Semiconductor Nanostructures the tailoring of electrical and optical properties

1
Semiconductor Nanostructures the tailoring of
electrical and optical properties
Gottfried H. Döhler Max Planck Research
GroupInstitute of Optics, Information and
Photonics University of Erlangen91058 Erlangen,
Germanydohler_at_physik.uni-erlangen.de,
http//kerr.physik.uni-erlangen.de/mpf/php/
4 lectures
Topics 1-dimensional quantum confinement in
multi-layer systems Heterostructures, Quantum
wells and Superlattices (design, electronic
structure, growth, transport and optical
properties) (lectures 1 3 ) 3-dimensional
quantum confinement in quantum dots (growth,
electronic structure transport and optical and
electrical properties) (lectures 4, 5)
Style interactive !!! (discussions, based on the
material presented)
2
semiconductor
Ec conduction band edge
Bandgap Eg
Ev valence band edge
3
2 semiconductors
4
heterostructure
5
double-heterostructure
LA

• charge carriers (electrons, holes) confined to
  potential well LA

• if LA sufficiently small quantum confinement ?
  quantum well

6
Quantum well (QW)
DEc cond. band off-set
DEv val. band off-set
LA
7
electron in a QW
DEc cond. band off-set
z
LA
energy of an electron in bulk s.c. A (near band
edge!) ec(k) Ec (?2/2mc)(kx2 ky2 kz2)
quantization of motion in z-direction ec(k)
Ec Ec,m (?2/2mc)(kx2 ky2), with
Ec,m (?2/2mc) kz,m2 , with kz,m? (m1)(p/LA)
m 0, 1, 2,
penetration of wave function into barrier (s.c.
B) has to be taken into account ? ? Ec,m
smaller ? at least 1 bound state in (2-dim.!)
QW (even if LA, DEc small)
8
electron in a QW
DEc cond. band off-set
z
LA
Schrödinger equation for electron in
semiconductor A -(?2/2m0)D vA(r) fcA(k,r)
ec(k) fcA(k,r), with Bloch function fcA(k,r)
exp(ikr) uc,kA(r)
ansatz for QW wave function fc,mj(k,r)
exp(ik?r?) xm (z) uc,k0j(r) j (A, B)
1-dim. effective mass Schrödinger equation for
QW envelope function xm(z) -(?2/2mc)(d2/dz2)
V(z) xm(z) Ec,m(k) xm(z) V(zltLA/2) 0,
V(zgtLA/2) DEc
9
electron in a QW
DEc cond. band off-set
z
LA
1-dim. effective mass Schrödinger equation for
QW envelope function xm(z) -(?2/2mc)(d2/dz2)
V(z)xm(z) Ec,m(k)xm(z)
V(zltLA/2) 0, V(zgtLA/2) DEc
kzA from e ecA(kz) (?2/2mcA)(kzA)2
xmA(z) a exp(ikzAz) a exp(-ikzAz), z lt
LA/2
kzB from e ecB(kz) DEc (?2/2mcB)(kzB)2
xmB(z) b exp(-kzBz),
z gt LA/2
kzB imaginary for e ecB(kz) lt DEc !
eigenvalues e Ec,m from continuity of (1)
xmj(z) and (2) (1/mj) (d/dx)xmj(z) at the
interfaces
10
electron in a QW
DEc cond. band off-set
z
LA
typical values (for GaAs/Al0.3Ga0.7As structure)
mcGaAs 0.067m0, DEc ? 250 meV
for LA 10 nm, 2 bound states Ec,0 ? 50 meV
and Ec,1 ? 180 meV
11
one QW
12
one QW ? many QWs superlattice
LA
LB
d
13
one QW ? superlattice
eigenstates ? minibands
LA
LB
d
14
Minibands in a superlattice superlattice
d
15
tailoring of minibands in a superlattice
superlattice
LA
LB
2-dimensonal subbands in a QW
d
ec(k) Ec Ec,m (?2/2mc)(kx2 ky2)
anisotropic 3-dimensional minibands in a
superlattice (Tight-binding appr.)
ec(k) Ec Ec,m - (Dc,m/2)coskzd
(?2/2mc)(kx2 ky2)
tailoring of the band structure
band off-set DEc depends on Al-content
x
miniband spacing Ec,m,, depends on well width
LA
miniband width Dc,m,, depends on barrier
width LB
16
Growth of Quantum wells and superlattices by
Molecular beam epitaxy (MBE)
schematic
Growth direction
Al
MBE
Growth
As
UHV
Ga
D
0.28nm
Conduction band
Electronic potential
Potential
3eV
1.5eV
Valence band
17
Growth of Quantum wells and superlattices by
Molecular beam epitaxy (MBE)
schematic
GaAs sub-strate (0.5mm, e.g.)
Growth direction
Al
MBE
Growth
As
UHV
Ga
D
0.28nm
Conduction band
Electronic potential
Potential
3eV
1.5eV
Valence band
18
molecular beam epitaxy chamber (MBE, Riber 32P,
e.g.)
19
TEM picture of grown structure (1 period of QCL
structure)
20
Original motivation for semiconductor
superlattices

• L. Esaki and R. Tsu, IBM J. Res. Dev. 14, 61
  (1970)
• Observation of NDC due to Bloch oscillations
  in superlattices
• ---------
• ) F. Bloch, Z. Physik 52, 555 (1928)