Georgia Institute of Technology
School of Electrical and Computer Engineering
Midterm Examination #3
Date: March 26, 2025 Course: ECE 3040
Section: A
Time: 75 minutes
Name: SOLUT IONS
Guidelines for Midterm #3:
1. Closed book, closed notes. Non-programmable calculators are permitted, as is
a single-sided handwritten formula sheet, plus the single-sided formula sheet
you used for Midterms 1 and 2.
The work you show on the exam paper itself is the only work which will be
graded. You may use the backs of the quiz pages, if you find you need additional
space.
. Plots, sketches and diagrams must be labeled in detail.
. Answers must include proper units, whenever applicable, and
vector quantities must be clearly indicated using the convention adopted
for this course.
It is required to show all work in order to receive full credit for your
answers, regardless of whether or not the answers are correct. Incorrect answers
may be awarded partial credit when appropriate. ~
- There are 7 pages to this exam, including the cover sheet. Please make sure you
have not overlooked any problems.
, Problem #1: MOS Structures (35 points)
A MOS capacitor has a silicon bulk region doped with 10%*¢ cm=3 acceptor atoms, a 6 nm thick SiO2
insulator layer, and a gate metal with a work function of 4 eV. The relative dielectric permittivities of
SiO2 and Si are 3.9 and 11.7, respectively, with €, = 8.85 - 107*2F/m. The effective densities of state
for electrons and holes in Siare N, = 6.2 - 101°T%/2cm™3 and N,, = 3.5 - 1015T3/2cm
™3, respectively.
s a) 7 pts.
[_\_‘:_ a What é(EC'EFy//(T
is the flatband voltage? \ng = = _ A
CI)A} A @W\ és/ é$: X%Lc EF
T ONa T € NeN 4 i Vfi BOOK’ Ne = 3\22x10'q(w\'3
= - - S T — ?Lf
LC ;F . KTLA( Y > €
=2 \IFB: \/‘ ’I“.OS —.C'\'RLl :_.q?H\/
b) 7 pts. What is the Fermi potential? (E:-E¢) /K'r S EEr - KT ,Q,\ l\\‘;fi_
\
& = Ei-EFl, ) v W = & K_r
*
k P - —%'JM (%>
CLF -.3592 V
c) 7pts. Assume instead (both now and henceforth in Problem #1) that the metal work
function is such that Vz3 = 0V, and that the Fermi potential is 0.2 V. (Note that this latter
assumption causes the acceptor density to deviate from the value given in the problem
statement above.) What are the minimum and maximum depletion region thicknesses one
might measure in each of the three biasing modes? .
i) Accumulation: Wnin = O 5 Winax = _O
ii) Depletion: Winin = @) 3 Wiaxr =_ 4. FF am
iii) Inversion: Winin = _ 4. FF AN, Woae =_HFF 0 m
w R/.e28%7E 2 3
Neow ‘/#F = ’07\/ — r\)A — 1D e = 22FUXID em
Thete 15 no deflefion in accumildio > wen - w.,. . o
Ta 5(")\94‘\0"\ , Wmay occurs whon b‘w\seg%o the om,@‘fr.,.( Taversion .
=> Ewmay = %MAWMAX (Fw\ Ma el éf)«flfmy
A+ onset of ‘vr\vers}m/ b, = 2 =4V
Rt &y = 4 Bwel/ = Bz NaWel, = 2de= -1t
P Wmex = 437 51078 = Wane =43 = Opm
un and Wein
LA itnvecsim | The ée@le‘{‘:m\ F@j"\w\ Aoog/\q— 7(@\”.
4\—/ Wam'in T WMAx — LL??—/M
7.
School of Electrical and Computer Engineering
Midterm Examination #3
Date: March 26, 2025 Course: ECE 3040
Section: A
Time: 75 minutes
Name: SOLUT IONS
Guidelines for Midterm #3:
1. Closed book, closed notes. Non-programmable calculators are permitted, as is
a single-sided handwritten formula sheet, plus the single-sided formula sheet
you used for Midterms 1 and 2.
The work you show on the exam paper itself is the only work which will be
graded. You may use the backs of the quiz pages, if you find you need additional
space.
. Plots, sketches and diagrams must be labeled in detail.
. Answers must include proper units, whenever applicable, and
vector quantities must be clearly indicated using the convention adopted
for this course.
It is required to show all work in order to receive full credit for your
answers, regardless of whether or not the answers are correct. Incorrect answers
may be awarded partial credit when appropriate. ~
- There are 7 pages to this exam, including the cover sheet. Please make sure you
have not overlooked any problems.
, Problem #1: MOS Structures (35 points)
A MOS capacitor has a silicon bulk region doped with 10%*¢ cm=3 acceptor atoms, a 6 nm thick SiO2
insulator layer, and a gate metal with a work function of 4 eV. The relative dielectric permittivities of
SiO2 and Si are 3.9 and 11.7, respectively, with €, = 8.85 - 107*2F/m. The effective densities of state
for electrons and holes in Siare N, = 6.2 - 101°T%/2cm™3 and N,, = 3.5 - 1015T3/2cm
™3, respectively.
s a) 7 pts.
[_\_‘:_ a What é(EC'EFy//(T
is the flatband voltage? \ng = = _ A
CI)A} A @W\ és/ é$: X%Lc EF
T ONa T € NeN 4 i Vfi BOOK’ Ne = 3\22x10'q(w\'3
= - - S T — ?Lf
LC ;F . KTLA( Y > €
=2 \IFB: \/‘ ’I“.OS —.C'\'RLl :_.q?H\/
b) 7 pts. What is the Fermi potential? (E:-E¢) /K'r S EEr - KT ,Q,\ l\\‘;fi_
\
& = Ei-EFl, ) v W = & K_r
*
k P - —%'JM (%>
CLF -.3592 V
c) 7pts. Assume instead (both now and henceforth in Problem #1) that the metal work
function is such that Vz3 = 0V, and that the Fermi potential is 0.2 V. (Note that this latter
assumption causes the acceptor density to deviate from the value given in the problem
statement above.) What are the minimum and maximum depletion region thicknesses one
might measure in each of the three biasing modes? .
i) Accumulation: Wnin = O 5 Winax = _O
ii) Depletion: Winin = @) 3 Wiaxr =_ 4. FF am
iii) Inversion: Winin = _ 4. FF AN, Woae =_HFF 0 m
w R/.e28%7E 2 3
Neow ‘/#F = ’07\/ — r\)A — 1D e = 22FUXID em
Thete 15 no deflefion in accumildio > wen - w.,. . o
Ta 5(")\94‘\0"\ , Wmay occurs whon b‘w\seg%o the om,@‘fr.,.( Taversion .
=> Ewmay = %MAWMAX (Fw\ Ma el éf)«flfmy
A+ onset of ‘vr\vers}m/ b, = 2 =4V
Rt &y = 4 Bwel/ = Bz NaWel, = 2de= -1t
P Wmex = 437 51078 = Wane =43 = Opm
un and Wein
LA itnvecsim | The ée@le‘{‘:m\ F@j"\w\ Aoog/\q— 7(@\”.
4\—/ Wam'in T WMAx — LL??—/M
7.
