IES/ESE Paper (Electronics) Mains Paper - I - 2024 | GATE, ISRO & IES/ESE Previous Year Solved Papers - Mechanical Engineering PDF Download

 Page 1


ELECTRONICS AND TELECOMMUNICATION 
Time 
Allowed 
: 
Three 
Hours 
Question Paper Specific Instructions 
ENGINEERING 
There are 
EIGHT 
questions divided in TWO sections. 
Please read each of the 
following instructions 
carefully before 
attempting 
questions: 
Candidate has to 
attempt FIVE 
questions in all. 
Paper -I 
Questions No. I and 5 are compulsory and out of the remaining, any THREE are to be 
attempted choosing at least ONE 
question from each 
section. 
The number of marks carried by a questionIpart is indicated against it. 
Wherever any assumptions are made for answering a question, they must be clearly 
indicated. 
Diagrams/figures, wherever required, shall be drawn in the space provided for answering 
the question itself. 
Unless otherwise mentioned, symbols and notations have their usual standard meanings. 
Attempts of questions shall be counted in sequential order. Unless struck off, attempt of a 
question shall be counted even if attempted partly. 
Answers must be written in ENGLISH only. 
Electron charge 
Any page or portion of the page left blank in the Question-cum-Answer (QCA) Booklet must 
be clearly struck off. 
Values of constants which may be required: 
Free space permeability 
Free space permittivity 
Maximum Marks : 300 
Boltzmann constant 
Velocity of light in free space 
Planck's constant 
|sGSE-OETE 
SGSE-O-ETE 
- I'6 x 1o19 Coulomb 
4n X 
10-
Henry/m 
3 x 108 m/s 
(1/36)x 10-9 Farad/m 
1:38 x 1o28 J/K 
6-626 x 1034J-s 
UPSC ESE Mains Question Paper EC 23 June 2024
Page 2


ELECTRONICS AND TELECOMMUNICATION 
Time 
Allowed 
: 
Three 
Hours 
Question Paper Specific Instructions 
ENGINEERING 
There are 
EIGHT 
questions divided in TWO sections. 
Please read each of the 
following instructions 
carefully before 
attempting 
questions: 
Candidate has to 
attempt FIVE 
questions in all. 
Paper -I 
Questions No. I and 5 are compulsory and out of the remaining, any THREE are to be 
attempted choosing at least ONE 
question from each 
section. 
The number of marks carried by a questionIpart is indicated against it. 
Wherever any assumptions are made for answering a question, they must be clearly 
indicated. 
Diagrams/figures, wherever required, shall be drawn in the space provided for answering 
the question itself. 
Unless otherwise mentioned, symbols and notations have their usual standard meanings. 
Attempts of questions shall be counted in sequential order. Unless struck off, attempt of a 
question shall be counted even if attempted partly. 
Answers must be written in ENGLISH only. 
Electron charge 
Any page or portion of the page left blank in the Question-cum-Answer (QCA) Booklet must 
be clearly struck off. 
Values of constants which may be required: 
Free space permeability 
Free space permittivity 
Maximum Marks : 300 
Boltzmann constant 
Velocity of light in free space 
Planck's constant 
|sGSE-OETE 
SGSE-O-ETE 
- I'6 x 1o19 Coulomb 
4n X 
10-
Henry/m 
3 x 108 m/s 
(1/36)x 10-9 Farad/m 
1:38 x 1o28 J/K 
6-626 x 1034J-s 
UPSC ESE Mains Question Paper EC 23 June 2024
QI. (a) 
(b) 
(c) 
(d) 
Consider an ideal pMOS capacitor of area 100 um x 100 um operated 
at T = 300 K. èM (work function for the metal) = 52 eV, 
X, (oxide 
thickness) = 3 nm and Nn = 101/em. 
Calculate the flat 
Assume 
band voltage VFB and 
the threshold voltage VTp. 
Eor = 3:43 x 10-18 Flem, V (thermal voltage) 
= 0-026 V, n; = 100/cm® 
Zs; 
(electron affinity of Si) = 4-05 eV, Eg = 112 eV and Esi = 10-12 
Flcm. 19 
In the circuit shown in the figure below, M, serves as an electronic 
switch. If v, is very small, determine W/L such that circuit attenuates 
the signal by 5%. 
Assume Vc = 18V and R, = 100 2. 
Hn 
Cor 
200 
4A 
Source. 
Vin 
SECTION A 
250 V + 
SGSE-O-ETE 
and VTN = 0:4 V. 
VG 
M 
Find the voltage v, in the circuit shown in the figure using source 
transformation. Also, find the power developed by the 250 V voltage 
25 S2 
oVout 
W 
)8A 
22 
Vo 100Q 
52 
An electrical load absorbs an average power of 85 kW at lagging power 
factor of 0-85. If the load operates at 240 V rms, calculate the complex 
power and 
impedance of the load. 
12 
12 
¿ 15 2 
12 
Page 3


ELECTRONICS AND TELECOMMUNICATION 
Time 
Allowed 
: 
Three 
Hours 
Question Paper Specific Instructions 
ENGINEERING 
There are 
EIGHT 
questions divided in TWO sections. 
Please read each of the 
following instructions 
carefully before 
attempting 
questions: 
Candidate has to 
attempt FIVE 
questions in all. 
Paper -I 
Questions No. I and 5 are compulsory and out of the remaining, any THREE are to be 
attempted choosing at least ONE 
question from each 
section. 
The number of marks carried by a questionIpart is indicated against it. 
Wherever any assumptions are made for answering a question, they must be clearly 
indicated. 
Diagrams/figures, wherever required, shall be drawn in the space provided for answering 
the question itself. 
Unless otherwise mentioned, symbols and notations have their usual standard meanings. 
Attempts of questions shall be counted in sequential order. Unless struck off, attempt of a 
question shall be counted even if attempted partly. 
Answers must be written in ENGLISH only. 
Electron charge 
Any page or portion of the page left blank in the Question-cum-Answer (QCA) Booklet must 
be clearly struck off. 
Values of constants which may be required: 
Free space permeability 
Free space permittivity 
Maximum Marks : 300 
Boltzmann constant 
Velocity of light in free space 
Planck's constant 
|sGSE-OETE 
SGSE-O-ETE 
- I'6 x 1o19 Coulomb 
4n X 
10-
Henry/m 
3 x 108 m/s 
(1/36)x 10-9 Farad/m 
1:38 x 1o28 J/K 
6-626 x 1034J-s 
UPSC ESE Mains Question Paper EC 23 June 2024
QI. (a) 
(b) 
(c) 
(d) 
Consider an ideal pMOS capacitor of area 100 um x 100 um operated 
at T = 300 K. èM (work function for the metal) = 52 eV, 
X, (oxide 
thickness) = 3 nm and Nn = 101/em. 
Calculate the flat 
Assume 
band voltage VFB and 
the threshold voltage VTp. 
Eor = 3:43 x 10-18 Flem, V (thermal voltage) 
= 0-026 V, n; = 100/cm® 
Zs; 
(electron affinity of Si) = 4-05 eV, Eg = 112 eV and Esi = 10-12 
Flcm. 19 
In the circuit shown in the figure below, M, serves as an electronic 
switch. If v, is very small, determine W/L such that circuit attenuates 
the signal by 5%. 
Assume Vc = 18V and R, = 100 2. 
Hn 
Cor 
200 
4A 
Source. 
Vin 
SECTION A 
250 V + 
SGSE-O-ETE 
and VTN = 0:4 V. 
VG 
M 
Find the voltage v, in the circuit shown in the figure using source 
transformation. Also, find the power developed by the 250 V voltage 
25 S2 
oVout 
W 
)8A 
22 
Vo 100Q 
52 
An electrical load absorbs an average power of 85 kW at lagging power 
factor of 0-85. If the load operates at 240 V rms, calculate the complex 
power and 
impedance of the load. 
12 
12 
¿ 15 2 
12 
Draw 
neat 
sketches 
of 
the 
edge 
and 
screw 
dislocations. 
IIlustrate 
the 
Burger's 
vector 
on 
the 
sketches 
of 
(1) 
6 
(e) 
Calculate 
the 
line 
energy 
of 
dislocation 
in 
BCC 
iron 
if 
the 
shear 
modulus 
and 
lattice 
parameter 
of 
BCC 
iron 
are 
80-2 
GN/m 
and 
2-87 Å, respectively. 
(ii) 
A p-n junction 
Q2. (a) 
N  
=3x 
1018 
/em, 
Np 
= 
2x 
1016/cm3 
D, 
= 
25 
cm²/s, 
D, 
= 
10 
cm/s 
Tn0 
= 
4 
x 
10-
s, 
Tno 
= 
10-
s 
20 
The 
photocurrent 
density 
J, 
= 
20 
mA/cm². 
Calculate 
the 
open 
circuit 
voltage 
of 
the 
solar 
cell 
at 
T 
= 
300 
K. 
Assume 
n; 
= 
1:5 
x 
1010/cm3. 
5 
though the armature 
What 
are 
the 
two 
functions 
of 
commutator 
in 
DC 
machines 
? 
Explain 
how 
the 
commutator 
keeps 
the 
armature 
mmf 
stationary 
in 
space, 
along 
the 
interpolar 
axis, 
even 
(i) 
(b) 
(ii) 
15 
rotates. 
10 
Explain why 
(i) 
(c) 
10 
Differentiate 
between 
different 
types 
of 
magnetic 
(ii) 
Design a 
Widlar 
(i) 
(a) 
10 
Q3. 
R$ 
V BE2 
VBE1 
10 
Design 
an 
amplifier 
that 
has 
a 
voltage 
gain 
of 
2 
if 
VÊN 
<0 
and 
1, 
if 
VIN 
> 
0. 
Assume 
ideal 
diodes 
and 
ideal 
op 
amps 
are 
availabie. 
(ii) 
3 
SGSE-O-ETE 
dislocations. 
solar 
cell 
is 
fabricated 
using 
silicon 
and 
has 
the 
following 
important parameters 
end-centred 
tetragonal 
geometry 
does 
not 
exist 
in 
Bravais crystal structures. 
materials on the 
basis 
of 
magnetic 
dipoles 
and 
hysteresis 
loops. 
current 
source 
shown in the 
figure 
below 
to 
give 
I, 
= 
5 
A 
and 
IR 
= 
1 
m¢. 
The 
parameters 
are 
Voc 
= 
30 
V, 
VBE1 
= 
07 
V, 
V 
= 
26 
mV 
and 
Bp 
= 
100. 
Page 4


ELECTRONICS AND TELECOMMUNICATION 
Time 
Allowed 
: 
Three 
Hours 
Question Paper Specific Instructions 
ENGINEERING 
There are 
EIGHT 
questions divided in TWO sections. 
Please read each of the 
following instructions 
carefully before 
attempting 
questions: 
Candidate has to 
attempt FIVE 
questions in all. 
Paper -I 
Questions No. I and 5 are compulsory and out of the remaining, any THREE are to be 
attempted choosing at least ONE 
question from each 
section. 
The number of marks carried by a questionIpart is indicated against it. 
Wherever any assumptions are made for answering a question, they must be clearly 
indicated. 
Diagrams/figures, wherever required, shall be drawn in the space provided for answering 
the question itself. 
Unless otherwise mentioned, symbols and notations have their usual standard meanings. 
Attempts of questions shall be counted in sequential order. Unless struck off, attempt of a 
question shall be counted even if attempted partly. 
Answers must be written in ENGLISH only. 
Electron charge 
Any page or portion of the page left blank in the Question-cum-Answer (QCA) Booklet must 
be clearly struck off. 
Values of constants which may be required: 
Free space permeability 
Free space permittivity 
Maximum Marks : 300 
Boltzmann constant 
Velocity of light in free space 
Planck's constant 
|sGSE-OETE 
SGSE-O-ETE 
- I'6 x 1o19 Coulomb 
4n X 
10-
Henry/m 
3 x 108 m/s 
(1/36)x 10-9 Farad/m 
1:38 x 1o28 J/K 
6-626 x 1034J-s 
UPSC ESE Mains Question Paper EC 23 June 2024
QI. (a) 
(b) 
(c) 
(d) 
Consider an ideal pMOS capacitor of area 100 um x 100 um operated 
at T = 300 K. èM (work function for the metal) = 52 eV, 
X, (oxide 
thickness) = 3 nm and Nn = 101/em. 
Calculate the flat 
Assume 
band voltage VFB and 
the threshold voltage VTp. 
Eor = 3:43 x 10-18 Flem, V (thermal voltage) 
= 0-026 V, n; = 100/cm® 
Zs; 
(electron affinity of Si) = 4-05 eV, Eg = 112 eV and Esi = 10-12 
Flcm. 19 
In the circuit shown in the figure below, M, serves as an electronic 
switch. If v, is very small, determine W/L such that circuit attenuates 
the signal by 5%. 
Assume Vc = 18V and R, = 100 2. 
Hn 
Cor 
200 
4A 
Source. 
Vin 
SECTION A 
250 V + 
SGSE-O-ETE 
and VTN = 0:4 V. 
VG 
M 
Find the voltage v, in the circuit shown in the figure using source 
transformation. Also, find the power developed by the 250 V voltage 
25 S2 
oVout 
W 
)8A 
22 
Vo 100Q 
52 
An electrical load absorbs an average power of 85 kW at lagging power 
factor of 0-85. If the load operates at 240 V rms, calculate the complex 
power and 
impedance of the load. 
12 
12 
¿ 15 2 
12 
Draw 
neat 
sketches 
of 
the 
edge 
and 
screw 
dislocations. 
IIlustrate 
the 
Burger's 
vector 
on 
the 
sketches 
of 
(1) 
6 
(e) 
Calculate 
the 
line 
energy 
of 
dislocation 
in 
BCC 
iron 
if 
the 
shear 
modulus 
and 
lattice 
parameter 
of 
BCC 
iron 
are 
80-2 
GN/m 
and 
2-87 Å, respectively. 
(ii) 
A p-n junction 
Q2. (a) 
N  
=3x 
1018 
/em, 
Np 
= 
2x 
1016/cm3 
D, 
= 
25 
cm²/s, 
D, 
= 
10 
cm/s 
Tn0 
= 
4 
x 
10-
s, 
Tno 
= 
10-
s 
20 
The 
photocurrent 
density 
J, 
= 
20 
mA/cm². 
Calculate 
the 
open 
circuit 
voltage 
of 
the 
solar 
cell 
at 
T 
= 
300 
K. 
Assume 
n; 
= 
1:5 
x 
1010/cm3. 
5 
though the armature 
What 
are 
the 
two 
functions 
of 
commutator 
in 
DC 
machines 
? 
Explain 
how 
the 
commutator 
keeps 
the 
armature 
mmf 
stationary 
in 
space, 
along 
the 
interpolar 
axis, 
even 
(i) 
(b) 
(ii) 
15 
rotates. 
10 
Explain why 
(i) 
(c) 
10 
Differentiate 
between 
different 
types 
of 
magnetic 
(ii) 
Design a 
Widlar 
(i) 
(a) 
10 
Q3. 
R$ 
V BE2 
VBE1 
10 
Design 
an 
amplifier 
that 
has 
a 
voltage 
gain 
of 
2 
if 
VÊN 
<0 
and 
1, 
if 
VIN 
> 
0. 
Assume 
ideal 
diodes 
and 
ideal 
op 
amps 
are 
availabie. 
(ii) 
3 
SGSE-O-ETE 
dislocations. 
solar 
cell 
is 
fabricated 
using 
silicon 
and 
has 
the 
following 
important parameters 
end-centred 
tetragonal 
geometry 
does 
not 
exist 
in 
Bravais crystal structures. 
materials on the 
basis 
of 
magnetic 
dipoles 
and 
hysteresis 
loops. 
current 
source 
shown in the 
figure 
below 
to 
give 
I, 
= 
5 
A 
and 
IR 
= 
1 
m¢. 
The 
parameters 
are 
Voc 
= 
30 
V, 
VBE1 
= 
07 
V, 
V 
= 
26 
mV 
and 
Bp 
= 
100. 
(b) 
(c) 
Q4. (a) 
() 
(ii) 
(i) 
(ii) 
Discuss the points of similarities between a transformer and 
induction machine. Explain, why an induction machine is called a 
generalized transformer. 
sGSEoETE| 
A 10 kVA/2500/250 V, single-phase transformer has the following 
parameters : 
Primary winding (h.v. side): Resistance rË = 24 2 
Leakage 
Reactance, x1 = 6-00 2 
Secondary winding (l.v. side): Resistance r = 0-03 S2 
Leakage 
Reactance, X, = 0:07 2 
With primary supply voltage held constant at 2500 V, calculate 
the secondary terminal voltage, when the low voltage winding is 
connected to a load impedance of 5 +j 35 2 and the transformer 
delivers its rated current at 08 p.f. lagging on the low voltage 
side. 
Discuss photoelectric efiect and find out the number of 
photoelectrons emitted per unit time from a transmitter operated 
at a frequency of 800 kHz and 10 kW power. 
Define dielectric strength. Discuss different types of dielectric 
breakdowns in solids. 
1 k2 
HE 
For the circuit shown in the figure below, determine the frequency of 
oscillation f, and overall voltage gain Ay. Also identify the type of 
Oscillator. (Assume op amps are ideal) 20 
A 
W 
1 kQ 
4 
1 k2 
W 
10 
1 uF 
10 
10 
10 
Page 5


ELECTRONICS AND TELECOMMUNICATION 
Time 
Allowed 
: 
Three 
Hours 
Question Paper Specific Instructions 
ENGINEERING 
There are 
EIGHT 
questions divided in TWO sections. 
Please read each of the 
following instructions 
carefully before 
attempting 
questions: 
Candidate has to 
attempt FIVE 
questions in all. 
Paper -I 
Questions No. I and 5 are compulsory and out of the remaining, any THREE are to be 
attempted choosing at least ONE 
question from each 
section. 
The number of marks carried by a questionIpart is indicated against it. 
Wherever any assumptions are made for answering a question, they must be clearly 
indicated. 
Diagrams/figures, wherever required, shall be drawn in the space provided for answering 
the question itself. 
Unless otherwise mentioned, symbols and notations have their usual standard meanings. 
Attempts of questions shall be counted in sequential order. Unless struck off, attempt of a 
question shall be counted even if attempted partly. 
Answers must be written in ENGLISH only. 
Electron charge 
Any page or portion of the page left blank in the Question-cum-Answer (QCA) Booklet must 
be clearly struck off. 
Values of constants which may be required: 
Free space permeability 
Free space permittivity 
Maximum Marks : 300 
Boltzmann constant 
Velocity of light in free space 
Planck's constant 
|sGSE-OETE 
SGSE-O-ETE 
- I'6 x 1o19 Coulomb 
4n X 
10-
Henry/m 
3 x 108 m/s 
(1/36)x 10-9 Farad/m 
1:38 x 1o28 J/K 
6-626 x 1034J-s 
UPSC ESE Mains Question Paper EC 23 June 2024
QI. (a) 
(b) 
(c) 
(d) 
Consider an ideal pMOS capacitor of area 100 um x 100 um operated 
at T = 300 K. èM (work function for the metal) = 52 eV, 
X, (oxide 
thickness) = 3 nm and Nn = 101/em. 
Calculate the flat 
Assume 
band voltage VFB and 
the threshold voltage VTp. 
Eor = 3:43 x 10-18 Flem, V (thermal voltage) 
= 0-026 V, n; = 100/cm® 
Zs; 
(electron affinity of Si) = 4-05 eV, Eg = 112 eV and Esi = 10-12 
Flcm. 19 
In the circuit shown in the figure below, M, serves as an electronic 
switch. If v, is very small, determine W/L such that circuit attenuates 
the signal by 5%. 
Assume Vc = 18V and R, = 100 2. 
Hn 
Cor 
200 
4A 
Source. 
Vin 
SECTION A 
250 V + 
SGSE-O-ETE 
and VTN = 0:4 V. 
VG 
M 
Find the voltage v, in the circuit shown in the figure using source 
transformation. Also, find the power developed by the 250 V voltage 
25 S2 
oVout 
W 
)8A 
22 
Vo 100Q 
52 
An electrical load absorbs an average power of 85 kW at lagging power 
factor of 0-85. If the load operates at 240 V rms, calculate the complex 
power and 
impedance of the load. 
12 
12 
¿ 15 2 
12 
Draw 
neat 
sketches 
of 
the 
edge 
and 
screw 
dislocations. 
IIlustrate 
the 
Burger's 
vector 
on 
the 
sketches 
of 
(1) 
6 
(e) 
Calculate 
the 
line 
energy 
of 
dislocation 
in 
BCC 
iron 
if 
the 
shear 
modulus 
and 
lattice 
parameter 
of 
BCC 
iron 
are 
80-2 
GN/m 
and 
2-87 Å, respectively. 
(ii) 
A p-n junction 
Q2. (a) 
N  
=3x 
1018 
/em, 
Np 
= 
2x 
1016/cm3 
D, 
= 
25 
cm²/s, 
D, 
= 
10 
cm/s 
Tn0 
= 
4 
x 
10-
s, 
Tno 
= 
10-
s 
20 
The 
photocurrent 
density 
J, 
= 
20 
mA/cm². 
Calculate 
the 
open 
circuit 
voltage 
of 
the 
solar 
cell 
at 
T 
= 
300 
K. 
Assume 
n; 
= 
1:5 
x 
1010/cm3. 
5 
though the armature 
What 
are 
the 
two 
functions 
of 
commutator 
in 
DC 
machines 
? 
Explain 
how 
the 
commutator 
keeps 
the 
armature 
mmf 
stationary 
in 
space, 
along 
the 
interpolar 
axis, 
even 
(i) 
(b) 
(ii) 
15 
rotates. 
10 
Explain why 
(i) 
(c) 
10 
Differentiate 
between 
different 
types 
of 
magnetic 
(ii) 
Design a 
Widlar 
(i) 
(a) 
10 
Q3. 
R$ 
V BE2 
VBE1 
10 
Design 
an 
amplifier 
that 
has 
a 
voltage 
gain 
of 
2 
if 
VÊN 
<0 
and 
1, 
if 
VIN 
> 
0. 
Assume 
ideal 
diodes 
and 
ideal 
op 
amps 
are 
availabie. 
(ii) 
3 
SGSE-O-ETE 
dislocations. 
solar 
cell 
is 
fabricated 
using 
silicon 
and 
has 
the 
following 
important parameters 
end-centred 
tetragonal 
geometry 
does 
not 
exist 
in 
Bravais crystal structures. 
materials on the 
basis 
of 
magnetic 
dipoles 
and 
hysteresis 
loops. 
current 
source 
shown in the 
figure 
below 
to 
give 
I, 
= 
5 
A 
and 
IR 
= 
1 
m¢. 
The 
parameters 
are 
Voc 
= 
30 
V, 
VBE1 
= 
07 
V, 
V 
= 
26 
mV 
and 
Bp 
= 
100. 
(b) 
(c) 
Q4. (a) 
() 
(ii) 
(i) 
(ii) 
Discuss the points of similarities between a transformer and 
induction machine. Explain, why an induction machine is called a 
generalized transformer. 
sGSEoETE| 
A 10 kVA/2500/250 V, single-phase transformer has the following 
parameters : 
Primary winding (h.v. side): Resistance rË = 24 2 
Leakage 
Reactance, x1 = 6-00 2 
Secondary winding (l.v. side): Resistance r = 0-03 S2 
Leakage 
Reactance, X, = 0:07 2 
With primary supply voltage held constant at 2500 V, calculate 
the secondary terminal voltage, when the low voltage winding is 
connected to a load impedance of 5 +j 35 2 and the transformer 
delivers its rated current at 08 p.f. lagging on the low voltage 
side. 
Discuss photoelectric efiect and find out the number of 
photoelectrons emitted per unit time from a transmitter operated 
at a frequency of 800 kHz and 10 kW power. 
Define dielectric strength. Discuss different types of dielectric 
breakdowns in solids. 
1 k2 
HE 
For the circuit shown in the figure below, determine the frequency of 
oscillation f, and overall voltage gain Ay. Also identify the type of 
Oscillator. (Assume op amps are ideal) 20 
A 
W 
1 kQ 
4 
1 k2 
W 
10 
1 uF 
10 
10 
10 
(b) 
(c) 
(i) 
Determine the 
impedance Z,, 
that results in 
maximum average 
power 
transferred to Z,. for the 
circuit shown in the 
figure. 
Calculate the maximum average power transferred to the oad 
impedance determined. 
20/0°,V 
5Q 
SGSE-O-ETE 
Given : erf (0-95) = 0-8209 
(ii) What are the major factors that have led to the acceleration and 
development of solar and wind power ? 
erf (1·0) = 0-8427 
To produce a p-type semiconductor, the boron is doped in pure 
silicon. Doping is done through a B,03 vapour phase of a surface 
concentration equivalent to 3-3 x 1028 boron atoms/m². Calculate the 
time required to get a boron content of 1028 atoms/m at a depth 
of 2 um. The doping temperature is 1000°C and Dg in Si at this 
temperature is 4 x 10-17 mn/s. 
erf (2-4)= 0-9993 
W 
erf (2-6)= 09998 
202 
5 
j3 2 
000 
a 
10 
10 
20