Lecture 2 Semiconductor Physics - Alexandria...
Transcript of Lecture 2 Semiconductor Physics - Alexandria...
Lecture 2
Semiconductor Physics
Semiconductor Physics 1-1
Outline Bond model: electrons and holes
Electron-hole pair generation and recombination
Intrinsic semiconductor
Doping: Extrinsic semiconductor
Charge Neutrality
Introduction to Charge Carrier Transport
Semiconductor Physics 1-2
Test Yourself
Can you differentiate between: Semiconductors
Conductors
Insulators
What is the difference between charge carriers and free charge carriers ?
Semiconductor Physics 1-3
Semiconductor Materials
Three most used semiconductors: carbon (C), silicon (Si) and germanium (Ge)
Semiconductor Physics 1-4
Carbon Silicon Germanium
Silicon (most common semiconductor material)
Bond Model
Si is column IV of the periodic table
Electronic structure of silicon atom: 10 core electrons (tightly bound)
4 valence electrons (loosely bound, responsible for most of the chemical properties
Other semiconductors: Single crystal: Ge, C (diamond form)
Compound: GaAs, InP, InGaAs, InGaAsP, GaP, ZnSe, CdTe (on the average, 4 valence electrons per atom)
Semiconductor Physics 1-5
Silicon crystal structure
Semiconductor Physics 1-6
Diamond structure: atoms tetrahedrally bonded by sharing valence electrons
covalent bonding
Each atom shares 4 electrons
eight covalent electrons associated with each atom
Si atomic density:
5 x 1022 cm-3
Simple “flattened” model of Si crystal
This bonding of atoms, strengthened by the sharing of
electrons, is called covalent bonding
Molecules or ions tend to be more stable when the outermost electron shells of their constituent atoms contain eight electrons
Semiconductor Physics 1-7
At 0 oK: • All bonds are satisfied (all valence electrons engaged in
bonding) • No “free” electrons (or holes)
Creation of electron-hole pair At room temperature (default 27 oC or 300 oK),
approximately 1.5X 1010 free carriers in 1 cm3 of intrinsic silicon material Intrinsic semiconductor material means material has
been refined to a very low level of impurities
Semiconductor Physics 1-8
Creation of electron-hole pair Electron-hole pairs in a silicon crystal. Free
electrons are being generated continuously while some recombine with holes
Electrons and holes
in semiconductors are
“fuzzier”: they span
many atomic sites
Semiconductor Physics 1-9
At finite temperature, some bonds are broken • “free” electrons – Mobile negative charge -1.6 x 10-19 C • “free” holes – Mobile positive charge, +1.6 x 10-19 C
Definitions
“electron” means free electron Not concerned with bonding electrons or
core electrons
Define: n ≡ free electron concentration [cm-3]
p ≡ free hole concentration [cm-3]
Mass action law (at thermal equilibrium)
Where ni ≡ intrinsic carrier concentration [cm−3 ]
Semiconductor Physics 1-11
pnni .2
Generation and Recombination Generation: break-up of covalent bond to form
electron and hole pairs In an intrinsic semiconductor, the number of holes is equal to the
number of free electrons
Generate new hole-electron pairs per unit volume per second requires energy from thermal or optical sources
Generation rate: G = Gthermal + Goptical + …. [cm−3. s−1 ]
Recombination: formation of covalent bond by bringing together electron and hole Releases energy in thermal or optical form
Recombination rate R [cm−3. s−1 ]
1 recombination event requires 1 electron + 1 hole
On an average, a hole (an electron) will exist for ζp (ζ n) seconds before recombination. This time is called the mean lifetime of the hole (electron)
Semiconductor Physics 1-12
Intrinsic Semiconductors Thermal Equilibrium
Steady state plus absence of external energy sources
With increasing temperature, the density of hole-electron pairs (free charge carriers) increases in an intrinsic semiconductor.
where ni ≡ intrinsic carrier concentration [cm−3 ] EG0 is the energy gap (the energy required to break a covalent
bond) at 0 K k is the Boltzmann constant in electron volts per degree
kelvin (J/K) [k = 1.38x10-23 J/K] A is a material-dependent constant independent of T
Semiconductor Physics 1-13
kT
E
i
G
eATn0
32
pnni .2
Intrinsic Semiconductors
In Si at 300 K (“room temperature”): ni ≈ 1x1010 cm-3
In a sufficiently pure Si wafer at 300K (“intrinsic semiconductor):
• Assume thermal equilibrium: n = p = ni ≈ 1 ×1010 cm−3
ni is a very strong function of temperature T ↑ ⇒ ni ↑
Why ?
Semiconductor Physics 1-14
Effect of Temperature on Conductivity
Conductor resistance increase with increase in heat (number of
free charge carriers decreases)
have a positive temperature coefficient
Semiconductor resistance decrease (i.e., conductivity increase) with
increase in heat (number of free charge carriers increases)
have a negative temperature coefficient
Semiconductor Physics 1-15
Controlling the properties of a Semiconductor
Doping = engineered introduction of foreign atoms to modify semiconductor electrical properties
Doping is the process of deliberately adding impurities to the crystal during manufacturing and increases the number of current carries (electrons or holes) Impurities (extraneous elements)
Doping process create n-type and p-type of semiconductors
A semiconductor material that has been subjected to the doping process is called an extrinsic material
Semiconductor Physics 1-16
Doping
Silicon: 4 valence electrons Each Si atom bonds to four
others Replace some Si atoms with atoms
that do not have four valence electrons
These atoms will have: - an extra electron (group V) Donors
- an extra hole (group III) Acceptors
Doping increases the number of carriers
Semiconductor Physics 1-17
Donors Introduce electrons to semiconductors (but not
holes)
For Si, group V elements (dopants) with 5 valence electrons (Arsenic “As”, phosphorus “P”, antimony “Sb”)
Semiconductor Physics 1-18
Donors 4 of five electrons participate in bonding
The 5th electron easy to release at room temperature, each donor releases 1 electron that is available
for conduction1 conduction
Donor site become positively charged (fixed charge)
Define:
Nd ≡ donor concentration [cm-3] If Nd << ni doping is irrelevant
• Intrinsic semiconductor → n = p = ni
If Nd >> ni, doping controls carrier
concentration
Extrinsic semiconductor ⇒
n = Nd and p = ni2/ Nd
Note: n >> p : n-type semiconductor
In general: Nd ≈ 1015
1020 atom or electron m-3 Semiconductor Physics 1-19
Acceptors Introduce holes to semiconductors (but not
electrons)
For Si, group III elements with 3 valence electrons (usually Boron(B) , Gallium (Ga) and Indium (In))
Semiconductor Physics 1-20
Acceptors 3 electrons participate in bonding
one bonding site “unsatisfied” making it easy to “accept” neighboring bonding electron to complete all bonds at room temperature, each acceptor “releases”
hole that is available for conduction
Acceptor site become
negatively charged
(fixed charge)
Semiconductor Physics 1-21
Acceptors
Define: Na ≡ acceptor concentration [cm-3] If Na << ni doping is irrelevant
• Intrinsic semiconductor → n = p = ni
If Na >> ni, doping controls carrier concentration
Extrinsic semiconductor ⇒ p = Na and n = ni2/ Na
Note: p >> n : p-type semiconductor
In general: Na ≈ 1015 1020 cm-3
Semiconductor Physics 1-22
Energy levels of donors and acceptors.
Semiconductor Physics 1-23
Summary of Charge Carriers
Semiconductor Physics 1-24
Majority and Minority Carriers
• n-type material, the electron is called majority carrier and hole the minority carrier
• p-type material, the hole is called majority carrier and electron the minority carrier
Semiconductor Physics 1-25
Charge Neutrality The semiconductor remains charge neutral even
when it has been doped Overall charge neutrality must be satisfied
In general: the net charge density ρ (C/cm3) in a semiconductor = ρ = q (p − n + Nd − Na) Where q: electric (elementary) charge = 1.6 Х 10-19 C
Semiconductor Physics 1-26
+ −
Charge Neutrality
Example Let us examine this for: Nd = 1017 cm-3, Na = 0
Then, n = Nd = 1017 cm−3, p = ni2/Nd = 103 cm−3
Using the equation ρ = q (p − n + Nd − Na), we find that ρ ≠ 0 !!
What is wrong??
Semiconductor Physics 1-27
Charge Neutrality
Nothing wrong!
We just made the approximation when we assumed that n = Nd
We should really solve the following system of equations (for Na=0):
Semiconductor Physics 1-28
p − n + Nd = 0 n.p = ni2
n2 - n. Nd - ni2 = 0 n ≠ Nd
+
Charge Carrier Transport
Any motion of free charge carriers in a semiconductor leads to a current
Different causes for having motion Associated random motion due to the thermal
energy (Thermal Motion)
Motion can be caused by an electric field due to an externally applied voltage (Carrier Drift)
Motion from regions where the carrier density is high to regions where the carrier density is low (Carrier Diffusion)
Semiconductor Physics 1-29
Thermal Motion In thermal equilibrium, carriers are not
sitting still: Undergo collisions with vibrating Si atoms
(Brownian motion)
Electrostatically interact with each other and with ionized (charged) dopants
Semiconductor Physics 1-30
Thermal Motion (cont’d) Characteristic time constant of thermal motion
mean free time between collisions • Tc ≡ Collison time (seconds)
In between collisions, carriers acquire high velocity: • vth ≡ thermal velocity (cm/second)
Characteristic length of thermal motion: • λ ≡ mean free path [cm] = vth Tc
Example: Put numbers for Si at room temperature (27 oC or 300 oK): Tc ≈ 10−13 seconds, vth ≈ 107 cm/second ⇒ λ ≈ 0.01 μm
Carriers undergo many collisions as they travel
Semiconductor Physics 1-31
Semiconductor Physics 1-32
Lecture Summary Covered material Continue Semiconductor Materials
Types of semiconductors Two types of “carriers” (mobile charge particles):
• electrons and holes
Creation of electron-hole pairs Doping
• Donors n-type semiconductor material • Acceptors p-type semiconductor material
Important equations under thermal equilibrium conditions: (p − n + Nd − Na = 0) and (n.p = ni
2)
Material to be covered next lecture Continue Semiconductor Physics
Carrier Transport (Carrier Drift and Carrier Diffusion)
pn junctions (or diodes) Basics