# Laser Diodes. Revised: 3/14/14 14: , Henry Zmuda Set 6a Laser Diodes 1

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1 Laser Diodes Revised: 3/14/14 14: , Henry Zmuda Set 6a Laser Diodes 1

2 Semiconductor Lasers The simplest laser of all. 2014, Henry Zmuda Set 6a Laser Diodes 2

3 Semiconductor Lasers 1. Homojunction Lasers 2. Heterojunction Lasers 3. Quantum Well Lasers 2014, Henry Zmuda Set 6a Laser Diodes 3

4 Homojunction Laser Unbiased In an unbiased equilibrium p-n junction, the Fermi level is constant with no current flowing. 2014, Henry Zmuda Set 6a Laser Diodes 4

5 Homojunction Laser Forward Biased When the junction is forward biased, the Fermi level splits because of the injection of minority carriers (electrons into the p region, holes into then region) and there exists a region near the junction where there is simultaneously a high density of electrons and a high density of holes. Because of the much higher mobility of electrons compared to that of holes, most of the injection is by electrons into the p region. These electrons recombine with the majority holes after diffusing a distance d which is more or less the diffusion length d: d = L n = Dτ 2014, Henry Zmuda Set 6a Laser Diodes 5

6 Homojunction Laser Forward Biased 2014, Henry Zmuda Set 6a Laser Diodes 6

7 Homojunction Laser For typical heavily doped GaAs: µ n = 600 cm 2 /V-sec (Mobility) D n = cm 2 /sec (Diffusivity) µ p = 30 cm 2 /V-sec D p = 0.78 cm 2 /sec Einstein Relation: d µ = kt e 2014, Henry Zmuda Set 6a Laser Diodes 7

8 Homojunction Laser What is the lifetime τ? Recall: dn dt = βnp + R Thus we see that the lifetime depends on the density of carriers. From the injected electrons perspective, once across the barrier they become a minority population, n p, in a sea of holes, p p. We can write: Thus: τ = 1 β p p dn p dt = βn p p p = n p τ 2014, Henry Zmuda Set 6a Laser Diodes 8

9 Homojunction Laser The lifetime depends on the doping of the device. A typical p-dopant density in a homojunction diode is approximately cm -3. As before, using β = 2 X 10-10, the effective lifetime for an injected electron is τ = 0.5 nsec This gives a diffusion distance L n equal to approximately 0.88 µm. 2014, Henry Zmuda Set 6a Laser Diodes 9

10 Homojunction Laser Thus the region of the inversion will be localized to a distance approximately 0.9 µm on the p-side of the junction. The injected electrons will, on average, recombine with holes within 0.5 nsec, only to be replaced by more electrons and holes flowing in from the surrounding regions of the junction. 2014, Henry Zmuda Set 6a Laser Diodes 10

11 Homojunction Laser As mentioned earlier, the homojunction laser has serious problems. Because the diffusion length of the injected current is controlled by recombination, there is little or no control over the dimensions of the gain region. The small gain region results in poor overlap of the spatial mode of the laser beam with the gain region. The wavelengths encountered in semiconductor lasers, generally 0.8 ~ 1.5 µm, will have spatial modes that are at least several wavelengths in diameter, which correspond to a larger area than provided by the pumped region of the pn junction. 2014, Henry Zmuda Set 6a Laser Diodes 11

12 Homojunction Laser 2014, Henry Zmuda Set 6a Laser Diodes 12

13 Homojunction Laser The poor overlap between the mode and the gain is not the most serious problem in the homojunction laser. The most significant problem is that the region outside of the inversion introduces a strong absorption loss. Remember that gain exists only for light with an energy slightly greater than the bandgap energy. When propagating through unpumped regions of the semiconductor, the same light will be absorbed, exciting electrons from the valence band up to the conduction band. 2014, Henry Zmuda Set 6a Laser Diodes 13

14 Heterojunction Laser The only way to get a homojunction laser to operate is to make the gain in the inverted region so great that it overcomes the passive losses experienced by the rest of the mode. This requires cryogenic operation to maximize the carrier density in the fewest number of states. Finally, there is no mode confinement or waveguiding of the laser mode. With the dimensions we have been talking about the laser beam will suffer a great deal of diffraction, and will spread to larger sizes in a short distance. This will further increase the absorption losses and reduce the overlap with the gain region. 2014, Henry Zmuda Set 6a Laser Diodes 14

15 Heterojunction Laser Many of the problems associated with homojunction lasers can be solved using the heterojunction laser. The energy band diagram of an AIGaAs/GaAs heterostructure laser is shown: 2014, Henry Zmuda Set 6a Laser Diodes 15

16 Heterojunction Laser There are two key advantages to the heterostructure: 1. Gain is established in the narrow bandgap region so absorption in the wings of the spatial mode is eliminated 2. The narrow bandgap region has a higher index of refraction, so it is possible to make a waveguide for the optical mode that coincides with the gain region. 2014, Henry Zmuda Set 6a Laser Diodes 16

17 Heterojunction Laser One key to making a heterojunction laser is to identify materials that can be grown together. The primary problem with growing one semiconductor material on another is that of lattice mismatch. If the crystal dimensions of the two materials are identical, the two can be joined without strain. However, if the lattice dimensions differ by even a fraction of 1 percent, the strain involved in growing one material on the other can lead to unacceptable numbers of dislocations and other defects which act to nonradiatively recombine holes and electrons. 2014, Henry Zmuda Set 6a Laser Diodes 17

18 Heterojunction Laser The semiconductor material is made into an allow with aluminum and asenide. Two major properties of the semiconductor are modified when an alloy is formed: the bandgap changes, and the index of refraction changes. GaAs has a bandgap of approximately 1.5 ev. AlAs has a bandgap of approximately 3 ev. The bandgap of an GaAIAs alloy falls somewhere in between, depending on the fractional content of aluminum. 2014, Henry Zmuda Set 6a Laser Diodes 18

19 Heterojunction Laser One can engineer the exact bandgap desired for a given application. 2014, Henry Zmuda Set 6a Laser Diodes 19

20 Heterojunction Laser Consider the double heterostructure laser shown: The laser-active layer is a thin region of p-doped GaAs. The active layer is p-doped since the density of states of the holes make it more difficult to move the quasi-fermi level into the band simply by injection, and due to the fact that electrons have higher mobility and will naturally inject into the p region in greater number than holes will inject into an n region. 2014, Henry Zmuda Set 6a Laser Diodes 20

21 Heterojunction Laser The surrounding layers are suitably doped AlGaAs, about µm thick. The AI concentration is commonly chosen to be quite large (70 percent) in these layers, so the index difference between the lasing layer and the cladding layers is large, yielding good mode confinement. Thinner cladding layers also save time and money in fabrication. A cap layer of highly doped GaAs is added to aid electrical contact, and a buffer layer of GaAs is grown on the substrate to effectively block the migration of any impurities or defects from the substrate up into the laser layers. 2014, Henry Zmuda Set 6a Laser Diodes 21

22 Heterojunction Laser Consider the energy bands for a strongly forward biased junction. 2014, Henry Zmuda Set 6a Laser Diodes 22

23 Heterojunction Laser From the sketch it is apparent why the double heterostructure has an advantage over the homojunction. First, the injected charge is effectively confined in the laseractive layer due to the potential well formed by the cladding layers. This improves laser efficiency. Second, the resulting index profile, with a high-index core and low-index cladding regions, causes optical-mode confinement where the gain is maximum. 2014, Henry Zmuda Set 6a Laser Diodes 23

24 Heterojunction Laser By maximizing the optical intensity in the region of the inversion, stimulated emission is encouraged. This further increases the efficiency. Finally, the evanescent tails of the optical mode which extend out into the cladding will see dramatically reduced absorption because the material has a larger bandgap than the gain layer. These three characteristics make the heterostructure laser an efficient, viable source of coherent radiation. 2014, Henry Zmuda Set 6a Laser Diodes 24

25 Quantum Well Lasers Growth techniques developed in the early 1980s have made it possible to reproducibly grow extremely thin layers of semiconductor material on top of other semiconductor substrates. These layers can be made as thin as a few monolayers of atoms. Such thin structures form what are called quantum wells. Most high performance semiconductor lasers (and LEDs) today are based on quantum well designs. The quantum well laser has much higher gain than the heterojunction, and allows access to new wavelength ranges. 2014, Henry Zmuda Set 6a Laser Diodes 25

26 Quantum Well Lasers Quantum well lasers perform better than the heterojunction laser due to the modification of the density of states in the gain region. Recall that for a bulk semiconductor with large dimensions in all three directions, we know that the density of available electronic states is: or: ρ( k)dk = k 2 dk π 2 ρ( E)dE = 1 2m * 2π EdE 2014, Henry Zmuda Set 6a Laser Diodes 26

27 Quantum Well Lasers When the size of one dimension become extremely small, as happens in a quantum well, the density of states changes in response to the quantization of momentum in that dimension. Consider the density of states in an ultrathin sample of semiconductor, with dimensions L x, L y, and L z. We will assume that L x and L y have macroscopic dimensions (> µm), while L z is on the order of tens of angstroms. The allowed electron wavevectors in this structure have components k x = nπ/l x, k y = mπ/l y, and k z = qπ/l z, where n, m, and q are integers greater than or equal to one. 2014, Henry Zmuda Set 6a Laser Diodes 27

28 Quantum Well Lasers The key point is to note that the small value of L z requires that the magnitude of k z be large. k z k z Density of States in a macroscopic semiconductor. k x k y Density of States in a ultra-thin semiconductor. 2014, Henry Zmuda Set 6a Laser Diodes 28 k x k y

29 Quantum Well Lasers The key point is to note that the small value of L z requires that the magnitude of k z be large. Since k x, k y, and k z can never equal zero, as this would violate the uncertainty principle (ΔxΔk > 1/2, etc.) there can be no allowed modes with k = 0 values. For the k-space representation of the allowed wavevectors for electrons in a thin semiconductor, the dots indicate allowed modes. Due to the small dimension in the z direction, the distance in k z space between allowed modes is relatively large. Obviously by the density of modes is quite different in the x-y plane than in the z-direction. 2014, Henry Zmuda Set 6a Laser Diodes 29

30 Quantum Well Lasers Since k z can never equal zero, there are no allowed states until k z π/l z, or until the energy in the system is at least E = 2 k 2 2m * = 2 π 2 2m * L z 2 Thus, unlike the bulk material where there were available states beginning at E E v = 0 or when E E c = 0, the quantum well has no low-energy states. Once the energy exceeds the above value electrons can occupy states which have momentum k x = nπ/l x and k y = nπ/ L y (and k x = π/l z ). 2014, Henry Zmuda Set 6a Laser Diodes 30

31 Quantum Well Lasers Since the dimensions L x and L y are large, the density of available states in the q = 1 plane follows a twodimensional density of states. To derive the proper expression, let's first count how many modes exist for a given value of k, and let's furthermore assume that k < 2π/L z, so that only states in the first level (q = 1) are occupied. The volume of k space we are interested in has a height of π/l z, and an area of k xy2 /4. Each point has two possible spins, and each point occupies a volume ink space of π 3 /L x L y L z. Thus, the number of modes is given by 2014, Henry Zmuda Set 6a Laser Diodes 31

32 Quantum Well Lasers The number of modes is given by: N = 2 πk 2 xy 4 π L L L x y z L z π 3 where k xy is the momentum in the x-y plane. The density of modes in the x-y plane is given by: dn dk xy = π k xy π L z L x L y L z π 3 In terms of the total k vector, k 2 = k 2 xy + π L z , Henry Zmuda Set 6a Laser Diodes 32

33 Quantum Well Lasers Differentiating: k 2 = k 2 xy + π L z 2 2kdk = 2k xy dk xy Substitute into: N = 2 πk 2 xy 4 π L L L x y z L z π 3 = 1 π 2 k xy dk xy π L z L x L y L z 1 Ndk = d π k 2 xy 2 2 π L L x L y L z z = 1 π 2 k xy dk xy π L z L x L y L z = 1 π 2 kdk π L z L x L y L z 2014, Henry Zmuda Set 6a Laser Diodes 33

34 Quantum Well Lasers Simplifying: ρdk = 1 π 2 kdk π L z Put in terms of energy: ρ( E)dE = 1 2m * 2π 2 2 Notice that the density of states is independent of energy for a specific value of q. This is consistent with the two-dimensional density of states we derived for an optical resonator. 3 2 π L z de 2014, Henry Zmuda Set 6a Laser Diodes 34

35 Quantum Well Lasers Comparison of the density of states of a quantum well and a bulk solid: 2014, Henry Zmuda Set 6a Laser Diodes 35

36 Quantum Well Lasers Note how the quantum well improves the laser. The overall gain at a given wavelength in a semiconductor laser is proportional to the quasi-fermi functions and the density of states. In a bulk semiconductor, the states with the highest probability of occupancy, namely those just above the edge of the conduction band, have the lowest density. The occupied electron states are thus spread over a large range of energies resulting in a gain curve is broad and highly energy dependent, and requires a large number of carriers to create a significant inversion. 2014, Henry Zmuda Set 6a Laser Diodes 36

37 Quantum Well Lasers In a quantum well, the lowest possible energy state already has a significant density of states. Therefore, it is possible to create a significant gain at a specific wavelength with only a small number of carriers. The lowest-energy states of the quantum well are not at the E c and E v levels of the material (see next slide). Because there is significant energy in establishing k z, the ground state of the quantum well will sit above the band edge. 2014, Henry Zmuda Set 6a Laser Diodes 37

38 Quantum Well Lasers The exact location of the energy levels depends on the dimensions of the well and the potential well depth. The ability to adjust the energy-level position by means of well dimensions provides another way to engineer the desired output wavelength for a semiconductor laser. 2014, Henry Zmuda Set 6a Laser Diodes 38

39 Quantum Well Lasers Charge Capture The dimensions of the quantum well are so small that injected electrons and holes can easily fly right past the well. The ballistic travel distance of an injected electron is on the order of 0.1 µm, times the dimension of a typical quantum well. Charge capture by the quantum well can be enhanced by appropriate choice of well dimensions and confinement structures. There are two popular structures for this. 2014, Henry Zmuda Set 6a Laser Diodes 39

40 Quantum Well Lasers Charge Capture 1. A rectangular potential well is grown using homogeneous layers of alloy semiconductor, with a single quantum well in the region, often displaced toward the hole injection side. Carriers are first trapped by the confinement layer where they form a standing wave. Phonon scattering will cool the carriers and allow them to drop into the quantum well. 2014, Henry Zmuda Set 6a Laser Diodes 40

41 Quantum Well Lasers Charge Capture 2. Another method uses graded-well structure which traps and directs charge into the quantum well. The electric field caused by the gradient forces the carriers toward the quantum well. 2014, Henry Zmuda Set 6a Laser Diodes 41

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