fundamentals of semiconductors - nptel · 2017-08-04 · fundam © dr. entals of semico g.vijaya...
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Fundam
© Dr.
1
2
mentals of Semico
. G.Vijaya Prakas
Aim:
1. Sketch th
2. . Draw thSymmetr
onductors: EPL213
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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
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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
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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
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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