Chapter 1-1

Microelectronics Microelectronics Circuit Analysis and Circuit Analysis and DesignDesign

Donald A. NeamenDonald A. Neamen

Chapter 1Chapter 1

Semiconductor Materials and Semiconductor Materials and DevicesDevices

Chapter 1-2

In this chapter, we will:In this chapter, we will: Gain a basic understanding of Gain a basic understanding of

semiconductor material propertiessemiconductor material properties– Two types of charged carriers that exist Two types of charged carriers that exist

in a semiconductorin a semiconductor– Two mechanisms that generate currents Two mechanisms that generate currents

in a semiconductorin a semiconductor

Chapter 1-3

Determine the properties of a pn Determine the properties of a pn junctionjunction

– Ideal current–voltage characteristics Ideal current–voltage characteristics of a pn junction diodeof a pn junction diode

Examine dc analysis techniques Examine dc analysis techniques for diode circuits using various for diode circuits using various models to describe the nonlinear models to describe the nonlinear diode characteristicsdiode characteristics

Chapter 1-4

Develop an equivalent circuit for a diode Develop an equivalent circuit for a diode that is used when a small, time-varying that is used when a small, time-varying signal is applied to a diode circuitsignal is applied to a diode circuit

Gain an understanding of the properties Gain an understanding of the properties and characteristics of a few specialized and characteristics of a few specialized diodesdiodes

Design a simple electronic thermometer Design a simple electronic thermometer using the temperature characteristics of a using the temperature characteristics of a diodediode

Chapter 1-5

Intrinsic Intrinsic SemiconductorsSemiconductors Ideally 100% pure materialIdeally 100% pure material

– Elemental semiconductorsElemental semiconductors Silicon (Si)Silicon (Si)

– Most common semiconductor used todayMost common semiconductor used today

Germanium (Ge)Germanium (Ge)– First semiconductor used in p-n diodesFirst semiconductor used in p-n diodes

– Compound semiconductorsCompound semiconductors Gallium Arsenide (GaAs)Gallium Arsenide (GaAs)

Chapter 1-6

Silicon Silicon (Si)(Si)

Covalent bonding of one Si atom with four other Si atoms to form tetrahedral unit cell.

Chapter 1-7

Effect of TemperatureEffect 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 1-8

Energy Energy Band Band DiagraDiagramm

EEvv – Maximum energy of a valence electron or hole – Maximum energy of a valence electron or hole

EEcc – Minimum energy of a free electron – Minimum energy of a free electron

EEgg – Energy required to break the covalent bond – Energy required to break the covalent bond

Chapter 1-9

Movement of HolesMovement 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 1-10

Intrinsic Carrier Intrinsic Carrier ConcentrationConcentration

kT

E

i

g

eBTn 223

B – coefficient related to specific semiconductorT – temperature in KelvinEg – semiconductor bandgap energy

k – Boltzmann’s constant(86х10-6eV/K)

310105.1)300,( cmxKSini

Chapter 1-11

Semiconductor Semiconductor constantsconstants

Material Eg(ev) B(cmMaterial Eg(ev) B(cm -3-3KK-3/2-3/2))

------------------------------------------------------------------------------------------------------------

Silicon 1.1 5.23X10Silicon 1.1 5.23X101515

Gallium arsenide(GaAs) 1.4 Gallium arsenide(GaAs) 1.4 2.10X102.10X101414

Germanium 0.66 1.66X10Germanium 0.66 1.66X101515

Chapter 1-12

Exercise Exercise

1.1 Calculate the intrinsic carrier 1.1 Calculate the intrinsic carrier concentration in silicon at concentration in silicon at T=300K.T=300K.

1.2 Calculate the intrinsic carrier 1.2 Calculate the intrinsic carrier concentration in Gallium arsenide concentration in Gallium arsenide and Germanium at T=300K.and Germanium at T=300K.

Chapter 1-13

Extrinsic Extrinsic SemiconductorsSemiconductors Impurity atoms replace some of Impurity atoms replace some of

the atoms in crystalthe atoms in crystal– Column V atoms in Si are called Column V atoms in Si are called

donor impurities.donor impurities.– Column III in Si atoms are called Column III in Si atoms are called

acceptor impurities.acceptor impurities.

Chapter 1-14

Phosphorous – Donor Impurity in SiPhosphorous – 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 1-15

Boron – Acceptor Impurity Boron – Acceptor Impurity in Siin 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 1-16

Electron and Hole Electron and Hole ConcentrationsConcentrationsn = electron concentrationn = electron concentration

p = hole concentrationp = hole concentrationpnni 2

n-type:n-type:

n = Nn = NDD, the donor concentration, the donor concentration

p-type:p-type:

p = Np = NAA, the acceptor concentration, the acceptor concentration

Ai Nnn /2

Di Nnp /2

Chapter 1-17

Drift Drift CurrentsCurrents

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 1-18

Diffusion CurrentsDiffusion 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 1-19

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 1-20

Built-in PotentialBuilt-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 1-21

Calculate VCalculate Vbibi

2 2ln lna d a d

bi Ti i

N N N NkTV V

e n n

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 1-22

Reverse BiasReverse Bias

Increase in space-charge width, W, as VR increases to VR+VR.

Creation of more fixed charges (-Q and +Q) leads to junction capacitance.

Chapter 1-23

Forward Biased p-n Forward Biased p-n JunctionJunction

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 1-24

Minority Carrier ConcentrationsMinority Carrier Concentrations

Gradients in minority carrier concentration generates diffusion currents in diode when forward biased.

Chapter 1-25

Ideal Current-Voltage (I-V) Ideal Current-Voltage (I-V) CharacteristicsCharacteristics

The p-n junction only conducts significant current in the forward-bias region.

iD is an exponential function in this region.

Essentially no current flows in reverse bias.

Chapter 1-26

)1( nkT

qv

sD

D

eII

Ideal Diode EquationIdeal Diode EquationA fit to the I-V characteristics of a diode yields the following equation, known as the ideal diode equation:

kT/q is also known as the thermal voltage, VT.

VT = 25.9 mV when T = 300K, room temperature.

Chapter 1-27

)1( T

D

V

v

sD eII

Chapter 1-28

Ideal Diode EquationIdeal Diode Equation

)log(log

)log( sDT

D IvnV

ei

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 1-29

Circuit SymbolCircuit Symbol

Conventional current direction and polarity of voltage drop is shown

Chapter 1-30

Breakdown VoltageBreakdown Voltage

Mechanism:

(1) Avalanche breakdown

(2) Zener breakdown

breakdown voltage (BV)

Chapter 1-31

Transient ResponseTransient Response

Chapter 1-32

Transient ResponseTransient Response

It is composed of a storage time, ts, and a fall time, tf.

Chapter 1-33

EX1.3 Determine VEX1.3 Determine Vbi bi for a silicon pn for a silicon pn junction at T=300K forjunction at T=300K for (a) N (a) Naa=10=101515cmcm-3-3, N, Ndd=10=101717cmcm-3-3, ,

and for and for

(b) N(b) Naa=N=Nd d =10=101717cmcm-3-3..

Chapter 1-34

dc Model of Ideal Diodedc Model of Ideal Diode

Equivalent Circuits

Chapter 1-35

Half-Wave Half-Wave Diode RectifierDiode 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 1-36

Graphical Analysis Graphical Analysis TechniqueTechnique

Simple diode circuit where ID and VD are not known.

PS D D

PS DD

PS D

V I R V

V VI

RV V

R R

Chapter 1-37

Load Line AnalysisLoad Line Analysis

PS D D

PS DD

PS D

V I R V

V VI

RV V

R R

Chapter 1-38

Piecewise Linear ModelPiecewise Linear Model

Two linear approximations are used to form piecewise linear model of diode.

Chapter 1-39

Diode Piecewise Equivalent CircuitDiode Piecewise Equivalent Circuit

The diode is replaced by a battery with voltage, V, with a resistor, rf, in series when in the ‘on’ condition (a) and is replaced by an open when in the ‘off’ condition, VD < V.

Chapter 1-40

Q-pointQ-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 1-41

Load Line: Reverse Biased DiodeLoad 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 1-42

PSpice AnalysisPSpice Analysis

V1 sweep from 0 to 5V.

Chapter 1-43

1.4 Diode Circuits: AC 1.4 Diode Circuits: AC Equivalent CircuitEquivalent Circuit

Objective: Develop an equivalent Objective: Develop an equivalent circuit for a diode that used when circuit for a diode that used when a small, time-varying signal is a small, time-varying signal is applied to a diode circuit.applied to a diode circuit.

Chapter 1-44

ac Circuit Analysisac Circuit AnalysisCombination of dc and sinusoidal input voltages modulate the operation of the diode about the Q-point.

Chapter 1-45

Sinusoidal AnalysisSinusoidal Analysis

T

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SD

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V

v

V

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S

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vV

SV

v

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v

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veIi

V

ve

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T

DQ

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T

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1

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Chapter 1-46

T

DQ

V

V

SDQ eII

dDQD iIi

DQ

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T

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Vrv

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Chapter 1-47

ExampleExample Objective: Analyze the circuit Objective: Analyze the circuit

shown in figure below.shown in figure below.

Assume circuit and diode parameters of VPS=5V, R=5KΩ, Vγ=0.6V, and vi=0.1sinwt(V).

Chapter 1-48

Solution: DC+AC Solution: DC+AC methodmethod

For the DC analysis: set vFor the DC analysis: set v ii=0,=0,

mAR

VVI PS

DQ 88.05

6.05

VKmARIV DQo 4.4)5()88.0(

The DC value of the output voltage is

Chapter 1-49

For the ac analysis, set VFor the ac analysis, set VPSPS=0. =0. The ac kirchhoff voltage law The ac kirchhoff voltage law (KVL) equation becomes(KVL) equation becomes

Chapter 1-50

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Chapter 1-51

EX1.4 Assume the circuit EX1.4 Assume the circuit and diode parameters for and diode parameters for the circuit in figure the circuit in figure 1.34(a) are 1.34(a) are VVPSPS=10V,R=20K=10V,R=20KΩΩ,V,Vγγ=0.7V,=0.7V,and vand vII=0.2sinwtV. =0.2sinwtV. Determine the quiescent Determine the quiescent diode current and the diode current and the time-varying diode time-varying diode current.current.

Chapter 1-52

!! !! Comment: Throughout the text, we Comment: Throughout the text, we will divide the circuit analysis into a will divide the circuit analysis into a dc analysis and an ac analysis. To do dc analysis and an ac analysis. To do so, we will use separate equivalent so, we will use separate equivalent circuit models for each analysis.circuit models for each analysis.

Chapter 1-53

Minority Carrier ConcentrationMinority Carrier Concentration

Time-varying excess charge leads to diffusion capacitance.

Frequency response

Chapter 1-54

Equivalent CircuitsEquivalent 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 1-55

Small Signal Equivalent Small Signal Equivalent ModelModel

Simplified model, which can only be used when the diode is forward biased.

Complete model

Chapter 1-56

1.5 Other Diode Types1.5 Other Diode Types

1.5.1 Solar cell1.5.1 Solar cell

1.5.2 Photodiode1.5.2 Photodiode

1.5.3 Light-Emitting Diode1.5.3 Light-Emitting Diode

1.5.4 Schottky Barrier Diode 1.5.4 Schottky Barrier Diode

1.5.5 Zener Diode1.5.5 Zener Diode

Chapter 1-57

1.5.1 Solar cell1.5.1 Solar cell

A solar cell is a pn junction device A solar cell is a pn junction device with no voltage directly applied with no voltage directly applied across the junction, which converts across the junction, which converts solar energy into electrical energy, solar energy into electrical energy, is connected to a load.is connected to a load.

Chapter 1-58

Chapter 1-59

1.5.2 Photodiode1.5.2 Photodiode

Attention: Reverse biasedAttention: Reverse biased

Chapter 1-60

1.5.3 Light-Emitting 1.5.3 Light-Emitting DiodeDiode

Chapter 1-61

Optical Transmission Optical Transmission SystemSystem

LED (Light Emitting Diode) and photodiode are p-n junctions.

Chapter 1-62

1.5.4 Schottky Barrier 1.5.4 Schottky Barrier DiodeDiode

A metal layer replaces the p region of the diode.

Circuit symbol showing conventional current direction of current and polarity of voltage drop.

Chapter 1-63

Comparison of I-V Characteristics: Comparison of I-V Characteristics:

Forward BiasForward Bias

The built-in voltage of the Schottky barrier diode, V(SB), is about ½ as large as the built-in voltage of the p-n junction diode, V(pn),.

Chapter 1-64

1.5.5 Zener Diode 1.5.5 Zener Diode

Usually operated in reverse bias region near the breakdown or Zener voltage, VZ.

Note the convention for current and polarity of voltage drop.

Circuit Symbol

Chapter 1-65

Example 1.13Example 1.13Given VZ = 5.6V

rZ = 0

Find a value for R such that the current through the diode is limited to 3mA

Chapter 1-66

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kmA

VV

I

VVR

R

VVI

ZZZ

ZPS

ZPS

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Chapter 1-67

Design example :Digital Design example :Digital ThermometerThermometer

Use the temperature dependence of the forward-bias characteristics to design a simple electronic thermometer.

Chapter 1-68

SolutioSolutionn

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21

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2

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22

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2

2

2

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1

1

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Given: IS = 10-13 A at T = 300K

Assume: Ideal diode equation can be simplified.

VeEg 12.1

Chapter 1-69

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Chapter 1-70

Chapter 1-71

Note:,Note:,

to complete this design, two to complete this design, two additional components must be additional components must be added to the circuit shown hereadded to the circuit shown here

Chapter 1-72

Two additional Two additional components:components:

An op-amp circuit to measure the An op-amp circuit to measure the diode voltage;diode voltage;

An ADC to convert the voltage to An ADC to convert the voltage to a temperature reading.a temperature reading.

Chapter 1-73

Problem 1.42Problem 1.42

First, determine if the diode is on or off. Is the open circuit voltage for the diode greater or less than V?

Chapter 1-74

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 ≥ V.

Chapter 1-75

EX1.5 (Solution can refer to next EX1.5 (Solution can refer to next page)page)

Design a circuit that has a voltage transfer function shown to the left.

(pp 60)

Chapter 1-76

SolutionSolution

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 1-77

solution con’tsolution 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 V = 8.2V.

Chapter 1-78

Circuit for 1.63Circuit for 1.63

Chapter 1-79

Or, if you assumed a more common V, say of 0.7V, then the circuit would be:

solution con’tsolution con’t