eee210( physical electronic)

8/2/2019 EEE210( Physical Electronic)

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EEE-210 Physical ElectronicsFirst Midterm Exam. 21.04.2000, 100 min. 100 points, questions, pages

Answers should be filled in the blanks.

NO PARTIAL CREDITS

SURNAME . . . . . . . . . . . NAME . . . . . .

1.(20) Find the probability of occupation of a level 0.045 eV above the coduction band

edge, if the Fermi level is 0.7 eV above the valence band, the energy gap is 1.1 eV and

the temperature is 300 K. How would you comment the result?

FFD = . . . ;

2.(20)Find the resistance of some semiconductor, 100 m long and 5 m2 in cross-section, if it isuniformly doped n-type with ND = 10

20 m-3, ni = 1016 m-3, e = 0.135 m2V-1s-1; h =0.05 m2V-1s-1.

R = . . . . .M ;


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3.(20) A uniformly doped n-type silicon semiconductor with 1016 donor atoms per cm3 is subjected

to a boron diffusion with a constant surface concentration of 5*1018 cm-3. It is desired to to form a

pn-junction at a depth of 2.7 m. At what temperature should this diffusion be carried out if it is tobe completed in 2 hours? Find the diffusivity.

D = . . . . . .cm2/s; T = . . . . K;

4.(20) An electron in GaAs has an effective mass of 0.068 m0. Its mean free path is 0.14 microns . If the

mean thermal velocity is 4.125*105 m s-1, find the electron mobility. Under which electric field the drift

velocity of electron would be equal to the thermal velocity.

= . . . .m2V-1s-1 ; E= . . . .V/m ;


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5.(20)Give the definitions for the:

a.Low level injection

b.Hall multiplier

c.Phonon scattering

d.Degenerate semiconductor

e.Traps


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EEE-210 Physical ElectronicsFirst Midterm Exam. 21.04.2000, 100 min. 100 points, questions, pages

Answers should be filled in the blanks.

NO PARTIAL CREDITS

SURNAME . . . . . . . . . . . NAME . . . . . .

1.(20) Find the probability of occupation of a level 0.045 eV above the coduction band

edge, if the Fermi level is 0.7 eV above the valence band, the valence band is 1.1 eV and

the temperature is 300 K.

FFD = . . . ;

2.(20)Find the resistance of some semiconductor, 100 m long and 5 m2 in cross-section, if it isuniformly doped n-type with ND = 10

20 m-3, ni = 1016 m-3, e = 0.135 m2V-1s-1; h =0.05 m2V-1s-1.

R = . . . . .M ;


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3.(20) A uniformly doped n-type silicon semiconductor with 1016 donor atoms per cm-3 is

subjected to a boron diffusion with a constant surface concentration of 5*1018 cm-3. It is

desired to to form a pn junction at a depth of 2.7 m. At what temperature should thisdiffusion be carried out if it is to be completed in 2 hours?

D = . . . . . .cm2/s; T = . . . . K;


mean thermal velocity is 4.125*105 m s-1, find the electron mobility. Under which electric field the dritf

velocity of electron is equal to the thermal.

= . . . .m2V-1s-1 ; E= . . . .V/m ;


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5.(20)Give the definitions for the:

a.Low level injection

If the injected carrier density is small compared with the impurity concentration,the majority carrier

density remains essentially unchanged while the minority carrier density is equal to the injected

carriers density. This condition isw called low-level injection.

b.Hall multiplier

The Hall multiplier is a semiconductor device, where the the output signal is the product of the input

Current I and the magnetic induction Bz.

c.Phonon scattering

The thermal vibrations may be treated quantum-mechanically as discreate particles called phonons.

The collisions of phonons with electrons and holes is called lattice or phonon scattering.

d.Degenerate semiconductor

When the impurity concentration is very high and approaches the effective density of states, the

Fermi level will be very close to Ec or Ev. For example, when Ec Ef < 3kT, the semiconductor issaid to be degenerate

e.Traps

Traps are the defects or impurities whose electronic states are deep in the forbidden gaps. They

capture electrons and holes thus contributing to the recombination processes.

EEE-210 Physical ElectronicsSecond Midterm Exam. 26.05.2000, 100 min. 100 points, 4 questions, 5 pages

Answers should be filled in the blanks.NO PARTIAL CREDITS; ALL CALCULATIONS ARE VALID UNTIL THE FIRST ERROR .

SURNAME . . . . . . . . . . . . . . NAME . . . . . .

1.(30) A Si p-n junction with area 10-4 cm2 has Na = 1017 cm-3 on the p side

and Nd = 1017 cm-3 on the n side. The diode has a forward bias of 0.7 V.

Assuming that n = 700 cm2/V s, p = 250 cm2/V s, and p = n = 1 s,find parameters given below. Plot Ip , In , I versus distance on a diagram.

Neglect recombination within W.

Lp = . . . .cm; Ln = . . . .cm; pn(0) = . . . . .cm-3;

np(0) = . . . . cm-3; Ip(0) = . . . A; In(0) = . . . A;


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Ip(xn) = . . . . . A; In(xp) = . . . . . A; I = . . A;

2.(15) A p+-n Si junction is doped with Nd = 1016 cm-3 on the n-side, where

Dp = 10 cm2/s and p = 0.1 s. The junction area is 10-4 cm2. Calculate the

reverse saturation current Ir, and the forward current If when V = 0.6 V.

Ir = . . . . . A; If = . . . . A;


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3.(15) A silicon diode operates at a forward voltage of 0.5 V. Calculate the factor F

by which the current will be multiplied when the temperature is increased from25 to 150

C. Assume that I I0 eV/ T and that I0 doubles every 6 C.

F = . . . . .

4.(40) In a silicon pnp transistor, the doping concentrations for the emitter, base, and

collector are 1019, 5*1017, and 1015 cm-3. The emitter and base widths are 1 and 0.7 m,respectively, and the diffusion length is 10 m for both electrons and holes. The collector

width is 50 m and the cross-sectional area is 10-4

cm

2

. If nE = 130 cm2

/V s; p = 250cm2/V s; nC = 1500 cm2/V s, then calculate: a)emitter injection efficiency; b)basetransport factor; c)normal alpha; d)common emitter current gain; e)inverse alpha; f)IE0;

g) IC0; h)collector-emitter voltage at saturation at IC = 1 mA and IB = 100 A.

a) . = . . . ; b) . = . . . ; c) . = . . . ;

d) . = . . . ; e) . = . . . ; f) . . . . A ;

g) . . . . . A ; h) . . . . . V ;


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EEE-210 Physical ElectronicsFinal Exam. 19.06.2000, 120 min. 100 points, 5 questions, 5 pages

Answers should be filled in the blanks.NO PARTIAL CREDITS; ALL CALCULATIONS ARE VALID UNTIL THE FIRST ERROR .

SURNAME . . . . . . . . . . . . . . NAME . . . . . .

1.(30) An ideal MOS capacitor has a 10 nm thick SiO2 layer and a

p-type Si with Na = 1016 cm-3. It operates under moderate inversion.

Find: a) depletion layer width; b) voltage for moderate inversion;

c) bulk charge; d) threshold voltage; e) oxide capacitance;

f) total capacitance; Take kT/q = 0.0259 v.

a) m; b) V; c) C/cm2;

d) vT = V ; e) F/cm2; f) F/cm2;


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2.(20) The potential is given by 1.5*1013 x2 volts. The charge in semiconductor is due

to a uniform distribution of singly charged carriers. Find the concentration of

carriers and their polarity (electrons or holes). The dielectric constant is 12.

N = cm-3 ; Polarity = ;

3.(15) A semiconductor is doped with Nd and has a resistance R1 ( Nd >> ni). The same

semiconductor is then doped with an unknown amount of acceptors Na (Na >> Nd),

yielding a resistance of 0.5 R1. Find Na in terms of Nd if Dn / Dp = 50.

Na = Nd.


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4.(15) In some newly developed semiconductor find the ratio of electron drift and

diffusion currents N = Idrift /Idiff at 300 K if the electric field is 105 Vm-1, the

concentration gradient is 1026 m-4 and the electron number density is 1020 m-3.

N = ;

5.(20) In some newly developed semiconductor the bandgap is 0.9 ev, and

ni = 1.5*1016 m-3 at 300 K. At what temperature does ni become 10

20, assuming

that Nc and Nv do not vary with temperature. Take kT/q = 0.0259 v.

T = K;

EEE-210 Physical ElectronicsFirst Midterm Exam. 20.04.2001, 100 min, 100 points, 4 questions, 6 pages

Answers should be filled in the blanks. No partial credits

SURNAME . . . . . . . . . . . NAME . . . . . .

1.(36) 1014 boron atoms are deposited on the surface of a silicon wafer of surface area 10 mm2.

The sample is then placed in a furnace. If the diffusivity of boron is 1.25*10-12 cm2/s find the

temperature T of the furnace. Find the boron concentration N at the surface after 2 hours. Find

the distance X from the surface where the boron concentration is 1017 atoms/cm3 after 2 hours.

T = K; N = atoms/cm3; X = m;


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2.(20) Calculate the concentration of impurities for p- and n-type silicon semiconductors if the

difference between intrinsic and Fermi levels is 3/2 kT.

nn = cm-3; pn = cm

-3;

np = cm-3; pp = cm

-3;

3.(24) (a) Calculate the conductivity and quasi-Fermi levels for a silicon sample with Nd = 1015

cm-3

, p = 1 s, and GL = 5*1019 cm-3 s-1. (b) Find the value of GL that produces 1015 holes/cm3. What are theconductivity and quasi-Fermi levels? Take p = 0.6*102 cm2/V s and n = 1.34*103 cm2/V s


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(a) n = p = cm-3; = / cm;Efn Ei = ev; Ei E fp = ev;

(b) GL = cm-3 s-1; = / cm;

Efn Ei = ev; Ei E fp = ev;

4.(20) A pn-junction is formed out of germanium ( ni = 2.4*1013 cm-3) with resistivity of 2 cm on

the p-side and 0.1 cm on the n-side. Assuming the junction to be at equilibrium at room temperature(300 K), find the contact potential VT. Take p = 1.7*103 cm2/V s and n = 3.6*103 cm2/V s

VT = v;

EEE-210 Physical ElectronicsSecond Midterm Exam. 25.05.2001, 100 min, 100 points, 3 questions, 3 pages

Answers should be filled in the blanks. No partial credits

SURNAME . . . . . . . . . . . NAME . . . . . .

1.(25) An oxide layer of a MOS transistor has a thickness of 0.1 m. Concentrationof acceptors in a p-type silicon is 3*1014 cm-3 at 300 K. Find: the surface band bending

under moderate inversion MI and strong inversion SI; the threshold voltage TV;depletion layer width W; total bulk charge Ch.


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MI = v; SI = v; TV =

v;

W= cm; Ch= C/cm2;

2.(25) A silicon npn semiconductor has the parameters: xB= 2 m, NA = 5 * 1016 cm-3 in a uniformlydoped base, n = 1 s, Dn = 22 cm2/s, and A = 0.01 cm2. If the collector is reversed-biased and InE = 1mA, calculate the the excess-electron density EED at the base side of the emitter junction, the emitter-

junction voltage VE , and the base transport factorBTF. What should be the mobility of electrons n anddiffusion length Ln.


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Ln = m; EED = cm-3; VE =v;

BTF = ; n =cm2/v s


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3.(50) A Si p-n junction of 50 m * 50 m area at T = 300 K has the following parameters: ND = 1017cm-3,

NA = 1015 cm-3, Dn = 38 * 10

-4 m2s-1, Dp = 13 * 10-4 m2s-1, n =50 s, p =10 s, ni = 1.4 * 1016 m-3.

Find: a) the saturation current I0; the potential difference 0; b) the depletion layer widths (Xd)-10, (Xd)+0.75 and the corresponding parallel plate capacitances (C0)-10, (C0)+0.75 at bias voltages of V = -10 v and

+ 0.75 v; c) the conductance GD and diffusion capacitance CD at V = + 0.75 v.

I0 (10) = A; 0 = v;(Xd)-10 = m; (Xd)+0.75(10)= m; (C0)-10 =

F;

(C0)+0.75 = F; GD = S; CD=

F;

EEE-210 Physical Electronics

The FINAL Exam 15.06.2001, 120 min, 100 points, 5 questions, 4 pages. All calculationsshould be done in detail, step by step.Calculations are valid until the first error. Answers

should be filled in the blanks, otherwise they are not valid. No partial credits

SURNAME . . . . . . . . . . . NAME . . . . . .

1.(20) A medium is neutral apart from a constant positive charge density Q C/m3 in the region

0 < x < d. The potential at x = 0 is zero and there is no electric field at x = d. Find the

expressions and sketch the diagrams for electric field E(x) and potentil V(x) as a function

of a distance x.

E(x) = ; V(x) = ;


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n(cm2/V s)

p(cm2/V s)

Width

( m)N

(cm-3)

Diffusion length L for

minorities ( m)emitter 150 90 1 1019

base 450 150 0.7 5*1017 20

collector 1500 450 50 1015 10

2.(25) Parameters of a n-p-n Si transistor of 10-4 cm2 area are given in the table. Calculate with a

precision

of no less than four digits: a) normal- NA and inverse- IA alpha; b) base transport factorBTF, common-

emitter current gain CECG, and common-collector current gain CCCG; c) if the lifetimes of carriers are

the same

all over the semiconductor, find the diffusion length LpE for holes in emitter.

NA = ; IA = ; BTF =;

CECG = ; CCCG = ; LpE=

m ;


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3.(20) The concentration of electrons in a semiconductor varies from 1020 m-3 to 1012 m-3 linearly over a

distance

of 4 m. Find: a) the electron diffusion current density Jn diff; b) the concentration of electrons n at the

midpoint of the 4 m distance; c) the electric field at the midpoint when the total current is zero.Take n = 0.135 m

2

V-1

s-1

and T = 200 K.

Jn diff= A/m2; n = m-3; =

V/m;


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4.(15) Determine the resistance to the lateral current flow of thin film semiconductor stripes of dimension

(length*width) 100*10 microns; 200*20 microns; 100*6 microns, if the sheet resistance is 50 ohms/unit

area.

R100*10 = ; R200*20 = ; R100*6 = ;


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5.(20) In n-type germanium with ni = 2.5 * 1019 m-3 and ND = 10

22 m-3, a flash of light doubles the hole

number

density. Calculate the generation rate GL and the time t taken for the hole density to decay to 8 * 1016 m-3 if

the hole lifetime is 3 ms.

t = ms; GL = m-3s-1;

EEE-210 Physical ElectronicsThe MAKE UP on FINAL Exam 25.06.2001, 120 min, 100 points, 5 questions, 4 pages.

All calculations should be done in detail, step by step.Calculations are valid until the first

error. Answers should be filled in the blanks, otherwise they are not valid. No partial credits

SURNAME . . . . . . . . . . . NAME . . . . . .

1.(15) In an n-type silicon, the donor concentration corresponds to 1 atom per 107 silicon

atoms, the electron effective mass is 0.33 m0. Calculate: (a) the concentration of donor atoms,

(b) The Fermi level with respect to the conduction band edge at room temperature, (c) if the

Fermi level coincide with Ec, what should be the concentration of donors?

2.(25) p-type silicon MOS capacitor doped 1023 m-3 , has an oxide thickness of 0.1 m. If the gate potential

is 5 V,find: (a) oxide capacitance; (b) derive the quadratic equation for the surface potential s and calculate s;(c) the voltage across oxide V0; (d) induced charge Qs; (e) depletion layer width Xd.

3.(20)Derive an expression of the anode current IA as a function of the gate current by using the two-

transistor

analog in an SCR.

4.(20) In a p+n junction diode, the width of the n region Wn is much smaller than Lp. Using Ip(x = Wn) =

qAS pnas one of the boundary conditions, derive the carrier and current distributions. Sketch the shape of minority

carriers in the n side for S = 0 and S = .

5.(20) The potential is given by 1.5*1013 x2 volts. The charge in semiconductor is due to a uniform

distribution of singly charged carriers. Find the concentration of carriers and their polarity (electrons orholes). The dielectric constant is 12.


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N = cm-3 ; Polarity = ;

EEE-210 Physical ElectronicsThe Ek snav Exam 11.09.2001, 120 min, 100 points, 6 questions,

All calculations should be done in detail, step by step.Calculations are valid until

the first error.

SURNAME . . . . . . . . . . . NAME . . . . . .

1.(20) Verify the following expression of the temperature dependence of the threshold

voltage for an MOS structure with an n substrate, assuming si = 2 f here and f< 0.

2.(15) a) The hole injection efficiency of a pn junction is defined as Ip / I at x = 0. Show that

this efficiency can be written

= Ip / I = 1 / (1 + nLp / pLn)

b) What should you do to make approach unity in a practical diode?

3.(20) Derive the expressions for the (a) electric field E(x), (b) potential distribution (x),(c) depletion layer width Xd, and (d) built-in-potential 0 for a linearly graded pn junctionwith a doping gradient a.

4.(10) The injection of carriers gives rises to the splitting of the electron and hole quasi-

Fermi levels. Show that the nonequilibrium product (pn) of a semiconductor with an energy

gap of Eg is the same as the equilibrium product pono of a semiconductor with a bandgap of

Eg (Efn Efp).

5.(20) Sketch the following diagrams: a) Capacitance-voltage characteristics for high and

low frequencies of MOS transistors; b) Electron and hole currents in forward-biased pnjunctions; c)The hybrid- circuit for bipolar transistor with output terminals short-circuited; d) Charge storage in the base and collector of transistor at cutoff and saturation.


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Show the active region; e) Static current-voltage characteristics of a typical tunnel diode.

Show its components.

6.(15) Give the definition for: a) Distribution function; b) Degenerate semiconductor; c)

Phonons;d) one-sided pn junction; e) Conditions for transistor to operate in normal mode.

EEE-210 Physical ElectronicsFirst Midterm Exam 21.03.2002, 100 min, 100 points, 4 questions, 3 pages. All

calculations should be done in detail, step by step.Calculations are valid until the first error.

Answers should be filled in the blanks, otherwise they are not valid. No partial credits

SURNAME . . . . . . . . . . . NAME . . . . . .

1.(20) Derive the electric field in an n-type semiconductor if: (a) Nd = ax, where a is a

constant; (b) Nd = N0 e

-ax

;

(a) = ; (b) = ;


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2.(25) An intrinsic silicon semiconductor is doped with donors to form a resistance of 10 k and abilityto handle

a current density of 50 A/cm2 when 5 volts are applied. Find the necessary concentration of donors Nd if

the

electric field inside the semiconductor should not exceed 100 V /cm. Take the mobility n = 410cm2/V s.

Nd = atoms/cm3.

This problem is modernised. Do not use it.

3.(25) Assume that, in an n-type gallium arsenide semiconductor at T = 300 K, the electron concentration

varies linearly from 1*1018 to 7*1017 cm-3 over a distance of 0.10 cm. Calculate the diffusion current

density

Jn diff if the mobility is n = 1000 cm2/V s.

Jn diff = A/cm2.


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4.(30) Calculate the density of states for free electrons in the conduction band per unit volume with

energies between zero and 1 ev.

N = m-3;

EEE-210 Physical Electronics

Second Midterm Exam 02.05.2002, 100 min, 100 points, 4 questions, 3 pages. All

calculations should be done in detail, step by step.Calculations are valid until the first error.

Answers should be filled in the blanks, otherwise they are not valid. No partial credits

SURNAME . . . . . . . . . . . NAME . . . . . .

1.(40) A Si p-n junction with area 10-4 cm2 has Na = 1017 cm-3 on the p side and

Nd = 10

17

cm

-3

on the n side. The diode has a forward bias of 0.7 V. Assuming that n = 700 cm2/V s, p = 250 cm2/V s, and p = n = 1 s, find parameters givenbelow. Calculate the numerical expressions for Ip(xn), In(xp), and I as a function of a

distance. Plot their diagram. Neglect recombination within W.

Lp = . . . . cm; Ln = . . . . cm; pn(0)

= . . . . . cm-3;

np(0) = . . . . cm-3; Ip(0) = . . . A; In(0) = . . . A;

Ip(xn) = . . . . . A; In(xp) = . . . . . A; I = . .

A;


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2.(40) In a silicon pnp transistor, the doping concentrations for the emitter, base, and collector are 1019,

5*1017, and 1015 cm-3. The emitter and base widths are 1 and 0.7 m, respectively, and the diffusionlength is

10 m for both electrons and holes. The collector width is 50 m and the cross-sectional area is 10-4cm2.

If nE = 130 cm2

/V s; p = 250 cm2

/V s; nC = 1500 cm2

/V s, then calculate: a)emitter injectionefficiency;b)base transport factor; c)normal alpha; d)common emitter current gain; e)inverse alpha; f) IE0; g) IC0;

h)collector-emitter voltage at saturation at IC = 1 mA and IB = 100 A. Use four significant digits inanswers.

a) . = . . . ; b) . = . . . ; c) . = . . . ;

d) . = . . . ; e) . = . . . ; f) . . . . A ;

g) . . . . . A ; h) . . . . . V ;


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3.(15) A p+-n Si junction is doped with Nd = 1016 cm-3 on the n-side, where Dp = 10 cm

2/s and p = 0.1 s. The junction area is 10-4 cm2. Calculate the reverse saturation current Ir, and the forward current Ifwhen V = 0.6 V.

Ir = . . . . . A; If = . . . . A;


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4.(5) Draw the voltage-current diagram for a tunnel diode. Show the components of a tunnel current

EEE-210 Physical ElectronicsFinal Exam 31.05.2002, 120 min, 100 points, 5 questions, 4 pages. All calculations should

be done in detail, step by step.Calculations are valid until the first error. Answers should be

filled in the blanks, otherwise they are not valid. No partial credits

SURNAME . . . . . . . . . . . . NAME . . . . . .

1.(20) The concentration of electrons in a semiconductor varies from 1020 m-3 to 1012 m-3

linearly over a distance of 4 m. Find: a) the electron diffusion current density Jn diff; b) theconcentration of electrons n at the midpoint of the 4 m distance; c) the electric field atthe midpoint when the total current is zero. Take n = 0.135 m2V-1s-1; T = 200K.

Jn diff = A/m2; n = m-3; =

V/m;


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2.(15) In an n-type silicon, the donor concentration corresponds to 1 atom per 107 silicon atoms, the

electron effective mass is 0.33 mo. Calculate: a) the concentration of donor atoms Nd, b) The Fermi level

with respect to the conduction band edge at room temperature. c) If the Fermi level coinside with E c, what

should be the concentration of donors Ncf EE ?

a) Nd = cm-3; b) E = eV; c) N

cf EE =

cm-3;


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3.(15) 0.5 mm long and 10-5 cm2 in cross section intrinsic silicon semiconductor is doped with donors to

form a resistance of 10 k . If the mobilities are n = p = 410 cm2/V s, find the necessaryconcentration of donors Nd.

Nd = atoms/cm3.

4.(20) A silicon diode operates at a forward voltage of 0.5 V. Calculate the factor1

2

I

Iby which the

current will be multiplied when the temperature is increased from t 1 = 25 C to t2 = 150 C. Assume that I= I0 exp(V / 2 T) and that I0 doubles every 6 C.

1T = V;

2T = V;

01

02

I

I= ;

1

2

I

I= ;


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2.(25) p-type silicon MOS capacitor doped 1023 m-3, has an oxide thickness of 0.1 m. If the gatepotential is 5 V: a) find the oxide capacitance C0; b) derive the quadratic equation for the surface potential

swith numerical coefficients. Calculate: c) the values of s from the equation; d) the voltage V0across the oxide; e) induced charge Qs; f) depletion layer width xd;

C0 = F/m2; (Equation for s) . . . .

= 0

s (solutions of the equation) = V;V0 = V; Qs = C; xd = m;

EEE-210 Physical ElectronicsMake up of the First Midterm Exam. 100 min, 100 points, 5 questions,

No partial credits

SURNAME . . . . . . . . . . . NAME . . . . . .

1.(20) (a) A semi-infinite slab of n-type silicon is uniformly illuminated with a generation rate

of GL. Obtain the hole-continuity equation under these conditions.

(b). If the surface recombination velocity is S at x = 0, solve the new continuity equation to

show that the steady-state hole distribution is given by

)1()(

/

0

pp

Lx

p

LpnnSL

SeGpxp

p

+

+=

2.(20) The p-type semiconductor is illuminated by steady-state radiation that uniformly generates GL

electron-hole pairs/cm3 s in the region L < x < L. The minority-carrier lifetime n is infinite. It is alsoknown that n(x = 2L) = 0. Find n(x = 0) (GL is a constant). Hint: n(x) and d n(x)/dx are continiousthroughout the semiconductor.


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3.(20) (a) From the definition of direct recombination, determine the average time an electron stays in the

conduction band and the average time the hole stays in the valence band.

(b) What is the relationship between the carrier lifetime and the average times obtained in (a)? Discussthis relationship for intrinsic and extrinsic semiconductors.

4.(20) Show that the effective density of states Nc represents a total number of states in the conduction

band 1.2 kT wide near the edge of the conduction-band edge. Explain the physical meaning of your result.

5.(20) Find the probability of occupation of a level 0.045 eV above the coduction band edge, if the Fermi

level is 0.7 eV above the valence band, the energy gap is 1.1 eV and the temperature is 300 K. How

would you comment the result?

EEE-210 Physical ElectronicsMake up of the Second Midterm Exam. 100 min, 100 points, 5 questions,

No partial credits

SURNAME . . . . . . . . . . . NAME . . . . . .

1.(20) (a) Ignoring the space-charge recombination currents,show that the exact expression for

the common-emitter output characteristics of a transistor is

N

I

T

ICBEO

NCBNCO

TCE ln)1(III

)1(IIIlnV

+

++

+=

Note: First solve explicitly for the junction voltages in terms of the currents.

(b) If IB>> IEO and IB>> ICO/ N, show that the foregoing equation reduces to

FENBC

FEIBCI

TCEhII

hIIV

/1

//1ln

+

=


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2.(20) (a) Derive an expression for the carrier concentration in the base in an npn transistor if xB and Lnare of the same order of magnitude.

(b) Simplify the result in (a) for xB


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2.(16) Calculate the the electron and hole concentration under steady-state illumination in an n-type silicon with

GL = 1016 cm-3 s-1, Nd = 10

15 cm-3, and n = p = 10 s.

n = cm-3; p = cm-3;

3.(20) An electron in GaAs has an effective mass of 0.068 m0 and a mean free path of 0.14 microns at

300 K. Find the electron mobility n. Under which electric field Ethe dritf velocity of electron wouldbe equal to their thermal velocity?

n = . . . . cm2/Vs; E= . . . . V/m ;


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4.(18) Find the probability of occupation of a level 0.045 eV above the coduction band edge, if the Fermi

level is 0.7 eV above the valence band, the energy gap is 1.1 eV and the temperature is 300 K. How

would you comment the result?

FFD = . . . ;

5.(15) a)Determine the number of atoms N in a unit cell of an fcc crystal.

b) What is the distance d in units of the lattice constant a between two nearest-neighboring atoms?

c) If each atom is assumed to be a sphere and the spherical surface of each atom comes into contact with its

nearest neighbors, what percentage P of the total volume of the unit cell is occupied?

N = ; d = a; P = %;


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6.(15) The lattice constant of silicon is 0.543 nm. Calculate the density of valence electrons.

D = cm-3;

EEE-210 Physical Electronics 2002-03Second Midterm Exam. 22.05.2003, 100 min. 100 points, 4 questions, 7 pages.

Calculations should be done in detail, step by step. Results are valid until the

first error. Answers should be filled in the blanks, otherwise they are not valid. No

partial credits.

SURNAME . . . . . . . . . . NAME . . . . .

1.(15) A silicon diode operates at a forward voltage of 0.5 V. Calculate the factor F by

which the current will be multiplied when the temperature is increased from 25 to 150C.

Assume that I I0 eV/ T and that I0 doubles every 6 C.

F = . . . . .

1

2

3

4


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2.(48) A Si p-n junction of 50 m * 50 m area at T = 300 K has the following parameters: ND = 1017cm-3,

NA = 1015 cm-3, Dn = 38 * 10

-4 m2s-1, Dp = 13 * 10-4 m2s-1, n =50 s, p =10 s. Find: a) the

saturation current I0 and the potential difference 0; b) the depletion layer widths (Xd)-10, (Xd)+0.75 andthe corresponding parallel plate capacitances (C0)-10, (C0)+0.75 at bias voltages of v = -10 V and + 0.75

V; c) the conductance GD and diffusion capacitance CD at V = + 0.75 v. Take ni = 1.4 * 1016

m-3

.

I0 = A; 0 = V;(Xd)-10 = m; (Xd)+0.75 = m; (C0)-10 =

F;

(C0)+0.75 = F; GD = S; CD=

F;


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3.(25) A silicon npn semiconductor has the parameters: xB= 2 m, NA = 5 * 1016 cm-3 in a uniformlydoped base, n = 1 s, Dn = 22 cm2/s, and A = 0.01 cm2. If the collector is reversed-biased and InE = 1mA, calculate the the excess-electron density EED at the base side of the emitter junction, the emitter-

junction voltage VE , and the base transport factorBTF (give four significant units). What should be themobility of electrons n and diffusion length Ln.

Ln = m; EED = cm-3; VE =V;

BTF = ; n =cm2/V s


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4.(12) Sketch the following diagrams:

a. The voltage-current diagram for a tunnel diode. Show the components of a tunnel current.

b. Electron and hole currents in forward biased pn-junctions.

c. Capacitance-voltage characteristics for high and low frequencies of MOS transistors.

EEE-210 Physical Electronics 2002-03Final Exam. 06.06.2003, 120 min. 100 points, 5questions, 6 pages. Calculations

should be done in detail, step by step. Results are valid until the first error.

Answers should be filled in the blanks, otherwise they are not valid. No partial

credits.

SURNAME . . . . . . . . . . NAME . . . . .

1.(20) A p+n silicon diode is used as a varactor. The doping concentrations on the two

sides of the junction are Na = 1019 cm-3and Nd = 10

15 cm-3, respectively. The diode area is

6.45*10-4

cm2

. a) Find the diode capacitance at the reverse bias voltage of 1V. b)Calculate the resonant frequencies of a circuit using this varactor with the inductance of 2mH.

1

2

3

4

5


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C = pF; f = Hz;

2.(14) The concentrtation of conductance electrons in germanium at room temperature is n = 1019 m-3.

What is the persentage P of conductance electrons out of all Ge atoms.

P = %;

3.(21) The potential is given by 1.5*10

13

x

2

volts. The charge in semiconductor is due to a uniformdistribution of singly charged carriers. Find the concentration of carriers and space-charge density.

Indicate the polarity of carriers (electrons or holes). Take the dielectric constant as 12.

N = cm-3 ; = C/m3; Polarity =;


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4.(15) A semiconductor is doped with Nd and has a resistance R1 ( Nd >> ni). The same semiconductor is

then doped with an unknown amount of acceptors Na (Na >> Nd), yielding a resistance of 0.5 R1. Find Nain terms of Nd if Dn / Dp = 50.

Na = Nd.

5.(30) An ideal MOS capacitor has a 10 nm thick SiO2 layer and a p-type Si with Na = 10

16

cm

-3

. Itoperates under moderate inversion. Find: a) depletion layer width; b) voltage for moderate inversion;

c) bulk charge; d) threshold voltage; e) oxide capacitance; f) total capacitance; Take kT/q = 0.0259 v.

a) m; b) V ; c)C/cm2;

d) VT = V ; e) F/cm2; f)

F/cm2;


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EEE-210 Physical Electronics 2003-04First Midterm Exam. 08.04.2004, 100 min. 100 points, 5 questions, 7 pages.



partial credits.

SURNAME . . . . . . . . . . NAME . . . . .

1.(30) The density of state related effective mass of electrons and holes in Si are 1.08 m oand 0.56 mo, respectively. The electron and hole mobilities at the temperature 250 Kare

1500 and 500 cm2 V-1s-1, respectively. If the band gap energy at T = 0 K is Eg(0) = 1.17

ev, find its value at 250 K with the precision of three significant digits. Take the material constants as

= 4.73*10-4 /K2, = 636 K. Calculate the effective density of states Nc and Nv , intrinsic concentration ni and

intrinsic resistivity of Si at 250 K.

Eg (250) = ev; Nc = cm-3; Nv = cm

-3;

ni = cm-3

; = cm;

1

2

3

4

5


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2.(20) A uniformly doped n-type silicon semiconductor with 1016 donor atoms per cm3 is subjected

to a boron diffusion with a constant surface concentration of 5*1018 cm-3. It is desired to to form a

pn-junction at a depth of 2.7 m. At what temperature should this diffusion be carried out if it is tobe completed in 2 hours? Find the diffusivity.

D = cm2/s; T = K;


mean thermal velocity is 4.125*105 m/s, find the electron mobility. Under what electric field the drift

velocity of electron would be equal to the mean thermal velocity.

= m2V-1s-1 ; E= V/m ;


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4.(21) a) Calculate the conductivity and quasi-Fermi levels for silicon sample with Nd = 1015 cm-3, p = 1

s, and GL = 5*1019 cm-3s-1. b) Find the value of GL that produces 10

15 holes/cm3. What are in this case the

conductivity and quasi-Fermi levels?

a) = ( cm)-1; Efn Ei = ev; Ei Efp = ev;

b) GL = cm-3s-1; = ( cm)-1;

Efn Ei = ev; Ei Efp = ev;


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5.(9) Give the definitions for the:

a. Hall multiplier

b. Degenerate semiconductor

c. Traps

EEE-210 Physical Electronics 2003-04Second Midterm Exam. 20.05.2004, 100 min. 100 points, 4 questions, 8 pages.



partial credits.

SURNAME . . . . . . . . . . NAME . . . . .

1.(20) A silicon Schottky-barrier diode has a contact area of 0.01 cm2, and the donor

concentration in the semiconductor is 1016 cm-3. Let o =0.7 V and VR=10.3 V.

Calculate

(a) the thickness xd of the depletion layer, (b) the barrier capacitance C, (c) the field strength at the

surface; (d) the field strength in the middle of the depletion layer.

(a) xd = cm; (b) C = pF;

(c) = V/cm; (d) = V/cm;

1

2

3

4


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2.(25) A silicon n-channel JFET has the following parameters: Na = 1018 cm-3, Nd = 10

15 cm-3, a = 2 m,

L = 20 m,, and W = 0.2 cm. Calculate (a) the built-in potential o, (b) the pinchoff voltages VPO and VP, (c)

the conductance Go, and (d) the actual channel conductance in the linear region with zero bias at the gate and

drain terminals. Take the mobility as n = 1000 cm

2

/Vs.

o = V; VPO = V; VP = V;

Go = S; gdl = S;


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3.(40) In a silicon pnp transistor, the doping concentrations for the emitter, base, and collector are 1019,

5*1017, and 1015 cm-3. The emitter and base widths are 1 and 0.7 m, respectively, and the diffusionlength is 10 m for both electrons and holes. The collector width is 50 m and the cross-sectional area

is 10-4

cm2

. If nE = 130 cm2

/V s; p = 250 cm2

/V s; nC = 1500 cm2

/V s, then calculate: a) emitterinjection efficiency; b) base transport factor; c) normal alpha; d) common emitter current gain; e)collector injection efficiency; f) inverse alpha; g) IE0; h) IC0; i) collector-emitter voltage VCE at saturation

at IC = 1 mA and IB = 100 A. Use four significant digits in answers.

a) = ; b) = ; c) =

;

d) = ; e) = ; f) =

;

g) IE0 = A ; h) IC0 = A ; i) VCE =V;


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4.(15) Give the definition for the:

a) electron affinity

b) Schottky barrier


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c) Heterojunction

d) Normally off or enhancement FET

e) Pinchoff curve

4.(15) Give the definition for the:

a) electron affinity

The electron affinity is the energy required to release an electron from the bottom of the conduction band to the vacuum level.

b) Schottky barrier

The Schottky barrier is the rectifying metal-semiconductor contact.

c) Heterojunction

A heterojunction is a junction formed by two semiconductor materials.

d) Normally off or enhancement FET

Normally off or enhancement FET is a FET with a lightly doped narrow channel in which the pinchoff happens at zero gate bias so

that it is necessary to apply a positive gate bias to induce a channel.


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e) Pinchoff curve

The pinchoff curve separates the linear and saturation regions in a junction field effect transistor.

EEE-210 Physical Electronics 2003-04

Final Exam. 9.06.2004, 120 min. 100 points, 6 questions, 8 pages. Calculationsshould be done in detail, step by step. Results are valid until the first error.

Answers should be filled in the blanks, otherwise they are not valid. No partial

credits.

SURNAME . . . . . . . . . . NAME . . . . .

1.(20) If we apply 500 mV to the contacts 3 and 4 of a semiconductor bar of a given

sizes

(50 mil * 10 mil * 4 mil), the current of 1 mA would flown through it. When additionally

we turn on the magnetic field of Bz = 10

-4

Wb/cm

2

, then the induced Hall voltage is 10 mV. Find the dopingconcentration n and taking into account the presence of the ionized impurity scattering calculate the mobility of electrons. 1 mil = 1 inch*10-3.

n = cm-3; = cm2/V s;

1

2

3

4

5

6


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2.(10) Sketch the two-dimensional diagram of a silicon lattice if you project all the atoms onto (a) the (111)

plane,

(b) the (110) plane.

3.(15) Determine the resistance to the lateral current flow of thin film semiconductor stripes of dimension

(length*width) 100*10 microns; 200*20 microns; 100*6 microns, if the sheet resistance is 60 ohms/unit

area.

R100*10 = ; R200*20 = ; R100*6 = ;


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4.(11) If the lattice constant of silicon were 0.700 nm what would be the density of valence electrons.

The density of valence electrons = cm-3;

5.(20) In n-type germanium with ni = 2.5 * 1019 m-3 and ND = 10

22 m-3, a flash of light doubles the hole

number

density. Calculate the generation rate GL and the time t taken for the hole density to decay to 8 * 1016 m-3 if

the hole lifetime is 3 ms.

t = ms; GL = m-3s-1;


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6.(24) (a) Sketch the energy band diagram for an ideal Schottky barrier with q m = 4.8 eV and q s = 4.05 eV.For Nd = 10

15 cm-3 calculate: (a1) the barrier height, (a2) the built-in potential, and (a3) the space charge width.

(b) Repeat (a) for Na = 1015 cm-3. Take kT = 0.026 eV. Use three significant digits and indicate all the

physical designations in answers. Show all numerical data on the pictures.

(a1) = eV; (a2) = V; (a3) =

m ;(b1) = eV; (b2) = V; (b3) =

m ;


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EEE-210 Physical Electronics 2004-05First Midterm Exam. 05.04.2005, 100 min. 100 points, 6 questions, 8 pages. Calculations

should be done in detail, step by step. Results are valid until the first error. Answers

should be filled in the blanks, otherwise they are not valid. No partial credits. Indicate

all data taken from formula sheet.

SURNAME . . . . . . . . . . NAME . . . . .

1.(16) In gallium arsenide both Nc and Nv vary with temperature. Assuming the bandgap

energy is 1.42 eV and does not vary with temperature over the range of T = 300 K and T =

450 K calculate the intrinsic carrier concentration at these temperatures. Take kT (300 K) =

0.0259 eV.

a) ni(300 K) = cm-3; b) ni(450 K) = cm

-3;

1

2

3

4

56


55/57

2.(12) A silicon wafer is doped with 1015phosphorus atoms/cm -3. Determine the probability P that an energy

level 3 kT above the Fermi energy is occupied by an electron at: a) T = 300 K; b) T = 250 K.

a) P300K = %; b) P250K = %;

3.(15) Consider silicon at T = 300 K. The Fermi energy is 0.25 eV below the conduction band. Calculate the

intrinsic carrier concentration (ICC) and the thermal equilibrium concentration of ionized donor and acceptor

atoms.

Nd = cm-3; Na = cm

-3; (ICC) =

cm-3;


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4.(20) A uniformly doped n-type silicon semiconductor with 1016 donor atoms per cm3 is subjected to a

boron diffusion with a constant surface concentration of 5*1018 cm-3. It is desired to to form a pn-junction

at a depth of 2.7 m. At what temperature should this diffusion be carried out if it is to be completed in 2hours? Find the diffusivity.

D = cm2/s; T = K;


mean thermal velocity is 4.125*105 m s-1, find the electron mobility. Under which electric field the drift

velocity of electron would be equal to the thermal velocity.

= m2V-1s-1 ; E= V/m ;


57/57

6.(21) In a silicon pn junction at T = 300 K the intercept of the curve per each 1 cm2 of area gives 0 =

0.855 volt. The slope is 1.32*1015 F-2V-1. Calculate the net concentration of impurities in both sides of

junction. Can we assume that the junction is oris not one sided? Describe why? Underline thenecessary. Take kT (300 K) = 0.0259 eV.

a) Na = cm-3

; b) Nd = cm-

3;

c) The junction is one sidedno

yes

eee210( physical electronic)

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