- Text
- Laser,
- Devices,
- Threshold,
- Znse,
- Density,
- Semiconductor,
- Lasing,
- Output,
- Characterisation,
- Thesis,
- Electro,
- Optical,
- Wavelength

Electro Optical Characterisation of Short Wavelength Semiconductor ...

Basic Concepts which by using 1.6 can be written as Adding up the band gap energy to both side leads to Efc + Efv > Ec + Ev. (1.11) Eg + Efc + Efv > Ec + Ev + Eg = hν > Eg. (1.12) Equation 1.12 represents the condition for optical gain. In the case **of** electrical pumping, this would imply that the externally applied electric field must result a separation **of** quasi Fermi energies, that exceeds the photon energy **of** the stimulated emission and the band gap energy **of** the semiconductor [37]. Macroscopic Aspects **Optical** gain is necessary but not sufficient for lasing. A second aspect called optical feedback is also needed. The feedback enables the selectivity for the stimulated emission in terms **of** direction and wavelength and thus enables the laser oscillation. The optical feedback could be reached through two parallel semi-transparent mirrors brought on the both sides **of** the gain medium. This forms a Fabry-Pérot resonator. From the macroscopic point **of** view the matter is considered as a homogeneous medium described by the complex dielectric ε(ω) or by the complex index **of** refraction ñ(ω). Laws **of** reflection, transmission and absorption can be described from this point **of** view. In case **of** a Fabry-Pérot resonator the concentration is on reflection and transmission, as depicted in Fig. 1.7. Transmission coefficients t1 and t2 and reflection coefficients r1 and r2 are defined respectively. A plane wave propagating in the positive z direction could be written as Ee −Γz , whereas Γ is the complex propagation constant. A wave Ei meets the input mirror at z = 0 perpendicular to the surface; a part will be reflected and a part transmitted. This happens every time the wave reaches any **of** both mirrors. For calculating the lasing conditions, it would be sufficient to only take the transmitted part on the output mirror at z = L into consideration. Summing up the transmitted fields delivers a geometric progression, Et = t1t2 Eie −ΓL + r1r2t1t2 Eie −3ΓL + · · · = Ei t1t2e −ΓL 1 − r1r2e −2ΓL · (1.13) Exactly at the laser threshold the cavity is invisible for the light. If the denominator **of** Eq. 1.13 approaches zero, the condition **of** lasing oscillation is obtained because **of** a finite transmitted intensity Et remaining from an incident wave with vanishing intensity Ei; r1r2e −2ΓL ! = 1. (1.14) The complex propagation constant Γ includes the damping factor α and the phase φ = 2π λ **of** the wave, where λ is the wavelength, 10

E i −2 L t 1 r1 r E 2 i e −2 L t 1 r E 2 i e t 1 E i Physics **of** **Semiconductor** Lasers input mirror output mirror L −3 L t 1 r1 r E 2 i e − L t 1 r E 2 i e − L t E 1 i e −3 L t 1t 2 r 1r E 2 i e − L t 1t E 2 i e Figure 1.7: Fabry-Pérot resonator **of** length L. t and r are transmission and reflection coefficients. Ei represents a plane wave, incident onto the input mirror [25]. Γ = α + i 2π · (1.15) λ The cavity **of** a laser is amplifying. This fact needs to be considered. Γ = (αi − g) + i 2πn , (1.16) λ where αi represents the whole internal loss, and g is the gain **of** the cavity. Propagation **of** light in matter **of** refractive index n = 1 leads to chromatic dispersion; thus λ. Combining n Eqs. 1.14 and 1.16 yields r1r2e (g−αi)2L −i2L e 2πn λ ! = 1, (1.17) which is representative for a wave covering a distance **of** 2L inside the cavity, returning to the input mirror with the same amplitude and in phase. Equating the real and imaginary parts **of** Eq. 1.17, two lasing conditions are obtained r1r2e (g−αi)2L cos 2L 2πn != 1 (1.18) λ sin 2L 2πn != 0 (1.19) λ z 11

- Page 1: University of Bremen Technical Univ
- Page 4 and 5: Preface ing the characterisation me
- Page 6 and 7: CONTENTS 4.2.1 Characterisation of
- Page 8 and 9: Basic Concepts Semiconductor lasers
- Page 10 and 11: Basic Concepts many problems appear
- Page 12 and 13: Basic Concepts 1.2.2 Light in Cryst
- Page 16 and 17: Basic Concepts Eq. 1.19 delivers di
- Page 18 and 19: Basic Concepts light below the mate
- Page 20 and 21: Developing Laser Diodes Metalorgani
- Page 22 and 23: Developing Laser Diodes 18 4. Lift
- Page 25 and 26: Chapter 3 Characterisation Life can
- Page 27 and 28: 3.1.3 SEM & FIB Opto-Electrical Cha
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- Page 34 and 35: Data Analysis As it can be seen the
- Page 36 and 37: Data Analysis Output Light Power [W
- Page 38 and 39: Data Analysis trometer. This could
- Page 40 and 41: Data Analysis Current [mA] 400 300
- Page 42 and 43: Data Analysis Following the trend o
- Page 44 and 45: Data Analysis can be due to the sub
- Page 46 and 47: Data Analysis It is worth mentionin
- Page 48 and 49: Data Analysis for the whole devices
- Page 50 and 51: Data Analysis Figure 4.18: Optical
- Page 52 and 53: Data Analysis current density 1.75
- Page 54 and 55: Data Analysis levels of the quantis
- Page 57 and 58: Chapter 5 Summary and Outlook Great
- Page 59: Appendix A Electrical Sources & Mea
- Page 62 and 63: ZnSe threshold current density valu
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Bibliography [1] N. G. Basov, O. N.

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BIBLIOGRAPHY [56] G. Snider, 1D Poi