Chapter 3 Spontaneous emission spectrum in light-emitting diodes
4.3 Temperature dependent
Figure 4.7 presents the normalized PL spectrum of the sample with varying temperatures from 20K to 340K. Figure 4.8 shows the S-shaped variation with temperature. The peak energy shifts from 2.76eV to 2.75eV when temperature increased from 20K to 80K, and shifts to 2.76eV when temperature increased to 200K. The peak energy shifts to 2.744eV when temperature further increased to 340K.
To further understand the S-shaped shift of the emission peak under various temperatures, the optical joint densities of states of the sample are determined under various temperatures from the measured spectra. Figure 4.9 shows the relative optical joint densities of states obtained from the PL spectra with varying temperature. Similar to the optical joint densities of states obtained from the EL spectra, these curves also show two distinct regions – a low-energy tail and a high-energy region. According to the previous result, the low-energy tails are attributed to the formation of localized states and the steep increase of the density of states in the high-energy regions are attributed to the unlocalized states of the two-dimensional quantum structure. Here, the unlocalized states of the two-dimensional quantum structure can be linear fitted as shown in Fig. 4.10.
43
To further consider the effects of the emission peak by these two regions, the theoretical emission spectra of these two regions were obtained. The theoretical emission spectra of the two-dimensional quantum structure were obtained by using the fitted dish lines multiplying the Boltzmann distribution function, as shown in Fig. 4.11. On the other hand, the optical joint densities of states of localized states can be obtained by divided from the origin optical joint densities of states and linear fitted lines as shown in Fig. 4.12. The theoretical emission spectra of localized states were obtained by multiplying the Boltzmann distribution function, as shown in Fig. 4.13.
To further compare these two theoretical emission spectra with varying temperatures, the theoretical emission peak of the localized states shows S-shaped shift, however, the theoretical emission peak of the two-dimensional quantum structure shows only redshifts, as shown in Fig. 4.14. This result indicates that the S-shaped shift is mainly attributed to the localized states and can be explained by the delocalization of excitons out of potential minima. The emission spectrum corresponded to the quantum structure is only affected by the Varshni redshift of the band gap energy. Furthermore, when the temperature increased to 200K, the emission peak positions are contributed by both localized states and quantum structure and redshifts with temperature. The value of the shifts is smaller than the theoretical emission peak of the localized states, which indicated that the emission spectrum corresponded to the unlocalizated two-dimensional quantum structures become to dominate the PL emission peak.
In summary, the optical joint densities of states of a nitride-based LED were determined with varying temperatures. The optical joint density of states can be divided into two regions, a low-energy tail is attributed to the localized states and a high-energy tail is attributed to the unlocalized states of the two-dimensional quantum well. The theoretical emission spectra of the two regions were obtained by multiplying the Boltzmann distribution function separately. Since the Boltzmann distribution can not be used in the lowest range
44
of temperatures due to the thermal equilibrium could not be obtained. Thus, the optical joint densities of states in the range of temperature were not discussed.
As temperature in the range of 80K to 200K, the emission spectrum corresponded to localized states dominates the PL emission peak, as shown in Fig. 4.15(a). The emission peak energy increased with temperature, which results the PL emission peak blue shift. This phenomenon can be explained by the delocalization of excitons out of potential minima. As temperature higher than 200K, the emission spectrum corresponded to the two-dimensional quantum well becomes to dominate the PL emission peak, as shown in Fig.
4.15(b). The emission peak energy was decreased with temperature, which results in the Varshni redshift of the band gap energy. In conclusion, the model for describing the spectra of quantum wells can be used not only to explain the blueshift of emission with varying currents but also explain the S-shift with varying temperatures in nitride LEDs.
45
References
[1] S. Nakamura, M. Senoh, N. Lwasa, and S. Nagaham, Jpn. J. Appl. Phys., Part 1 34 (1995) 797.
[2] S.D. Lester, F.A. Ponce, M.G. Craford, and D.A. Steigerwald, Appl. Phys.
Lett. 66 (1995) 1249.
[3] S. Chichibu, T. Azuhata, T. Sota, and S. Nakamura, Appl. Phys. Lett. 70 (1997) 2882.
[4] Y. Narukawa, Y. Kawakami, M. Funato, Sz. Fujita, Sg. Fujita, and S.
Nakamura, Appl. Phys. Lett. 70 (1997) 981.
[5] S. Chichibu, T. Azuhata, T. Sota, and S. Nakamura, Appl. Phys. Lett. 69 (1997) 4188.
[6] M. Sugawara, Phys. Rev. B 51 (1995) 10743.
[7] S.J. Rosner, E.C. Carr, M.J. Ludowise, G. Girolami, and H.I. Erikson, Appl.
Phys. Lett. 70 (1997) 420.
[8] S.Y. Karpov and Y.N. Makarov, Appl. Phys. Lett. 81 (2002) 4721.
[9] P. Riblet, H. Hirayama, A. Kinoshita, A. Hirata, T. Sugano, and Y. Aoyagi, Appl. Phys. Lett. 75 (1999) 2241.
[10] M. E. Aumer, S. F. LeBoeuf, S. M. Bedai, M. Smith, J. Y. Lin, and H. X.
Jiang, Appl. Phys. Lett. 77 (2000) 821.
[11] R. Zheng and T. Taguchi, J. Appl. Phys. 89 (2001) 6260.
[12] Y.D. Qi, H. Liang, D. Wang, Z.D. Lu, W. Tang, and K.M. Lau, Appl. Phys.
Lett. 86 (2005) 101903.
[13] S. Chichibu, T. Sota, K. Wada, and S. Nakamura, J. Vac. Sci. Technol. B 16 (1998) 2204.
[14] T. Li, A. M. Fischer, Q. Y. Wei, F. A. Ponce, T. Detchprohm, and C. Wetzel, Appl. Phys. Lett. 96 (2010) 031906.
46
[15] A. Bell, S. Srinivasan, C. Plumlee, H. Omiya, F. A. Ponce, J. Christen, S.
Tanaka, F. Fujioka, and Y. Nakagawa, J. Appl. Phys. 95 (2004) 4670.
[16] Y. Kawakami, K. Omae, A. Kaneta, K. Okamoto, Y.Narukawa, T. Mukai, and S. Fujita, J. Phys.: Condens. Matter 13 (2001) 6993.
[17] Y. H. Cho, G. H. Gainer, A. J. Fischer, J. J. Song, S. Keller, U. K. Mishra, and S. P. DenBaars, Appl. Phys. Lett. 73 (1998) 1370.
[18] H. P. D. Schenk, M. Leroux, and P. de Mierry, J. Appl. Phys. 88 (2000) 1525.
[19] J. Li, K. B. Nam, J. Y. Lin, and H. X. Jiang, Appl. Phys. Lett. 79 (2001) 3245.
[20] B.E.A. Saleh and M.C. Teich, Fundamentals of Photonics, (Wiley, New York, 1991), p. Chap. 15.
[21] C.H. Henry, R.A. Logan, H. Temkin, and F.R. Merritt, IEEE J. Quantum Electron. QE-19 (1983) 941.
[22] C.H. Henry, R.A. Logan, and F.R. Merritt, J. Appl. Phys. 51 (1980) 3042.
[23] C.H. Henry, R.A. Logan, and K.A. Bertness, J. Appl. Phys. 52 (1981) 4453.
[24] P. Blood, A.I. Kucharska, J.P. Jacobs, and K. Griffiths, J. Appl. Phys. 70 (1991) 1144.
[25] P. Blood, E.D. Fletcher, P.J. Hulyer, and P.M. Smowton, Appl. Phys. Lett.
48 (1986) 1111.
[26] J.D. Thomson, H.D. Summers, P.J. Hulyer, P.M. Smowton, and P. Blood, Appl. Phys. Lett. 75 (1999) 2527.
[27] G.M. Lewis, P.M. Smowton, J.D. Thomson, H.D. Summers, and P. Blood, Appl. Phys. Lett. 80 (2002) 1.
[28] H.D. Summers, J.D. Thomson, P.M. Smowton, P. Blood, and M. Hopkinson, Semocon. Sci. Tech. 16 (2001) 140.
47
[29] N.C. Chen, W.C. Lien, Y.K. Yang, C. Shen, Y.S. Wang, and J.F. Chen, J.
Appl. Phys. 106 (2009) 074514.
[30] N.C. Chen, C.M. Lin, C. Shen, W.C. Lien, and T.Y. Lin, Opt. Express 16 (2008) 20759.
[31] S.M. Sze and K.K. Ng, Physics of Semiconductor Devices 2nd Edition (Wiley, New York, 1982), p. 61.
[32] R. André, J. Cibert, and L.S. Dang, Phys. Rev. B 52 (1995) 12013.
[33] S.F. Chichibu, A.C. Abare, M.P. Mack, M.S. Minsky, T. Deguchi, D. Cohen, P. Kozodoy, S.B. Fleischer, S. Keller, J.S. Speck, J.E. Bowers, E. Hu, U.K.
Mishra, L.A. Coldren, S.P. DenBaars, K. Wada, T. Sota, S. Nakamura, Mater.
Sci. Eng. B 59 (1999) 298.
[34] C.K. Choi, Y.H. Kwon, B.D. Little, G.H. Gainer, J.J. Song, Y.C. Chang, S.
Keller, U.K. Mishra, and S.P. DenBaars, Phys. Rev. B 64 (2001) 245339.
48
2.8 3.0 3.2 3.4 3.6
(a)
80 mA 70 mA 60 mA 50 mA 40 mA 10 mA 20 mA 30 mA
EL IN T EN SI T Y (a .u .)
PHOTON ENERGY (eV) VIOLET
2.4 2.6 2.8 3.0 3.2
(b) 18 meV
EL INTENSITY (a. u.)
PHOTON ENERGY (eV)
80 mA 70 mA 60 mA 50 mA 40 mA 10 mA 20 mA 30 mA
BLUE
49
2.0 2.2 2.4 2.6 2.8
(c) 32 meV
80 mA 70 mA 60 mA 50 mA 40 mA 30 mA 20 mA
EL INT ENSITY (a. u.)
PHOTON ENERGY (eV)
10 mA
GREEN
Fig. 4.1. EL spectra of (a) violet, (b) blue, and (c) green InGaN/GaN-based LEDs at various currents from 10 to 80 mA at 300K. Emission peak shifts in the three spectra are 0 meV, 19 meV, and 37 meV, respectively
50
2.2 2.4 2.6 2.8 3.0 3.2 3.4
80 mA 70 mA 60 mA 50 mA 40 mA 30 mA 20 mA 10 mA
Green Blue Violet
(h ) (arb. units)
PHOTON ENERGY (eV)
Fig. 4.2. Relative optical joint density of states in violet, blue, and green LEDs under currents from 10 to 80 mA, calculated by dividing EL spectra by thermal distribution
51
E
cE
v(a)
E
cE
v(b)
Fig. 4.3. Band diagrams and wave functions of elections and holes under (a) piezoelectric field and (b) screened piezoelectric field
52
3.2 3.3 3.4
VIOLET
10 mA 20 mA 30 mA 40 mA 50 mA 60 mA 70 mA 80 mA
OPTICAL JOINT DENSITY (a.u.)
PHOTON ENERGY (eV)
2.75 2.80 2.85 2.90 2.95
10 mA 20 mA 30 mA 40 mA 50 mA 60 mA 70 mA 80 mA
OPTICAL JOINT DENSITY (a.u.)
PHOTON ENERGY (eV) BLUE
53
2.45 2.50 2.55 2.60
10 mA 20 mA 30 mA 40 mA 50 mA 60 mA 70 mA 80 mA
OPTICAL JOINT DENSITY (a.u.)
PHOTON ENERGY (eV) GREEN
Fig. 4.4. Theoretical emission spectra obtained by two-dimensional quantum structure at various currents from 10 to 80 mA at 300K
54
0.00 0.02 0.04 0.06 0.08
0.00 0.01 0.02 0.03 0.04
CURRENT (A) BLUE SHIFT (eV) Blue
Green
Fig. 4.5. Experimental and theoretical EL peak shifts with current in blue (green) LED are denoted by solid circles (solid squares) and open circles (open squares), respectively
55
0.00 0.02 0.04 0.06 0.08
0.04
0.00 0.02 0.04 0.06 0.08
0.04
56
0.00 0.02 0.04 0.06 0.08
0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20
FWHM (eV)
CURRENT (A)
GREEN
EXPERIMENT SIMULATION
Fig. 4.6. The FWHMs of the experimental spectra and simulated spectra for violet, blue and green LEDs
57
360 400 440 480 520
INTENSITY (a.u.)
Fig. 4.7. PL spectra of an LED at various temperatures from 20 to 340K
0 50 100 150 200 250 300 350
Fig. 4.8. The emission peak positions of the PL spectra at various temperatures from 20 to 340K
58
2.4 2.5 2.6 2.7 2.8 2.9
Op ti c al j oi nt de ns ity of s tat es (a .u. )
20K 340K, calculated by dividing PL spectra by thermal distribution
2.7 2.8 2.9 3.0
Optical joint density of states (a.u.)
Energy (eV)
140K 240K 340K
Fig. 4.10. The linear fitted lines of the steep increased of optical joint density of states at 140K, 240K and 340K
59
2.70 2.75 2.80 2.85 2.90
0.0 0.2 0.4 0.6 0.8 1.0
Intensity (a.u.)
Energy (eV)
60K 80K 100K 120K 140K 160K 180K 200K 220K 240K 260K 280K 300K 320K 340K
Fig. 4.11. The theoretical emission spectra obtained by two-dimensional quantum structure from 20 to 340K
60
2.4 2.5 2.6 2.7 2.8
Optical joint density of states (a.u.)
Energy (eV)
140K 240K 340K
Fig. 4.12. The optical joint density of states with eliminating linear fitted lines at 140K, 240K and 340K
Fig. 4.13. The theoretical emission spectra obtained by localized states from 20 to 340K
61
50 100 150 200 250 300 350 2.72
2.74 2.76 2.78 2.80 2.82 2.84
Peak Energy (eV)
Temperature (K)
Experimental emission Localized states
Two-dimensional quantum structure
Fig. 4.14. The peak positions of experimental emission spectrum and theoretical emission spectrum obtained by two-dimensional quantum structure and localized states from 60 to 340K
62
2.4 2.5 2.6 2.7 2.8 2.9 3.0 140K
quantum wells
Intensity (a.u.)
Energy (eV) localized states
2.4 2.5 2.6 2.7 2.8 2.9 3.0 quantum wells localized states
Intensity (a.u.)
Energy (eV) 340K
Fig. 4.15. The experimental emission spectrum and theoretical emission spectrum obtained by two-dimensional quantum structure and localized states at (a) 140 K and (b) 340K
63