Band Discontinuities at Heterointerfaces
Effective Masses and Density of States
Donors and Acceptors

Basic Parameters for Ga_xIn_1-xAs_yP_1-y

Zinc Blende crystal structure

Energy gaps, E_g	0.354(InAs) ÷2.27(GaP) eV	300 K
Direct energy gaps, E_g min max	0.354 (InAs) 2.17
Direct energy gaps composition, E_g	1.35 +0.668x -1.068y +0.758x² +0.078y² -0.069xy -0.332x²y +0.03xy² eV	300 K

	Ga_0.47In_0.53As_yP_1-y	Remarks	Referens
Energy gaps, E_g	(1.344-0.738y+0.138y²) eV	300 K	Goldberg Yu.A. & N.M. Schmidt (1999)
Electron affinity	##### eV	300 K
*Conduction band*
Energy separation between X valley and top of the valence band E_X;	(2.19-0.86y) eV	300 K	Goldberg Yu.A. & N.M. Schmidt (1999)
Energy separation between L valley and top of the valence band E_L	(1.93-0.73y) eV	300 K
Effective conduction band density of states	2.5x10¹⁹(0.08-0.039y)^3/2 cm^-3	300 K
*Valence band*
Energy separation of spin-orbital splitting E_so	(0.11+0.24y) eV	300 K
Effective valence band density of states	2.5x10¹⁹(0.6-0.18y)^3/2 cm^-3	300 K
Intrinsic carrier concentration	4.3 x 10⁸ cm^-3 (for y=0.27) 4.4 x 10⁹ cm^-3 (for y=0.47) 6.7 x 10¹¹ cm^-3 (for y=1.0)	300 K

Band structure for Ga_xIn_1-xAs_yP_1-y

	Ga_xIn_1-xAs_yP_1-y (zinc blende, cubic). Band structure of alloys lattice-matched to InP. Important minima of the conduction band and maxima of the valence band.. For details see Goldberg Yu.A. & N.M. Schmidt (1999) .
	+Energy gap E_g of vs. lattice constant Solid lines represent direct band region. Dashed lines represent indirect band region Foyt (1991) For direct band region (300K): E_g = 1.35+0.68x -1.068y +0.758x²+ 0.78y² -0.069 xy -0.332 x²y +0.3 xy², (eV)
	Ga_xIn_1-xAs_yP_1-y. Energy gap E_g of vs. x and y. 300K Dashed lines represent the compositions lattice- matched to GaAs (1) and InP (2) Gorelenok et al. (1981)
	Ga_xIn_1-xAs_yP_1-y. Energy gap E_g of vs. concentration y for lattice-matched. 300K 1 -- GaAs; 2 -- ZnSe Adachi (1982)
	Ga_xIn_1-xAs_yP_1-y. Energy gap E_g of vs. x and y. 300K Dashed lines represent the compositions lattice- matched to GaAs (1) and InP (2) Gorelenok et al. (1981)

For direct band region (300K):
E_g = 1.35 +0.68x -1.068y +0.758x²+ 0.078y² -0.069 xy -0.332 x²y +0.3 xy², (eV)
For compositions lattice-matched to InP (300K):
E_g = 1.344 -0.738y +0.138 y² , (eV)
For compositions lattice-matched to InP (4.2K):
E_g = 0.41(1-x)y +1.42(1-x)(1-y)+ 1.51xy +2.34x(1-y) -0.54x(1-x) -0.17y(1-y) = 1.42 - y +0.37 y², (eV)
Benzaquen et al.(1994)

Brillouin zone of the face centered cubic lattice, the Bravais lattice of the diamond and zincblende structures.

Brillouin zone of the hexagonal lattice.

Temperature Dependences

The energy gap versus temperature for Ga_xIn_1-xAs_yP_1-y lattice-matched
to InP :

E_g = E_g(0) - 4.3·10^-4x T²/(T + 224)	(eV)	Satzke et al. (1988)
E_g(0) = **** eV		Satzke et al. (1988)

where T is temperature in degrees K

Ga_xIn_1-xAs_yP_1-y. Energy gap E_g of vs. temperature for three compositions lattice-matched to InP.
1 -- y=0.3;
2 -- y=0.48;
3 -- y=0.69.
Yamazoe et al. (1981)

Lasing wavelength λ₀

Lasing wavelength λ₀ versus temperaturefor GaInAsP/InP double-hetero-structure lasers:


dλ₀/dt ~= 4A/K	at dλ₀=1.3 μm	(y=0.6)	Arai et al.(1980)
dλ₀/dt ~= 5A/K	at dλ₀=1.55μm	(y=0.9)

Intrinsic carrier concentration:

n_i = (N_c·N_v)^1/2exp(-E_g/(2k_BT))

Ga_xIn_1-xAs_yP_1-y. Intrinsic carrier concentration vs. temperature for Ga_xIn_1-xAs_yP_1-yalloys lattice-matched to InP.
1 -- y= 1;
2 -- y= 0.47;
3 -- y= 0.27;
3 -- y= 0.0.
Yamazoe et al. (1981)

Effective density of states in the conduction band: N_c

N_c ~= 4.82 x 10¹⁵ · (m_Γ/m₀)^3/2T^3/2 (cm^-3) ~= 4.82 x 10¹⁵ · (0.08-0.039)^3/2T^3/2 (cm^-3) :
(for GaInAsP alloys lattice-matched to InP)

Effective density of states in the valence band: N_v

N_v ~= 4.82 x 10¹⁵ · (m_h/m₀)^3/2T^3/2 (cm^-3)= 4.82 x 10¹⁵ · (0.6-0.18y)^3/2T^3/2 (cm^-3)
(for GaInAsP alloys lattice-matched to InP)

Dependence on Hydrostatic Pressure

Ga_xIn_1-xAs_yP_1-y. Hydrostatic-pressure coefficient dependence of the energy gap E_g vs. concentration y for
Adachi (1992)

Band Discontinuities at Heterointerfaces

GaInAsP/InP			Referens
Conduction band discontinuity	ΔE_c = 268y+3y² meV	77K	Adachi (1992)
Valence band discontinuity	ΔE_v = 0.7 eV	77K
Band discontinuities at Ga_0.47In_0.53As and Al_0.48In_0.52As heterojunction
Conduction band discontinuity	ΔE_c = 520 meV	300K	see also Adachi (1992)

The conduction-band discontinuities DEc versus band-gap
differences DEg between
composition and InP for GaInAsP/InP
heterojunctions. 300K.
(after Forrest et al.(1984)).

Ga_xIn_1-xAs_yP_1-y. Conduction band discontinuity ΔE_c vs. band-gap
differences ΔE_g between Ga_xIn_1-xAs_yP_1-ycomposition and InP
heterojunctions.
300K
Forrest et al.(1984)

Effective Masses and Density of States:

Electrons

For wurtzite crystal structure the surfaces of equal energy in Γ valley should be ellipsoids, but effective masses in z direction and perpendicular directions are estimated to be approximately the same:

Effective Electron Masses		Remarks	Referens
Effective electron mass m_e	0.08-0.05y+0.017y² m_o~= ~=0.08-0.039y m_o	Ga_0.47In_0.53As_yP_1-y; 300K for alloys lattice-matched to InP	Goldberg Yu.A. & N.M. Schmidt (1999)

	Ga_xIn_1-xAs_yP_1-y. Electron effective mass in GaInAsP alloys vs. concentration y for compositions lattice-matched to InP 300K Pearsall (1982
	Ga_xIn_1-xAs_yP_1-y. Electron effective mass in Ga_0.1In_0.9As_0.3P_0.7 alloys vs. electron concentration 80K Vilkotsky et al.(1986)

Holes

Effective Masses for Zinc Blende GaN		Remarks	Referens

Effective hole masses (heavy) m_h	m_h ~= (0.6 -0.18y) m_o	Ga_0.47In_0.53As_yP_1-y; 300K	Goldberg Yu.A. & N.M. Schmidt (1999)
Effective hole masses (light) m_lp	m_lp ~= (0.12 -0.099y +0.03y ²) m_o	Ga_0.47In_0.53As_yP_1-y; 300K
Effective hole masses (split-off band) m_s	m_so ~= (0.21 -0.01y -0.05y ²) m_o	Ga_0.47In_0.53As_yP_1-y; 300K

Donors and Acceptors

For composition alloys lattice-matched to InP:

Ionization energies of Shallow Donors		Remarks
Sn, Ge, Si, Te, S	~ 3 meV		Goldberg Yu.A. & N.M. Schmidt (1999)
Ionization energies of Shallow Acceptor
Mg	~ 35 meV		Goldberg Yu.A. & N.M. Schmidt (1999)
Zn	37.5-22 eV	for y=0.3-0.9
Cd	~ 60-30 meV	for y=0.2-0.9
Be	~ 40 meV

	Ga_xIn_1-xAs_yP_1-y. Ionization energy of Cd vs. concentration y y for GaInAsP alloys lattice-matched to InP Wehmann et al.(1986)
	Ga_xIn_1-xAs_yP_1-y. Ionization energy of Cd vs. acceptor concentration Na for four GaInAsP alloys lattice-matched to InP 77K 1 - y=0 (InP); 2 - y=0.47; 3 - y=0.64; 4 - y=1 Wehmann et al.(1986)