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Microelectronics
Circuit Analysis and Design
Donald A. Neamen
Chapter 1
Semiconductor Materials and Devices
Chapter 1-1
In this chapter, we will:

Gain a basic understanding of
semiconductor material properties
– Two types of charged carriers that exist in a
semiconductor
– Two mechanisms that generate currents in a
semiconductor
Chapter 1-2

Determine the properties of a pn
junction
– Ideal current–voltage characteristics of a
pn junction diode

Examine dc analysis techniques for
diode circuits using various models to
describe the nonlinear diode
characteristics
Chapter 1-3



Develop an equivalent circuit for a diode
that is used when a small, time-varying
signal is applied to a diode circuit
Gain an understanding of the properties and
characteristics of a few specialized diodes
Design a simple electronic thermometer
using the temperature characteristics of a
diode
Chapter 1-4
Intrinsic Semiconductors

Ideally 100% pure material
– Elemental semiconductors

Silicon (Si)
– Most common semiconductor used today

Germanium (Ge)
– First semiconductor used in p-n diodes
– Compound semiconductors

Gallium Arsenide (GaAs)
Chapter 1-5
Silicon (Si)
Covalent bonding of one Si atom with four other Si
atoms to form tetrahedral unit cell.
Chapter 1-6
Effect of Temperature
At 0K, no bonds are broken.
Si is an insulator.
As temperature increases, a bond can
break, releasing a valence electron and
leaving a broken bond (hole).
Current can flow.
Chapter 1-7
Energy
Band
Diagram
Ev – Maximum energy of a valence electron or hole
Ec – Minimum energy of a free electron
Eg – Energy required to break the covalent bond
Chapter 1-8
Movement of Holes
A valence electron in a
nearby bond can move to
fill the broken bond,
making it appear as if the
‘hole’ shifted locations.
Chapter 1-9
Intrinsic Carrier
Concentration
ni  BT e
32
 Eg
2 kT
B – coefficient related to specific semiconductor
T – temperature in Kelvin
10
3
 1.5 x10
cm
i ( Si,300 K ) bandgap
Eg –nsemiconductor
energy
k – Boltzmann’s constant(86х10-6eV/K)
Chapter 1-10
Semiconductor constants
Material
Eg(ev)
B(cm-3K-3/2)
-----------------------------------------------------Silicon
1.1
5.23X1015
Gallium arsenide(GaAs) 1.4
2.10X1014
Germanium
0.66
1.66X1015
Chapter 1-11
Exercise


1.1 Calculate the intrinsic carrier
concentration in silicon at T=300K.
1.2 Calculate the intrinsic carrier
concentration in Gallium arsenide and
Germanium at T=300K.
Chapter 1-12
Extrinsic Semiconductors

Impurity atoms replace some of the
atoms in crystal
– Column V atoms in Si are called donor
impurities.
– Column III in Si atoms are called acceptor
impurities.
Chapter 1-13
Phosphorous – Donor Impurity in Si
Phosphorous (P) replaces a Si atom and forms four covalent bonds with
other Si atoms.
The fifth outer shell electron of P is easily freed to become a conduction
band electron, adding to the number of electrons available to conduct
current.
Chapter 1-14
Boron – Acceptor Impurity in Si
Boron (B) replaces a Si atom and forms only three covalent bonds with
other Si atoms.
The missing covalent bond is a hole, which can begin to move through
the crystal when a valence electron from another Si atom is taken to form
the fourth B-Si bond.
Chapter 1-15
Electron and Hole
Concentrations
n = electron concentration
p = hole concentration
n-type:
n = ND, the donor concentration
p-type:
p = NA, the acceptor concentration
Chapter 1-16
n  n p
2
i
p  ni2 / N D
n  n / NA
2
i
Drift Currents
Electrons and hole flow in opposite directions when under the
influence of an electric field at different velocities.
The drift currents associated with the electrons and holes are in
the same direction.
Chapter 1-17
Diffusion Currents
Both electrons and holes flow from high concentration to low.
The diffusion current associated with the electrons flows in the
opposite direction when compared to that of the holes.
Chapter 1-18
p-n Junctions
A simplified 1-D sketch of a p-n
junction (a) has a doping profile
(b).
The 3-D representation (c) shows
the cross sectional area of the
junction.
Chapter 1-19
Built-in Potential
This movement of
carriers creates a
space charge or
depletion region
with an induced
electric field near
x = 0.
A potential
voltage, vbi, is
developed across
the junction.
Chapter 1-20
Calculate Vbi
kT  Na Nd
Vbi 
ln  2
e  ni

 Na Nd 
  VT ln  2 

 ni 
Where VT=kT/e, k=Boltzmann’s constant. T=absolute
temperature, e=the magnitude of the electronic charge,
and Na and Nd are the net acceptor and donor
concentrations in the p- and n- regions, respectively.
Chapter 1-21
Reverse Bias
Increase in space-charge width, W, as VR increases to VR+DVR.
Creation of more fixed charges (-DQ and +DQ) leads to junction
capacitance.
Chapter 1-22
Forward Biased p-n Junction
Applied voltage, vD, induces an electric field, EA, in the opposite
direction as the original space-charge electric field, resulting in a
smaller net electric field and smaller barrier between n and p
regions.
Chapter 1-23
Minority Carrier Concentrations
Gradients in minority carrier concentration generates
diffusion currents in diode when forward biased.
Chapter 1-24
Ideal Current-Voltage (I-V) Characteristics
The p-n junction only
conducts significant
current in the forwardbias region.
iD is an exponential
function in this region.
Essentially no current
flows in reverse bias.
Chapter 1-25
Ideal Diode Equation
A fit to the I-V characteristics of a diode yields the
following equation, known as the ideal diode equation:
I D  I s (e
qvD
nkT
 1)
kT/q is also known as the thermal voltage, VT.
VT = 25.9 mV when T = 300K, room temperature.
Chapter 1-26
I D  I s (e
Chapter 1-27
vD
VT
 1)
Ideal Diode Equation
log e
log( iD ) 
vD  log( I s )
nVT
The y intercept is equal to IS.
The slope is proportional to 1/n.
When n = 1, iD increased by ~
one order of magnitude for
every 60-mV increase in vD.
Chapter 1-28
Circuit Symbol
Conventional current direction and polarity of voltage
drop is shown
Chapter 1-29
Breakdown Voltage
Mechanism:
(1) Avalanche
breakdown
(2) Zener breakdown
breakdown voltage (BV)
Chapter 1-30
Transient Response
Chapter 1-31
Transient Response
It is composed of a storage time, ts, and a fall time, tf.
Chapter 1-32
EX1.3 Determine Vbi for a silicon pn junction at
T=300K for
(a) Na=1015cm-3, Nd=1017cm-3,
and for
(b) Na=Nd =1017cm-3.
Chapter 1-33
dc Model of Ideal Diode
Equivalent Circuits
Chapter 1-34
Half-Wave Diode
Rectifier
Diode only allows current to flow through the resistor when
vI ≥ 0V. Forward-bias equivalent circuit is used to determine
vO under this condition.
Chapter 1-35
Graphical Analysis Technique
VPS  I D R  VD
VPS  VD
 ID 
R
VPS VD


R
R
Simple diode circuit where ID and VD are not known.
Chapter 1-36
Load Line Analysis
VPS  I D R  VD
VPS  VD
 ID 
R
VPS VD


R
R
Chapter 1-37
Piecewise Linear Model
Two linear
approximations are
used to form piecewise
linear model of diode.
Chapter 1-38
Diode Piecewise Equivalent Circuit
The diode is replaced by a battery with voltage, Vg, with a
resistor, rf, in series when in the ‘on’ condition (a) and is
replaced by an open when in the ‘off’ condition, VD < Vg.
Chapter 1-39
Q-point
The x intercept of the load line is the open circuit voltage and the
y intercept is the short circuit current.
The Q-point is dependent on the power supply voltage and the
resistance of the rest of the circuit as well as on the diode I-V
characteristics.
Chapter 1-40
Load Line: Reverse Biased Diode
The Q-point is always ID = 0 and VD = the open circuit voltage
when using the piecewise linear equivalent circuit.
Chapter 1-41
PSpice Analysis
V1 sweep
from 0 to
5V.
Chapter 1-42
1.4 Diode Circuits: AC
Equivalent Circuit
Objective: Develop an equivalent circuit
for a diode that used when a small,
time-varying signal is applied to a
diode circuit.
Chapter 1-43
ac Circuit Analysis
Combination of dc and
sinusoidal input
voltages modulate the
operation of the diode
about the Q-point.
Chapter 1-44
Sinusoidal Analysis

iD  I S  e


VDQ  vd

VT

1  I S e  I S e


VDQ vd

VT VT
VDQ
 ISe e 
vd

VT 
vd
  iD  I S e 1 
vd 
VT
VT

e  1
VT 
vD
vT
vD
VT
Chapter 1-45



iD  I DQ  id
VDQ
I DQ  I S e
VT
I DQ
VT
id 
vd  rd 
VT
I DQ
Chapter 1-46
Example

Objective: Analyze the circuit shown in
figure below.
Assume circuit and
diode parameters of
VPS=5V, R=5KΩ,
Vγ=0.6V, and
vi=0.1sinwt(V).
Chapter 1-47
Solution: DC+AC method
For the DC analysis: set vi=0,
I DQ 
VPS  Vg
R

5  0.6
 0.88mA
5
The DC value of the output voltage is
Vo  I DQ R  (0.88mA)  (5K)  4.4V
Chapter 1-48
For the ac analysis, set VPS=0. The
ac kirchhoff voltage law (KVL)
equation becomes
Chapter 1-49
vi  id rd  id R  id (rd  R)
VT
0.026V
rd 

 0.0295K
I DQ 0.88mA
The ac diode current is
vi
0.1sin t
id 

 19.9 sin t A
rd  R 0.0295  5
The ac component of the output vol tage is
vo  id R  0.0995 sin t V 
Chapter 1-50
EX1.4 Assume the circuit and
diode parameters for the
circuit in figure 1.34(a) are
VPS=10V,R=20KΩ,Vγ=0.7V,an
d vI=0.2sinwtV. Determine
the quiescent diode current
and the time-varying diode
current.
Chapter 1-51
!! Comment: Throughout the text, we
will divide the circuit analysis into a dc
analysis and an ac analysis. To do so,
we will use separate equivalent circuit
models for each analysis.
Chapter 1-52
Frequency response
Time-varying excess
charge leads to
diffusion capacitance.
Minority Carrier Concentration
Chapter 1-53
Equivalent Circuits
When ac signal is small, the dc operation can be decoupled from the ac
operation.
First perform dc analysis using the dc equivalent circuit (a).
Then perform the ac analysis using the ac equivalent circuit (b).
Chapter 1-54
Small Signal Equivalent Model
Simplified model, which
can only be used when the
diode is forward biased.
Complete model
Chapter 1-55
1.5 Other Diode Types
1.5.1
1.5.2
1.5.3
1.5.4
1.5.5
Solar cell
Photodiode
Light-Emitting Diode
Schottky Barrier Diode
Zener Diode
Chapter 1-56
1.5.1 Solar cell
A solar cell is a pn junction device with
no voltage directly applied across the
junction, which converts solar energy
into electrical energy, is connected to a
load.
Chapter 1-57
Chapter 1-58
1.5.2 Photodiode
Attention: Reverse biased
Chapter 1-59
1.5.3 Light-Emitting
Diode
Chapter 1-60
Optical Transmission System
LED (Light Emitting Diode) and photodiode are p-n junctions.
Chapter 1-61
1.5.4 Schottky Barrier Diode
A metal layer replaces the
p region of the diode.
Circuit symbol showing
conventional current
direction of current and
polarity of voltage drop.
Chapter 1-62
Comparison of I-V Characteristics:
Forward Bias
The built-in voltage of
the Schottky barrier
diode, Vg(SB), is about
½ as large as the builtin voltage of the p-n
junction diode, Vg(pn),.
Chapter 1-63
1.5.5 Zener Diode
Circuit Symbol
Usually operated in reverse bias
region near the breakdown or
Zener voltage, VZ.
Note the convention for current
and polarity of voltage drop.
Chapter 1-64
Example 1.13
Given VZ = 5.6V
rZ = 0
Find a value for R such
that the current through the
diode is limited to 3mA
Chapter 1-65
VPS  VZ
I
R
VPS  VZ 10V  5.6V
R

 1.47k
I
3mA
PZ  I ZV Z 3mA  5.6V  1.68mW
Chapter 1-66
Design example :Digital Thermometer
Use the temperature dependence of the
forward-bias characteristics to design a
simple electronic thermometer.
Chapter 1-67
Solution
Given: IS = 10-13 A at T = 300K
E g e  1.12V
Assume: Ideal diode equation can be simplified.
I D  I Se
VD
VT
 Eg
 Eg
 ni2 e kT e
VD
VT
eVD1
kT1
I D1 e kT1 e
  E g eV
if assume I D1  I D 2
D2
I D2
e kT2 e kT2
E g T2 E g
T2
T2
T2
VD 2   ( ) 
 VD1 ( )  1.12(1  )  VD1 ( )
e T1
e
T1
T1
T1
15V  VD
ID 
 I Se
R
VD
VT
Chapter 1-68
Thermometer con’t
VD
VT
15V  VD
13
ID 

10
A  e at T  300K
3
15 x10 
Through tr ial and error : VD  0.5976V and I D  0.960mA
To find temperatu re dependence , let T1  300K.
T
VD  1.12  0.522(
)V
300
Chapter 1-69
Chapter 1-70
Note:,

to complete this design, two additional
components must be added to the
circuit shown here
Chapter 1-71
Two additional components:


An op-amp circuit to measure the
diode voltage;
An ADC to convert the voltage to a
temperature reading.
Chapter 1-72
Problem 1.42
First, determine if the diode is on or
off. Is the open circuit voltage for
the diode greater or less than Vg?
Chapter 1-73
The voltage at the node connected to the p side of the diode is
2kW 5V/(4kW) = 2.5V
The voltage at the node connected to n side of the diode is
2kW 5V/(5kW) = 2V
The open circuit voltage is equal to the voltage at the p side minus
the voltage at the n side of the diode:
Voc = 2.5V – 2V = 0.5V.
To turn on the diode, Voc must be ≥ Vg.
Chapter 1-74
EX1.5 (Solution can refer to next page)
Design a circuit that
has a voltage
transfer function
shown to the left.
(pp 60)
Chapter 1-75
Solution
For 0V ≤ vI < 8.2V, the voltage transfer function is linear.
When vI = 0V, vO = 0V so there is no need to include a battery
in the piecewise linear model for this voltage range.
Since there is a 1:1 correspondence
between vI and vO, this section of
the transfer function can be
modeled as a 1 resistor.
Chapter 1-76
solution con’t
When vI ≥ 8.2V, the output voltage is pinned at 8.2V, just as if
the device suddenly became a battery.
Hence, the model for this section is a battery, where Vg = 8.2V.
Chapter 1-77
Circuit for 1.63
Chapter 1-78
solution con’t
Or, if you assumed a more common Vg, say of 0.7V, then
the circuit would be:
Chapter 1-79