Chapter 1-Semiconductor Materials

Chapter 1Chapter 1Semiconductor Materials and Semiconductor Materials and DiodesDiodes

Semiconductor Materials and Semiconductor Materials and Properties Properties

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© Electronics© Electronics ECE 1231ECE 1231

Classification of MaterialsClassification of Materials

Classification according to the way materials react to the current when a voltage is applied across them:

Insulators Materials with very high resistance Oppose the flow of current (mica, rubber)

Conductors Materials with very low resistance Allow the current to flow easily (copper, aluminum)

Semiconductors Neither good conductors nor insulators (silicon, germanium) Can be controlled to either insulators by increasing their

resistance or conductors by decreasing their resistance

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Semiconductor MaterialsSemiconductor Materials

Electronic devices are fabricated by using semiconductor along with conductors and insulators.

Silicon is the most common semiconductor material used for devices and integrated circuits.

Other semiconductor materials are used for specialized applications.

For example, gallium arsenide and related compounds are used for very high speed devices and optical devices.

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Semiconductor Materials and Semiconductor Materials and PropertiesProperties

An atom is composed of a nucleus, which contains positively An atom is composed of a nucleus, which contains positively charged protons and neutral neutrons, and negatively charged charged protons and neutral neutrons, and negatively charged electrons that orbit the nucleus.electrons that orbit the nucleus.

The electrons are The electrons are distributed in various shell distributed in various shell at different distances from at different distances from the nucleus, and electron the nucleus, and electron energy increases as shell energy increases as shell radius increases.radius increases.

Electrons in the outermost Electrons in the outermost shell are called shell are called valence valence electronselectrons..

Atomic structure: (a) Germanium(b) Silicon

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A portion of the periodic table in which the more common semiconductors are found

Elemental Semiconductors Silicon (Si) and germanium (Ge) are in group IV.

Compound Semiconductor

Gallium arsenide (GaAs) is a group III-V.

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This figure shows five noninteracting silicon atoms, with four valence electrons of each atom shown as dashed lines emanating from the atom

Atoms come into close proximity to each other, the valence electrons interact to form a crystal.

The valence electrons are shared between atoms, forming what are called covalent bonds.

This figure is a two-dimensional representative of the lattice formed by five silicon atoms

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Ec

Ev

Eg

Conduction band

Valence band

Forbidden bandgap

In order to break the covalent bond, valence electron must gain a minimum energy, Eg , called the bandgap energy and becomes a free electron.

The energy Ev is the maximum energy of the valence energy band and the energy Ec is the minimum energy of the conduction energy band. The bandgap energy Eg is the difference between Ec and Ev, and the region between these two energies is called the forbidden bandgap.

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Energy Gaps and Energy Levels

Electrons can jump from one level to another if they absorb the enough energy to make the difference between their level and the level they are jumping to.

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The net charge of the material is neutral. If a negative charged electron breaks its covalent bond and moves away from its original position, a positively charged “empty state” is created at that position. This positively charged “particle” is called a hole.

In semiconductor, two types of charged particles contribute to the current: the negatively charged free electron and the positively charged hole.

A two-dimensional representation of the silicon crystal showing the movement of positively charged “empty state”

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Intrinsic SemiconductorIntrinsic Semiconductor

Intrinsic Semiconductor A single-crystal semiconductor material with no other types of

atoms within the crystal.

The densities of electrons and holes are equal.

The notation ni is used as intrinsic carrier concentration for the concentration of the free electrons as well as that of the hole:

B = a coefficient related to the specific semiconductor materialEg = the bandgap energy (eV)T = the temperature (K)k = Boltzmann’s constant (86 x 10-6 eV/K)

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Intrinsic SemiconductorIntrinsic Semiconductor

The values of B and Eg for several semiconductor materials:

Example: Calculate the intrinsic carrierconcentration in silicon at T = 300 K.

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Extrinsic SemiconductorExtrinsic Semiconductor

Impurity with five valence electrons is diffused in silicon are called donor atoms.

The phosphorous atom is called a donor impurity, since it donates an electron that is free to move.

When a donor impurity is added, free electrons are created without generating holes. This process is called doping.

A semiconductor that contains donor impurity is called n-type semiconductor.

For example, when a phosphorous atom diffused in a silicon atom: • Four of its valence electrons are used to

satisfy the covalent bond requirements.

• The fifth valence electron is free to move.

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Impurity with three valence electrons is diffused in silicon are called acceptor atoms.

The boron atom is called an acceptor impurity, since it accepts a valence electron.

Acceptor atoms lead to creation of holes without electrons being generated. This process is also called doping.

A semiconductor that contains acceptor impurity is called p-type semiconductor.

For example, when a boron atom replaces for a silicon atom: • Its three valence electrons are used to

satisfy the covalent bond for three.

• This leaves one bond position open.

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Extrinsic Semiconductor The materials containing impurity atoms are called extrinsic

semiconductors, or doped semiconductors.

The doping process, which allows to control the concentrations of free electronics and holes, determines the conductivity and currents in the materials.

The relation between the electron and hole concentrations in thermal equilibrium:

no = the thermal equilibrium concentration of free electrons po = the thermal equilibrium concentration of holes ni = the intrinsic carrier concentration

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At room temperature (T = 300 K), each donor atom donates a free electron to the semiconductor.

• If the donor concentration Nd is much larger than the intrinsic concentration, approximately:

• Then, the hole concentration:

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Similarly, at room temperature, each acceptor atom accepts a valence electron, creating a hole.

• If the acceptor concentration Na is much larger than the intrinsic concentration, approximately:

• Then, the electron concentration:

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ExampleCalculate the thermal equilibrium electron and hole concentrations.

Consider silicon at T = 300 K doped with phosphorous at a concentration of Nd = 1016 cm-3 and ni = 1.5 x 1010 cm-3.

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Drift and Diffusion CurrentsDrift and Diffusion Currents

Current Generated by the movement of charged particles(negatively charged electrons and positively charged holes).

CarriersThe charged electrons and holes are referred to as carriers

The two basic processes which cause electrons and holes move in a semiconductor:

Drift - the movement caused by electric field. Diffusion - the flow caused by variations in the concentration.

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Drift Current Density (n-type semiconductor) An electric field E applied to n-type semiconductor with a

large number of free electrons.• Produces a force on the electrons in the opposite direction,

because of the electrons’ negative charge.• The electrons acquire a drift velocity (in cm/s):

µn = a constant called electron mobility (cm2/ V-s)(typically 1350 cm2/ V-s for low-doped silicon)

• The electron drift produces a drift current density (A/cm2):

n = the electron concentration (#/cm3)e = the magnitude of the electronic charge

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Drift Current Density (p-type semiconductor) An electric field E applied to p-type semiconductor with a

large number of holes.• Produces a force on the holes in the same direction, because of

the positive charge on the holes.• The holes acquire a drift velocity (in cm/s):

µp = a constant called hole mobility (cm2/ V-s)(typically 480 cm2/ V-s for low doped silicon)

• The hole drift produces a drift current density (A/cm2):

p = the hole concentration (#/cm3)e = the magnitude of the electronic charge

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Since a semiconductor contains both electrons and holes, the total drift current density is the sum of the electron and hole components:

where

σ = the conductivity of the semiconductor (Ω-cm)-1

• ρ = 1/σ, the resistivity of the semiconductor (Ω-cm)• The conductivity is related to the concentration of electrons

and holes

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Diffusion Current Density The basic diffusion process

Flow of particles from a region of high-concentration to a region of low-concentration. • The diffusion of electrons produces a flow of electrons in the

negative x direction.• The conventional current direction is in the positive x direction.

The diffusion current density due to the diffusion of electrons:

Jn = eDn dn/dx

e = the magnitude of the electronic chargedn/dx = gradient of the electron concentrationDn = the electron diffusion coefficient

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The diffusion of holes from a high-concentration region to a low-concentration region: • Produces a flow of holes in the negative x direction.• The conventional current direction is in the negative x direction.

The diffusion current density due to the diffusion of holes:

Jp = - eDp dp/dx

e = the magnitude of the electronic chargedp/dx = gradient of the hole concentrationDp = the hole diffusion coefficient

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Excess CarriersExcess Carriers

Valence electrons may acquire sufficient energy to break the covalent bond.

Become free electrons. Both electron and hole are produced. Generating an electron-hole pair. The additional electrons and holes are called excess

electrons and excess holes. A free electron may recombine with a hole, in a process

called electron-hole recombination.

no = the thermal equilibrium concentrations of electronspo = the thermal equilibrium concentrations of holesδn = the excess electron concentrationsδp = the excess hole concentrations

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Electron-Hole Pair:

When an electron jumps from the valence shell to the conduction band, it leaves a hole in the covalent bond. This action creates an electron-hole pair.

Recombination:

Within a short time an electron in the conduction band will give up its energy and fall into one of the valence shell holes in the covalent band.


The pn Junction The pn Junction

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n-type versus p-type n-type versus p-type

n-type materials make the Silicon (or Germanium) atoms more negative.

In n-type semiconductor the electrons are called the majority carriers and holes are the minority carriers.

p-type materials make the Silicon (or Germanium) atoms more positive.

In p-type semiconductor the holes are called the majority carriers and electrons are the minority carriers.

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The Equilibrium pn JunctionThe Equilibrium pn Junction

Join n-type and p-type doped Silicon (or Germanium) to form a p-n junction.

It shows respective p-type and n-type doping concentrations, assuming uniform doping, and minority carrier concentrations, assuming thermal equilibrium.

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Diffusion of hole from p-region into n-region & electron from n-region into p-region.

If no voltage applied, diffusion of holes and electrons must eventually cease.

Direction of induced electric field repels further diffusion of holes and electrons.

Thermal equilibrium occurs when the force produced by the electric filed and force produced by the density gradient exactly balance.

Modest space-charge region or depletion region formed at pn junction.

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Potential difference across the depletion region is called the built-in potential barrier, or built-in voltage:

VT = kT/ek = Boltzmann’s constantT = absolute temperaturee = the magnitude of the electronic chargeNa = the net acceptor concentration in the p-regionNd = the net donor concentration in the n-region

VT = thermal voltage, approximately 0.026 V at temp, T = 300 K

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ExampleCalculate the built-in potential barrier of a pn junction.

Consider a silicon pn junction at T = 300 K, doped Na = 1016 cm-3 in the p-region, Nd = 1017 cm-3 in the n-region and ni = 1.5 x 1010 cm-3.

Solution

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Reverse-Biased pn JunctionReverse-Biased pn Junction

Positive voltage is applied to the n-region of the pn junction. Applied voltage VR induces an applied electric field EA. Direction of the applied field is the same as that of the E-field in

the space-charge region. Magnitude of the electric field in the space-charge region

increases above the thermal equilibrium value. Increased electric field holds back the holes in the p-region and

the electrons in the n-region. No current across the pn junction. This applied voltage polarity is

called reverse bias. Reverse-bias voltage increases,

space-charge width W increases.

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Additional positive and negative charges induced in the space-charge region with increasing in reverse-bias voltage.

Capacitance is associated with the pn junction when a reverse-bias voltage is applied.

This junction capacitance, or depletion layer capacitance:

Cjo = the junction capacitance at zero applied voltage

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ExampleCalculate the junction capacitance of a pn junction.

Consider a silicon pn junction at T = 300 K, with doping concentrations of Na = 1016 cm-3 and Nd = 1015 cm-3.

Assume that ni = 1.5 x 1010 cm-3

and Cjo = 0.5 pF.

Calculate the junctioncapacitance Cj

at VR = 1 V and VR = 5 V.

*Capacitance decreases as the reverse-bias voltage increases.

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Forward-Biased pn JunctionForward-Biased pn Junction

Positive voltage vD is applied to the p-region of the pn junction. The potential barrier decreases. Direction of the applied electric field EA is the opposite as that of

the E-field in the space-charge region. The net result is that the electric field in the space-charge region

lower than the thermal equilibrium value. Majority carrier electrons from the n-region diffuse into p-region

and the majority carrier holes from the p-region diffuse into n-region.

Creating current in the pn junction. This applied voltage polarity is

called forward bias. vD must always be less than Vbi.

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Ideal Current-Voltage RelationshipIdeal Current-Voltage Relationship

The theoretical relationship between voltage and current in the pn junction:

IS = the reverse-bias saturation current (for silicon 10-15 to 10-13 A)

VT = the thermal voltage (0.026 V at room temperature)

n = the emission coefficient (1 ≤ n ≤ 2)

This pn junction, with nonlinear rectifying current characteristics, is called a pn junction doide.

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Ideal Current-Voltage RelationshipIdeal Current-Voltage Relationship

ExampleDetermine the current in a pn junction diode.

Consider a pn junction at T = 300 K in which IS = 10-14 A and n = 1. Find the diode current for vD = +0.70 V and vD = -0.70 V.

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pn Junction Diodepn Junction Diode

The basic pn junction diode circuit symbol, and conventional current direction and voltage polarity.

Ideal I-V characteristics of a pn junction diode.

The diode current is an exponential function of diode voltage in the forward-bias region.

The current is very nearly zero in the reverse-bias region.

The pn junction diode is a nonlinear electronic device.

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Actual Diode Characteristics:

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Temperature Effects on Semiconductor Materials The conductivity of semiconductor is directly proportional to temperature. Means that an increase in temp (T) will cause an increase in conductance (C)

and current (I).

Semiconductor materials has a negative temp coefficient of resistance which means as temp increases (T), their resistance decreases (R).

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Temperature Effects Both IS and VT are functions of temperature. The diode characteristics vary with temperature. For silicon diodes, the change

is approximately 2 mV/oC.

Forward-biased pn junction characteristics versus temperature.

The required diode voltage to produce a given current decreases

with an increase in temperature.

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Diode Circuits: DC Analysis and ModelsDiode Circuits: DC Analysis and Models

The ideal Diode

The I -V characteristics of the ideal diode.

Equivalent circuit in the conducting state (a short circuit)

Equivalent circuit under reverse bias (an open circuit)

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ExampleConsider a circuit with a dc voltage VPS applied across a resistor and a diode.Applying KVL, we can write,

or,

The diode voltage VD and current ID are related by the ideal diode equation: (IS is assumed to be known for a particular diode)

Equation contains only one unknown, VD:

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QuestionDetermine the diode voltage and current for the circuit.Consider IS = 10-13 A.

or,

and

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Load Line

The Load Line plots all possible current (ID) conditions for all voltages applied to the diode (VD) in a given circuit. VPS/R is the maximum ID and VPS is the maximum VD.

Where the Load Line and the Characteristic Curve intersect, the point is referred as the quiescent point or Q-point, which specifies a particular ID and VD for a given circuit.

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Piecewise Linear Model

For VD ≥ Vγ, assume a straight-line approximation whose slope is 1/rf.

Vγ = turn on voltagerf = forward diode resistance

For VD < Vγ, assume a straight-line approximation parallel with the VD axis at the zero current level.

Components of the piecewise-linear equivalent circuit

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Diode piecewise equivalent circuit in the “on” condition when VD ≥ Vγ

Diode piecewise equivalent circuit in the “off” condition when VD < Vγ

The piecewise linear diodecharacteristics by assuming rf = 0

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ExampleDetermine the diode voltage and current using

a piecewise linear model.

Assume piecewise linear diode parameters of Vf = 0.6 V and rf = 10 Ω.

Solution:The diode current is determined by:

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Diode Circuits: AC Equivalent CircuitDiode Circuits: AC Equivalent Circuit

Sinusoidal AnalysisThe total input voltage vI = dc VPS + ac vi

iD = IDQ + idvD = VDQ + vd

IDQ and VDQ

are the dcquiescent diode current and voltage respectively.

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Current-voltage Relation

The relation between the diode current and voltage can be written as:

VDQ = dc quiescent voltage

vd = ac component

The -1 term in the equation is neglected.

The equation can be written as:


If vd << VT, the equation can be expanded into linear series as:

The quiescent diode current as:

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or,

gd = diode small signal incremental conductance or diffusion conductance.rd = diode small signal incremental resistance or diffusion resistance.

or,

Current-voltage Relation

The diode current –voltage relationship canthen be written as:

id = ac component

The relationship between the ac componentsof the diode voltage and current is then:


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ExampleAnalyze the circuit (by determining VO & vo ).

Assume circuit and diode parameters ofVPS = 5 V, R = 5 kΩ, Vγ = 0.6 V & vi = 0.1 sin ωt (V)


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Analyze the circuit (by determining VO & vo ).

Assume circuit and diode parameters ofVPS = 5 V, R = 5 kΩ, Vγ = 0.6 V & vi = 0.1 sin ωt (V)


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Frequency Response

If the frequency of the ac input signal increases, the diffusion capacitance associated with forward-biased pn junction becomes important.

The diffusion capacitance is the change in the stored minority carrier charge that caused by a change in the voltage, or

The diffusion capacitance Cd

is normally much larger than the junction capacitance Cj ,

because of the magnitude of the changes involved.


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Small-Signal Equivalent Circuit

The small-signal equivalent circuit of the forward-biased pn junction is developed partially from the equation for the admittance, which is given by:

gd = the diffusion conductance

Cd = the diffusion capacitance


Simplified version small-signal equivalent circuit of the diode

Complete circuit of small-signal equivalent circuit of the diode

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Light-Emitting Diode

Light-Emitting Diode (LED) A semiconductor device that produces light when an electrical current or voltage is

applied to its terminal.

Because of the recombination of electrons and holes some energy will be given off.

1) Si and Ge energy will emitted in the form of heat.

2) Gallium Arsenide Phosphide (GaAsP) and (GaP) will emit the energy in form of photons of light.

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The LED V-I Characteristic Curve

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Zener Diode

Breakdown Voltage When a reverse-bias voltage is applied to a pn junction, the electric field in

the space-charge region increases.

The electric field may become large enough that covalent bonds are broken and electron-hole pairs are created.

Electrons are swept into the n-region and holes are swept into the p-region by the electric field, generating a large reverse bias current. This phenomenon is called breakdown.

The reverse-bias current created by breakdown mechanism is limited only by the external circuit.

If the current is not sufficiently limited, a large power can be dissipated in the junction that may damage the device and cause burnout.

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Breakdown Voltage

Avalanche Breakdown The most common breakdown mechanism is called avalanche breakdown. It occurs when carriers crossing the space-charge

region gain sufficient kinetic energy from the high electric field to be able to break covalent bonds during a collision process.

The generated electron-hole pairs can themselves be involved in a collusion process generating additional electron-hole pairs, thus the avalanche process.

The breakdown voltage is a function of the doping concentrations in the n- and p-region of the pn junction.

Large doping concentrations result in smaller break-down voltage.

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Breakdown Voltage

Zener Breakdown A second breakdown mechanism is called zener breakdown. It is a result of tunneling of carriers across the

junction.

This effect is prominent at very high doping concentrations and results in breakdown voltage less than 5 V.

The voltage at which breakdown occurs is usually in the range of 50 to 200 V for discrete devices.

A pn junction is usually rated in terms of its peak inverse voltage or PIV.

The PIV of a diode must never be exceeded in circuit operation if reverse breakdown is to be avoided.

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Zener Diode

Diodes are fabricated with a specifically design breakdown voltage and are designed to operate in the breakdown region. These diodes are called Zener diodes. Circuit symbol of the Zener diode:

The large current that may exist at breakdown can cause heating effects and catastrophic failure of the diode due to the large power dissipated in the device.

Diodes can be operated in the breakdown region by limiting the current to a value within the capacities of the device.

Such a diode can be used as a constant-voltage reference in a circuit.

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Chapter 1-Semiconductor Materials

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