固体物理导论

(Ohm’s law)
! E =0
! ! vd = v (t ) = 0 ! ! ! vd = v (t ) = − µE
v rms =
L = v rms τ (mean free path)
! 3kBT v (t )2 = m
eτ 2 s = vd τ = E m
2 τ ne −1 σ=ρ = y t i m ity tiv v c i u t nd sis co re ne 2L ne 2L = = mv rms 3kBTm
experimentally ρ~T and not T1/2 !!!
Heat conduction: Wiedemann-Franz law
Heat current density:
dQ dT = −K JT ≡ Adt dx
thermal conductivity
1 1 2 = K = C v L k nv v rms " rms τ B " 3 3 2 v τ
Electrical conduction: Ohm’s Law
! ! J = envd , ! ! vd = v (t )
drift velocity
Βιβλιοθήκη Baidu
! ! vd = − µE ,
current density
electron density
eτ µ= m
! ! J = σE
mobility
mean free time
Classical free electron theory of metals
• Free electron model of metals: metal = an ideal gas of conduction electrons moving through the fixed lattice of positive ion cores • Features of the free electron model: • explains the high electrical (σ) and σ ~ 106 (Ωm) −1 − ~ 10 100 W/mK K thermal (K) conductivity of metals ! ! J = σE • explains the functional form of Ohm’s law • explains the relationship between σ and K [K / σT = const ] (Wiedemann-Franz law) • fails to predict accurately the experimental values of σ and K
Crystal
Glass (amorphous)
Gas
Degree of (dis)ordering in a solid
can be quantified by the two particle correlation (radial distribution) function g2(r) = probability of finding a 2nd atom at a distance r from a given atom; g2(r) can be measured experimentally and calculated theoretically/numerically.
Bonding in solids: Covalent solids
Atoms in the crystal are held together by covalent bonding C atoms in diamond form a tetragonal crystal structure Properties of covalent crystals: • very hard and stable • high melting point • good insulators • do not absorb light • larger cohesive energies (~10 eV) than in ionic crystals
Classification of solids
• Phases of matter: • solid (well defined shape and volume) • liquid (only well defined volume) • gas (no defined shape or volume) • plasma (an overall neutral collection of charged and neutral particles) • Solids • crystalline (atoms form a regular periodic structure) • amorphous (atoms have irregular spatial distribution) • Solids • metals (good electrical/heat conductors) • semiconductors • insulators (poor electrical/heat conductors)
K mkB 2 3kB2 v = 2T = 2 rms 2e σ 2e ⇓ K 3kB2 −8 2 1.1 10 W Ω /K = const = = × ⋅ 2e 2 $ σT #$$$$$$ %$$$$$$$ &
= Lorentz number
2
kB n
rms
is different from the experimental value !!!
Metal ion
Conduction electron gas
Bonding in solids: Molecular crystals
Molecules in the crystal are held together by: • weak Van der Waals bonds exp: solid methane (Ec=0.10 eV/molecule) solid argon (Ec=0.076 eV/molecule) • relatively strong hydrogen bonds exp: solid ice (Ec=0.53 eV/molecule)
Amorphous solids
• Ideal solid crystals exhibits structural long range order (LRO) • Real crystals contain imperfections, i.e., defects and impurities , which spoil the LRO • Amorphous solids lack any LRO [though may exhibit short range order (SRO)]
Bonding in solids: Ionic solids
Ionic solid crystals (e.g. NaCl) are held together by the Coulomb attractive interaction between ions with opposite sign (ionic bonding)
1 m −1
Bonding in solids: Ionic solids
Properties of ionic solid crystals: • relatively stable and hard • poor electrical/heat conductors • high melting/boiling temperatures • transparent to visible light • strong IR absorption • soluble in polar solvents (e.g., water)
Bonding in solids: Metallic solids
Atoms in a metallic crystal are held together by the effective attractive electrostatic interaction mediated by the conduction (valence) electron gas (metallic bonding) Properties of metallic crystals: • smaller cohesive energies (~1 eV) than in covalent/ionic crystals • sufficiently hard and stable • good electrical/heat conductors • strong interaction with light • form solid solutions
e2 b U = −αk + m r r
(α = 1.7476 for Na +Cl − )
(m ~ 10)
k = 1 / 4πε 0
Madelung constant
Ionic cohesive energy:
11 α = − − U0 = min U r k ( ) 1 m r0 mb r0 = αk
Physics 215 Winter 2002
Introduction to Modern Physics
Prof. Ioan Kosztin Lecture #23
Solid State Physics
• Bonding in solids (metals, isolators, semiconductors) • Classical free electron theory of metals • Quantum theory of metals • Band theory of solids • Semiconductors • Lasers