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Nanophotonics Atilla   Ozgur Nanophotonics Atilla   Ozgur

Nanophotonics Atilla Ozgur - PowerPoint Presentation

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Nanophotonics Atilla Ozgur - PPT Presentation

Cakmak PhD Unit 2 Lecture 17 Quantum Confinement Effects in Solids and Quantum DevicesPart1 Outline Quantum Confinement in Solids Quantum Wells Quantum Wires Nanorods A couple of words ID: 811570

band quantum conduction wells quantum band wells conduction electron inp valance confined states effective wavelength confinement mass state solution

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Slide1

Nanophotonics

Atilla Ozgur Cakmak, PhD

Slide2

Unit 2

Lecture 17: Quantum Confinement Effects in Solids and Quantum Devices-Part1

Slide3

Outline

Quantum Confinement in SolidsQuantum WellsQuantum Wires/Nanorods

Slide4

A couple of words…

Now, since we have just covered the fundamentals of semiconductor physics and also covered quantum effects/potentials in the previous lectures, it is the high time we start looking into quantum confinement devices that are used for photodetection or photoemission. This lecture will initiate that analysis.

Suggested reading: Sergey V. Gaponenko, “Introduction to

Nanophotonics”, 4th Chapter.

Slide5

Quantum Confinement in Solids

Let us remember de Broglie wavelength from the previous lectures:

(The book uses m

0

for m

e

in

vaccum

)

A thin film, hence would confine the electron motion in 1D => Quantum Wells

If we create a rod, wire, we can confine the electron motion in 2D => Quantum Wires

Crystalline nanoparticles (nanocrystals) can offer confinement in 3D => Quantum dots

Slide6

Quantum Confinement in Solids

Remember that we had derived the 3D D(E) as an assignment for particles:

Slide7

Quantum Wells

D(E) gets quantized for confined structures:

Quantum wells can be fabricated by means of epitaxial growth of a multilayer semiconductor structure. A narrow band gap material is buried into a wider band gap material =>

Heterostructure

This is feasible only when the crystal lattices match (

ie

lattice symmetry, chemical

compability

)

Slide8

Quantum Wells

We need perfect lattice match at the

heterostructure interface. Some examples are:GaAs-GaAl

xAs1-x , ZnS-ZnSxSe1-x

, Ge-Ge

x

Si

1-x

, CdSe-CdSe

x

Te

1-x

. Quantum well devices can be cascaded and will result in

quantum well

superlattices

similar to the case we investigated in quantum mechanics review.

An example with GaAs-GaAl

x

As

1-x Quantum Wells:

GaAs is sandwiched between

two

GaAl

x

As

1-x

layers. Band gap of GaAs is 1.42 eV. GaAl

x

As

1-x

has empirically 1.42+1.247x for x < 0.45. There is also a relative offset in the conduction band minimum between the two materials: 0.836x. The electron effective mass is given to be m*=0.063+0.083x. We can construct quantum wells,

superlattices

, by changing the composition of the alloy. Likewise, we can create the quantum well using the valance band offsets. Valance band offset is -0.412x. The effective mass is m*=-(0.51+0.25x).

Let us look at the

wavefunctions

in these possible structures.

Slide9

Quantum Wells

Conduction band quantum well

Valance band quantum well

Slide10

Quantum Wells

An amazing property is their strong sensitivity of the absorption spectrum to an external electric field. Si-Ge offers an easy and cheap integration with CMOS electronic circuitry. Electro-absorptive multiple quantum wells can be tuned to the 1.55um of the optical networks. Their electro-absorptive properties yield electro-refractive effects (changes in the refractive index).

Slide11

Quantum Wells

A step discontinuity in the conduction and valance band offsets create the key capability for the invention of the room temperature semiconductor lasers. The conduction band offset blocks the flow of the electrons, whereas the valance band offset blocks the flow of holes. Electrons and holes get trapped in the active region.

We can adjust the quantum well width to play with the emission wavelength + play with the stoichiometry .

Slide12

Quantum Wells

Quantum well widths are very small compared to the optical communication wavelengths. Most practical applications stack quantum wells to overlap the size of the cascaded quantum wells with the optical mode.

Band diagram and

wavefunctions

in cascaded quantum

wells

Slide13

Quantum Wells

They can also be used as photodetectors due to the absorption capability. In quantum well lasers, these absorption processes happen based on

interband transitions (from valance confined states to the conduction confined states). There can be some

intersubband transitions as well. Whereas for the photodetectors, they have to be intersubband (from one confined state to the other in the conduction band).

Slide14

Quantum Wells

We have to conduct current. Therefore, transition to the conduction band confined state is not good enough. There are several ways of doing this:

Send the electron to the next level of conduction band confined state, which can tunnel through the barrier. Large dark current (unwanted signal) - > Disadvantage

There is only one confined state in the conduction band and electron jumps up to the conduction band continuum. Lowered dark current.

Coupled quantum wells produce a

miniband

that coincides with the upper confined state in the conduction band. The electron will be conducted just like as in the case of b).

a)

b)

c)

Slide15

Quantum Wells

Light polarization (as we will see what it means in the upcoming lectures) will be crucial in the absorption mechanism. Only red colored wave (shown below, not the wavelength!) will be absorbed. There is a dipole moment defined between the confined states of the quantum well (perpendicular to the well) and the direction of this dipole moment has to match the moment of the incoming light.

Slide16

Quantum Wells (problem)

Find the emission wavelength of the InP|In

0.53

Ga

0.4

As|InP laser. The bandgap of

InP

is 1.35eV. The bandgap of In

0.53

Ga

0.4

As is 0.75eV. The conduction band and valance band offsets are 0.25eV and 0.35eV, respectively. The

InP

and In

0.53

Ga

0.4

As effective electron masses in the conduction band are 0.08 and 0.041, respectively. Likewise, it is -0.6 and -0.45 for the valance band for

InP

and In

0.53Ga0.4

As, respectively. The graph of the configuration is shown below. Drawn out of scale.

InP

InP

In

0.53

Ga

0.4

As

1.35eV

0.7eV

0.25eV

0.35eV

Slide17

Quantum Wells (solution)

Remember the bound states in TMM solutions. Focus on each well, separately, in conduction and valance band sections. The only difference are the effective mass changes. Define two different electron masses and use the same formulas as before. For the conduction band:

Slide18

Quantum Wells (solution)

Here V

0

is 0.25eV and m

1

, m

2

are the effective masses in

InP

and

In

0.53

Ga

0.4

As, respectively, multiplied with the electron mass.

Slide19

Quantum Wells (solution)

Here V

0

is 0.25eV and m

1

, m

2

are the effective masses in

InP

and

In

0.53

Ga

0.4

As, respectively, multiplied with the electron mass.

We are 54.4meV away from the conduction band

Slide20

Quantum Wells (solution)

Here V

0

is 0.35eV and m

1

, m

2

are the effective masses in

InP

and

In

0.53

Ga

0.4

As, respectively, multiplied with the electron mass for the valance band part. Since the electron is much heavier, we have more states available.

Slide21

Quantum Wells (solution)

If we look at the options. Laser can emit (band gap=0.75eV):

54.04meV+0.75eV+7.04meV=> Convert to nm wavelength => 1529 nm, this is between the first confined states.

OR

54.04meV+0.75eV+28.7meV=>1488.8nm

All the other options will result in wavelengths that are outside of the telecommunication wavelength regime (1,55um). Hence, 1527nm seems to be the viable option.

Slide22

Quantum Wires/Nanorods

A one dimensional conductor: Quantum wire exhibits the conductivity named as conductivity quantum.

An electron with a high speed will have a lower density of states (D(E)). The speed of the electron determines the conductivity but

speedxD(E) will be constant in this case revealing a constant conductivity.

CdSe

nanowires have been synthesized with size dependent optical properties.

Slide23

Quantum Wires/Nanorods