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Lecture 2
OUTLINE
• Semiconductor Basics
Reading: Chapter 2
EE105 Fall 2011
Lecture 2, Slide 1
Prof. Salahuddin, UC Berkeley
Announcement
• Office Hours for tomorrow is cancelled
(ONLY for this week)
There will be office hours on Friday (2P-3P)
(ONLY for this week)
Thursday’s class will start at 4P
(ONLY for this week)
EE105 Fall 2011
Lecture 2, Slide 2
Prof. Salahuddin, UC Berkeley
What is a Semiconductor?
• Low resistivity => “conductor”
• High resistivity => “insulator”
• Intermediate resistivity => “semiconductor”
– conductivity lies between that of conductors and insulators
– generally crystalline in structure for IC devices
• In recent years, however, non-crystalline semiconductors have
become commercially very important
polycrystalline amorphous crystalline
EE105 Fall 2011
Lecture 2, Slide 3
Prof. Salahuddin, UC Berkeley
Semiconductor Materials
Phosphorus
(P)
Gallium
(Ga)
EE105 Fall 2011
Lecture 2, Slide 4
Prof. Salahuddin, UC Berkeley
Energy Band Description
•For current flow, one needs to have electrons in the conduction
band or holes in the valence band
•Completely full or completely empty bands cannot carry current
EE105 Fall 2011
Lecture 2, Slide 5
Prof. Salahuddin, UC Berkeley
Energy Band Description
Current due to electron flow and hole flow will add up
EE105 Fall 2011
Lecture 2, Slide 6
Prof. Salahuddin, UC Berkeley
Silicon
• Atomic density: 5 x 1022 atoms/cm3
• Si has four valence electrons. Therefore, it can form
covalent bonds with four of its nearest neighbors.
• When temperature goes up, electrons can become
free to move about the Si lattice.
EE105 Fall 2011
Lecture 2, Slide 7
Prof. Salahuddin, UC Berkeley
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;
Holes are positively charged.
 The concentration
(#/cm3) of conduction electrons & holes in a
semiconductor can be modulated in several ways:
1.
by adding special impurity atoms ( dopants )
2.
3.
4.
by applying an electric field
by changing the temperature
by irradiation
EE105 Fall 2011
Lecture 2, Slide 8
Prof. Salahuddin, UC Berkeley
Electron-Hole Pair Generation
• When a conduction electron is thermally generated,
a “hole” is also generated.
• A hole is associated with a positive charge, and is
free to move about the Si lattice as well.
EE105 Fall 2011
Lecture 2, Slide 9
Prof. Salahuddin, UC Berkeley
Carrier Concentrations in Intrinsic Si
• The “band-gap energy” Eg is the amount of energy
needed to remove an electron from a covalent bond.
• The concentration of conduction electrons in intrinsic
silicon, ni, depends exponentially on Eg and the
absolute temperature (T):
ni  5.2 10 T
15
3/ 2
exp
 Eg
2kT
electrons / cm3
ni  11010 electrons / cm3 at 300K
ni  11015 electrons / cm3 at 600K
EE105 Fall 2011
Lecture 2, Slide 10
Prof. Salahuddin, UC Berkeley
Doping (N type)
• Si can be “doped” with other elements to change its
electrical properties.
• For example, if Si is doped with phosphorus (P), each
P atom can donate a conduction electron, so that the
Si lattice has more electrons than holes, i.e. it
becomes “N type”:
Notation:
n = conduction electron
concentration
EE105 Fall 2011
Lecture 2, Slide 11
Prof. Salahuddin, UC Berkeley
Doping (P type)
• If Si is doped with Boron (B), each B atom can accept
an electron (creating a hole), so that the Si lattice has
more holes than conduction electrons, i.e. it
becomes “P type”:
Notation:
p = hole concentration
EE105 Fall 2011
Lecture 2, Slide 12
Prof. Salahuddin, UC Berkeley
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 = ni
extrinsic semiconductor: doped semiconductor
EE105 Fall 2011
Lecture 2, Slide 13
Prof. Salahuddin, UC Berkeley
Intrinsic vs. Extrinsic Semiconductor
EE105 Fall 2011
Lecture 2, Slide 14
Prof. Salahuddin, UC Berkeley
Electron and Hole Concentrations
• Under thermal equilibrium conditions, the product
of the conduction-electron density and the hole
density is ALWAYS equal to the square of ni:
2
np  ni
N-type material
P-type material
n  ND
p  NA
2
2
n
p i
ND
EE105 Fall 2011
n
n i
NA
Lecture 2, Slide 15
Prof. Salahuddin, UC Berkeley
Dopant Compensation
• An N-type semiconductor can be converted into Ptype material by counter-doping it with acceptors
such that NA > ND.
• A compensated semiconductor material has both
acceptors and donors.
N-type material
(ND > NA)
P-type material
(NA > ND)
n  ND  N A
p  N A  ND
2
2
ni
p
ND  N A
EE105 Fall 2011
ni
n
N A  ND
Lecture 2, Slide 16
Prof. Salahuddin, UC Berkeley
Doping
What is the electron and hole density if you
dope Si with Boron to 1018 /cm3 ?
EE105 Fall 2011
Lecture 2, Slide 17
Prof. Salahuddin, UC Berkeley
Charges in a Semiconductor
• Negative charges:
– Conduction electrons (density = n)
– Ionized acceptor atoms (density = NA)
• Positive charges:
– Holes (density = p)
– Ionized donor atoms (density = ND)
• The net charge density (C/cm3) in a semiconductor is
  q p  n  N D  N A 
EE105 Fall 2011
Lecture 2, Slide 18
Prof. Salahuddin, UC Berkeley
Carrier Drift
• The process in which charged particles move because
of an electric field is called drift.
• Charged particles within a semiconductor move with
an average velocity proportional to the electric field.
– The proportionality constant is the carrier mobility.

Hole velocity
vh   p E

Electron velocity


ve    n E
Notation:
p  hole mobility (cm2/V·s)
n  electron mobility (cm2/V·s)
EE105 Fall 2010
Lecture 2, Slide 19
Prof. Salahuddin, UC Berkeley
Velocity Saturation
• In reality, carrier velocities saturate at an upper limit,
called the saturation velocity (vsat).

0
1  bE
vsat 
0
b
v 
1
EE105 Fall 2010
Lecture 2, Slide 20
0
E
0 E
vsat
Prof. Salahuddin, UC Berkeley
Drift Current
• Drift current is proportional to the carrier velocity
and carrier concentration:
Total current Jp,drift= Q/t
Q= total charge contained in the
volume shown to the right
t= time taken by Q to cross the
volume
Q=qp(in cm3)X Volume=qpAL=qpAvht
 Hole current per unit area (i.e. current density) Jp,drift = q p vh
EE105 Fall 2010
Lecture 2, Slide 21
Prof. Salahuddin, UC Berkeley
Conductivity and Resistivity
• In a semiconductor, both electrons and holes
conduct current:
J p ,drift  qp p E
J n ,drift  qn(  n E )
J tot,drift  J p ,drift  J n ,drift  qp p E  qn n E
J tot,drift  q( p p  n n ) E  E
• The conductivity of a semiconductor is   qp p  qn n
– Unit: mho/cm
• The resistivity of a semiconductor is  
– Unit: ohm-cm
EE105 Fall 2010
Lecture 2, Slide 22
1

Prof. Salahuddin, UC Berkeley
Resistivity Example
• Estimate the resistivity of a Si sample doped with phosphorus
to a concentration of 1015 cm-3 and boron to a concentration
of 6x1017 cm-3.
EE105 Fall 2010
Lecture 2, Slide 23
Prof. Salahuddin, UC Berkeley