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Solids and Semi-conductor 1

genius PHYSICS

Energy Bands.In isolated atom the valence electrons can exist only in one of the allowed orbitals each

of a sharply dened energy called energy levels !ut when two atoms are brought nearer toeach other" there are alterations in energy levels and they spread in the form of bands

#nergy bands are of following types

$%& Valence band

'he energy band formed by a series of energy levels containing valence electrons is(nown as valence band )t * K" the electrons lls the energy levels in valence band startingfrom lowest one

$i& 'his band is always fulll by electron$ii& 'his is the band of maximum energy

$iii& #lectrons are not capable of gaining energy from external electric eld

$iv& +o ,ow of current due to such electrons

$v& 'he highest energy level which can be occupied by an electron in valence band at *Kis called fermi level

$& Conduction band

'he higher energy level band is called the conduction band

$i& It is also called empty band of minimum energy

$ii& 'his band is partially lled by the electrons

$iii& In this band the electrons can gain energy from external electric eld

$iv& 'he electrons in the conduction band are called the free electrons 'hey are able tomove any where within the volume of the solid

$v& Current ,ows due to such electrons

$.& Forbidden energy gap (Eg)

#nergy gap between conduction band and valence band maxmin &$&$ BVBCEg =

$i& +o free electron present in forbidden energy gap

$ii& /idth of forbidden energy gap upon the nature of substance$iii& )s temperature increases $&" forbidden energy gap decreases $& very slightly

Types of Solids.

min

max

min

max

Eg

C!

0!

Ge

P Ge

Ge

Ge


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2 Solids and Semi-conductor

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1n the basis of band structure of crystals" solids are divided in three categories

S.No

.

roperties Conductors !nsulators Se"iconductors

$%& #lectrical conductivity %*to %*234m %*5 234m %*5 6to %**34m

$& 7esistivity %*5to %*52-m

$negligible&

%*2-m %*6to %**-m

$.& !and structure

$8& #nergy gap 9ero or very small 0ery large: fordiamond it is ; eV

eVfor SiEg= %% eV

$6& Current carries


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Solids and Semi-conductor #

genius PHYSICS

Types of Se"iconductors.

$%& !ntrinsic se"iconductor) pure semiconductor is called intrinsic semiconductor It has thermally generated

current carriers

$i& 'hey have four electrons in the outermost orbit of atom and atoms are held togetherby covalent bond

$ii&


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& Solids and Semi-conductor

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#onates e&ta 'ee electon. as the$ accept electon.

$iv& 'he number of atoms of impurity element is about % in 2%* atoms of thesemiconductor

$v& he nn

$vi& In these fermi level shifts towards valence or conduction energy bands$vii& 'heir conductivity is high and they are practically used

$.& Types of e$trinsic se"iconductor

N'type se"iconductor P'type se"iconductor

$i&

$ii& aGority charge carriers 5 electrons

inority charge carriers 5 holes

aGority charge carriers 5 holes

inority charge carriers 5 electrons

$iii& neMM nh: ieMM ih nhMM ne: ihMM ie

$iv& Conductivity neee Conductivity nhhe

$iv& N-type semiconductor is electrically neutral$not negatively charged&

P-type semiconductor is also electricallyneutral $not positively charged&

$v& Impurity is called Aonar impurity becauseone impurity atom generate one e5

Impurity is called )cceptor impurity

$vi& Aonor energy level lies Gust below theconduction band

)cceptor energy level lies Gust above thevalence band

P-Nunction iode.

/hen a P-type semiconductor is suitably Goined to an N-type semiconductor" thenresulting arrangement is called P(NGunction or P(NGunction diode

Ge

P GeGe

Ge


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Solids and Semi-conductor *

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$%& epletion region

1n account of di@erence in concentration of charge carrier in the two sections of P-NGunction" the electrons from N(region di@use through the Gunction into P-region and the holefrom Pregion di@use into N(region

Aue to di@usion" neutrality of both Nand P(type semiconductor is disturbed" a layer ofnegative charged ions appear near the Gunction in the P(crystal and a layer of positive ionsappears near the Gunction in N(crystal 'his layer is called depletion layer

$i& 'he thic(ness of depletion layer is % micon = %*5;m

$ii& /idth of depletion layerAoppin

%

$iii& Aepletion is directly proportional to temperature

$iv& 'he P(NGunction diode is eFuivalent to capacitor in which

the depletion layer acts as a dielectric$& otential barrier

'he potential di@erence created across the P(NGunction due to the di@usion of electronand holes is called potential barrier

*=

1n the average the potential barrier in P(NGunction is D *6 Vand the width of depletionregion D %*5;

So the barrier electric eld mV

#

VE 4%*6

%*

6* 6;

===

Some important graphs

$.& i+usion and drift current

!ecause of concentration di@erence holes4electron try to di@use from their side to otherside 1nly these holes4electrons crosses the Gunction" having high (inetic energy 'hisdi@usion results is an electric current from the P-side to the N-side (nown as di@usion current$i#'&

)s electron hole pair $because of thermal collisions& are continuously created in thedepletion region 'hese is a regular ,ow of electrons towards the N-side and of holes towardsthe P-side 'his ma(es a current from the N-side to the P-side 'his current is called the driftcurrent $i#&

+ote L In steady state ##' ii = so *=neti /hen no external source is connected" diode is called unbiased

Charge density

distance5ve

)ve

NP

Potential

Aistance

NP#lectric eld

Aistance

NP

NPAepletion layer

5

VB


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, Solids and Semi-conductor

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$8& Biasing

eans the way of connectingem'source to P(NGunction diode

For-ard biasing e%erse biasing

$i& Positive terminal of the battery is connectedto the P-crystal and negative terminal of thebattery is connected to N-crystal

$i& Positive terminal of the battery isconnected to the N-crystal and negativeterminal of the battery is connected to P-crystal

$ii& /idth of depletion layer decreases $ii& /idth of depletion layer increases

$iii& *


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covalent bonds" generating more carriers ) chain reaction is established" giving rise to highcurrent 'his mechanism is called a%alance brea/do-n.

$.& Special purpose diodes

0ener diode 4igt e"itting

diode (4E)

oto diode Solar cells

It is a highly dopedp(nGunction which is notdamaged by highreverse current 'he

brea(down voltage ismade very sharp Inthe forward bias" theEener diode acts asordinary diode It canbe used as voltageregulator

Specially designeddiodes" which give outlight radiations whenforward biases #AQS

are made of GaAsp"Gapetc

In these diodeselectron and hole pairsare created byGunction photoelectric

e@ect 'hat is thecovalent bonds arebro(en by the #radiations absorbedby the electron in the0! 'hese are usedfor detecting lightsignals

It is based on thephotovoltaic e@ect1ne of thesemiconductor regionis made so thin thatthe light incident on itreaches the p(n

Gunction and getsabsorbed It convertssolar energy intoelectrical energy

P-Nunction iode as a ecti5er.

6alf -a%e recti5er Full -a%e recti5er

Auring positive half cycleAiode forward biased1utput signal obtained

Auring negative half cycleAiode reverse biased1utput signal not obtained

Auring positive half cycleAiode L +% forward biased

+ reverse biased1utput signal obtained due to +%only

Auring negative half cycleAiode L +% reverse biased

+ forward biased

7 7

7 7

8 8

Inputac signal

1utputdc signal D2 D2D1 D1

7 7

8 8

Inputac signal

1utputdc signal


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1utput signal obtained due to +only

+ote L


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Solids and Semi-conductor Solids and Semi-conductor

genius PHYSICS

valve of #clies between *6 to * valve of aclies between %6 and *

$ii& 0oltage gain

&$voltageinputinChange

&voltage$outputinChange

i

ov

V

VA

=

Av= ac7esistance gain

$ii& 0oltage gain

gain7esistance=

= ac

i

ov

V

VA

$iii&&power$inputinChange

&power$outputinChangegainPower

c

o

P

P

=

gai7esistancegainPower -ac=

$iii&

gai7esistanceP

PgainPower -

i

o=

= ac

+ote L Trans conductance (gm) ;'he ratio of the change in collector currentto the change in emitter base voltage is

called trans conductance i.e.EB

cm

V

ig

=

)lso,

Vm*Ag = : *,= oad resistance

$6& elation bet-een and L

=%

or

+=%

$;& Co"parison bet-een CB? CEand CC a"pli5er

S.No.

Caracteristic "pli5er

CB CE CC$i& Input resistance $*i& 6*to ** low % to -medium %6* 5 2** -high

$ii& 1utput resistance$*o&

% 5 -high 6*-medium -low

$iii& Current gain *2 5 * low * 5 ** high * 5 ** high$iv& 0oltage gain edium High ow$v& Power gain edium High ow$vi& Phase di@erence

between input andoutput voltages

9ero %2*o 9ero

$vii& sed as amplier for current Power 0oltage

Example; 2 ) Ge specimen is doped with Al 'he concentration of acceptor atoms is D%*%

atoms4m. Tiven that the intrinsic concentration of electron hole pairs is .% 4%*D m " theconcentration of electrons in the specimen is

@!!AS 2>>&

$a& .%> 4%* m $b& .%6 4%* m $c& .8 4%* m $d& .- 4%* m

Solution L $a& ehi nnn =- en=

-%-% %*&%*$ 4%* .%> mne =

Example; # ) silicon specimen is made into a P-type semi-conductor by doping" on an average" oneIndium atom per >%*6 silicon atoms If the number density of atoms in the silicon

specimen is -2%*6 atoms4m." then the number of acceptor atoms in silicon will be

@A AT 1#

$a& .*%*6- atoms4cm. $b& %.%**% atoms4cm. $c& %6%**% atoms4cm. $d& .;%*6- atoms4cm

.

Examples

Examples


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genius PHYSICS

Solution L $c& +umber density of atoms in silicon specimen = 6 %*2atomm.= 6 %*atom4cm.

Since one atom of indium is doped in 6 %*> Siatom So number of indium atomsdoped per cm-.of silicon

4%*%

%*6

%*6 .%6>

--

cmatomn =

=

Example; & ) P-type semiconductor has acceptor levels 6> meV above the valence band 'hemaximum wavelength of light reFuired to create a hole is $Planc(Qs constant h =

.8%*;; /(s& @A ET 1 $c& %>%**0 $d&

0..%*;%%%

Solution L $c&

hcE =

E

hc=

%.

2.8

%*;%%*6>

%*.%*;;

= = %>%** U

Example; * ) potential barrier of *6*V exists across a P(N Gunction If the depletion region ism>%**6 wide" the intensity of the electric eld in this region is

@SET 2>>2

$a& mV 4%**% ; $b& mV 4%**% 6 $c& mV 4%**- 6 $d&

mV 4%**- ;

Solution L $a&>%*6

6**

==#

VE = % %*;Vm

Example; , ) Vbattery is connected across the pointsAand Bas shown in the gure given below)ssuming that the resistance of each diode is Eero in forward bias and innity in reversebias" the current supplied by the battery when its positive terminal is connected to Ais

@SET 2>>2

$a& *A

$b& *8A$c& 9ero$d& *%A

Solution L $a& Since diode in upper branch is forward biased and in lower branch is reversed biased

So current through circuit#*

Vi

+= : here # = diode resistance in forward biasing = *

So A*

Vi -*

%*

-===

Example; 3 Current in the circuit will be@CBSE AT 2>>1

$a& A8*

6

$b& A6*

6

$c& A%*

6

$d& A-*

6

Solution L $b& 'he diode in lower branch is forward biased and diode in upper branch is reverse biased

Ai6*

6

.*-*

6=

+=

Example; 9 >1

$a& *

A B

%*

%*

5 8V

. 5 %V

*

6V*

.*

i


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genius PHYSICS

$b& % amp$c& *% amp$d& * amp

Solution L $a& Aiode is reverse biased 'herefore no current will ,ow through the circuitExample; < 'he diode used in the circuit shown in the gure has a constant voltage drop of *6 Vat

all currents and a maximum power rating of %** milliwatts /hat should be the value ofthe resistor *" connected in series with the diode for obtaining maximum current

@CBSE AT 1>&

$a& 5 6 $b& 5 %6> $c& 5 82 $d& 5 82>2

Solution L $d& In common emitter conguration current gain.;

%*%*-6%

6*

% +

=

+

=

,oe

'ei

*h

hA = 5

82>2

Example; 11 In the following common emitter conguration an NPNtransistor with current gain =%** is used 'he output voltage of the amplier will be@!!AS 2>>#

$a& %* mV$b& *% V$c& %* V$d& %* V

Solution L $c& 0oltage gainvoltageInput

voltag1utput= Vout= Vin0oltage gain

Vout= VinCurrent gain 7esistance gain = VinBE

,

*

*=

%%

%*

%**%*

.

V=

Example; 12 /hile a collector to emitter voltage is constant in a transistor" the collector currentchanges by 2 mAwhen the emitter current changes by 2. mA 'he value of forwardcurrent ratio h'eis @DCET 2>>2$a& 2 $b& 2. $c& 2 $d& 2.

Solution L $a& 2--2.2

-2=

=

=ceV

"

c'e

i

ih

Example; 1# 'he transfer ratio of a transistor is 6* 'he input resistance of the transistor when usedin the common-emitter conguration is % K 'he pea( value for an ac input voltage of**% Vpea( is @CBSE AT 1


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Solids and Semi-conductor 1#

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Solution L $d& AA*

Vii

i

i"c 6**%*6**

%***

*%*6*

; =====

Example; 1& In a common base amplier circuit" calculate the change in base current if that in theemitter current is mAand = *2

@B6 1

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