02 dol solid state physics

7/30/2019 02 DOL Solid State Physics

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Detection of Light: Lecture 2

Detection of Light

Lecture 2: Solid State Physics

1Thursday 10 February 2011


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Overview of Course Topics

Before solid state TODAY: Solid State Physics

Intrinsic and Extrinsic Photoconductors

Detector Arrays Artifacts, multiplexers, readout schemes

Bolometers

Heterodyne Receivers



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Photon Detectors respond directly to individual photons

Incoming photons energy....

DetectorMaterial

Wavelengths: From X-ray to infrared

Examples:

Photoconductors, photodiodes,

photoemissive detectors,photographic plates

...is converted into releasing bound charge carriers

+

+--

E = hc



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Electrons

Are fundamental, point-like particles

Carry an electric charge

Are fermions (only one fermion per quantum state)

e

me = 9.11 1031kg

Charge = 1.60 1019C



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Energy Units

1eV = 1.602 1019

J

The electron volt is the amount of energy a free electron gets after

passing through an electrical potential of 1 Volt:

E 1.240

(m)eV



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Photons

Are massless (but have momentum)

Quantized as particles (and as a continuous wave...) Carry no electric charge

Are bosons

E =

hc

p =h



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Electrons and Photons interact through Electromagnetism

The photon is the gauge boson for EM

Accelerating charges make photons

...and photons can be absorbed in bound charge systems

e



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z

Classical Mechanics treat electric charges as pointparticles interacting with electric fields

e

UE =1

40q1

q2

r12Electric Potential Energy between two charges:

r12

Atomic Nucleus with N protons

Np+

Electron with mean separation



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The QM properties of electrons lead to atomic linesand semiconductor bands

i

t(x, t) = H(x, t)

Electrons (and other particles) are described

with Schrodingers Wave Equation:

Multiple electrons around a positively charged

nucleus have four quantum numbers:

n, l, ml, ms

Only ONE FERMION can have one set of

quantum numbers!

Electrons are described by probability clouds

called ORBITALS with specific energies.



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Electrons can absorb or emit photons and change toa different allowed orbital

m = 2 to n = , 4, 5,

Photons of only specific energiescan be absorbed or emitted

e.g. the Hydrogen atom with one electron

Energy level diagram



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Incomplete orbitals provide electrons for bonding

Forming a crystal sharing electrons with other

Si atoms forms a stable LATTICE:

i iii

i iii

i iii

i iiiSi

Energetically they want to have 8

electrons to form a stable configuration:Si

Silicon and Germanium have 4 electrons

in their outermost (n=2) orbital:Si d = 0.230 nm

(In the Periodic Table these are GROUP IV elements)



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Semiconductors can be formed with pairs of elements

Ga atoms alternating with As atoms

form a stable LATTICE:

Ga

Ga

Ga

Ga

Ga

Ga

Ga

Ga

As

As

As

As

As

As

As

As

Gallium has 3 electrons, Arsenic has 5 electrons: Ga As



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Dopants in Silicon

We can dope a pure silicon crystal with small amounts of Group V or Group III elements

i iii

iii

i iii

i iii

Adding a Group V element introduces

conduction electrons and creates n-typesilicon, called a donor.

As

i iii

iii

i iii

i iii

Ga

Adding a Group III element introduces an

electron hole and creates p-type silicon,

called an acceptor.

Pure semiconductors are INTRINSIC,doped semiconductors are EXTRINSIC



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Metals

Metals and Semiconductors on the Periodic Table

Classical

Semiconductors

New Semiconductors



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Atomic orbitals overlap in a crystal to form electronic bands

Isolated atoms Lattice spacing

Decreasing atomic separation

Energy

Outermost orbitals begin

to overlap....

Eg

...bands form at

crystal spacing

1s

s

2p

s

3p



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Semiconductors



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Energy Band Diagram

Energy

g

Ec

Ev

CONDUCTION BAND

VALENCE BAND

BAND GAPhc

> Eg

Electrons can also be THERMALLY excited



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Energy Band Diagram

EnergyCONDUCTION BAND

VALENCE BAND

BAND GAP

Insulator Metal

T > 0K

Intrinsic Semiconductor

T = 0K

Extrinsic

Semiconductor



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Energy Band Diagram for Donors and Acceptors


VALENCE BAND

BAND GAP

Intrinsic

Semiconductor

Extrinsic n-type

Semiconductor

T = 0K

Extrinsic p-type

Semiconductor

Acceptor ionization energy Ea

Donor ionization energy Ed



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Energy Band Diagram for Donors and Acceptors


VALENCE BAND

BAND GAP

Intrinsic

Semiconductor

T > 0K

Extrinsic n-type

Semiconductor

Extrinsic p-type

Semiconductor

Donor ionization energy Ed

Acceptor ionization energy Ea



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Metals, Semiconductors and Insulators

Metals have high electricalconductivity and consist ofpositive ions in a crystal lattice

surrounded by delocalisedelectrons

Insulators (also called dielectrics)resist the flow of electric current

Semiconductors have electricalresistivity between metals andinsulators, which is temperature

dependent

Metals

Semimetals

Semiconductors



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The wavevector k

Electrons are FERMIONS and so they cannot occupy the same quantum states

Even in a material with T=0, the electrons have momentum!

So, we talk about the electrons wavevector, which is related to their momentum:

k = U(k, r)eik.r

Atom



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In reality, band structure is complicated...

SiliconGermanium



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The Size of Bandgaps

For semiconductors, typically: 0 < Eg < 3.6 eV



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Bandgaps and Lattice Struture



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Direct and Indirect Band Gaps

Minimum in the conduction band and maximum in the

valence band are characterized by the wavevector k

If the k-vectors for minimum and maximum are the

same, it is called a DIRECT GAP.

If the k-vectors for minimum and maximum are different

it is called an INDIRECT GAP, and a transition must

involve the absorption or emission of a phonon to

conserve momentum.

source: Wikipedia



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Direct and Indirect Band Gaps

Indirect gaps make electronic transitions less likely, so light-emitting

and laser diodes are almost always made of direct band gap

materials (e.g., GaAs), and not indirect ones (e.g. Si)

Consider a compound material like:

Al and Ga have ~ same atomic size within the lattice are exchangeable

If x 0.7 then bandgap is direct

If x > 0.7 then bandgap is indirect

(Fletcher et al. 1993)



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Electrical Conductivity of a material quantifies how a

material conducts electrical current flow

=1

= R.

A

l

R = electrical resistance (ohms) A = cross-section area (m2)l = length of material (m)

A

R

l

Electrical ResistivityElectrical Conductivity

A sample of uniform material



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Thermal Excitation and the Fermi Energy

The distribution of electrons amongst the energy states is described by the Fermi distribution f()



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f(E) =

1

1 + eEEF

kT

The Energy Distribution of Electrons (1)

n2

n1=e

(E2E1)/kT=e

Eg/kT

n0

=

Ec f(E)N(E) dE

In the classical picture, the energeticdistribution of electrons would be givenby Maxwell Boltzmann statistics:

In the QM picture the concentrationof electrons in the conduction bandis given by:

...where N(E) dE is the density of

states and f(E) the Fermidistribution (Fermi-Dirac statistics):



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For intrinsic semiconductors: Ec EF = EF EV = Eg /2"

T = 0 K



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n0 = Ncf(Ec) where Nc = 2

2meffkT

h2

3/2

n0 = Ncf(Ec) = 2

2meffkT

h2

3/2e(EcEF)/kT

f(Ec) =1

1+e(EcEF)

kT

EcEF>>kT

e(EcEF)

kT

Even at room temperature, the conduction electrons occupy onlythe lowest states in the conduction band.

If f(E)N(E) is close to zero at E>Ec, it can be described by an averageeffective density of states Nc near E ~ Ec:

Hence the Fermi-Dirac statistics become:

...and we get:



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The Fermi Energy in Extrinsic Materials



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Donor and Acceptor Energies

Observed donor Ed and acceptor Eaionization energies:

Donor Si (meV) Ge (meV)

intrinsic 1100 700

P 45 12

As 49 13

Sb 39 10

B 45 10

Ga 65 11

In 157 11

For T = 300K,kT 26 meV



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Summary

Semiconductors can detect photons by absorbing the photon and raising anelectron from a valence band to a conduction band

The energy between the two bands is called the band gap energy

For intrinsic semiconductors, the band gap is large compared to roomtemperature

Doping intrinsic semiconductors forms intrinsic semiconductors, whichintroduce energy levels much smaller than the intrinsic semiconductor bandgap

The conductivity of a semiconductor is dependent on the doping and thetemperature of the detector

Read Detection of Light Chapters 1 and 2Do the Exercise sheet 1


S


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Reference Properties of Semiconductor Materialssecondcolumn:i=indirect,d=direct,D

=diamond,Z=zincblende

,W=wurtzite,H=NaCl;

source:Streetman&Banerjee,Appen

dixIII

02 dol solid state physics

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