Solid statee divice lecture, Thesis of Solid State Physics

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Lecture 2

OUTLINE

• (^) Important quantities
• (^) Semiconductor Fundamentals

(cont’d)

• (^) Energy band model
• (^) Band gap energy
• (^) Density of states
• (^) Doping

Reading: Pierret 2.2-2.3, 3.1.5; Hu 1.3-1.4,1.6, 2.

Important Quantities

• (^) Electronic charge, q = 1.6 10 -19^ C
• (^) Permittivity of free space, o = 8.854 10 -14^ F/cm
• (^) Boltzmann constant, k = 8.62 10 -5^ eV/K
• (^) Planck constant, h = 4.14 10 -15^ eVs
• Free electron mass, m o = 9.1 10 -31^ kg
• (^) Thermal voltage kT / q = 26 mV at room

temperature

• (^) kT = 0.026 eV = 26 meV at room temperature
• (^) kTln ( 10 ) = 60 meV at room temperature

1 eV = 1.6 x 10-19^ Joules

Energy Band Diagram

• (^) Simplified version of energy band model, showing only the bottom edge of the conduction band ( E c ) and the top edge of the valence band ( E v )
• E c and E v are separated by the band gap energy E G

E c

E v electron energy

distance

Electrons and Holes

(Band Model)

• (^) Conduction electron = occupied state in the conduction band
• (^) Hole = empty state in the valence band
• (^) Electrons & holes tend to seek lowest-energy positions  Electrons tend to fall and holes tend to float up (like bubbles in water)

Increasing hole energy^ Increasing electron energy

E c

E v

electron kinetic energy

hole kinetic energy

P.E.  E c  E reference

E c represents the electron potential energy.

• (^) E G can be determined from the minimum

energy of photons that are absorbed by

the semiconductor

Measuring the Band Gap

Energy

Band gap energies of selected semiconductors Semiconductor Ge Si GaA s Band gap energy (eV)

E c

E v

photon h  > E G

g ( E ) dE = number of states per cm^3 in the energy range betw

Near the band edges:

Density of States

c (^ )^83 2 ^ m * n , DOS ^3 /^2 ^ E Ec 

h

g E ^ ^  for E  E c

for E  E v

EE130/230M Spring 2013 Lecture 2, Slide 8

E c

E v

dE

E

density of states, g ( E

E c

E v

( )^83 2  m * ,  3 /^2  E E 

h

g (^) v E ^  pDOS v 

Si Ge GaA s m n,DOS/* m o

1. 8

6

7 m p,DOS/* m

0. 1

9

Electron and hole density-of-states effective mas

• (^) By substituting a Si atom with a special impurity atom (Column V or Column III element), a conduction electron or hole is created.

Doping

Donors: P, As, Sb

N D ≡ ionized donor concentration (cm-3)

Acceptors: B, Al , Ga, In

N A ≡ ionized acceptor concentration (cm-3)

Doping Silicon with a

Donor

Example: Add arsenic (As) atom to

the Si crystal

The loosely bound 5th valence electron of the As atom “breaks free” and becomes a mobile electron for current conduction.

Doping (Band Model)

Ionization energy of selected donors and acceptors in silicon Donors Acceptors

Dopant Sb P As B Al In

Ionization energy (meV) E c- E D or E A- E v

E c

E v

Donor ionization energy E D

E A

Acceptor ionization energy

Dopant Ionization

n-type Material ( n > p )

N D > N A (more specifically, N D – N A >> n i) :

p-type Material ( p > n )

N A > N D (more specifically, N A – N D >> n i) :

Terminology

donor: impurity atom that increases n

acceptor: impurity atom that increases p

n-type material: contains more electrons than holes

p-type material: contains more holes than electrons

majority carrier: the most abundant carrier

minority carrier: the least abundant carrier

intrinsic semiconductor: n = p = n i

extrinsic semiconductor: doped semiconductor such that majority carrier concentration = net dopant concentration

Summary

• (^) Allowed electron energy levels in an atom give

rise to bands of allowed electron energy levels

in a crystal.

• (^) The valence band is the highest nearly-filled band.
• (^) The conduction band is the lowest nearly-empty band.
• (^) The band gap energy is the energy required to

free an electron from a covalent bond.

• E G for Si at 300 K = 1.12 eV
• Insulators have large E G; semiconductors have small E G