Band gap, spin orbit splitting and radiative transitions of GaNAsBi ...

URHEA
2 nd International Workshop on Bismuth-Containing
Semiconductors : Theory, Simulation and Experiment
18 th - 20 th July 2011, Guildford, Surrey, UK
Band gap, spin orbit splitting and
radiative transitions of GaNAsBi layers
matched on GaAs substrates
M ed Mourad Habchi*, Ahmed Rebey and Belgacem El Jani
Monastir University, Faculty of Sciences, Physics Department
Research Unit on Hetero-Epitaxy and Applications (URHEA)
TUNISIA
e-mail : mohamedmourad.habchi@fsm.rnu.tn
1

URHEA Outline
‣ Background
‣ Theory & Models
‣ GaAsBi Ternary Alloys
‣ GaNAsBi Quaternary Alloys
‣ Conclusion
2

HMAs
URHEA
Background
• Group II-VI based : ZnX 1-y Te y , X = O, S, Se
• Group III-V based : Ternary & Quaternary Alloys
Dilute nitrides : GaN y As 1-y , In x Ga 1-x N y As 1-y
Dilute bismides : GaAs 1-y Bi y , InAs 1-y Bi y
Dilute nitride-bismides : GaN x As 1-x-y Bi y
Dilute Alloys || (eV) || (%) |R co | (pm) |R co | (%)
GaAs - N 0.86 39.4 48 40.3
GaAs - Bi 0.16 7.3 26 21.8
HMAs : Highly Electronegativity Mismatched Alloys
3

GaN x As 1-x-y Bi y Alloys
URHEA
Background
Lattice parameter : (Vegard’s Law)
a =
1 − y − x a GaAs + xa GaN + ya GaBi
(GaNAsBi/GaAs) Pseudomophic Structure :
Band Offset :
Δa/a = 0 ⟶ x N = 0. 58 y Bi
Interface CBO (eV) VBO (eV) so Offset (eV)
GaN/GaAs - 0.03 - 1.84 - 1.52
GaBi/GaAs - 2.1 - 2.3 0.8 0.6 - 1.1 - 1.3
4

The k.p Method
URHEA
Theory & Models
k
H = H 0 + H k.p + H k + H so + H so
Applied to GaAs near Γ point :
Valence Band (H 6×6 )
• Luttinger Model
• Six-Band Model
• Group Theory & Crystallo.
VB + CB (H 8×8 )
• Second-Order Kane Model
• Eight-Band Model
• Löwdin Perturbation Theory
• {|J, M J >} Basis, J=1/2; 3/2
• {|U n >} Basis, n= 1..8
5

Différent Situations :
BAC Models
URHEA
Theory & Models
CB
(1) : N in GaAs
Gap
(2) : N in GaP
(3) : Bi in GaP
VB
(4) : Bi in GaAs
BAC : Band Anti-Crossing
6

BAC Models
(GaAsBi)
URHEA
Theory & Models
VB : BAC Model (H 12×12 ) BS : BAC Model (H 14×14 )
[1]
[2]
V 6×6 = diag 6 (V Bi )
V Bi = C Bi
y
[1] Alberi et al, Phys. Rev B 75 (2007) 045203
[2] Imhof et al, Semicond. Sci. Technol. 23 (2008) 125009
Reference [1]
E Bi (eV) - 0.4
E Bi-so (eV) - 1.9
C Bi (eV) 1.55 1.6
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BS : BAC Model (H 16×16 )
BAC Model
(GaNAsBi)
URHEA
Theory & Models
H 16×16 =
mod
H 8×8
V N(2×8)
V Bi(6×8)
V N(8×2) V Bi(8×6) H N,Bi(8×8)
V N = C N
V Bi = C Bi
x
y
Reference [1]
E N (eV) 1.65
C N (eV) 2.7
• No interaction between
Bi localized level and CB
states.
• No coupling between N
localized level and VB
states of GaAs.
[1] Wu et al, Semicond. Sci. Technol. 17 (2002) 860
8

E(eV)
E(eV)
URHEA
GaAsBi Ternary Alloys
GaAs .96 Bi .04
Band Structure
@300K
(a) : BAC Model (12x12)
(b) : BAC Model (14x14)
0.5
0.0
-0.5
-1.0
-1.5
-2.0
E hh+
E lh+
E hh-
E so-
E lh-
E so+
0.1(2/a)
(a)
E Bi
E Bi-so
• E g = 1.145 eV
• so+ = 0.518 eV
-2.5
1.8
1.5
1.2
E bc
0.1(2/a)
(b)
• E qad = - 0.687 eV
0
E hh+
E lh+
E so+
between E so+ and E hh- levels in
direction @ k = 0.175(2π/a).
-1
-2
E hh-
E lh-
E so-
E Bi
E Bi-so
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Energy, E(eV)
Energy, E(eV)
0.5
E hh+
(a)
URHEA
GaAsBi Ternary Alloys
0.0
-0.5
-1.0
-1.5
E so+
E lh+
E lh-
E hh-
BS of GaAs .96 Bi .04
@300K along ,
and directions
-2.0
E so-
-2.5
30.00 0.05 0.10 0.15 0.20
2
0.0
-0.5
-1.0
-1.5
-2.0
E so+
E so-
E lh+
E lh-
(b)
Vecteur d'onde, k (2/a)
E hh+
E hh-
0.00 0.05 0.10 0.15 0.20
Wavevector, k (2/a)
E bc
• E c & E so+/- are invariant under high
symmetry direction changes in
the vicinity of Γ.
• This isotropic nature results from
the symmetry “s” of bands.
• E n+/- (k) has Γ 8 -symmetry and
depends on k-direction because
of the symmetry “p” of bands.
10

Energy, E(eV)
URHEA
Energy levels vs Bi content
GaAsBi Ternary Alloys
Using BAC Model (14x14)
2
1
0
-1
E bc
E so+ ↗
• If y Bi ↗ E hh/lh+ ↗
E hh/lh+
E so+
E hh/lh-
• VBM shifts toward the top.
• If y Bi ↗ E cb ↘
E hh/lh- ↘
E so- ↘
-2
E so-
0.00 0.01 0.02 0.03 0.04 0.05
Bi content, y
• Like GaAs, E hh/lh+ & E hh/lh-
Levels are degenerate
@ Γ point.
11

Energy, E (eV)
URHEA
GaAsBi Ternary Alloys
Interband Radiative Transitions
3.5
3.0
T (bc/so-)
Using BAC Model (14x14)
2.5
2.0
1.5
1.0
• Reduction of E g with increase of y Bi
with a rate of 81 meV/%Bi.
T (bc/hh-)
- Literature : (42-84 meV/%Bi)
T (bc/so+)
- URHEA : 42 meV/%Bi [1]
E
g
so-
so+
0.5
0.00 0.02 0.04 0.06 0.08 0.10 0.12
Bi content, y
• Increase of spin-orbit splitting with
a rate of 56 meV/%Bi.
- Exp. Val. : 59 meV/%Bi [2]
‣ Resonance of E g & so+ for y Bi = 0.12 (with E res = 0.733 eV)
[1] Fitouri et al, Semicond. Sci. Technol. 25 (2010) 065009
[2] Fluegel et al, Phys. Rev. Lett. 97 (2006) 067205
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E(eV)
URHEA
GaNAsBi Quaternary Alloys
BS of GaN .023 As .937 Bi .040 @ 300K
Using BAC Model (16x16)
• GaNAsBi is matched to GaAs.
2
E bc+
E N
• Each band is divided into two
1
E bc-
0.1(2/a)
sub-bands.
• Bandgap E g = 0.860 eV
0
-1
E hh+
E lh+
E so+
E hh-
E lh-
E Bi
for y Bi = 0.040 then x N = 0.023
• Bismuth reduces the amount of
Nitrogen to achieve lower gap
-2
E so-
E Bi-so
energy.
- In fact, for GaNAs :
E g = 0.860 eV x N > 5%
13

Energy, E(eV)
Energy levels
vs
URHEA
GaNAsBi Quaternary Alloys
y Bi coupled to x N
Using BAC Model (16x16)
• Like GaAsBi, E hh/lh+ & E hh/lh-
2
1
0
E bc+
E bc-
E hh/lh+
E so+
Levels are degenerate @ Γ
point and VBM shifts toward
the top.
-1
-2
E hh/lh-
E so-
0.00 0.01 0.02 0.03 0.04 0.05
Bismuth composition, y
• If y Bi ↗
+ E cb+ ↗, E hh/lh+ ↗ and E so+ ↗
+ E cb- ↘, E hh/lh- ↘ and E so- ↘
14

Energy, E(eV)
URHEA
GaNAsBi Quaternary Alloys
Interband Radiative Transitions
4
3
T (bc+/so-)
T (bc+/hh-)
T (bc-/so-)
• Strong reduction of E g with
increase of y Bi with a rate of
2
T (bc+/so+)
T (bc+/hh+)
198 meV/%Bi.
1.5
so-
E g
T (bc-/hh-)
T (bc-/so+)
• Like GaAs 1-y Bi y, We note the
1.0
same increase of spin-orbit
0.5
so+
0.00 0.02 0.04 0.06 0.08
Bismuth composition, y
splitting in GaN .58y As 1-1.58y Bi y
with the rate of 56 meV/%Bi.
Resonance of :
E g & so+ for y Bi = 0.068 (with E res = 0.604 eV)
E cb+/hh+ & E cb-/so+ for y Bi = 0.005 & (with E res = 1.685 eV)
E cb+/hh+ & E cb-/hh- for y Bi = 0.014 & (with E res = 1.715 eV)
15

Energy, E(eV)
BS of GaN .023 As .937 Bi .040
@300K along
, and directions
URHEA
GaNAsBi Quaternary Alloys
3
2
1
0
-1
-2
0.00 0.05 0.10 0.15 0.20
Wavevector, k (2/a)
• Qualitatively, the same
behavior of GaAs .96 Bi .04 band
structure is observed
(see Slide n.10).
• The symmetries “s” or “p”
affect the CB and the
restructured VB near Γ point.
• E hh+ () is the similar tp E hh+ (),
but it’s different to E hh+ ()
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URHEA
GaNAsBi Quaternary Alloys
Emissions 1.3 m & 1.55 m
GaN .027 As .927 Bi .046 & GaN .018 As .951 Bi .031
T 1 = E g
hh/lh+ → bc-
T 2
so+ → bc-
T 3
hh/lh- → bc-
T 4
hh/lh+ → bc+
T 5
so+ → bc+
T 6
hh/lh- → bc+
T 7
so- → bc-
T 8
so- → bc+
Emission 1.55 μm 1.3 μm
GaN x As 1-x-y Bi y (x, y) = (.027, .046) (x, y) = (.018, .031)
E (eV) 0.801 0.955
(nm) 1547.0 ≈ 1.55 μm 1298.4 ≈ 1.3 μm
E 1.339 1.441
925.8 (NIR) 860.5 (NIR)
E 1.597 1.646
776.4 (R) 753.3 (R)
E 1.743 1.737
711.4 (R) 713.9 (R)
E 2.280 2.223
543.9 (G) 557.8 (G)
E 2.538 2.428
488.6 (G-B) 510.7 (G)
E 2.988 3.060
415.0 (V) 405.2 (V)
E 3.929 3.842
315.6 (UV) 322.7 (UV)
17

Energy, E(eV)
URHEA
GaNAsBi Quaternary Alloys
GaNAsBi/GaAs Mismatched Structures
1.6
1.4
1.2
1.0
E g
so-
x = 0
0.001
0.005
0.010
0.020
0.030
0.040
0.050
• x N & y Bi are independent.
• E g (y) ↘ x &
E g (x) ↘ y , too
• Nitrogen has no effect on so±
0.8
when Bi content is changing.
0.6
• If y ↗ so+ ↗ & so- ↘
0.4
so+
• Resonance of E g & so+ cannot
0.00 0.01 0.02 0.03 0.04 0.05
Bismuth composition, y
be done for different (x, y)
couples where x, y ≤ 0.05.
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Conclusion
URHEA
Conclusion
We have studied theoretically the electronic band structure of GaAsBi and
GaNAsBi within the framework of the band anti-crossing model .
Using the valence-BAC, the conduction-BAC and the k.p method, BS was
calculated near the Brillouin zone center ( point) for three non-equivalent
directions (, and ).
We have determined also the variation of energy levels and interband
transitions with Bi content, in particular the band gap energy and the spin-orbit
splitting.
In addition, we have treated the case of GaNAsBi leading to the wavelength
emissions of 1.3 m and 1.55 m.
Finally, we note the possibility to obtain the resonance of band gap and
spin-orbit splitting when Bi content increases.
19

Thank
You Very
Much
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