VCSEL Industry. Babu Dayal Padullaparthi
in 1963, a double heterostructure laser had been proposed by Herbert Kromer by using semiconductor layers with varying bandgap and refractive index [9]. Herbert Kroemer and Zhores Alferov [7] both received the 2000 Nobel Prize in Physics for the idea.
This DH structure is used only for confining light field as shown in Figure 1.4b. More descriptions can be found in related textbooks [10–14].
1.1.3.2 Quantum Well Lasers
Present semiconductor lasers utilize quantum wells (QWs) as shown in Figure 1.5 for the light emitting and amplification layer for almost all semiconductor lasers and LEDs. The QW [15] has a thickness of several nanometers (1 nm = 10–9 m). Grain‐shaped quantum dots [16, 17] that have a several‐nanometer box size can be used to further reduce the threshold current in semiconductor lasers. The optical gain necessary for lasing using multiple quantum wells (MQWs) is further explained in Chapter 2.
Figure 1.5 Quantum well structure with separate optical confinement. (a) The carrier densities of electron and holes in a quantum well structure. (b) The quantum well laser where the optical field is confined by the double heterostructure.
Source:[8]. [Image Courtesy of Genichi Hatakoshi.]
1.1.4 Amplification of Light in Semiconductors
The relationship between the density of states and energy in semiconductors is shown in Figure 1.6. This is determined by the product of the parabolic density of states in the conduction band and the valence band and the Fermi‐Dirac distribution according to Pauli exclusion principle. In the case of bulk semiconductors, it has the shape shown in the Figure 1.6. Ec and Ev are Fermi levels in thermal equilibrium in the conduction band and valence band, respectively, and Eg is the bandgap energy. If the electrons and holes are excessive due to photoexcitation or current injection, the distribution changes. The electron and hole levels in each band are called quasi‐ or degenerate‐Fermi level and are indicated by Efc and Efv. The condition for the population inversion from the thermal equilibrium state (also called quasi equilibrium) is expressed by:
Efc − Efv > Ec − Ev: negative temperature or amplifying (condition for gain).
When the light with angular frequency ω comes in the semiconductor, the following characteristics appear, where ħ is the reduced Planck’s constant: ħ = h/2π (h: Planck’s constant). Here, ħω is a quantized photon energy, which appears in Chapter 8.
Figure 1.6 Population distribution of electrons and holes in semiconductor well vs. energy.
Source:[18]. (After Masahiro Asada and Yasuharu Suematsu)
ħω < Ec − Ev: transparent
ħω > Ec − Ev: absorptive
As shown in Figure 1.6, in the excited state, the carrier distribution representing the gain is distributed in a mountain shape with respect to energy. The result of the calculation is also shown in Figure 1.7.
Figure 1.7 Optical gain of semiconductor vs. energy.
Source:[19]. (After Masahiro Asada and Yasuharu Suematsu)
1.1.5 Oscillation Conditions in Semiconductor Lasers
1.1.5.1 Laser Resonators
The schematics of the edge‐ and surface‐emitting laser (VCSEL) are shown in Figure 1.8. The edge‐emitting (EE) laser, shown in Figure 1.8(a), includes Fabry‐Pérot (FP) laser, distributed feedback (DFB) laser, and distributed Bragg reflector (DBR) laser. These laser types will be compared with VCSEL in Figure 1.8b in subsequent chapters.
Let us consider the oscillation conditions of a semiconductor laser. As shown in Figure 1.8(a) and (b), the target semiconductor laser is composed of a Fabry‐Pérot (FP) cavity. Both resonators are generalized in Figure 1.9(a). By using the field reflectance including phase shift, which will be given later, this model can be applied to edge‐emitting Fabry‐Pérot lasers, DFB lasers, DBR lasers, and VCSELs as well.
Figure 1.8 Schematic of edge‐emitting Fabry‐Pérot lasers and VCSELs. The coupling of light through standing waves in laser resonators (a) Fabry‐Pérot (edge‐emitting laser/EEL), and (b) surface emitting laser (VCSEL).
Source: Figure by K. Iga and B. D. Padullaparthi [copyright reserved by authors].
Figure 1.9 Fabry‐Pérot cavity and resonant spectra. (a) Fabry‐Pérot cavity. (b) Resonant spectra.
<Parameters>
L: cavity length
d: thickness of active layer
φ 1, φ 2: phase shift of each reflection
r1, r2: electric field reflectance coefficients of the mirrors at both ends
R1, R2 ,: power reflection coefficients