From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005) Sinai University Faculty of Engineering Science Department of Basic sciences 4/25/2020 1

Course name: Electrical materials Code: ELE163

Text references

1- Principles of Electronic Materials and Devices, 3 rd 2- Kittel, Introduction to Solid State Physics 3-College Physics , Serway, 7 th edition 4-Lecture notes (power points) 5- Internet sites edition Prepared by

Pr Ahmed Mohamed El-lawindy

From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

[email protected]

Faculty site: www.engineering.su.edu.eg

2

From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

These PowerPoint color diagrams can only be used by instructors if the 3 rd Edition has been adopted for his/her course. Permission is given to individuals who have purchased a copy of the third edition with CD-ROM Electronic Materials and Devices to use these slides in seminar, symposium and conference presentations provided that the book title, author and © McGraw-Hill are displayed under each diagram.

4.3 Semiconductors, Si, Ge, GaAs The electronic structure of

14

Si

Need explanation n=3 n=2 n=1 Very close to the nucleus Full and stable orbits From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw Hill, 2005) Fig 4.15

Explanation

(b) When Si is about to bond, the one 3s orbital and the three 3p orbitals become perturbed and mixed to form four hybridized orbitals,  hyb , called sp 3 orbitals, which are directed toward the corners of a tetrahedron. The  hyb orbital has a large major lobe and a small back lobe. Each  hyb orbital takes one of the four valence electrons.

sp

3

hybridization

The 3s and 3p energy levels are quite close, and when five Si atoms approach each other, the interaction results in the four orbitals   (3s),  (3p

x

), (3p

y

) and  (3p

z

) mixing together to form four new hybrid orbitals, which are directed in tetrahedral directions; that is, each one is aimed as far away from the others as possible.

Other examples: Ge, Silane- SiH

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw Hill, 2005) 4 , methane-CH Fig 4.16

4 , InP, GaAS

Si- Solid

(a) Formation of energy bands in the Si crystal first involves hybridization of 3s and 3p orbitals to four identical  hyb orbitals which make 109.5

o with each other as shown in (b). (c) neighboring Si atoms can overlap to form 

B

or  hyb orbitals on two 

A

. The first is a bonding orbital (full) and the second is an antibonding orbital (empty). In the crystal yB overlap to give the valence band (full) and 

A

overlap to give the conduction band (empty).

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw Hill, 2005) Fig 4.17

Energy band diagram of a semiconductor. CB is the conduction band and VB is the valence band. At T =0 0 K, the VB is full with all the valence electrons.

From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005) Fig 4.18

4.4 Electron Effective mass

(a) An external force F acceler ext applied to an Electron in a vacuum results in an ation a vac = F ext / m e .

(b) An external force F ext applied to an Electron in a crystal results in an acceleration a cryst = F cryst / m e* From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw Hill, 2005) Fig 4.19

Ch 5: Objectives

• • • • 1-Develop a basic understanding of the properties of intrinsic and extrinsic semiconductors 2- Understand the conduction mechanisms for both p- and n type semiconductors 3- Illustration of the importance of Fermi level 4- Calculate the concentration of donors and acceptors via solved examples and problems From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

Chapter 5: Semiconductors

• Intrinsic semiconductors The crystal consists of Si atoms perfectly bonded to each other in the diamond structure, • number of free electrons equals the number of free holes Extrinsic Semiconductors Contains impurities or crystal defects, such as dislocations and grain boundaries • number of free electrons not equals the number of free holes, • extra acceptors, p-type or donors, n-type semiconductors+ .

•

At T> T 0

• Si vibrates in its lattice, with an average energy, 3kT, not enough to break Si Si bond.

• In some region, this energy is sufficient to break a bond, creating an electron and a hole in its bond site.

• Free electrons and holes are created, wonder in the lattice, so that both contribute to electrical conduction.

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

5.1 Intrinsic semiconductor

5.1.1 Silicon crystal and energy band diagram The width of conduction band is called electron affinity,

(d)

(a) A simplified two-dimensional illustration of a Si atom with four hybrid orbitals  hyb . Each orbital has one electron.

(b) A simplified two-dimensional view of a region of the Si crystal showing covalent bonds.

(c) The energy band diagram at absolute zero of temperature.

(d) A two-dimensional pictorial view of the Si crystal showing covalent bonds as two lines where each line is a valence electron.

Fig 5.1

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

5.1.2 Electrons and holes

( a) A photon with an energy greater than E g excite an electron from the VB to the CB.

can Thermal vibrations of atoms can break bonds and (b) When a photon breaks a Si-Si bond, a free electron and a hole in the Si-Si bond is created.

Fig 5.3

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) thereby create electron-hole pairs.

Explanation A pictorial illustration of a hole in the valence band wandering around the crystal due to the tunneling of electrons from neighboring bonds.

Fig 5.5

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

5.1.3 Conduction in semiconductors

Total energy, E In case of no electric field, E

x , E=KE + PE

In case of electric Field, E=KE+PE+PE(x)

(dV/dx)=-E x , V(x)=-Ax+B, PE(x)= -eV(x)

So as x increases, PE(x) increases When an electric field is applied, electrons in the CB and holes in the VB can drift and contribute to the conductivity.

(a) A simplified illustration of drift in E direction of E

x

, whereas PE increases.

x

.

(b) Applied field bends the energy bands since the electrostatic PE of the electron is –eV(x) and V(x) decreases in the Fig 5.6

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

Electron and Hole Drift Velocities

Current density: J=env

de

v

de

=



e

E

x

and

v

dh

=



h

E

+ epv

dh x v de

= drift velocity of the electrons, electric field, v

dh



e

= electron drift mobility, E

x

= drift velocity of the holes, 

h

= applied = hole drift mobility

Conductivity of a Semiconductor



e

 

e



e m

*

e

= en



e



h



e



+ ep

m h

* 

h h

 = conductivity, e = electronic charge, n = electron concentration in the CB, 

e

electron drift mobility, p = hole concentration in the VB,

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005) 

h

= hole drift mobility =

5.1.4 Electron and hole concentration

(a) Energy band diagram.

(b) Density of states (number of states per unit energy per unit volume).

(c) Fermi-Dirac probability function (probability of occupancy of a state).

(d) The product of g (E) and f (E) is the energy density of electrons in the CB (number of electrons per unit energy per unit volume). The area under n

E

(E) versus E is the electron concentration.

Fig 5.7

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

Electron Concentration in CB

n



N c

exp    (

E c



kT E F

)   5.6

n = electron concentration in the CB, N

c

edge, E

c

= conduction band edge, E

F

= effective density of states at the CB = Fermi energy, k = Boltzmann constant, T = temperature

Effective Density of States at CB Edge

N

c

 2   2 

m

e

*

h

2

kT

  3 / 2 5.7

N c

= effective density of states at the CB edge, m

e *

= effective mass of the electron in the CB, k = Boltzmann constant, T = temperature, h = Planck’s constant From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

Hole Concentration in VB

p



N v

exp   (

E F



kT E v

)   5.8

p = hole concentration in the VB, N

v

= Fermi energy, E

v

= effective density of states at the VB edge, E = valence band edge, k = Boltzmann constant, T = temperature

F

Effective Density of States at VB Edge

N

v

 2  2 

m

h

*

h

2

kT

  3 / 2 5.9

N v

= effective density of states at the VB edge, m

h *

= effective mass of a hole in the VB, k = Boltzmann constant, T = temperature, h = Planck’s constant From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

np



n i

2

Mass Action Law



N c N v

exp   

E g kT

 

n i

= intrinsic concentration

5.11

The np product is a constant, n

i

2 , that depends on the material properties N

c

, N

v

,

E g

, and the temperature. If somehow n is increased (e.g. by doping), p must decrease to keep np constant.

From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

Fermi Energy in Intrinsic Semiconductors

E Fi



E v

 1 2

E g

 1 2

kT

ln  

N c N v

  5.12

E Fi

= Fermi energy in the intrinsic semiconductor, E

v

= valence band edge, E

g

is the bandgap energy, k = Boltzmann constant, T = temperature, N

c

= E = effective

c

density of states at the CB edge, N

v

= effective density of states at the VB edge

- E v E Fi



E v

 1 2

E g

 3 4

kT

ln  

m e

*

m h

*  

m e *

= electron effective mass (CB), m

h *

= hole effective mass (VB) 5.13

From equations 5.6, 5.7, 5.8, 5.9, 5.10, 5.11

Proof equations 5.12 and 5.13

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

Since n i 2 =np=constant means that if n increases p decreases If intrinsic semiconductor ,

n=p

N c =N v , or m* e =m* h Then E Fi =E v + ½ E g E F

in the middle If n-type semiconductor ,

n>p

Then E

c -E F

Then E

F

is closer to E

c

than E

v

If p-type semiconductor ,

p>n

Then E

c -E F

Then E

F

is closer to E

v

than E

c

Fig 5.8

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Energy band diagrams for (a) Intrinsic, (b) n-type, and (d) p-type semiconductors.

In all cases, np = n

i

2

Average Electron Energy in CB

E

CB 

E c

 3 2

kT E

C B = average energy of electrons in the CB, E

c

constant, T = temperature = conduction band edge, k = Boltzmann (3/2)kT is also the average kinetic energy per atom in a monatomic gas (kinetic molecular theory) in which the gas atoms move around freely and randomly inside a container. The electron in the CB behaves as if it were “free” with a mean kinetic energy that is (3/2)kT and an effective mass m

e *.

From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

Important notes for examination Don’t memorize equations but know the physical meaning for each physical parameter

From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

5.2 Extrinsic semiconductors

5

B 2p

1 14

Si 3s

2

3p

2 15

p 3s

2

3p

3 31

Ga 4s

2

4p

1 32

Ge 4s

2

4p

2 33

As 4s

2

4p

3

1As: 10

6

Arsenic-doped Si crystal.

The four valence electrons of As allow it to bond just like Si, but the fifth electron is left orbiting the As site. The energy required to release the free fifth electron into the CB is very small.

Fig 5.9

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

Si

Binding energy E b

 

E I



me

4 8 

o

2

h

2  2 .

18  10  18 J  13.6

eV, for n  1

for an electron around E b Si

 8 

m

*

e o

2 

e r

2 4

h

2  0 .

032 eV notice that 3kT  0.07

eV

As



in Si environmen t

, 

r

,

and m



m e

* Fig 5.10

Energy band diagram for an n-type Si doped with 1 ppm As. There are donor energy levels just below E c around As + sites.

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

n-Type Conductivity

 

eN d



e

 

e



n i N d

2   

h



eN d



e

 = electrical conductivity e = electronic charge

N d

= donor atom concentration in the crystal 

e

= electron drift mobility, n

i

= intrinsic concentration, 

h

= hole drift mobility From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

5.2.2 p-type doping

5

B 2s

2

2p

1 14

Si 3s

2

3p

2 15

p 3s

2

3p

3 31

Ga 4s

2

4p

1 32

Ge 4s

2

4p

2 33

As 4s

2

4p

3 Boron-doped Si crystal.

B has only three valence electrons. When it substitutes for a Si atom, one of its bonds has an electron missing and therefore a hole, as shown in (a). The hole orbits around the B site by the tunneling of electrons from neighboring bonds, as shown in (b). Eventually, thermally vibrating Si atoms provide enough energy to free the hole from the B site into the VB, as shown.

Fig 5.11

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

 

eN a



h

Energy band diagram for a p-type Si doped with 1 ppm B. There are acceptor energy levels E

a

just above E

v

around B sites. These acceptor levels accept electrons from the VB and therefore create holes in the VB.

Fig 5.12

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

Compensation Doping

If both donors or acceptors are doped to an intrinsic semiconductor

More donors than acceptors

n

More acceptors than donors

p

 

N N d a

From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)  

N N a d N d p



N a



n i

2

n



n i



N d n i

2 

N a N a



N d



n i n



n i

2

p



N a n i

2 

N d