Liberation of electron using a photon

photoelectric effect/photoemission

Science By The Slice

Xiaoshan Xu

July 22, 2016

PHOTOELECTRIC EFFECT

The complete absorption of a photon by a solid with the emission of an

electron. (Handbook of chemistry and physics, David Lide, 87th edition,

Boca Raton, FL : CRC Press, 2006)

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Light (𝐼, 𝜈 ) Electron (𝐸𝑘 , 𝐼𝐸)

Metal: Li, Na, K

Photoelectric effect

https://phet.colorado.edu/en/simulation/photoelectric

𝐼: light intensity

𝜈: light frequency

𝐸𝑘: kinetic energy of

emitted electron

𝐼𝐸: photoelectric

current

Light (𝐼, 𝜈 )

Electron (𝐸𝑘 , 𝐼𝐸)

Properties of the photoelectric effect

𝐼𝐸 ∝ 𝐼 (The intensity of light is

proportional to the induced photo

electric current.)

There is an threshold for the light

frequency to generate photocurrent.

The maximum kinetic energy

increases with the light frequencyhttp://hyperphysics.phy-astr.gsu.edu/hbase/mod2.html

Na

Quantization of light: photon

• The energy of the light propagates in discrete wave packets (photons):

𝐸𝑝 = ℎ𝜈, ℎ is the Plank constant

• Conservation of energy:

𝐸𝑘𝑚𝑎𝑥 = 𝐸𝑝 − 𝜙 = ℎ𝜈 − 𝜙

Vacuum level

Metal

𝜙:𝑤𝑜𝑟𝑘 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛

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Light (𝐼, 𝜈 )

Measurement of Plank constant

Robert Millikan

ℎ = 6.6 × 10−34 Js

http://hyperphysics.phy-astr.gsu.edu/hbase/mod2.html

𝐸𝑘𝑚𝑎𝑥 = 𝐸𝑝 − 𝜙 = ℎ𝜈 − 𝜙

Work functions of metals (eV)Ag 4.26 – 4.74 Al 4.06 – 4.26 As 3.75

Au 5.1 – 5.47 B ~4.45 Ba 2.52 – 2.7

Be 4.98 Bi 4.31 C ~5

Ca 2.87 Cd 4.08 Ce 2.9

Co 5 Cr 4.5 Cs 2.1

Cu 4.53 – 5.10 Eu 2.5 Fe: 4.67 – 4.81

Ga 4.32 Gd 2.90 Hf 3.9

Hg 4.475 In 4.09 Ir 5.00 – 5.67

K 2.29 La 3.5 Li 2.9

Lu ~3.3 Mg 3.66 Mn 4.1

Mo 4.36 – 4.95 Na 2.36 Nb 3.95 – 4.87

Nd 3.2 Ni 5.04 – 5.35 Os 5.93

Pb 4.25 Pd 5.22 – 5.6 Pt 5.12 – 5.93

Rb 2.261 Re 4.72 Rh 4.98

Ru 4.71 Sb 4.55 – 4.7 Sc 3.5

Se 5.9 Si 4.60 – 4.85 Sm 2.7

Sn 4.42 Sr ~2.59 Ta 4.00 – 4.80

Tb 3.00 Te 4.95 Th 3.4

Ti 4.33 Tl ~3.84 U 3.63 – 3.90

V 4.3 W 4.32 – 5.22 Y 3.1

Yb 2.60 [13] Zn 3.63 – 4.9 Zr 4.05

Visible light:

1.6-3.1 eV

Light: Wave and particle

• Klein–Gordon equation (Relativistic)

−ℏ2𝜕2

𝜕𝑡2𝜓 = −ℏ2𝑐2𝛻2 +𝑚2𝑐4 𝜓 = 𝐸2

m=0 for photon:

−ℏ2𝜕2

𝜕𝑡2𝜓 = −ℏ2𝑐2𝛻2𝜓 = 𝐸2

𝜓 = Ae𝑖(2𝜋𝜆𝑥−𝜔𝑡)

, 𝐸 = ℏ𝜔 = ℎ𝜈

𝜔 ≡ 2𝜋𝜈, ℏ ≡ℎ

2𝜋

Light Induced Quantum Transitions

• Transition matrix

𝐻12 = 𝜓1 𝐸0𝑒−𝑖𝜔𝑡 𝜓2

= 𝜓10 𝐸0 𝜓2

0 𝑒−𝑖(𝐸2−𝐸1

ℏ−𝜔)𝑡

Transition probability

𝑃 𝑡 ∝ න0

𝑡

𝐻12𝑑𝑡

2

∝ න0

𝑡

𝑒−𝑖

𝐸2−𝐸1ℏ

−𝜔 𝑡𝑑𝑡

2

∝ 𝜓10 𝐸0 𝜓2

0 2𝛿(𝐸2 − 𝐸1

ℏ− 𝜔)

Light e−𝑖𝜔𝑡

𝜓1 = 𝜓10𝑒−𝑖

𝐸1ℏ𝑡

𝜓2 = 𝜓20𝑒−𝑖

𝐸2ℏ𝑡

Application of photoelectric effect

• Photoelectric cell for light sensing

• Photomultiplier tube for single-photon

detection

Excitation in an insulator (semiconductor)

Vacuum level

Metal

𝜙:𝑤𝑜𝑟𝑘 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛

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Light (𝐼, 𝜈 )

Vacuum level

Insulator

𝐸𝑔: 𝑏𝑎𝑛𝑑 𝑔𝑎𝑝

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Light (𝐼, 𝜈 )

𝑉𝑎𝑙𝑒𝑛𝑐𝑒 𝑏𝑎𝑛𝑑

𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑏𝑎𝑛𝑑 Si

Si

Si

Si

Si

Si

Si

Si

Si

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Light induced electron-hole pair

Photovotaic effect

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h+++

---

𝑥

𝑉𝑑𝑟𝑜𝑝

Electric potential

Depletion zone

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+-

Photodetector: charge coupled device (CCD)

Gate

SiO2

p-Si

𝑉𝐺

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PHOTOEMISSION

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Light (𝐼, 𝜈 ) Electron (𝐸𝑘 , 𝐼𝐸)

Metal and insulators

Photoemission

Binding energy: 𝐸𝐵 = ℎ𝜈 − 𝐸𝑘Binding energy of valence electron

< 100 eV ultraviolet light

Binding energy of core electron:

> keV x-ray

K, n=1

L, n=2M, n=3N, n=4Valence

Vacuum

https://en.wikipedia.org/wiki/X-ray_photoelectron_spectroscopy

Ultraviolet photoelectron spectroscopy (UPS)

http://en.wikipedia.org/wiki/File:ARPESgeneral.png

Fix photon energy

Measure kinetic energy

• Surface sensitive due to small kinetic energy

• Must be in UHV (typically <10-9 Torr)

X-ray photoelectron spectroscopy (XPS)

J. Phys.: Condens. Matter 27 (2015) 175004 .

h-LuFeO3

Auger effect (Secondary photoemission)

• 1st , x-ray excites electron to

conduction band and

generate a core hole

• 2nd , electron recombine

with the hole; the emitted

energy expels another

electronK, n=1

L, n=2M, n=3N, n=4Valence

Vacuum

K, n=1

L, n=2M, n=3N, n=4Valence

Vacuum

X-ray absorption Electron-hole recombination and

emission of another electron

ABSORPTION SPECTROSCOPY

𝜓1 = 𝜓10𝑒−𝑖

𝐸1ℏ𝑡

𝜓2 = 𝜓20𝑒−𝑖

𝐸2ℏ𝑡 𝑃 𝑡 ∝ 𝜓1

0 𝐸0 𝜓20

2𝛿(𝐸2 − 𝐸1

ℏ− 𝜔)

Optical absorption spectroscopy

1.2 1.4 1.6 1.8 2.0 2.20

100

200

300

400

500

600

700

(

cm-1

)

Energy (eV)

300 K

4 K

6A

1g

4T

1g

6A

1g

4T

2g

PHYSICAL REVIEW B 79, 134425 2009

BiFeO3

t2g

eg

Fe3+ 3d5

Spin Parity

Initial 5/2 Even

Final 3/2 Even6A1g

4T1g

Color of BiFeO3 comes from the absorption

X-ray absorption spectroscopy (XAS)

Transmission

Incident x-ray

Secondary

photoemission

(surface sensitive,

a few nm)Fluorescence

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• Transmission is normally

difficult to measure,

especially for thin films

• Fluorescence spectra is

often distorted by self

absorption

• Photoemission is often

used for its surface

sensitivity, especially for

thin films.

XAS using synchrotron x-ray

• Unlike XPS, UPS, the x-ray

energy is canned, which

requires synchrotron source

• UHV is also necessary

X-ray

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XAS at Canadian Light Source

Electronic structures by XAS

LuFeO3

hexagonal

orthorhombic

hexagonal

orthorhombic

X-ray magnetic circular dichroism (XMCD)

Stohr, Siegmann, Magnetism From Fundamentals to Nanoscale Dynamics, Springer, 2006.

Photoemission electron microscopy (PEEM)

Fe magnetic domains

Magnetic domains

hexagonal

orthorhombic

hexagonal

orthorhombic

Structural

domains

Thank you for your attention !