Population inversion occurs when there are more atoms in the excited state than in the ground state. This is achieved through the following:

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1 Lasers and SemiconductorsTutorial Lasers 1. Fill in the table the differences between spontaneous emission and stimulated emission in atoms: External stimulus Direction of emission Phase & coherence of emitted photons Spontaneous Occurs naturally without any external stimulus. Photons travel in different directions. The photons produced from different spontaneous emissions have phases different from each other. Stimulated Occurs when stimulated by an incoming photon having the energy equivalent to that of the energy level transition. Photontravel in the same direction as the incoming photon. The photon produced from stimulated emissionis in phase with the incoming photon. Polarisation of emitted photons Photons have different planes polarization. Photons have the same plane of polarization. 2. What is population inversion and how can one achieve this? Population inversion occurs when there are more atoms in the excited state than in the ground state. This is achieved through the following: Energy pumped in E 3 Spontaneous emission E 2 Metastable state E 1 B19

2 i. The atoms involved must have a metastable state. ii. Energy is pumped into the system of atoms to bring them into level E 3, eg. through optical pumping (using lamps that produce light over all wavelengths) iii. The excited state is not stable, and some of the atoms fall spontaneously into the lower metastable state. iv. As the metastable state lasts much longer than normal excited states, many atoms will remain in this state. When there are more atoms in this state compared to the grounds state, population inversion is achieved. 3. Even though lasers are supposed to produce collimated light beams, a typical laser system may still produce a beam with some degree of divergence. What is the beam divergence caused by? As the beam exits the laser it undergoes diffraction and hence has some degree of spreading. Typically this beam divergence is as small as 0.05 o but even this small amount will be apparent if the beam travels long distances. 4. Why isstimulated emission important in the operation of a laser? Stimulated emission is important as this process produces photons which have the same frequency, direction and phase as the incoming photon, and thus the light produced travels in one direction and is coherent. B20

3 5. Why is a population inversionimportant in the operation of a laser? Population inversion is important so that there is a net emission of photons instead of absorption of photons. (If there are equal number of atoms in the ground and excited states, there is no net emission of photons. If there are more atoms in the ground state, there will be a net absorption of photons. ) Why is there a need for a metastable state in the operation of a laser? Since the lifetime of an atom in excited state is very short ( 10-8 s), spontaneous emission will take precedence over stimulated emission. For lasing action to take place there must be amplification of identical photons. Therefore to ensure that stimulated emission dominates over spontaneous emission, the upper lasing state must have a relatively long lifetime, ie be a meta-stable state so that population inversion can then be achieved. 6. Which of the following is not true regarding pumping in a laser? A The purpose of pumping is to maintain population inversion which is necessary for lasing. B Other than pumping by optical means, there are other ways such as electrically and chemically. C Due to the amplification effect, the output power of the laser will be greater than the input power during pumping. D In optical pumping, the light used should not have the same wavelength as the laser light to be produced. Answer: C B21

4 N08/I/38 7. In a helium-neon laser, helium atoms collide with neon atoms and excite them. This produces a population inversion which allows stimulated emission. Which neon energy level diagram correctly shows the excitation of the neon atoms by the helium atoms, the spontaneous infra-red emission from the neon, and the stimulated emission of red light? A B spontaneous emission stimulated emission excitation stimulated emission excitation spontaneous emission spontaneous emission C D spontaneous emission excitation stimulated emission excitation stimulated emission Answer: D B22

5 Energy Band Theory Electrons in an atom may only occupy permitted energy levels. In isolated atoms, there are distinct permitted levels. When 2 atoms come close to one another, each energy level splits into two. When the atoms of a metal are brought together in a periodic lattice to form the solid,the energy levels associated with each atom are changed because of the electronic interactions between the atoms. This process leads to a band of energies instead of a discrete energy for the atomic levels. Energy bands consisting of a large number of closely spaced energy levels exist in crystalline materials. The bands can be thought of as the collection of the individual energy levels of electrons surrounding each atom. B23

6 N10/I/37 1. Energy levels in low-pressure gases are represented as lines whereas in solids, the levels are shown as bands.what is responsible for the formation of bands? A B C D Atoms in solids are much closer together than those in gases. Atoms in solids are much denser than those in gases. Solids are better electrical conductors than gases. Solids are not fluids but gases are fluids. Answer: A When 2 atoms come close to one another, each energy level splits into two. When many atoms are close to each other, the energy levels form bands. 2. The diagram below shows the energy bands of sodium. In the boxes provided, identify which is the conduction band, the valence band, and the forbidden band gaps. Conduction band Forbidden band gaps Valence band N07/I/38 B24

7 3. The diagram illustrates the upper energy bands in two different classes of solid at absolute zero. The shaded areas represent occupied electron energy levels. solid X solid Y band P energy band Q What are bands P and Q, and what are the classes X and Y of the solids? band P band Q solid X Solid Y A conduction valence intrinsic semiconductor metal B conduction valence metal intrinsic semiconductor C valence conduction intrinsic semiconductor metal D valence conduction metal intrinsic semiconductor 3. Answer: B See summary. 4. a) The upper energy band of a metal is only partially filled with electrons; that is, the band does not contain the maximum number of electrons that can have energies in its range. How does this fact account for the ability of metals to conduct electric current? Due to the partially filled energy band, electrons are able to move to slightly higher energy levels due to thermal excitation. When an electric field is applied, the electrons are able to drift across the lattice of ions, occupying the unfilled energy levels in the partially filled band in each atom. The metal is thus able to conduct electric current. B25

8 (N12/III/5b) (See Question 6) B26

9 b) The resistance of a metal increases with increase of temperature. By making reference to band theory, account for this change [3] (N12/III/5b) A metal has low resistivity because it has either a partially filled valence band or the conduction band overlaps with the valence band. With some thermal energy, electrons are able to move easily into the unfilled energy levels. or Conduction band Filled valence band Forbidden band Filled energy band When the temperature of a metal increases, the lattice ions vibrate more and electrons collide more with the vibrating ions. This reduces the rate at which they drift across the metal. For the same pd applied, the current flow is smaller. Thus, the resistance of the metal increases. N09/I/38 5. Which statement about the energy bands in an ideal intrinsic semiconductor is correct? A The conduction band lies just below the valence band. B The number of electrons in the conduction band equals the number of holes in the valence band. B27

10 C There is an energy gap of 5 ev to 10 ev between the valence and conduction bands. D There is a small overlap between the valence and conduction bands. Answer: B A conduction band lies just above the valence band C energy gap is about 1 ev D there is an energy gap of about 1 ev 6. Describe, in terms of band theory, the conduction of electronsthrough an intrinsic semiconductor. (Specimen Paper 3, Q5a) For a semi-conductor, there is a small energy gap of about 1 ev between the filled valence band and the conduction band. Electrons at the top of the valence band can gain sufficient energy through thermal excitation to jump into the conduction band. This results in electrons in the conduction band and holes in the valence band as charge carriers. B28

11 When a potential difference is applied, the electrons and holes drift in opposite directions, producing a current flow. N07/I/37 7. Which statement about conduction of electricity in solids is correct? A Free electrons are found both in the conduction band and in the valence band. B In a metal, there is a large energy gap between the conduction and valence bands. C The presence of impurities in an intrinsic semiconductor is used to increase its resistance. D In an intrinsic semiconductor, electrons travel in the opposite direction to holes. A Free electrons are found both in the conduction band and in the valence band. No; only in the conduction band. B In a metal, there is a large energy gap between the conduction and valence bands. No. Metals either have the conduction band overlapping with the valence band, or have a partially filled valence band. C The presence of impurities in an intrinsic semiconductor is used to increase its resistance. Impurities in semiconductor is to increase its conductivity. D In an intrinsic semiconductor, electrons travel in the opposite direction to holes.yes. B29

12 8. What kind (p-type or n-type) of semiconductor is made if pure silicon (4 valence electrons) is doped with a small amount of (a) gallium (3 valence electrons) p-type semiconductor (b) antimony (5 valence electrons) n-type semiconductor 9(a) The effect of doping a group IV intrinsic semiconductor with group V donors is to add some energy levels in the band gap just below the conduction band. How do the additional donor energy levels help to increase the conductivity? Answer: - As there is only a small gap between the added energy level and the conduction band, electrons at the added energy level can easily jump to the conduction band through thermalexcitation to become free electrons. - These electrons become the majoritycharge carriers, and thus increase conductivity. B30

13 (b) Similarly, the addition of group III dopants lead to additional acceptor energy levels in the band gap just above the valence band. How do the additional energy levels help to increase the conductivity? Answer: As there is only a small gap between the added energy level and the valence band, electrons at the top of the valence band can easily jump to the added energy level through thermal excitation, resulting in holes in the valence band as the majority charge carriers. N07/II/5 10. A junction is formed between slices of p-type and n-type semiconductor material, as shown in Fig p-type material n-type material Fig (a) On Fig. 20.1, draw an arrow to show the direction of movement of electrons as the two slices are brought into contact. [1] B31

14 p-type material n-type material Fig (b) Describe the origin of the depletion region at the junction. [4] n-type semiconductor has a higher concentration of electrons while p-type semiconductor has a higher concentration of holes. When a p-type and n-type semiconductor are fused, electrons from the n-type migrate to the p-type, combine with the holes and produce a region with no charge carriers and a lattice of negative ions. p-type material - - n-type material Fig Holes near the junction from the p-type migrate to the n-type, combine with the electrons and produce a region with no charge carriers and a lattice of positive ions. At the junction, an electric field is set up. This electric field opposes further diffusion of electrons and holes across the junction. B32

15 (c) On Fig. 20.1, draw the symbol for a battery, connected so as to increase the width of the depletion region. [1] p-type material n-type material Fig B33

16 N08/I/ In the diagrams below, the symbols and represent the majority carriers in the p-type and n-type sides of a p-n junction.which pair of diagrams illustrates how a p-n junction acts as a rectifier? A voltage source _ p n _ conventional current _ p n nocurre nt B voltage source _ p n _ conventional current _ p n nocurre nt C voltage source _ p n _ conventional current _ p n nocurre nt D voltage source _ p n _ conventional current _ p n nocurre nt Answer: D B34

17 12. The resistivity of the intrinsic semiconductor silicon decreases from 400 Ωm at 20 o C to 40 Ωm at 60 o C. Which statement, using band theory, best explains the change in resistivity of silicon with increase in temperature? [N12/I/38] A. Conduction band electrons which carry current move faster B. More electrons can move through the valence band taking part in conduction C. More valence band electrons can be promoted to the conduction band D. The energy gap between the valence and conduction band decreases Answer: C B35

18 13. [N11/1/38] Answer: B _ F E I B B36

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