1. Which of the following best describes the meaning of population inversion?
A The incident photons’ frequency is the same as the frequency of the stimulated photons.
B An atom in an excited state undergoes a transition to the ground state and emits a photon.
C The number of electrons at a lower energy level exceeds the number of electrons at a higher
D The number of electrons at a higher energy level exceeds the number of electrons at a lower
2. Which of the characteristic below describes the energy band structure of a typical semiconductor?
valence band energy gap / eV conduction band
A completely filled 1 eV almost filled
B completely filled 1 eV almost empty
C partially filled 10 eV almost empty
D partially filled 10 eV almost filled
3. (a) (i) With reference to conduction electrons and holes, explain why electrons in solids are
represented by energy bands, whereas those in isolated gas atoms are be
represented by energy levels. 
(ii) Using band theory, explain how p-type and n-type extrinsic semiconductors are
produced from intrinsic semiconductors for better electrical conduction.
Hint: You may draw relevant diagrams to help you in your explanations. 
(iii) Fig 7 shows a p-type semiconductor placed in contact with another of n-type.
1. Explain how a depletion region is formed between the n- and p-type.
Hint: You may draw relevant diagrams to help you in your explanations. 
2. Explain how the depletion layer acts as a rectifier. 
4. In the action of a laser, population inversion refers to
A the rate of stimulated emission being smaller than the rate of absorption.
B more atoms in a high energy state than in a lower one.
C photons causing other photons of the same frequency to be emitted from excited atoms.
D charged particles causing light to be emitted from excited atoms.
5. The diagrams illustrate the conduction band (CB), forbidden band (FB), valence band (VB) and an
energy level of different materials.
Which diagram depicts a semiconductor doped with boron?
6. Which of the following statements about a semiconductor diode in forward bias is incorrect?
A The applied potential difference from the source of e.m.f. opposes the junction potential.
B Electrons and holes are urged away from the p-n junction.
C The n-type material of the diode is connected to the negative terminal of the source of e.m.f.
D Electrons in the n- type side of the diode will cross steadily to the p- type side.
7. Junjie tried to build a laser himself and failed for the hundredth time. Which of the following is not a
possible reason for failing to achieve lasing?
A Population inversion failed to take place.
B The mirrors were misaligned such that stimulation emission did not occur.
C The absence of a metastable state prevented stimulation emission from taking place.
D The potential difference applied was too high and prevented spontaneous emission from
emitting the correct wavelength.
8. (a) Explain why population inversion is important in lasers. 
(b) Light emitting diodes of different colours can be produced using semiconductor materials with a
small band gap. A p-n junction is made using doped semiconductors to produce the light
emitted by the diodes.
(i) Describe how a band gap is formed in a semiconductor. 
(ii) Explain how doping affects the conduction properties of a p-type semiconductor. 
(iii) Describe how a depletion region can be formed at a p-n junction. 
9. (a) One property of a laser is that it can direct a large amount of energy to a very small spot. In
one particular application, the laser emits a 3.0 mJ pulse in 1.0 ns, focused to a spot 8.0 × 10
in area. Calculate the power per unit area at the target. 
(b) Using the ideas of population inversion and stimulated emission, explain how a laser could
deliver an intense and directed light beam. 
10. Solar cells are p-n junctions which can convert solar energy into electrical energy. The basic principle of
a solar cell can be summarized in two sentences:
1. Incident photons arriving at the depletion region are absorbed to generate electron-hole pairs
2. The electron-hole pairs generated in the depletion region are immediately swept by the internal
electric field from the depletion region into the neutral regions giving rise to a current through
an external load.
(a) With the help of a clearly labelled energy band diagram, explain how a photon arriving
at the depletion region is able to generate an EHP. 
(b) Shade the region in Fig. 5 where the positive fixed ions reside. 
(c) Indicate using arrows in Fig. 5, the directions of the electric forces experienced by the
electron-hole pair in the depletion region. 
(d) Hence deduce and indicate in Fig. 5 the direction of current through the external load.
11. Which of the following statements about LASER is incorrect?
A Laser light is highly monochromatic.
B Laser light is coherent and cannot be diffracted.
C Laser light occurs when there is a population inversion between two atomic levels.
D Laser light is due to stimulated emission.
12. At room temperature, the charge carriers inside a p-type semi-conductors are
A holes only.
B free electrons only.
C positive ions.
D both holes and free electrons.
13. (a) (i) To produce laser light the following conditions must be satisfied:
1. The higher of two energy states must be metastable. 
2. A population inversion must exist between the two states. 
Explain the meaning of the terms in italics.
(ii) An atom has two energy levels with a transition wavelength of 632.8 nm. There are
7.0 × 10
atoms pumped into the upper state with 4.0 × 10
atoms in the lower state.
Assuming that the emission of a single laser pulse stops when the two energy levels
have equal numbers of atoms, how much energy could be released in a single laser
(iii) The He-Ne laser emits light at a wavelength of 632.8 nm and has an output of 2.3 mW.
How many photons are emitted each minute by this laser when it is operating? 
(iv) The He-Ne laser with a beam aperture of diameter 12 cm is aimed at the moon 3.8 ×
m away from the Earth. The laser beam will spread due to diffraction effects when
it emerges from the aperture. The angular location of the edge of the central diffraction
is given by
where d is the diameter of the beam aperture.
What is the diameter of the laser beam at the Moon’s surface? 
[ Take sin θ ≈ tan θ, for small values of θ ]
(b) (i) With the help of suitable energy diagrams, explain the difference in electrical
conductivity of metals and that of intrinsic semiconductors using the band theory of
(ii) The process of adding impurities, also known as doping can change the conductivity
of an intrinsic semiconductor. Describe using suitable diagrams, the formation of an n-
type semiconductor. 
14. In a stimulated emission of a photon, as shown in Fig. 37.1 below, which of the following statements is
A The electron in the excited state de-excites to the ground state in a random process and
produce an photon of energy E1.
B An incident electron of energy E1 moves pass the excited atom. The atom then de-excites to
give off an electron of energy E1. The incident electron is being absorbed by the atom.
C An incident photon of energy E1 moves pass the excited atom. The atom then de-excites to
give off a photon of energy E1 which moves together with the incident photon with the same
D An incident electron of energy E1 moves pass the excited atom. The atom then de-excites to
give off a photon of energy E1 – E which moves together with the incident electron with the
same phase, where E is the kinetic energy of the incident electron.
15. Which of the following statements about laser is false?
A The laser beam is monochromatic if there is only one laser transition.
B The laser beam is extremely unidirectional.
C The dispersion of a laser beam is due to diffraction around the edge of the aperture.
D All photons in the laser cavity are generated by stimulated emission.
16. (a) A person’s vision may be improved significantly by having the corneal reshaped with a laser
beam, in a procedure known as photorefractive keratectomy. The excimer laser used in these
treatments produces UV radiation of wavelength 193 nm.
(i) What is the energy difference between the two levels that participate in the stimulated
emission in the laser? 
(ii) How many photons from this laser are required to deliver 1.58 x 10
J of energy? 
(b) Electromagnetic radiation can promote an electron from the top of a nearly complete valence
band to the bottom of an unfilled conduction band. The lowest frequency for this to be possible
is 2.75 x 10
Hz for Si and 1.79 x 10
Hz for Ge at room temperature. Calculate the energy
gap between the valence and conduction bands for Si and Ge. 
(c) Explain how the depletion region in a p-n junction is formed. 
(d) (i) The tip of a STM probe is positioned at a distance d from a sample surface which has
a work function energy of 6.0 eV. Find the value of d at which the tip-surface
transmission coefficient T is 0.0001. 
(ii) An electron with de Broglie wavelength λ = 0.10 nm has an uncertainty in momentum
of Δp = 6.6 × 10
kg m s
. What is the uncertainty in the electron’s wavelength? 
17. Which statement about conduction of electricity in semiconductors is correct?
A The presence of impurities in a semiconductor is used to decrease its resistance.
B In a semiconductor, there is a large energy gap between the conduction and valence bands.
C At low temperatures, free electrons are found both in the conduction band and in the valence
D In an intrinsic semiconductor, electrons travel in the same direction as the holes.
18. When a p-n junction is under reverse bias mode, the width of the depletion region will be increased.
Which of the following statements is true?
A The applied voltage moves the electrons from n-type region to p-type region.
B The applied voltage moves the holes from p-type region to n-type region.
C The applied voltage drives the electrons towards n-type region.
D The applied voltage drives the holes towards n-type region.
19. Figure 6.1 illustrates the upper energy bands in two different classes of solid at absolute zero. The
shaded areas represent occupied electron energy levels.
(a) State the classes of solids for X and Y. 
(b) At absolute zero, which solids, X or Y, will conduct electricity? Explain your choice using band
(c) At higher temperatures, solid X conducts electricity. Explain, using band theory, why this is so.
20. In a piece of n-type silicon,
A the number of electrons in the valence band exceeds the number of holes in the
B the number of holes in the valence band is less than the number of electrons in the
C conduction is due to electrons only and the conduction and valence bands overlap.
D the impurity element with which silicon is doped has fewer valence electrons than
21. Which of the following statements is not related to laser production?
A Light amplification
B Stimulated emission
C Population inversion
D Electron deceleration
22. Electric currents in semiconductors are considered to be due to the motion of electrons and holes. Holes
A atomic vacancies.
B positively charged electrons.
C positive ions.
D electronic vacancies in atoms.
23. When a beam of laser is shown on to a vertical slit as shown in Fig. 1, we can see a spot of light on the
screen as expected. As the slit is made narrower and narrower, the spot of light becomes wider and
wider in the X direction.
(a) By considering the laser beam as an electromagnetic wave, explain the phenomenon using wave
(b) By considering the laser beam as consisting of a stream of photons, use Heisenberg Uncertainty
Principle to explain this phenomenon. 
(c) A laser beam of wavelength 635 nm is used in the above experiment. Find the momentum of a
photon in this laser beam. 
(d) If the width of the slit is 2.0 x 10
m, and the uncertainty x of the position of a photon passing
through the slit is approximately of the same value, calculate the uncertainty of the momentum px
of the photon using the following Heisenberg uncertainty equation: x
x p h . 
Image when slit is wide
Image when slit is made
narrower and narrower
(e) Find sin using the results from (c) and (d). 
(f) In wave theory, the angle of such single slit diffraction experiment is given by
sin where a is the width of the slit
and is the wavelenght of the light.
Calculate the angle using this equation. 
(g) Comment on your answers obtained in (e) and (f). 
24. (a) A three-level laser system is shown in Fig. 4.1, where E2 is the meta-stable state.
(i) Explain what is meant by meta-stable state. 
(ii) Using Fig. 4.1, explain the action of a laser in terms of population inversion and stimulated
(iii) A four-level laser system is shown in Fig. 4.2. A student commented that this system is more
efficient than a three-level laser system.
Explain why the student is correct. 
(b) (i) On Fig. 4.3, draw and label clearly the changes to the band diagrams for semiconductors due to n- and p-
type doping. 
(ii) Using Fig. 4.3, explain how the n-type doping changes the conduction property of a semiconductor.
(iii) What is the difference between n- and p-type semiconductors in terms of conduction?
25. In comparing a semiconductor and an insulator, what are the relative dimensions of the energy gaps of
the semiconductor and the insulator?
A Narrow Narrow
B Narrow Wide
C Wide Narrow
D Wide Wide
26. What is the overall electrical charge of the isolated n-type semiconductor?
A Depending upon the balance of electrons, it will be positive or negative
27. In the production of laser light, atoms are excited to energy level E4 using light of wavelength 550 nm.
After which it falls to its metastable state at energy level E3. Population inversion is achieved between
energy levels E2 and E3. What is the wavelength, λ of the laser light emitted?
A 550 nm B 598 nm C 694 nm D 772 nm
28. Which of the following statements below on intrinsic semiconductors is true?
A The total current flow is the sum of both ‘hole’ and ‘electron’ currents.
B The valence band is completely filled and the conduction band is partially filled.
C There are more electrons in the conduction band than there are holes in the valence band.
D The valence band is completely filled and the conduction band is empty at room temperature.
29. (a) A laser constructed of the semiconductor Gallium Aluminium Arsenide (GaAlAs) can continuously
deliver 5.0 mW of power at a wavelength of 0.80 μm.
(i) At what rate does it generate photons? 
(ii) State any two important conditions required to produce a laser beam. 
(b) Beryllium (Be) is the most common dopant in GaAlAs.
(i) With the help of the partial periodic table in Fig. 6, state if a n-type or p-type semiconductor will
be obtained. 
(ii) Explain how such a doped semiconductor in (b)(i) increases the electrical conductivity of
30. This question is about the charge carrier density of intrinsic silicon semiconductor.
The density of energy states in a semiconductor near the bottom of a band is similar to that of a free electron
gas but decreases back to zero at the top of a band. The energies at the top of the valence band and at the
bottom of the conduction band are EV and EC respectively with a band gap energy EG of 1.1 eV. The
probability of occupation of these energy states is governed by Fermi-Dirac distribution. The density of
energy states near the bottom of the conduction band is
(a) Sketch the density of states around the top of the valence band and the bottom of the conduction band.
Indicate the position of the Fermi level in your sketch. 
(b) The average thermal energy of electrons is kT where k is Boltzmann constant and T is the
(i) Explain why the number of electrons in the conduction band for an intrinsic semiconductor at
room temperature is very low. 
(ii) Show that at room temperature, the probability of occupation of the energy states in the
conduction band is 
(iii) On the sketch you have made in (a), sketch how the states in the conduction band will be
(iv) Given that
show that the number density of electrons in the conduction band is
(v) Determine the number density of electrons in the conduction band at room temperature of 300
31. In a p–n junction, free electrons near the junction in the n–type material diffuse across the junction into
the p–type material. Diffusion occurs because
A the concentration of free electrons in n–type material is small and in p–type material is large.
B the concentration of free electrons in n–type material is large and in p–type material is small.
C the small potential across the depletion layer cause electrons to diffuse continuously across the
D of different thermal agitation of atoms in the n–type and p–type material.
32. (a) Explain how stimulated emission accounts for the properties of laser.
(b) Describe, with an appropriate energy level diagram, the production of lasers.
(c) A diode can be formed by joining a p-type semiconductor and an n-type semiconductor, to form a p-n
junction. Explain the formation of the depletion layer in the diode and state the effect of reverse-bias
condition on the depletion layer.
33. (a) Give two reasons why a 1 W laser may appear brighter than a 10 W filament lamp. 
(b) Draw and label the energy band diagram for an intrinsic semiconductor at room temperature,
showing clearly how the bands might be filled. 
(c) Use the band theory to explain why the addition of a small concentration of boron (Group III element)
will decrease the resistivity of the semiconductor significantly. 
34. Why is laser light monochromatic?
A The atoms in the laser medium are in a state of population inversion.
B The excited atoms in the laser medium are in a metastable state.
C Photons which trigger off stimulated emission produce more photons of the same energy.
D The photons produced by stimulated emission are reflected back by the use of reflecting
mirrors in the laser system.
35. Metals and semiconductors have different electrical properties because semiconductors have
A more valence electrons
B a small energy band gap
C fewer valence electrons
D a higher atomic mass
36. Which of the statements is correct for a p-type semiconductor?
A There are excess holes in the valence band.
B There are excess holes in the conduction band.
C There are excess electrons in the conduction band.
D There are excess electrons in the valence band.
37. The addition of one part per million of arsenic will decrease the resistivity of silicon by a factor of 10
This dopped silicon is an n-type semiconductor.
(a) State two differences between p-type semiconductors and n-type semiconductor. 
(b) Explain, in terms of band theory, how doping in an n-type semiconductor increases its conductivity.
(c) Discuss with an aid of a diagram and using the idea of a depletion layer, how a p-n junction can act
as a rectifier. 
38. The diagram below shows the energy levels and electron transitions for the
He-Ne laser, which produces a bright red light. The helium atoms are used to
excite the neon atoms into excited states by collision.
Identify the metastable state and the laser transition.
Metastable State Laser Transition
A E2, He E3,Ne to E2,Ne
B E2, Ne E2,Ne to E1,Ne
C E3, Ne E3,Ne to E2,Ne
D E3, Ne E3,Ne to E1,Ne
39. Which of the following statements concerning a laser system is true?
A An external energy source is needed to create population inversion
because at thermal equilibrium, the electrons will occupy the lower
B High-end laser systems can produce perfectly collimated beams, i.e.
beams that would not spread.
C The laser beam achieves its brightness because of the two fully
reflecting mirrors placed at the ends of the tube containing the lasing
D The laser beam produced is coherent and of a single wavelength
because of spontaneous emission.
40. (c) Light from a laser is produced via stimulated emission, whereas
light from a fluorescent tube is produced via spontaneous emission. Compare the light from these two
sources in terms of phase difference and deduce the effect this has on the experimental setup for a
double-slit interference experiment using laser light.