Fundam

© Dr.

1

2

mentals of Semico

. G.Vijaya Prakas

Aim:

1. Sketch th

2. . Draw thSymmetr

onductors: EPL213

sh, IIT, Delhi

understandi

he unit cell in

he Wigner-Sry points ( H

3 (2012)

Fun

ing unit cell

n these two e

Seitz cell of How many yo

ndamental

Prob

l, crystal stru

examples. C

f a cubic lattou can see in

s of SemicEPL213 blem sheet 1

uctures, Bril

Can you ident

tice using thn this 2D (x

conductors

1

llouin zone,

tify how ma

he procedure-y) plane?)

symmetry r

any lizards (

e given in y

representatio

now basis) f

your lecture

1

on

for unit cell?

notes. Labe

1

?

el

Fundam

© Dr.

3

mentals of Semico

. G.Vijaya Prakas

3. List the pnotes, sin[110] andatoms?

onductors: EPL213

sh, IIT, Delhi

positions of tnce this is a d [111] direc

3 (2012)

the atoms in very impor

ctions, labell

the basis of rtant lattice tling the heigh

a face centretype). Draw ht of each at

ed cubic lattia plan view

tom. Which p

ice. Draw a uw of the lattiplane has the

unit cell (seeice seen alone densest arr

2

e your lectureng the [100]rangement o

2

e ], f

Fundam

© Dr.

mentals of Semico

. G.Vijaya Prakas

onductors: EPL213

sh, IIT, Delhi

3 (2012)

33

Fundam

© Dr.

4

5

mentals of Semico

. G.Vijaya Prakas

4. You havwidth is ain the cel

5. Find num

onductors: EPL213

sh, IIT, Delhi

e been told a, can you finll multiplied

mber of Silic

3 (2012)

that the hardnd the packin

d by volume

on atoms/cm

d spheres nang fraction? of sphere( at

m2 in (100) s

atural assem( packing fratom) divided

surface of Sil

mbly is fcc paction is defid by volume

licon wafer.

acked latticefined as numbe of unit cell)

(a=5.43x10

e. Now, if thber of sphere)

0-8cm)

4

he cubic celes ( or atoms

4

ll )

Fundam

© Dr.

6

7

mentals of Semico

. G.Vijaya Prakas

6. Similarly

7. Now youstructuredensity o

onductors: EPL213

sh, IIT, Delhi

y do it for (1

u are in a pos? Refer you

of Silicon. ( I

3 (2012)

10) surface

sition to exteur lecture noIf necessary

end the samotes). Find N

use, Avogad

***

e philosophyNumber Si adro Number=

*** *****

y to 3D modatoms ( per u= 6.02x1023a

del ( Do youunit volumeand Mol We

u remember t) in an unit ight of Si= 2

5

the Si crystacell and the

28.08g/mol)

5

al e

Fundam

© Dr.

1

2

mentals of Semico

. G.Vijaya Prakas

Aim: undeund

1. Using N(a=0.30 n10.00 nmscatters t

2. We havethe densimlh*=0.1

onductors: EPL213

sh, IIT, Delhi

erstanding thderstanding

early-free elnm) are fou

m-1 and –10.9them and als

effective mity of states6m0 and mhh

3 (2012)

Fun

he band struof band gap

lectrons (conund to have a94 nm-1 respo find the po

masses of vars masses forh*=0.49m0

ndamental

Probuctures, effeps, density of

nsider one dallowed ene

pectively. Byossible energ

rious branchr respective

s of SemicEPL213 blem sheet 2ective mass aof states, intr

dimension) nergies of 3.6y calculatinggy separation

hes in conduconduction

conductors

2 and the condrinsic proper

near the Bri6eV and 4.6 E1,2, find thn.

ction and vaand valanc

duction valarties of semi

illouin zone 66eV when he strength in

alance bandsce bands. ml

ance energy iconductors

edge of a cgiven a momn eV of the p

s of Si as foll*=0.98m0, m

6

levels,

cubic crystamentum kx =potential tha

lowing. Findmt*=0.19m0

6

al = at

d 0,

Fundam

© Dr.

3

mentals of Semico

. G.Vijaya Prakas

3. CalculateThe GaA

onductors: EPL213

sh, IIT, Delhi

e the conducAs effective m

3 (2012)

ction band enmass ( you a

nergy level falready know

for the givenw this) is 0.0

n k vector 0.4067m0. How

42nm-1 ( mew about free

easured fromspace electro

7

m band edge)on energy?

7

).

Fundam

© Dr.

4

5ooo

mentals of Semico

. G.Vijaya Prakas

4. A conduc

measured

5. Commeno Direct ano Effectiveo Heavy-ho

onductors: EPL213

sh, IIT, Delhi

ction band ed from the co

nt briefly on nd indirect bae masses at cole, light-ho

3 (2012)

electron in Sonduction ba

the followinand gap

conduction aole and split-

Si(100) occuand edge.

ng terms that

and valance boff bands

upy in k spac

t are very mu

bands

ce (2π/a)*(0

uch useful in

0.9,0.2,0). Es

n understand

stimate the e

ding band str

InxGa InGax

InxGa InxGa InxGa InxGa

8

energy level

ructures.

a1-xAs

xAs1-x

a1-xAsyP1-y

ayAs1-x P1-y

ayAlAs1-x-y

ayAl1-x-y As

8

l,

Fundam

© Dr.

6

ypwm

mentals of Semico

. G.Vijaya Prakas

6. You havelecture. T

Conductio

Calculate reyou to say thpoints energiweight averame why?

onductors: EPL213

sh, IIT, Delhi

e seen screenThis is based

on band enerGaAs

Γ point= 1.4Χ point= 1.

espective Γ hat GaAs is aies. How aboage of energi

3 (2012)

n shots of thd on virtual

rgies measur

43eV .91eV

and Χ pointa direct bandout the abovies) . Give a

e applet for crystal appro

red from valaAlA

Γ poΧ po

s for intermed gap materive compositio

hint if the co

alloy, AlGaAoximation u

ance band edAs

oint= 2.75eVoint= 2.15eV

ediate compal and AlAs ons? ( hint: (ompositions

As conditionsing the foll

dge

V V

ositions Al0

is an indirec(Here in thisgiven in the

n and valancowing data a

.3Ga0.7As, Act one by juss approximate left side box

ce band estimat 300K

Al0.6Ga0.4As. st looking attion, one simx are possib

9

mation n you

It is easy fot the Γ and Χmply uses thele or not, tel

9

ur

r Χ e ll

Fundam

© Dr.

7

mentals of Semico

. G.Vijaya Prakas

7. Estimate concentra

onductors: EPL213

sh, IIT, Delhi

the (a) effeation for sili

3 (2012)

ective densiticon at 300K

ty of states K

for valance and conducction bands and (b) intr

10

rinsic carrie

0

r

Fundam

© Dr.

8

(

mentals of Semico

. G.Vijaya Prakas

8. An intrin

emitted l( any help?: R

onductors: EPL213

sh, IIT, Delhi

nsic GaAs liight wavelenRefer your l

3 (2012)

ight emittingngth with temecture notes

g device is omperature. s for tempera

operating at

ature depend

room temp

dence of band

perature. Esti

d gap )

imate any c

11

hange in the

1

e

Fundam

© Dr.

mentals of Semico

. G.Vijaya Prakas

onductors: EPL213

sh, IIT, Delhi

3 (2012)

122

Fundam

© Dr.

9

mentals of Semico

. G.Vijaya Prakas

9. Find the

( Any help?

onductors: EPL213

sh, IIT, Delhi

intrinsic Fer

? kB= 8.617

3 (2012)

rmi level gra

7e-5 eVK-1)

adient with r

)

espect to temmperature ( ddEfi/dT) and

. discuss yo

13

our findings

3