Intrinsic Semiconductor as Conductor
(End of part1)
Intrinsic Semiconductor as Conductor
•
At room temperature, some of the covalent bonds are broken by thermal generation.
Each broken bond gives rise to a free electron and a hole (as the electron leaves its
parent atom, it leaves behind a net positive charge, that is a hole), both of which
become available for current conduction
Self questions:
free electron, hole
Chapter 1-1
Concentration of free electrons (𝑛) and holes (𝑝)
𝑛𝑖 : Concentration of intrinsic semiconductor
𝑛 = 𝑝 = 𝑛𝑖
𝑝𝑛 = 𝑛𝑖2
3 −𝐸𝑔
𝑛𝑖 = 𝐵𝑇 2 𝑒 2𝑘𝑇
B – coefficient related to specific semiconductor
T – temperature in Kelvin
𝐸𝑔 – semiconductor bandgap energy
k – Boltzmann’s constant
𝑛𝑖 𝑆𝑖, 300𝑘 = 1.5 × 1010 𝑐𝑎𝑟𝑟𝑖𝑒𝑟𝑠/𝑐𝑚3 : considered as insulator
(concentration of intrinsic silicon semiconductor at room temperature)
Self questions: Why 𝑛 = 𝑝 = 𝑛𝑖 ?
Chapter 1-2
1.8 Doped Semiconductors
Intrinsic silicon carrier concentration are far too small for
silicon to conduct appreciable current at room temperature.
At this condition we will consider semiconductor as
insulator.
How to make Semiconductor as conductor ?
Develop the method to increase the carrier concentration.
This process is called Doping.
Doped silicon is generated.
(high concentration enough to conduct)
Chapter 1-3
Doped Semiconductors
Intrinsic Semiconductor
Used as Insulator
Doped Semiconductor (Extrinsic Semiconductor)
used as conductor
Extrinsic Semiconductor (Doped Semiconductor)
Intrinsic Semiconductor
=> contain relatively small current
Extrinsic Semiconductor (Doped Semiconductor)
=> concentration greatly increased (why?)
Doping involves introducing impurity atom into
silicon (intrinsic Semiconductor)
Chapter 1-4
Doped Semiconductors
Intrinsic Semiconductor
(with valence of 4)
Add Impurity atoms into intrinsic
semiconductor
Doped Semiconductor (Extrinsic Semiconductor)
Impurity atoms
Group V elements
(with valence of 5 such as phosphorus)
Group III elements
(with valence of 3 such as boron)
Self questions:
Why do you add the impurity atoms?
What is the doped semiconductor?
Chapter 1-5
Doped Semiconductors : 𝑛-type Semiconductor
𝑝-type Semiconductor
Intrinsic Semiconductor
(with valence of 4)
Add Impurity atoms
Doped Semiconductor
(Extrinsic Semiconductor)
𝑛-type Semiconductor
•
•
•
•
Group V element impurity is doped.
Donor impurity.
Increase the concentration of free
electrons.
Majority is electrons & minority is
holes
𝑝-type Semiconductor
•
•
•
Group III element impurity is doped.
Acceptor impurity.
Increase the concentration of holes.
•
Majority is holes & minority is
electrons
Self questions:
𝑛-type semiconductor, 𝑝-type Semiconductor
Chapter 1-6
𝑛-type Semiconductor
𝑛-type Semiconductor
•
•
•
•
•
•
•
•
Group V element impurity is doped.
Donor impurity.
Increase the concentration of free electrons.
Majority is electrons & minority is holes
A silicon crystal doped by a pentavalent element.
Impurity atoms replace some of the atoms in crystal.
Each dopant atom donates a free electron and is thus called a donor.
The doped semiconductor becomes n type.
Chapter 1-7
𝑝-type Semiconductor
𝑝-type Semiconductor
•
•
•
•
•
•
•
•
Group III element impurity is doped.
Acceptor impurity.
Increase the concentration of holes.
Majority is holes & minority is electrons
A silicon crystal doped with a trivalent impurity.
Impurity atoms replace some of the atoms in crystal.
Each dopant atom gives rise to a hole and is thus called a acceptor.
The doped semiconductor becomes p type.
Chapter 1-8
Doped Semiconductors
Intrinsic Semiconductor
(with valence of 4)
Add Impurity atoms
Doped Semiconductor
(Extrinsic Semiconductor)
𝑛-type Semiconductor
•
•
•
•
Group V element impurity is doped.
Donor impurity.
Increase the concentration of free electrons.
Majority is electrons & minority is holes
𝑝-type Semiconductor
•
•
•
•
Group III element impurity is doped.
Acceptor impurity.
Increase the concentration of holes.
Majority is holes & minority is electrons
Group V atoms(pentavalent) in Si are called donor impurities.
 N-type semiconductor
Group III in Si atoms(trivalent) are called acceptor impurities.
 P-type semiconductor
Chapter 1-9
Electron and Hole Concentrations
Concentration of free electrons in the 𝑛-type silicon , 𝑛𝑛
Concentration of hole in the 𝑛-type silicon , 𝑝𝑛
𝑁𝐷 = 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑑𝑜𝑛𝑜𝑟 𝑎𝑡𝑜𝑚𝑠 in the n-type
(𝑁𝐷 𝑖𝑠 𝑢𝑠𝑢𝑎𝑙𝑙𝑦 𝑚𝑢𝑐ℎ 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛 𝑛𝑖 )
Why?
𝑛𝑛 = 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑓𝑟𝑒𝑒 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑛_𝑡𝑦𝑝𝑒 𝑠𝑖𝑙𝑖𝑐𝑜𝑛
Thus will be,
𝑛𝑛 ≅ 𝑁𝐷
𝑝𝑛 = 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 ℎ𝑜𝑙𝑒 in the 𝑛-type silicon will be
𝑝𝑛 𝑛𝑛 = 𝑛𝑖2
𝑝𝑛 ≅
𝑛𝑖2
𝑁𝐷
Note: 𝑛𝑛 is determined by the doping concentration and not by temperature.
𝑝𝑛 , however, is determine by the thermal ionization.
electrons are the majority charge carriers and holes the minority carriers
Chapter 1-10
Electron and Hole Concentrations
Concentration of holes in the 𝑝-type silicon , 𝑝𝑝
𝑁𝐴 = 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑎𝑐𝑐𝑒𝑝𝑡𝑜𝑟 𝑎𝑡𝑜𝑚𝑠 in the p-type
(𝑁𝐴 𝑖𝑠 𝑢𝑠𝑢𝑎𝑙𝑙𝑦 𝑚𝑢𝑐ℎ 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛 𝑛𝑖 )
Why?
𝑝𝑝 = 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 ℎ𝑜𝑙𝑒𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑝_𝑡𝑦𝑝𝑒 𝑠𝑖𝑙𝑖𝑐𝑜𝑛
Thus will be,
𝑝𝑝 ≅ 𝑁𝐴
𝑛𝑝 = 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑓𝑟𝑒𝑒 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 in the 𝑝-type silicon
𝑝𝑝 𝑛𝑝 = 𝑛𝑖2
𝑛𝑝 ≅
𝑛𝑖2
𝑁𝐴
Note: 𝑝𝑝 is determined by the doping concentration and not by temperature.
minority electrons will have the same temperature dependence as that of the 𝑛𝑖2
holes are majority charge carriers and electrons the minority carriers
Chapter 1-11
1.9 In current flow in semiconductors
There are two distinctly different mechanisms for the movement of charge carrier
Drift current
Diffusion current
Drift current
: Movement(displacement) caused by electric field
𝑣𝑑 = 𝜇𝐸 (drift velocity of electron accelerated by electric field E)
Diffusion current
: Flow caused by variations in concentration
Self questions:
What is Drift velocity?
What is group velocity?
What is phase velocity?
What is ohm’s law?
Chapter 1-12
Drift current
Drift velocity (drift velocity: 𝑣𝑑 = 𝜇𝐸 = 𝜇
•
•
•
•
𝑉
𝐿
: caused by electric field)
Electric field 𝐸 is established in a semiconductor.
Holes are accelerated in the direction of 𝐸.
Free electrons are accelerated in the direction opposite to that of 𝐸
Both the hole and electron drift currents are in the direction of E
𝑉 = 𝑅𝐼
Drift velocity of holes :
velocity: 𝑣 = 𝜇𝐸 = 𝜇
𝑣𝑝−𝑑𝑟𝑖𝑓𝑡 = 𝜇𝑝 𝐸
Drift velocity of free electrons : 𝑣𝑛−𝑑𝑟𝑖𝑓𝑡 = −𝜇𝑛 𝐸
𝑉
𝐿
480𝑐𝑚2
𝜇𝑝 = 𝑉∙𝑠
hole mobility
1350𝑐𝑚2
𝜇𝑛 = 𝑉∙𝑠 electron mobility
Self questions:
Can you drive a ohm’s law with current density?
𝜇𝑛 is about 2.5 times 𝜇𝑝 ⇒ electron move with ease through the silicon crystal than do holes
Chapter 1-13
Drift current (generally called as current)
𝐼𝑝 : Drift current due to the holes
•
•
Holes are accelerated in the direction of 𝐸.
Both the hole and electron drift currents are in the direction of E
Drift velocity of holes :
𝑣𝑝−𝑑𝑟𝑖𝑓𝑡 = 𝜇𝑝 𝐸
𝜇𝑝 =
480𝑐𝑚2
: hole mobility
𝑉∙𝑠
Charge Q (within imaginary volume)
𝑄 =𝐴∙𝑞∙𝑝∙𝐿
e𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑐ℎ𝑎𝑟𝑔𝑒 = 𝑞 = 1.6 × 10−19 𝐶
A: cross sectional area (a plane perpendicular to the 𝑥 direction)
Drift current 𝐼𝑝
𝑄
𝐼𝑝 = ∆𝑡
𝑄
𝐼𝑝 = ∆𝑡 =
∆𝑡 = 𝑣
𝐿
𝑝_𝑑𝑟𝑖𝑓𝑡
𝐴∙𝑞∙𝑝∙𝐿
𝑉
𝐴
=
𝐴𝑞𝑝
∙
𝑣
=
𝐴𝑞𝑝
∙
𝜇
𝐸
=
𝐴𝑞𝑝𝜇
=
𝑞𝑝𝜇
𝑉
𝑝
𝑝
𝑝
𝑝
𝑑𝑟𝑖𝑓𝑡
∆𝑡
𝐿
𝐿
𝐴
𝐼𝑝 = 𝑞𝑝𝜇𝑝 𝐿 𝑉
⇒
𝑉 = 𝑅𝐼
Chapter 1-14
Drift current
End of Part2
𝑣 = 𝜇𝐸 = 𝜇
Drift current 𝐼𝑝 due to the holes
𝑄
𝐼𝑝 = ∆𝑡
𝑄
𝐼𝑝 = ∆𝑡 =
𝐿
∆𝑡 = 𝑣
𝑝_𝑑𝑟𝑖𝑓𝑡
𝐴∙𝑞∙𝑝∙𝐿
𝑉
𝐴
=
𝐴𝑞𝑝
∙
𝑣
=
𝐴𝑞𝑝
∙
𝜇
𝐸
=
𝐴𝑞𝑝𝜇
=
𝑞𝑝𝜇
𝑝𝑑𝑟𝑖𝑓𝑡
𝑝
𝑝𝐿
𝑝𝐿 𝑉
∆𝑡
𝐴
𝑉 = 𝑅𝐼 (ohm’s Law)
𝐼𝑝 = 𝑞𝑝𝜇𝑝 𝐿 𝑉
1
𝐿
1
𝑉 = 𝑅𝐼 = 𝑞𝑝𝜇 𝐴 𝐼
𝐿
1𝐿
𝑅 = 𝑞𝑝𝜇 𝐴 = 𝜎 𝐴
𝑝
𝑝
𝜎 = 𝑞𝑝𝜇𝑝 = 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦
𝜌=
Current density:
𝐼𝑝
1
= 𝑟𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑖𝑡𝑦
𝜎
𝑉
𝐽𝑝 = 𝐴 = 𝑞𝑝𝜇𝑝 𝐿 = 𝜎𝐸
Chapter 1-15
𝑉
𝐿