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计算代写-PX4131/PXT301

时间：2021-01-20

PX4131/PXT301

1

CARDIFF UNIVERSITY

EXAMINATION PAPER

Academic Year:

2018-2019

Examination Period:

Autumn

Examination Paper Number:

PX4131/PXT301

Examination Paper Title:

Semiconductor Fabrication

Duration:

1 Hour

Do not turn this page over until instructed to do so by the Senior Invigilator

Structure of Examination Paper:

There are five pages.

There are three questions in total.

There are no appendices.

The maximum mark for the examination paper is 50 (50% of the module mark) and the mark

obtainable for a question or part of a question is shown in brackets alongside the question.

Students to be provided with:

The following items of stationery are to be provided:

1 answer book.

The following books are to be provided:

Mathematical Formulae and Physical Constants.

Instructions to Students:

Answer TWO questions. If an additional question is attempted, be clear which should be marked,

otherwise only the first two written answers will be marked.

Calculators which have been pre-programmed and calculators with an alphabetical keyboard are not

permitted in any examinations.

The use of translation dictionaries between English, Welsh and/or other languages, bearing an

appropriate departmental stamp, is permitted in this examination.

PX4131/PXT301

2

Useful formulae. Note that many of these equations are specific to their particular applications.

Variables may mean different things depending on the context.

= + ×

() = (0) −

2

+

= exp (

2

)

=

(∗ − )

0

= −

//

∗

=

Δ//

Δ∗

=

= 2//

2 1 +

1 −

sin =

=

−1

=

0.6

= 0.9 (

)

3

2

1 =

2 =

2

= {exp (

) − 1}

Γ =

√2

=

Γ

22

()

= −()

= exp (−

)

() = 0 exp(−)

=

1

2

3

=

Δ

=

1.2

√

=

ln

ln

= |log (

2

1

)|

−1

=

2 sin

() =

1

(1 + )

(

1

2

exp [−

2

2

] +

2

exp [−

2

2

])

< > =

2

( + )2

Δ

=

< >

4

√

8

=

0

≈ (

)

4

PX4131/PXT301

3

1. GaAs InP

Crystal structure zinc-blende zinc-blende

Lattice constant (nm) 0.565 0.587

Poisson’s ratio 0.31 0.36

(a) Molecular beam epitaxy can be used to grow thin films of a semiconductor. Briefly explain

the molecular beam epitaxy procedure. Briefly outline the advantages of molecular beam

epitaxy over other epitaxial growth methods such as MOCVD.

[3]

(b) What is the definition of the critical thickness when growing an epitaxial layer?

[1]

(c) Refer to the table above.

(i) Briefly explain what a zinc-blende structure is.

[1]

(ii) Calculate the length of the Ga-As bond.

[1]

(iii) Calculate the length of the In-P bond.

[1]

(d) What is the lattice mismatch between InP and GaAs?

[1]

(e) In the epitaxial growth of InP on a GaAs substrate, the indium K-cell is maintained at a

temperature of 1000°C. A calibration procedure measures the mass loss as Δ = 30 mg

over a duration Δ of 6 hours when the circular aperture is opened to a diameter d of

2.0 mm. Note: the atomic mass of indium is = 114.8 g/mol.

(i) Given that the total mass loss is Δ = ΓΔ (where Γ is the effusion flux and is the

mass of one indium atom), show that the partial pressure of indium in the K-cell is

given by

=

4Δ

2Δ

√

2

where = 8.314 J/mol/K is the universal gas constant. Use this formula to estimate

the partial pressure of indium in the K-cell.

[5]

(ii) Estimate the indium atom flux for a sample placed 8 cm away. What are the

assumptions involved in your calculation?

[3]

(iii) Assuming pseudomorphic growth, estimate the growth rate.

[6]

(iv) Comment on this growth rate. How would you increase the growth rate? What are

the limits?

[3]

PX4131/PXT301

4

2. (a) Define what is meant by the sensitivity of a resist used in electron beam lithography.

Estimate the dwell time or exposure time for a pattern with a total exposed area of 3 cm2 if

the beam current is 0.2 A and the resist sensitivity is 25 C/cm2.

[3]

(b) A certain device requires a minimum feature size of 13 nm. If the electron beam has a

diameter at the focus of 5 nm and an energy of 30 keV, what is the maximum resist

thickness that can be used?

[6]

(c) The point scattering function describing the two dominant electron scattering processes in

a resist is

() =

1

(1 + )

(

1

2

exp [−

2

2

] +

2

exp [−

2

2

])

For a certain resist/substrate combination, the parameters in the above function are =

93 nm, = 1.306 m and = 1.4.

Name and briefly describe the two processes.

Which of the two processes contributes the most to the proximity effect?

[5]

(d) A device requires two identical small features to be written in close proximity, with a

300 nm centre-to-centre separation.

The proximity effect correction can be framed as a set of simultaneous equations in matrix

form:

(

1

2

) = (

11 12

21 22

) (

1

2

)

1,2 is the intended exposure dose to each feature for correct writing.

1,2 is the corrected exposure dose to adjust for the proximity effect.

are the proximity interaction matrix elements.

Assuming each of the features is written in a point-like exposure, give an expression for,

and calculate the values of, 11, 12, 21 and 22.

[5]

(e) By solving the simultaneous equation in part (d), or otherwise, show that the dose factor

(relative to the uncorrected dose 0) required for each of the features to correct for the

proximity effect is given by

1

0

=

11

11 + 12

Use your values of 11 and 12 from above to give a value for the proximity effect corrected

dose factors.

[6]

PX4131/PXT301

5X

3. (a) Define what is meant by a positive tone resist. Provide an example of a positive tone

resist.

[2]

(b) A certain semiconductor resist combination has a selectivity under reactive ion etching of

0.8. Give the definition of the selectivity. Calculate the maximum etch depth into the

semiconductor if the resist thickness is 200 nm.

[2]

(c) What is a hard mask, and when might its use be considered?

[2]

(d) What is a plasma? Briefly describe the properties of a plasma used during reactive ion

etching.

[3]

(e) Which process will generally give higher etch rates: capacitively coupled plasma etching or

inductively coupled plasma etching? Briefly explain the difference(s) that allow the higher

etch rate.

[4]

(f) Trimethylaluminium (TMAl) and water are used in the atomic layer deposition of

aluminium oxide (Al2O3). Using diagrams briefly outline this atomic layer deposition

process.

[4]

(g) The rate of change of concentration of surface hydroxyl groups in the first step is

proportional to the concentration of surface hydroxyl groups:

= −1

where the reaction rate coefficient depends on the chemical activation energy

1 = exp (−

1

)

Write down the solution for COH as a function of time.

[1]

(h) In the first step, the reaction rate is measured to drop to half its initial value after 0.08 s.

What length of time is required for the reaction to complete such that only 1 in 106 surface

OH groups remain?

[3]

(i) In the second step, the reaction rate is measured to drop to half its initial value after 0.06s.

What is the difference between the chemical activation energies of the two steps 2 – 1?

Show your working and provide a numerical answer. You may assume that the reaction

conditions between the steps are constant, and the temperature is 300K.

[4]

1

CARDIFF UNIVERSITY

EXAMINATION PAPER

Academic Year:

2018-2019

Examination Period:

Autumn

Examination Paper Number:

PX4131/PXT301

Examination Paper Title:

Semiconductor Fabrication

Duration:

1 Hour

Do not turn this page over until instructed to do so by the Senior Invigilator

Structure of Examination Paper:

There are five pages.

There are three questions in total.

There are no appendices.

The maximum mark for the examination paper is 50 (50% of the module mark) and the mark

obtainable for a question or part of a question is shown in brackets alongside the question.

Students to be provided with:

The following items of stationery are to be provided:

1 answer book.

The following books are to be provided:

Mathematical Formulae and Physical Constants.

Instructions to Students:

Answer TWO questions. If an additional question is attempted, be clear which should be marked,

otherwise only the first two written answers will be marked.

Calculators which have been pre-programmed and calculators with an alphabetical keyboard are not

permitted in any examinations.

The use of translation dictionaries between English, Welsh and/or other languages, bearing an

appropriate departmental stamp, is permitted in this examination.

PX4131/PXT301

2

Useful formulae. Note that many of these equations are specific to their particular applications.

Variables may mean different things depending on the context.

= + ×

() = (0) −

2

+

= exp (

2

)

=

(∗ − )

0

= −

//

∗

=

Δ//

Δ∗

=

= 2//

2 1 +

1 −

sin =

=

−1

=

0.6

= 0.9 (

)

3

2

1 =

2 =

2

= {exp (

) − 1}

Γ =

√2

=

Γ

22

()

= −()

= exp (−

)

() = 0 exp(−)

=

1

2

3

=

Δ

=

1.2

√

=

ln

ln

= |log (

2

1

)|

−1

=

2 sin

() =

1

(1 + )

(

1

2

exp [−

2

2

] +

2

exp [−

2

2

])

< > =

2

( + )2

Δ

=

< >

4

√

8

=

0

≈ (

)

4

PX4131/PXT301

3

1. GaAs InP

Crystal structure zinc-blende zinc-blende

Lattice constant (nm) 0.565 0.587

Poisson’s ratio 0.31 0.36

(a) Molecular beam epitaxy can be used to grow thin films of a semiconductor. Briefly explain

the molecular beam epitaxy procedure. Briefly outline the advantages of molecular beam

epitaxy over other epitaxial growth methods such as MOCVD.

[3]

(b) What is the definition of the critical thickness when growing an epitaxial layer?

[1]

(c) Refer to the table above.

(i) Briefly explain what a zinc-blende structure is.

[1]

(ii) Calculate the length of the Ga-As bond.

[1]

(iii) Calculate the length of the In-P bond.

[1]

(d) What is the lattice mismatch between InP and GaAs?

[1]

(e) In the epitaxial growth of InP on a GaAs substrate, the indium K-cell is maintained at a

temperature of 1000°C. A calibration procedure measures the mass loss as Δ = 30 mg

over a duration Δ of 6 hours when the circular aperture is opened to a diameter d of

2.0 mm. Note: the atomic mass of indium is = 114.8 g/mol.

(i) Given that the total mass loss is Δ = ΓΔ (where Γ is the effusion flux and is the

mass of one indium atom), show that the partial pressure of indium in the K-cell is

given by

=

4Δ

2Δ

√

2

where = 8.314 J/mol/K is the universal gas constant. Use this formula to estimate

the partial pressure of indium in the K-cell.

[5]

(ii) Estimate the indium atom flux for a sample placed 8 cm away. What are the

assumptions involved in your calculation?

[3]

(iii) Assuming pseudomorphic growth, estimate the growth rate.

[6]

(iv) Comment on this growth rate. How would you increase the growth rate? What are

the limits?

[3]

PX4131/PXT301

4

2. (a) Define what is meant by the sensitivity of a resist used in electron beam lithography.

Estimate the dwell time or exposure time for a pattern with a total exposed area of 3 cm2 if

the beam current is 0.2 A and the resist sensitivity is 25 C/cm2.

[3]

(b) A certain device requires a minimum feature size of 13 nm. If the electron beam has a

diameter at the focus of 5 nm and an energy of 30 keV, what is the maximum resist

thickness that can be used?

[6]

(c) The point scattering function describing the two dominant electron scattering processes in

a resist is

() =

1

(1 + )

(

1

2

exp [−

2

2

] +

2

exp [−

2

2

])

For a certain resist/substrate combination, the parameters in the above function are =

93 nm, = 1.306 m and = 1.4.

Name and briefly describe the two processes.

Which of the two processes contributes the most to the proximity effect?

[5]

(d) A device requires two identical small features to be written in close proximity, with a

300 nm centre-to-centre separation.

The proximity effect correction can be framed as a set of simultaneous equations in matrix

form:

(

1

2

) = (

11 12

21 22

) (

1

2

)

1,2 is the intended exposure dose to each feature for correct writing.

1,2 is the corrected exposure dose to adjust for the proximity effect.

are the proximity interaction matrix elements.

Assuming each of the features is written in a point-like exposure, give an expression for,

and calculate the values of, 11, 12, 21 and 22.

[5]

(e) By solving the simultaneous equation in part (d), or otherwise, show that the dose factor

(relative to the uncorrected dose 0) required for each of the features to correct for the

proximity effect is given by

1

0

=

11

11 + 12

Use your values of 11 and 12 from above to give a value for the proximity effect corrected

dose factors.

[6]

PX4131/PXT301

5X

3. (a) Define what is meant by a positive tone resist. Provide an example of a positive tone

resist.

[2]

(b) A certain semiconductor resist combination has a selectivity under reactive ion etching of

0.8. Give the definition of the selectivity. Calculate the maximum etch depth into the

semiconductor if the resist thickness is 200 nm.

[2]

(c) What is a hard mask, and when might its use be considered?

[2]

(d) What is a plasma? Briefly describe the properties of a plasma used during reactive ion

etching.

[3]

(e) Which process will generally give higher etch rates: capacitively coupled plasma etching or

inductively coupled plasma etching? Briefly explain the difference(s) that allow the higher

etch rate.

[4]

(f) Trimethylaluminium (TMAl) and water are used in the atomic layer deposition of

aluminium oxide (Al2O3). Using diagrams briefly outline this atomic layer deposition

process.

[4]

(g) The rate of change of concentration of surface hydroxyl groups in the first step is

proportional to the concentration of surface hydroxyl groups:

= −1

where the reaction rate coefficient depends on the chemical activation energy

1 = exp (−

1

)

Write down the solution for COH as a function of time.

[1]

(h) In the first step, the reaction rate is measured to drop to half its initial value after 0.08 s.

What length of time is required for the reaction to complete such that only 1 in 106 surface

OH groups remain?

[3]

(i) In the second step, the reaction rate is measured to drop to half its initial value after 0.06s.

What is the difference between the chemical activation energies of the two steps 2 – 1?

Show your working and provide a numerical answer. You may assume that the reaction

conditions between the steps are constant, and the temperature is 300K.

[4]