Lecture 16: Continue Semiconductors
Shrinkage of the band gap:
High doping leads to shrinkage of the band gap. How?
High doping leads to an increase in the density of
impurities. Thus, the wave functions of the electrons
bound to impurity start to overlap, then form energy
band rather than discrete levels. Since the energy band
level is shallow, this reduces the band gap of the host
material. You start to see this effect for doping level
higher than 1018 /cm3 . At this level (1018 /cm3 ) the
distance between impurity atoms is ≈ 10nm.
Compound Semiconductors
Example: Ga As (group III-V)
Lets consider compounds from group III and V,
compounds from group II and VI, and compounds from
group IV and VI. There are also compounds of group IV
and IV.
These are insulators at low temperatures because all
electrons participate in the bonding. At higher
temperatures thermal excitation break the bonds and
electrons can be excited into the conduction band.
What are the differences between them and the
elemental semiconductors as Si and Ge?
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They have ionic contribution to the bonding.
Ionic bonding causes a harder bond (more difficult to
break) → leads to higher energy gap
Example III-V Materials (Ga As):
GaAs has higher electron mobility relative to Si and Ge
because of small value of effective electron mass (band
reduction)
Energy gap= 1.4eV
Look to the following table and to the periodic table and
note that:
Energy gap of:
GaN= 3.42 eV
GaP= 2.25 eV
GaAs= 1.4 eV
GaSb= 0.7 eV
Which means the gap gets smaller as we move down
through the periodic table.
The melting point also decreases, why??
- Let’s go back to Ga As:
 n-type or p-type: It depends on excess As
or excess Ga
 It can be also doped with (for example IV
material).
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Ga As versus Si:
 High electron mobility (high speed application)
 Large band gap (prevents intrinsic contribution)
 Direct band gap (good optical properties)
 Lower ionization energies of donors and acceptors
(complete ionization even at low temperature)
Problems:
 Density of GaAs= 5.3g/cm3
 Density of Si= 2.3 g/cm3
Ga As→ heavy and somewhat expensive
-Another semiconductor in group III-V is (GaN)
II-VI Compounds:
Examples: ZnTe, ZnO, ZnS
They have more ionic bonding than III-V.
Let’s discuss ZnO as an example.
IV-VI compounds:
Examples: PbS, PbSc, PbTe
IV-IV compounds:
Si-C
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Engineering (or tailoring) of the band gap:
By adding a third element
Example: add Al to GaAs
Al will occupy the Ga site and the energy gap will
increase
- the more Al added, the larger the band gap.
Another Example: add Mg to ZnO
The energy gap will increase
Third Example: add In to GaN
The energy gap will decrease
What are the benefits of that??
Control of conductivity in some compounds
p-type or n-type
Common problem (Bipolar Doping)
In principal, it should be simple to make p-type or ntype
However, this is not the case in some compounds as (IIVI group)
Wide band gap semiconductor always have Biopolar
doping problems (Important).
Let’s discuss the reasons behind this problem
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Measurements of energy gap:
1. The energy gap can be determined from conductivity
measurements versus temperature
𝜎 = (𝑁𝑒 𝜇𝑒 + 𝑁ℎ 𝜇ℎ )𝑒
For intrinsic use
𝑁𝑒 − 𝑁ℎ = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
3
𝑇 ⁄2
∙
−𝐸𝑔
⁄
2𝑘𝑇
𝑒
𝜎 is a function of temperature
𝜎 ≡ 𝑐𝑜𝑛𝑠𝑡
𝐸
− 𝑔⁄2𝑘𝑇
𝑒
The behavior is a little bit difference for doped
semiconductors
2. The energy gap can be determined for: optical
transmission measurements
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