semiconductors fundamentals.pdf

Semiconductor Fundamentals
• Yuan-Huei Chang

Lattice: periodical arrangement of atoms
Body-centered
Zinc-Blende

Periodical potential of a lattice and the electron
wavefunction
http://www.mtmi.vu.lt/pfk/funkc_dariniai/quant_mech/bands.htm

• Bloch theorem
• U (r)= U (r+R),
R is any lattice vector
• H=P 2 /2m+ U (r)
• H Φ = E Φ
• Φ k (r)= = e ik·r u (r)
• u (r) = u (r+R)
• k could be used to specify the electronic
state and p=ћk, is the crystal momentum of
the electron in the lattice

From energy level to
energy band
○
○
△E
○
○
△E
○
○

Relation between width of the energy
band and the inter-atomic distance
△E
d

Band structure of solid
Conduction
band
E F : Fermi evel
Energy gap
Valence
band
insulator
metal

What is a hole
The collective motion of n-1 electrons.
When a filled band has holes, it can
conduct electricity.
Net effect
missing
電 洞
Sum=0

E-k relation for an electron in a lattice
• For an electron in the vacuum E = ћ 2 k 2 /2m.
• In a lattice E(k) is usually a very complicated function
http://zh.wikipedia.org/wiki/%E5%8D%8A%E5%AF%BC%E4%BD%93

E- k and v-k relation for an electron
in a lattice
•
A filled band does not conduct

有 效 質 量 (effective mass)
• In vacuum E = ћ 2 k 2 /2m and m is independent of E.
• In a lattice E=E(k).
• E(k)= ћω(k), and v g =dω/dk /dk v g =(1/ ћ) dE/dk
• a=d v g /dt=(1/ ћ) d 2 E/dkdt=(1/ ћ) d 2 E/dk 2 (dk/dt)
• p= ћk, F=dp/dt= ћ dk/dt dk/dt= (1/ ћ) F
• a=(1/ ћ 2 )F d 2 E/dk 2
• m* - 1 = (1/ ћ 2 ) d 2 E/dk 2
• m*
-1 ij = (1/ ћ 2 ) ∂ 2 E/ ∂k i ∂k j

semiconductors
1. Intrinsic semiconductor is an insulator
2. The conduction property of the SC is
determined by the impurity in the SC.
3. Whether a semiconductor is useful depends
on
a. Low defect density pure substrate could
be obtained.
b. Controlled doping of n and p type
impurities can be achieved

Donor and acceptor
http://www.physics.udel.edu/~watson/scen103/colloq2000/doping-donor.html

Binding energy of donor and acceptor