Electronics lecture 1

1
Basic Physics of Semiconductors

Basic Physics of Semiconductors 2
Semiconductor Physics
➢ Semiconductor devices serve
as heart of microelectronics.
➢ PN junction is the most fundamental
semiconductor device.

3
Charge Carriers in Semiconductor
➢ To understand PN junction’s IV characteristics, it is
important to understand:
– Charge carriers’ behavior in solids,
– How to modify carrier densities,
– and different mechanisms of charge flow.

4
Periodic Table
➢ This abridged table contains elements with three to five
valence electrons, with Si being the most important.

5
Silicon
➢ When temperature goes up,
electrons in the covalent bond
can become free.
➢ Si has four valence electrons.
➢ Therefore, it can form covalent
bonds with four of its neighbors

6
Electron-Hole Pair Interaction
➢ Holes can be filled by
absorbing other free electrons
➢ With free electrons breaking off
covalent bonds, holes are generated.
➢ So, effectively there is a flow of
charge carriers.

7
Free Electron Density at a Given Temperature
➢ Eg, or bandgap energy determines how much effort is
needed to break off an electron from its covalent bond.
➢ There exists an exponential relationship between the free-
electron density and bandgap energy.
32/3
/
2
exp cmelectrons
kT
E
BTn g
i
−
=

8
Doping (N type)
➢ Pure Si can be doped with other elements to change its
electrical properties.
➢ For example, if Si is doped with P (phosphorous), then
it has more electrons, or becomes type N (electron).

9
Doping (P type)
➢ If Si is doped with B (boron), then it has more holes,
or becomes type P.

10
Summary of Charge Carriers

11
Electron and Hole Densities
➢ The product of electron and hole densities is ALWAYS
equal to the square of intrinsic electron density
regardless of doping levels.
2
innp =
D
i
D
A
i
A
N
n
p
Nn
N
n
n
Np
2
2



Majority Carriers :
Minority Carriers :
Majority Carriers :
Minority Carriers :
type N
type P

12
First Charge Transportation Mechanism: Drift
➢ The process in which charge particles move because of
an electric field is called drift.
➢ Charge particles will move at a velocity that is proportional
to the electric field.
→→
→→
−=
=
Ev
Ev
ne
ph


Semiconductor

13
Current Flow: General Case
➢ Electric current is calculated as the amount of charge
that passes thru a cross-section if the charge travel with a
velocity of v m/s.
qnhWvI −=
(current density)

14
Current Flow: Drift
➢ Since velocity is equal to E, drift characteristic is obtained
by substituting v with E in the general current equation.
➢ The total current density consists of both electrons and holes.

15
Second Charge Transportation Mechanism:
Diffusion
➢ Charge particles move from a region of high concentration
to a region of low concentration. It is analogous to an
every day example of an ink droplet in water.

16
Current Flow: Diffusion
➢ Diffusion current is proportional to the gradient of charge
(dn/dx) along the direction of current flow.
➢ Its total current density consists of both electrons and holes.

17
Example: Linear vs. Nonlinear Charge
Density Profile
➢ Linear charge density profile means constant diffusion
current, whereas nonlinear charge density profile means
varying diffusion current.
L
N
qD
dx
dn
qDJ nnn −==
dd
n
n
L
x
L
NqD
dx
dn
qDJ
−−
== exp

18
Einstein's Relation
➢ While the underlying physics behind drift and diffusion
currents are totally different, Einstein’s relation provides
a mysterious link between the two mechanisms.
q
kTD
=

26 mV @ 300 K

19
PN Junction (Diode)

20
PN Junction
➢ When N-type and P-type dopants are introduced side-
by-side in a semiconductor, a PN junction or a diode
is formed.

21
Diode’s Three Operation Regions
➢ In order to understand the operation of a diode, it is
necessary to study its three operation regions:
– equilibrium,
– reverse bias,
– and forward bias.

22
Current Flow Across Junction: Diffusion
➢ Because each side of the junction contains an excess of
holes or electrons compared to the other side, there exists
a large concentration gradient. Therefore, a diffusion
current flows across the junction from each side.

23
Depletion Region
➢ As free electrons and holes diffuse across the junction, a
region of fixed ions is left behind. This region is known as
the “depletion region.”

CH2 Basic Physics of Semiconductors 24
Current Flow Across Junction: Drift
➢ The fixed ions in depletion region create an electric field
that results in a drift current.

25
Current Flow Across Junction: Equilibrium
➢ At equilibrium, the drift current flowing in one direction
cancels out the diffusion current flowing in the opposite
direction, creating a net current of zero.
➢ The figure shows the charge profile of the PN junction.
ndiffndrift
pdiffpdrift
II
II
,,
,,
=
=

26
Built-in Potential
➢ Because of the electric field across the junction, there
exists a built-in potential (Vo).
20 ln
i
DA
n
NN
q
kT
V =

27
Diode in Reverse Bias
➢ When the N-type region of a diode is connected to a
higher potential than the P-type region, the diode is under
reverse bias, which results in wider depletion region and
larger built-in electric field across the junction.

28
Reverse Biased Diode’s Application:
Voltage-Dependent Capacitor
➢ The PN junction can be viewed as a capacitor. By
varying VR, the depletion width changes, changing its
capacitance value; therefore, the PN junction is actually
a voltage-dependent capacitor.

29
Voltage-Dependent Capacitance
➢ The equations that describe the voltage-dependent
capacitance are shown above.
0
0
0
0
1
2
1
VNN
NNq
C
V
V
C
C
DA
DAsi
j
R
j
j
+
=
+
=


30
Voltage-Controlled Oscillator
➢ A very important application of a reverse-biased PN
junction is VCO, in which an LC tank is used in an
oscillator. By changing VR, we can change C, which
also changes the oscillation frequency.
LC
fres
1
2
1

=

31
Diode in Forward Bias
➢ When the N-type region of a diode is at a lower potential
than the P-type region, the diode is in forward bias.
➢ The depletion width is shortened and the built-in electric
field decreased.

32
Minority Carrier Profile in Forward Bias
➢ Under forward bias, minority carriers in each region
increase due to the lowering of built-in field/potential.
Therefore, diffusion currents increase to supply the
increase in minority carriers.
T
F
fp
fn
V
VV
p
p
−
=
0
,
,
exp
T
ep
en
V
V
p
p
0
,
,
exp
=

33
Diffusion Current in Forward Bias
➢ Diffusion current will increase in order to supply the
increase in minority carriers.
)(
2
pD
p
nA
n
is
LN
D
LN
D
AqnI +=
)1(exp −=
T
F
stot
V
V
II

34
Forward Bias Condition: Summary
➢ However, as we go deep into the P and N regions,
recombination currents from the majority carriers
dominate. These two currents add up to a constant
value.
➢ In forward bias, there are
large diffusion currents of
minority carriers through
the junction.

35
IV Characteristic of PN Junction
➢ The current and voltage relationship (I/V characteristic)
of a PN junction is exponential in forward bias region,
and relatively constant in reverse bias region.
)1(exp −=
T
D
SD
V
V
II

36
Parallel PN Junctions
➢ Since junction currents are proportional to the junction’s
cross-section area. Two PN junctions put in parallel are
effectively one PN junction with twice the cross-section
area, and hence twice the current.

37
Constant-Voltage Diode Model
➢ Diode operates as an open circuit if VD< VD,on and a
constant voltage source of VD,on if VD tends to exceed
VD,on.

38
Example: Diode Calculations
➢ This example shows the simplicity provided by a constant-
voltage model over an exponential model.
➢ For an exponential model, iterative method is needed to
solve for current, whereas constant-voltage model
requires only linear equations.
S
X
TXDXX
I
I
VRIVRIV ln11 +=+=
mAI
mAI
X
X
2.0
2.2
=
=
VV
VV
X
X
1
3
=
=for
for

39
Reverse Breakdown
➢ When a large reverse bias voltage is applied, breakdown
occurs and an enormous current flows through the diode.

40
Zener vs. Avalanche Breakdown
➢ Zener breakdown is a result of the large electric field
inside the depletion region that breaks electrons or holes
off their covalent bonds.
➢ Avalanche breakdown is a result of electrons or holes
colliding with the fixed ions inside the depletion region.

41
Effect of Temperature on the behavior of Diode

42
Diode Types
Signal diodes:

43
Diode Types
Zener diode:

44
Diode Types
Light Emitting Diodes:

45
Diode Types
Schottky Diodes:

46
Diode Types
Varactor Diode:

47
Diode Types

48
Testing Diodes

49
Testing Diodes

50
Exercise 1
Consider a pn junction at T = 300 K.
Assume IS = 1.4 x 10-14 A and n = 1.
Find the diode current for vD = +0.75 V and vD = -0.75 V.
For VD = +0.75 V, the diode is forward-biased.
Solution:
For VD = -0.75 V, the diode is reverse-biased.

51
Exercise 2
Determine the diode voltage and current in the circuit
using ideal model for a silicon diode. Also determine the
power dissipated in the diode.
Solution:

52
Exercise 3
(using constant voltage model) for a silicon diode.
Also determine the power dissipated in the diode.
Consider the cut-in voltage V = 0.65 V.
Solution:

53
Exercise 3
using piecewise linear model for a silicon diode. Also
determine the power dissipated in the diode. Consider
the cut-in voltage V = 0.65 V and the diode DC forward
resistance, rf = 15 Ω.
Solution:

54
Exercise 4
Determine the diode voltage and current for the circuit.
Consider IS = 10-13 A.
Solution:
&

55
Discussion
Ideal Model
Constant-
Voltage Model
Piecewise
Linear Model
Direct
Approach
Model

56
Diode - DC Load Line

57
Diode - DC Load Line

58
Exercise 5
A diode circuit and its load line are as shown in the
figure below:
Design the circuit when the diode is operating in forward bias
condition. Determine the diode current ID and diode forward
resistance rf in the circuit using a piecewise linear model.
Consider the cut-in voltage of the diode, Vγ = 0.65.

Electronics lecture 1

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