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Midterm

MATLS 1M03 Study Guide - Midterm Guide: Fermi Level, Electron Mobility, Thermal Conductivity


Department
Materials Science and Engineering
Course Code
MATLS 1M03
Professor
Joey Kish
Study Guide
Midterm

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=
OHM’S LAW
=
=

ELECTRICAL RESISTIVITY
units = (m)
=
1
ELECTRICAL CONDUCTIVITY
ease with which a material
generates an electric current
units = (m)
CURRENT DENSITY
=
=
CONDUCTIVITIES
Metals 10 (m)
Semi-conductors 10

 10
(m)

Insulators10  10 (m)
CURRENT
result of motion of charged particles responding to
forces from externally applied electric field
[
+
moves with current direction,
-
moves opposite]
ELECTRIC CONDUCTION: flow of electron causing a current (within most solids)
IONIC CONDUCTION: possible current produced from net motion of charged ions (diffusion of ions)
BAND STRUCTURE = how electrons fill orbitals in an atom
- electrons acted upon by the electrons & nuclei of adjacent atoms when in close proximity
- may split into series of closely spaced electronic states (electron energy bands)
- extent of splitting depends on separation
- energy band gaps = the gaps between adjacent bands
- total # states in each band = total states from N atoms
(s band = N states, p band = 3N states)
FERMI ENERGY (E
f
)
energy of last filled
state at 0K.
CONDUCTOR if bands
partially full/overlap
INSULATOR/
SEMICONDUCTOR
if valence bond full &
conduction band
empty
FREE ELECTRON participates in conduction process
HOLE (semiconductor/insulators)
electrons with
energy LESS than Ef and still participate in conduction
- acceleration is counteracted by friction
friction from scattering e- from lattice impurities
impurity atoms, vacancies, thermal vibrations,
dislocations, interstitial atoms
- scattering—e- loses kinetic energy, motion changes
direction, resistance to passage of current
- net motion opposite field
- drift velocity (Vd) = average e- velocity opposite field
CONDUCTION IN METALS
-
electron excited to empty state about the Fermi energy (free electron)
requires little energy because there are vacant states adjacent to
highest-filled state at Fermi energy (provided by electric field)
-
very high conductivity many electrons excited into empty state above Ef
RESISTIVITY depends on TEMPERATURE
as T increases, # of impurities increases, BUT u
e
decreases (dominates)
=
+ a is the material constant
==+ for T > -200oC
RESISTIVITY depends on # OF IMPURITIES
as T increases, # of impurities increases, BUT u
e
decreases (dominates)
= (1 ) A is the constant
concentration is in terms of atomic fraction (%at / 100)
Matthieson’s Rule:
 =++
(temp + impurities + deformation)
CONDUCTION IN SEMICONDUCTORS & INSULATORS
-
electron must be thermally promoted across band gap into empty
states at bottom of conduction band to become a free electron
- band gap energy (Eg) ~ 1eV … from non-electric source
- Eg > 3eV = insurmountable gap = insulating material
- Eg increase = larger band gap & decreased electrical conductivity
-
Semiconductors have a narrow band gap
-
Insulators have a relatively wide band gap
INTRINSIC SEMICONDUCTIVITY
-
narrow band gap (less than 2eV)
- At T = 0K, conductivity = 0
- At T > 0K heat helps e- jump over band gap (ehole pair)
- Hole is created for every e- excited to conduction band
INTRINSIC CONDUCTION
- Free electrons (n = # e- / m3)
- Holes (p = # holes / m3)
- =||+||
- since # holes = # free e- for intrinsic semi-conductors
= || (+)
-
electrons and holes move in response to electric field
- e/atom = e/volume x volume/atom
N-TYPE EXTRINSIC SEMICONDUCTION
-
e- loosely boundweak attraction promotes conduction band
- e- binding energy = E requited to excite e- to state within
conduction band (ED)
- each excitation donates an e- to the conduction band (donor)
- no corresponding hole created in valence bond
-
Fermi level shifted up in band gap
-
ED << Eg, n >> p many donor e- promoted at room T
=||
P-TYPE EXTRINSIC SEMICONDUCTION
-
Dopant atoms (each with a valence bond deficient in an e
-
)
- Hole for electron… new level above valence (acceptor state)
- Hole left in valence bond when e- fills acceptor state
- p >> n … =||
-
Fermi level positioned within
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