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```Semiconductor Device Physics
Lecture 2
Dr. Gaurav Trivedi,
EEE Department,
IIT Guwahati
Electronic Properties of Si
 Silicon is a semiconductor material.
 Pure Si has a relatively high electrical resistivity at room
temperature.
 There are 2 types of mobile charge-carriers in Si:
 Conduction electrons are negatively charged,
e = –1.602  10–19 C
 Holes are positively charged,
p = +1.602  10–19 C
 The concentration (number of atom/cm3) of conduction electrons &
holes in a semiconductor can be influenced in several ways:
 Adding special impurity atoms (dopants)
 Applying an electric field
 Changing the temperature
Bond Model of Electrons and Holes
 2-D Representation
Si
Si
Si
Si
Si
Si
Si
Si
Si
Hole
 When an electron breaks loose
and becomes a conduction
electron, then a hole is created.
Si
Si
Si
Si
Si
Si
Si
Si
Si
Conduction
electron
What is a Hole?
 A hole is a positive charge associated with a half-filled covalent bond.
 A hole is treated as a positively charged mobile particle in the
semiconductor.














Conduction Electron and Hole of Pure Si
• Covalent (shared e–) bonds exists
between Si atoms in a crystal.
• Since the e– are loosely bound,
some will be free at any T,
creating hole-electron pairs.
ni = intrinsic carrier
concentration
ni ≈ 1010 cm–3 at room temperature
Si: From Atom to Crystal
Energy states
(in Si atom)
Energy bands
(in Si crystal)
• The highest mostly-filled
band is the valence band.
• The lowest mostly-empty
band is the conduction band.
Electron energy
Energy Band Diagram
Ec
EG, band gap energy
Ev
• For Silicon at 300 K, EG = 1.12 eV
• 1 eV = 1.6 x 10–19 J
Simplified version of energy band model, indicating:
Lowest possible conduction band energy (Ec)
Highest possible valence band energy (Ev)
Ec and Ev are separated by the band gap energy EG.
Measuring Band Gap Energy
 EG can be determined from the minimum energy (hn) of photons that
can be absorbed by the semiconductor.
 This amount of energy equals the energy required to move a single
electron from valence band to conduction band.
Electron
Ec
Photon
photon energy: hn = EG
Ev
Hole
Band gap energies
Semiconductor
Band gap (eV)
Ge
0.66
Si
1.12
GaAs
1.42
Diamond
6.0
Carriers
 Completely filled or empty bands do not allow current flow, because
no carriers available.
 Broken covalent bonds produce carriers (electrons and holes) and
make current flow possible.
 The excited electron moves from valence band to conduction band.
 Conduction band is not completely empty anymore.
 Valence band is not completely filled anymore.
Band Gap and Material Classification
Ec
Ev
Ec
E G = ~8 eV
Ec
Ev
SiO2
EG = 1.12 eV
Si
Ec
Ev
Ev
Metal
Insulators have large band gap EG.
Semiconductors have relatively small band gap EG.
Metals have very narrow band gap EG .
Even, in some cases conduction band is partially filled,
E v > E c.
Carrier Numbers in Intrinsic Material
 More new notations are presented now:
 n : number of electrons/cm3
 p : number of holes/cm3
 ni : intrinsic carrier concentration
 In a pure semiconductor, n = p = ni.
 At room temperature,
ni = 2  106 /cm3 in GaAs
ni = 1  1010 /cm3 in Si
ni = 2  1013 /cm3 in Ge
Manipulation of Carrier Numbers –
Doping
By substituting a Si atom with a special impurity atom
(elements from Group III or Group V), a hole or
conduction electron can be created.
Acceptors: B, Ga, In, Al
Donors: P, As, Sb
Doping Silicon with Acceptors
 Example: Aluminium atom is doped into the Si crystal.
Al– is immobile
 The Al atom accepts an electron from a neighboring Si atom,
resulting in a missing bonding electron, or “hole”.
 The hole is free to roam around the Si lattice, and as a moving
positive charge, the hole carries current.
Doping Silicon with Donors
 Example: Phosphor atom is doped into the Si crystal.
P is immobile
 The loosely bounded fifth valence electron of the P atom can “break
free” easily and becomes a mobile conducting electron.
 This electron contributes in current conduction.
Donor / Acceptor Levels (Band Model)
▬
+
Donor Level
Ec
ED
Donor ionization energy
Acceptor ionization energy
▬
Acceptor Level
EA
Ev
+
Ionization energy of selected donors and acceptors in Silicon
Donors
Ionization energy of dopant
EC – ED or EA – EV (meV)
Sb
39
P
45
Acceptors
As
54
B
45
Al In
67 160
Dopant Ionization (Band Model)
 Donor atoms
 Acceptor atoms
Carrier-Related Terminology
Donor: impurity atom that increases n (conducting
electron).
Acceptor: impurity atom that increases p (hole).
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: undoped semiconductor n = p =
n i.
Extrinsic semiconductor: doped semiconductor.
Density of States
E
DE
Ec
gc(E)
Ec
Ev
Ev
density of states g(E)
gv(E)
 g(E) is the number of states per cm3 per eV.
 g(E)dE is the number of states per cm3 in the energy range between
E and E+dE).
Density of States
DE
Ec
E
Ec
Ev
Ev
gc(E)
density of states g(E)
gv(E)
 Near the band edges:
g c (E ) 
g v (E ) 
mn* 2mn*  E  Ec 
2h3
mp* 2mp*  Ev  E 
 h
2
3
E  Ec
E  Ev
mn* : effective mass of electron
For Silicon at 300 K,
mn*  1.18mo
mp*  0.81mo
mo  9.1 10 31kg
mo: electron rest mass
Fermi Function
 The probability that an available state at an energy E will be
occupied by an electron is specified by the following probability
distribution function:
f (E) 
1
1 e
( E  EF ) / kT
k : Boltzmann constant
T : temperature in Kelvin
EF is called the Fermi energy or the Fermi level.
If E  EF , f ( E )  0
If E  EF , f ( E )  1
If E  EF ,
f (E)  1 2
Effect of Temperature on f(E)
Effect of Temperature on f(E)
Equilibrium Distribution of Carriers
n(E) is obtained by multiplying gc(E) and f(E),
p(E) is obtained by multiplying gv(E) and 1–f(E).
 Intrinsic semiconductor material
Energy band
diagram
Density of
states
Probability
of occupancy
Carrier
distribution
Equilibrium Distribution of Carriers
n-type semiconductor material
Energy band
diagram
Density of
States
Probability
of occupancy
Carrier
distribution
Equilibrium Distribution of Carriers
p-type semiconductor material
Energy band
diagram
Density of
States
Probability
of occupancy
Carrier
distribution
Important Constants
Electronic charge, q = 1.610–19 C
Permittivity of free space, εo = 8.85410–12 F/m
Boltzmann constant, k = 8.6210–5 eV/K
Planck constant, h = 4.1410–15 eVs
Free electron mass, mo = 9.110–31 kg
Thermal energy, kT = 0.02586 eV (at 300 K)
Thermal voltage, kT/q = 0.02586 V (at 300 K)
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