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Compact Models for Integrated Circuit Design
2.4 Summary
This chapter presented a brief overview of the basic semiconductor physics and basic theory of extrinsic semiconductors forming pn-junctions.
First of all, the basic properties of intrinsic semiconductor materials
including bond and band structures, intrinsic carrier concentration, and
energy levels are discussed. Then the behavior of extrinsic semiconductors, carrier  statistics of electrons and holes, carrier transport, and
transport equations are discussed. After the discussion of p-type and
n-type semiconductors, the basic properties of n- and p-type semiconductors forming pn- junctions are described. Then the basic theory of pnjunctions,  current transport,  and dynamic characteristics are discussed.
Finally, a basic equivalent circuit model of pn- junction for circuit CAD is
presented.
Physical Constants
Constants
Symbol
Magnitude
Units
Electronic charge
q
1.602 × 10 –19
C
Free-electron mass
m
9.11 × 10 –28
g
Boltzmann’s constant
k
1.38 × 10 –23
J K –1
8.62 × 10 –5
eV K –1
Planck’s constant
h
6.25 × 10 –34
J s
Permittivity of free space
ε 0
8.854 × 10 –14
F cm –1
Thermal voltage at 300 K
kT/q = v kT
0.02586
V
Thermal energy at 300 K
kT
0.02586
eV
g d
r s
C d
C j
FIGURE 2.29
An equivalent circuit for a pn-junction showing the relevant circuit elements: r s is the series
resistance of the neutral n- and p-regions; C j is junction capacitance; C d is the diffusion capacitance; and g d is the small-signal conductance.