Semiconductor Optics

1. Chapter 10
Electro-Optical properties of Semiconductors
Introduction to the Semiconfductor Optics
1/18 Quantum Functional Material & Device Lab.
21-5-2019
Presented by
P. Kedhareswara Sairam

2.  1.Franz-Keldysh effect
 2. DC Stark effect
 3.Electric Field Effect in Two Dimensions
 Quantum-Confined Franz-Keldysh and
 Quantum-Confined Stark effect
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Introduction

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 Effect of electric filed on optical interband transition in semiconductors by ignoring columbic interaction.
 Broadening and low energy shift to the band edge absorption spectra and red shift towards low energies.
 Change in the e-h columbic interaction due to e field and its free carrier absorption.
 Oscillatory structure, and broadening splitting in addition to the broadening shifting and absorption
coefficients .
 Application of electric field over the bulk semiconductor and interaction of Hamiltonian due to e field.
 Application of electric field with e-h pairs (DC-Stark effect).
 Effect of field ionization and (Uncertainty principle) life time of excition, and calculated absorption coefficients
effects of different excitons spectra with increase in field magnitude and changes in absorption.
 Electric field in 2-D
 Quantum-Confined Franz-Keldysh and
 Quantum-Stark effect.
Outline

4.  The Schrodinger equation for the above Hamiltonian
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 Application electric field over bulk semiconductor leads to motion of
electron through lattice associated with interaction Hamiltonian
 Total Hamiltonian of e-h pair in uniform electric field is given by
Relative coordinate eqn of field
 Assuming electron is moving in the Z direction Calculated absorption coefficient
1.FRANZ-KELDYSH EFFECT
Here is the eigen function εn
indicates the energy eigen values for
relative motion and mr and Φn are the
reduced mass of e-h pair and eigen
function.
He
int is Hamiltonian of electric field.

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 The final calculated absorption spectra for direct-allowed transitions.
 Where ε/and Ai is the Airy function given as
Calculated free-carrier absorption with zero
field and field of 105 V/cm for abulk
semiconductor is given in the Fig 10.1
 Airy function shows two types of properties that decaying
exponentially for positive valus and oscillatory motion for
negative values.
 Amplitude of oscillations decreased with in creased in ℏ𝜔
Shift towards the lower energies
called the red shift which can be
explained by photon assisted
tunneling.

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 Field induced tunneling of an electron from VB to CB
Fig.(a) without field
Fig.(b) due to electric field tilts the electron states in
direction for both the bands.
 Band edge absorption of semiconductors in the
absence of columbic interaction leads to the
appearance of absorption below the bandgap and to o
oscillatory absorption variations for energies above
the gap.
 Free carrier absorption in electric field is often called Franz-Keldysh
electroabsorption
Fig.10.2

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 Improving bandgap analysis by including the columbic
interaction between the e and h in a bulk semiconductor.
 The combined potential of e-h pair with e field is given by
 is plotted between the potential and Z
direction
a. Major effect is modification of purely attractive columb wellin
to apotential barrier due the field.
b. Field ionization decreases the life time of exciton leads to the
broadening of resonances (Uncertainty principle) and also
widening of potential well resulting in a red shifting of
excitonic lines.
c. Second order effect of shift is known as dc –Stark effect.
2.DC Stark effect
Fig.10.3

8. The Schrodinger equation by replacing the potential term
Solution of this eqn
Where
Eqn 10.6 - Shows the enhancement of the free
carrier Franz-Keldysh absorption due o the e-h
Columb attraction
 The electric field energy should provide which is at
least equal to the binding energy of exciton across
the Bhor radius.
 The ionization field is about 5x103 V/cm in GaAs
EB –Binding energy
aB- Bhor radius of the excitons
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• As the electric field increases , the
excitons shifts towards lower energies
and broadens.
• If the field strength is increased to
ionization , the bound exicton level
becomes broadened and mixed with
continuum.
• Here the shift is relatively small and
broadening usually dominates the
spectra.
 For exciton n=2 corresponds to degenerated S-like and P-like.
 In addition to the Stark Shifting also we have Stark splitting of degenerate
exciton states.
 For n=2 the p exciton is forbidden and s exciton is allowed, due to the Crystal
inversion symmetry from Ch.4
Fig.10.4

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• The field along the Z direction leads to a
combination of s and pz results to be in the
form of doublet in the absorption spectrum.
• Here also we can observe the broadening
and shifting as increase in field.
Fig.10.6
 Shows the calculated elctroabsorption for a temaparture-
brodended exciton and continuum states at different field
magnitudes.
 Also shows the oscillations on the high energy side of the
exciton as well as broadening and shifting.
Fig.10.5

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 Displays the elctroabsorption coefficient of PbI2 ,with
and without field, and the absorption difference Δα.
 The experimental theories are in good agreement with
theory of excitonic effects.
 Fig.10.8
 Shows the change in absorption spectra with and without an
electric field of 2.85 X 105 V/cm in comparison to excitonic
absorption and free carrier absorption theories
Fig.10.7

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 Shows the changes in GaAs, induced by various field
strength also about the oscillatory structure in Δn( 𝜔).
 Important note that changes in
electroabsorption ,discussed so far gives rise to the
refractive index changes .In the vicinity of the
bandgap energy through the Kramers - Kronig
transformation.
 It will changes in the few orders of the percentages
with the applied field magnitude of ~ 105 V/cm
Fig. 10.9

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3.Electric Field Effect in Two Dimensions
 Quantum-Confined Franz-Keldysh and
 Quantum-Confined Stark effect
 Considering the quasi 2D GaAs-AlxGa1-xAs MQWs and study
about the optical properties in the presence of electric field.
 Applied field may be both in Parallel and perpendicular to the
quantum wells layers.
 The main effect of field is broadening and exciton resonance
 Fig10.10 shows EA spectra for the 3 field magnitudes applied
parallel to the GaAs-AlxGa1-xAs MQWs layers.
 Exicton in MQWs having large binding energy than bulk,
consequently are not easy to ionize.
 Effect of field perpendicular to the layers in MQWs, where e-h Coulomb interaction is neglected ,leads
to the EA spectra May be descried as Quantum Confined Franz-Keldysh effect.
 Where as with Coulomb interaction spectra referred to as Quantum Confined Stark effect.

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Shows the modified energy levels and wave
function for the e and h in an infinite dep
potential well.
 QWs are distorted by the field as shown in
the fig.
 The field pushes the e and h in the opposite
walls of well.
 The field ionization of exciton is inhibited in
2D by the walls of QW where it is dominated
in 3D bulk materials.
 Hence the exciton shifts and persist up to
high fields.
Fig.10.11

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Displays the observed large red shift of the excitonic peak.
 The exciton persists for field strength as high as 1.8 X 105
V/cm (20V)
 In experiment using two 94 A0 GaAs QW centered in
superlattice, in the perpendicular fields.
 Opposite to the behavior of Fig.10.11.
 One more consequence is lowering of symmetry and thus
removal of strict transition rules for
a. The allowed transitions are those between e and h confined states with Δj = 0.
b. The transitions with Δj ‡ 0 are forbidden in the absence of external field.
c. The transitions with Δj ‡ 0 are allowed due to the e and h wave functions are
overlap and is generally zero for i ‡ j
Fig.10.12

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Shows the observed forbidden transitions and their
enhancement with larger field.
 The subscript letters l and h, refer as light and heavy hole
states
 The allowed transitions in the absence of electric field are
 The transitions are forbidden
that have become as allowed due the electric field.
 The consequences of the forbidden transitions in the EA
of the MQWs has derived by using sum rules for the
interband transitions
 It states that, increase of absorption at heigher photon
energiesis acompained by the reduction of peak of the
allowed transition at low photon energies.
Fig.10.13

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Summary
 Electric field effects on electro-absorption coefficients in Bulk semiconductors.
 Electric field induced changes of optical spectra near band edge.
 Role of excitons in variation of field magnitudes.
 Exciton Stark shifting, Stark splitting.
 Broadening and red shift and Franz-Keldysh oscillations.
 Electric field effects in 2D Multi Quantum Wells.
 QCSC and QCFK.

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Thanks for your attention.