Byungwoo Park Semiconductor

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Byungwoo Park

Department of Materials Science and Engineering Seoul National University

http://bp.snu.ac.kr

Semiconductor

http://bp.snu.ac.kr

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Semiconductors

Semiconductor ^Dae-Ryong http://bp.snu.ac.kr 2

Kittel, Solid State Physics (Chapters 7 and 8).

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Forbidden band Empty

Filled

C.B.

V.B.

Valence band edge Conduction band edge

E

_g

• Intrinsic semiconductor Energy band (at 0 K)

• As the temperature increases, electrons are thermally excited from the valence band to the conduction band.

• Both the electrons in the conduction band and holes in valence band

contribute to the electrical conductivity.

Semiconductor Hongsik http://bp.snu.ac.kr 3

Semiconductor Crystal

Kittel, Solid State Physics (Chapter 8).

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Semiconductor ^Jongmin http://bp.snu.ac.kr 4

Energy Band of Semiconductors

_ ___

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Direct Bandgap vs. Indirect Bandgap

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___

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 In the direct absorption process, a photon is absorbed by the crystal with the creation of an electron and a hole.

• Crystal with Direct Gap

• Measurement of band gap: Optical absorption

E

_g

ω

g



e

The threshold of continuous optical absorption at frequency ω

_g

determines the bandgap E

_g

= ħω

_g

e

ω



C.B.

V.B.

C.B.

edge V.B. edge

E

_g

eV Absorption

g

ω

E = 

Semiconductor Hongsik

Direct Bandgap

http://bp.snu.ac.kr 6

http://hynsr.korea.ac.kr/lecture/solid_state_physics/

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e

C.B.

V.B.

C.B. edge V.B. edge

Ω ωg

photon process phonon

process

E_g

Onset of direct transition (no phonon involved)

Ω

g + 

E (Onset of indirect phonon transition)

E_vert eV

Absorption

• Optical absorption E

^g

>>  Ω (~ 0.01 eV - 0.03 eV)

In general

Ω E

(photon)

ω

_g



 = +

∴

Phonon energy involved.

• Crystal with Indirect Gap

Semiconductor Hongsik

Indirect Bandgap

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Semiconductor ^BP ⁸

Direct Bandgap and Indirect Bandgap

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MRS Bulletin (1999)

Semiconductor ^BP ⁹

Bandgap Energy for Semiconductors

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n-Type and p-Type Doping

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Donor state (n-type semiconductor) Acceptor state (p-type semiconductor)

By donor, an excess electron exists near to the conduction band.

Donors (Electrons increased) P

As Sb

By acceptor, a positive hole exists near to the valence band.

Acceptors (Holes increased) B

Ga In Al

E

0

C.B

V.B

acceptor level

Si

Si Si

Si

B

^-

positive hole

acceptor

E

0

C.B

V.B

donor level

Si

Si Si

Si

As

⁺

e-

electron

donor

Column Ⅴ elements

Column Ⅲ elements

Doping

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( ) [

^E ^E ^k ^T

]

T k

n m^e ^B exp _F _C / _B

2 2 ²

3

2  −



 



= 

π

∫

= D ε f ε d ε n ( ) ( )

DOS Fermi-Dirac distribution

 ‘n-p’ constant and independent of impurity concentration at a given temperature.

(

^E ^k ^T

)

m T m

np k^B ( _e _h) exp _g / _B

4 2 ²

3 3

2  −



 



= 

π



( ^E ^k ^T )

m T m

p k

n

_i _i ^B

(

_e _h

) exp

_g

/ 2

_B

2 2

⁴

2 3 3

2

 −



 



= 

= π 

e

h

f

f = 1 − ε

ε ε

f d D

p

= ∫

^E∞^v _h _h

-

( ) ( )

( )

[

^E ^E ^k ^T

]

T

p k^B exp _V _F / _B 2

2 m ²

3

2

h  −



 



= 

π



 

 

 + 

=

e h B

g

F

m

T m k E

E ln

4 3 2

1 ① m

_e

= m

_h

② T = 0

The Fermi level is on the middle of E_g

E

_F

= ½ E

_g

• Carrier Concentration

T k

E

B

• Intrinsic conductivity & carrier concentration (n) controlled by 

g

is large → the concentration of intrinsic carrier → low the conductivity → low

T k

E

B g

Intrinsic Carrier Concentration

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Fermi-Dirac distribution

If

Intrinsic Carrier Concentration

Density of State for Electron

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Thus

, If

Intrinsic Carrier Concentration

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Thus

Intrinsic Carrier Concentration

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(a) Isolated, neutral regions of p-type and n- type material and energy bands for the isolated regions

(b) Junction, showing space charge in the transition region W, the resulting electric field ℇ and contact potential V₀, and the separation of the energy band.

(c) Directions of the four components of particle flow within the transition region, and the resulting current directions.

For the same bandgap energy between p-type and n-type.

Solid State Electronic Devices (6^thedition, Chapter 5) B. G. Streetman and S. K. Banerjee

Semiconductor ^Yumin http://bp.snu.ac.kr 16

Properties of an Equilibrium p-n Junction

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Depletion Layer

Ashcroft, Solid State Physics

_______

____

σ (x) ρ (x) Ф (x)

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Carrier Density at a p-n Junction

Ashcroft, Solid State Physics

Equilibrium

Forward bias

Reverse bias

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Typical한 Si diode에서는 ideal 한 I-V characteristic 이 보인다.

applied forward voltage 는 보통 1 V 보다 작고, breakdown voltage는 impurity concentration 과 다른 parameter에 따라 1 V 보다 작은 값에서부터 수천 voltage 까지 변할 수 있다.

77 K에서 Ge, Si, GaAs, GaAsP diode의

I-V curve.

heavy doping되어 p-type 쪽과 n-type 쪽의 Fermi level이 각각 valence band와 conduction 에 거의 근접했다고 가정하였을 때, 각 물질 의 band gap energy에 가까운 voltage가 가해지 면 current가 급격히 증가한다.

Solid State Electronic Devices (6^thedition, Chapter 5) Ben G. Streetman, Sanjay Kumar Banerjee

A Typical Silicon p-n Junction

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V. I. Klimov, Los Alamos National Laboratory

J. Am. Chem. Soc. (2007)

Type-I and Type-II Band-Edge Alignment

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(b)

A Schottky barrier formed by contacting on n-type semiconductor with a metal having a larger work function:

(a) Band diagrams for the metal and the semiconductor before joining.

(b) Equilibrium band diagram for the junction.

(a)

Schottky Barriers

_____ e

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(b)

A Schottky barrier between a p-type semiconductor and a metal having a smaller work function:

(a) Band diagrams before joining.

(b) Band diagram for the junction at equilibrium.

(a)

Schottky Barriers

h

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The absence of minority carrier injection.

Since the forward current in each case is due to the injection of majority carriers from the semiconductor into the metal.

Switching speed of Schottky barriers is generally better than p-n junction.

A Feature of Schottky Barriers

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Ohmic metal-semiconductor contacts:

(a) q Ф

_m

< q Ф

_s

for an n-type semiconductor.

(b) The equilibrium band diagram for the junction.

Solid State Electronic Devices (6^th edition, Chapter 5) Ben G. Streetman, Sanjay Kumar Banerjee

Ohmic Contact

_____

_____ e

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Ohmic metal-semiconductor contacts:

(a) Ф

_m

> Ф

_s

for an p-type semiconductor.

(b) The equilibrium band diagram for the junction.

Ohmic Contact

_____

h

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Linear I-V characteristics.

No depletion region.

Aligning the Fermi levels at equilibrium calls for accumulation of majority carriers in the semiconductor.

A Feature of Ohmic Contacts

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I-V Characteristics of Ohmic and Schottky Barriers

Current-voltage characteristics of Ohmic and Schottky barrier metal-semiconductor contacts to GaAs.

Schottky contact to GaAs is doped at 10

¹⁵

cm

^-3

, and the Ohmic contact resistance is 10

⁴

Ωcm

²

.

http://www.mtmi.vu.lt/legacy/pfk/funkc_dariniai/diod/schottky.htm

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____

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Schottky junction (n-type semiconductor) Ohmic junction (n-type semiconductor) Barrier

Metal to semiconductor = Ф

_M

- χ

_S

Semiconductor to metal = Ф

_M

- Ф

_S

Negligible Barrier depletion layer is

thin (1-3 atomic layer) at metal

H. Bube, Electrons in Solids (Chapter 10)

Semiconductor ^Yejun http://bp.snu.ac.kr 28

Barrier Height

Vacuum Level Vacuum Level

- 2010-09-29

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Semiconductor ^BP ²⁹

Electron-Hole Recombination of a p-n Junction

Electron Energy

×

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Double Heterostructure Injection Laser

Semiconductor ^BP

h

e

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nonrad rad

rad

k k

k

= + η

Radiative and Nonradiative Recombination

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We know that

Thus

Effective mass m*

Typical variation of group velocity v

_g

and effective mass m as a function of k.*

Effective Mass

H. Bube, Electrons in Solids (Chapter 10)

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Hole = Missing Electron

Kittel, Solid State Physics (Chapter 8)

________________________

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Lorentz force induces charge accumulation at the x – z plane:

→ E

_H

field generation

x

y z

Majority carrier and carrier density can be calculated by Hall measurement.

A

w d

Hall Measurement

34 http://bp.snu.ac.kr

Semiconductor ^Changwoo

http://en.wikipedia.org

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j

_x

B

_z

E

_H

+ + + + + + + + + + + +

<Hall effect of p-type semiconductor>

Hall coefficient

Hall mobility

(n-type) (p-type)

Hall mobility = Major carrier mobility

at high doping concentration

<by theoretical calculation>

Hall Mobility

Semiconductor ^Changwoo - - - -

Electron mobility or hole mobility

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Kittel, Solid State Physics (Chapter 6, Eqs. 53 -55)

σ = ne ² τ/m = neµ _e

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Highly Resistive Substrate

→ accurate Hall measurement of thin-film

substrate thin film

Hall Measurement for Thin Film

Semiconductor ^Changwoo

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기판 : 한 변의 길이는 2-2.1 cm

박막 :

한 변의 길이는 약 1.8 cm

metal contact

위의 schematic figure와 같이 박막의 네 귀퉁이에 metal contact 붙여 Hall measurement를 측정하러 가면 됩니 다. Metal contact으로는 silver나 indium을 쓰는데 저의 경우(Al-doped ZnO 경우)에는 indium을 사용했을 시 에 측정이 더 잘되었습니다.

오른쪽 그림의 (b)와 같이 삼각형 모양의 metal contact을 정확히 귀퉁이에 맞도록 붙이는 것이 가장 좋겠지 만 손으로 붙이는 과정에서 현실적으로 정확히 그림과 같이 붙이기는 어려울 것입니다. 최소한 그림 (c)의 오른쪽 그림 처럼 metal contact이 박막 안쪽으로 들어가지는 않게 하는 것이 좋을 것 같습니다.

Metal contact의 크기는 사람 눈으로 보일 정도의 크기가 되는 선에서 되도록 작게 (현실적으로 위의

schematic figure와 같이 한변의 길이가 1-2 mm 정도 되는 것이 한계일 것 같습니다.) 붙이는 것이 좋을 것 입 니다.

http://www.nist.gov/eeel/semiconductor/hall.cfm

1-2 mm

Hall Measurement ( 반도체공동연구소 ₎

Semiconductor ^Yumin http://bp.snu.ac.kr

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Annealed at 473 K Annealed at 523 K

Sample Preparation: Average size (PbSe nanoparticles) ~5.5 nm ( σ<5.5%) Capped with oleic acid (~1 nm)

Three-monolayers thick

Si SiO₂

Au PbSe QD Au

* Coulomb blockade 양자점에서의전자의 capacity는 온도에 의해

fluctuations이 있음. 그fluctuation이 single electron 이하가 되려면 온도를 낮 추거나 양자점이 아주 작아야함. Si의 경우 10 nm 가 전자 1개의 fluctuation에 해당하고, 안정적으로 전자를 갖고 있으려면 1 nm 가량이 되어야 함. 그렇게 전자가 1-2개 order로 control이 될 경우 양자점에 1개의 전자가 들어가 있으면 coulomb repulsion 때문에 다음 전자가 들어 가는데 더 많은 에너지가 필요하 게 되는 현상을 Coulomb blockade 현상이이라고 함. 본 논문은 5 nm 정도 PbSe 나노입자가 상온에서 Coulomb blockade 현상을 보이고 있음.

Annealing: Tuning the distance between QDs Tunable Quantum Dots

입자간 간격 멀때--> Coulomb Blockade

입자간 간격 중간 정도--> Electronic Hopping 입자간 간격 가까울 때--> QuantumTunneling

Semiconductor ^Tae-Gon ³⁸