NSM Archive - Gallium Indium Arsenide Phosphide (GaInAsP) - Band structure

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 GaxIn1-xAsyP1-y

Zinc Blende crystal structure
Energy gaps, Eg 0.354(InAs) ÷2.27(GaP) eV 300 K  
Direct energy gaps, Eg
    min
    max

    0.354 (InAs)
    2.17
   
Direct energy gaps composition, Eg 1.35 +0.668x -1.068y +0.758x2 +0.078y2
-0.069xy -0.332x2y +0.03xy2 eV
300 K  
       

Ga0.47In0.53AsyP1-y Remarks Referens
Energy gaps, Eg
(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 EX;
(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 EL
(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 Eso

(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 GaxIn1-xAsyP1-y

GaxIn1-xAsyP1-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 Eg of vs. lattice constant
Solid lines represent direct band region.
Dashed lines represent indirect band region Foyt (1991)
For direct band region (300K):
Eg = 1.35+0.68x -1.068y +0.758x2+ 0.78y2 -0.069 xy -0.332 x2y +0.3 xy2, (eV)
GaxIn1-xAsyP1-y. Energy gap Eg of vs. x and y. 300K
Dashed lines represent the compositions lattice- matched to GaAs (1) and InP (2)
Gorelenok et al. (1981)
GaxIn1-xAsyP1-y. Energy gap Eg of vs. concentration y for lattice-matched.
300K
1 -- GaAs;
2 -- ZnSe
Adachi (1982)
GaxIn1-xAsyP1-y. Energy gap Eg 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):
Eg = 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):
Eg = 1.344 -0.738y +0.138 y2 , (eV)
For compositions lattice-matched to InP (4.2K):
Eg = 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 GaxIn1-xAsyP1-y lattice-matched
to InP :
  Eg = Eg(0) - 4.3·10-4x T2/(T + 224)  
  (eV) Satzke et al. (1988)
      Eg(0) = **** eV    
     
where T is temperature in degrees K    
GaxIn1-xAsyP1-y. Energy gap Eg 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:
       
0/dt ~= 4A/K   at 0=1.3 μm   (y=0.6)   Arai et al.(1980)
0/dt ~= 5A/K   at 0=1.55μm   (y=0.9)  

Intrinsic carrier concentration:

ni = (Nc·Nv)1/2exp(-Eg/(2kBT))
GaxIn1-xAsyP1-y. Intrinsic carrier concentration vs. temperature for GaxIn1-xAsyP1-y alloys 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: Nc

Nc ~= 4.82 x 1015 · (mΓ/m0)3/2T3/2 (cm-3) ~= 4.82 x 1015 · (0.08-0.039)3/2 T3/2 (cm-3) :
(for GaInAsP alloys lattice-matched to InP)

Effective density of states in the valence band: Nv

Nv ~= 4.82 x 1015 · (mh/m0)3/2 T3/2 (cm-3)= 4.82 x 1015 · (0.6-0.18y)3/2 T3/2 (cm-3)
(for GaInAsP alloys lattice-matched to InP)


Dependence on Hydrostatic Pressure

GaxIn1-xAsyP1-y. Hydrostatic-pressure coefficient dependence of the energy gap Eg vs. concentration y for
Adachi (1992)


Band Discontinuities at Heterointerfaces

GaInAsP/InP     Referens
Conduction band discontinuity ΔEc = 268y+3y2 meV   77K Adachi (1992)
Valence band discontinuity ΔEv = 0.7 eV   77K  
Band discontinuities at Ga0.47In0.53As and Al0.48In0.52As heterojunction      
Conduction band discontinuity ΔEc = 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)).
GaxIn1-xAsyP1-y. Conduction band discontinuity ΔEc vs. band-gap
differences ΔEg
between GaxIn1-xAsyP1-y composition 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 me 0.08-0.05y+0.017y2 mo~=
~=0.08-0.039y mo
Ga0.47In0.53AsyP1-y; 300K
for alloys lattice-matched to InP 
Goldberg Yu.A. & N.M. Schmidt (1999)
GaxIn1-xAsyP1-y. Electron effective mass in GaInAsP alloys vs. concentration y for compositions lattice-matched to InP
300K
Pearsall (1982
GaxIn1-xAsyP1-y. Electron effective mass in Ga0.1In0.9As0.3P0.7 alloys vs. electron concentration
80K
Vilkotsky et al.(1986)

Holes

Effective Masses for Zinc Blende GaN   Remarks Referens
       
Effective hole masses (heavy) mh mh ~= (0.6 -0.18y) mo Ga0.47In0.53AsyP1-y; 300K Goldberg Yu.A. & N.M. Schmidt (1999)
Effective hole masses (light) mlp mlp ~= (0.12 -0.099y +0.03y 2) mo
Ga0.47In0.53AsyP1-y; 300K  
Effective hole masses (split-off band) ms mso ~= (0.21 -0.01y -0.05y 2) mo Ga0.47In0.53AsyP1-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

GaxIn1-xAsyP1-y. Ionization energy of Cd vs. concentration y y for GaInAsP alloys lattice-matched to InP
Wehmann et al.(1986)
GaxIn1-xAsyP1-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)