**6. Sb-based QD-SOA structures**

Sb-based QD semiconductors suffer from the difficulty of QD growth methods, like the selfassembled growth method, due to kinetic effects. Sb-based QD crystals growth hinders due to large mismatch (>7 or 8%) with GaAs semiconductors. Now it is possible to grow GaSb QDs on GaAs substrate [18]. In addition, an interfacial misfit array method can be used now to grow Sb-based layers on a GaAs platform although the (8%) lattice mismatch between GaAs and GaSb [19].

Accordingly, we choose a large number of structures, it is classified here in a five types, as in Table 1. In these structures, we change the composition of QD ( structure Nos. 1, 4 and 5), WL (No. 2) or barrier layer (No. 3). This is to examine the effect of these layers on the QD-SOA and also to specify the possible spectral ranges in the Sb-based QD structures. In all of these structures there is a lattice mismatch between layers (dot and WL or WL and barrier) not exceeds (6%) and in some cases its value is very small. This is to intend these structures to the ease of QD growing. QD energy levels are calculated using parabolic band quantumdisc model [20] where the dots are assumed to be in the form of a disc with radius (14 ) *nm* and height (2) *h nm* , unless states otherwise. Quantum well WL thickness is taken as (9 nm). The accuracy of the quantum disc model is checked by a comparison with the experimental data and numerical methods [20, 21]. The parameters used in the calculations of Sb-based structures are stated in Tables 2 and 3. Thus, it is adequate to calculate energy levels without time consumption. An example of QD energy levels calculated using parabolic band model is shown in Fig. 3 for InAs0.1Sb0.9 /GaAs.1Sb.9/Al.1Ga.9As QD-SOA. In the calculation of quasi-Fermi energy Eqs. (3) and (4) are used. Gain is then calculated, using Eq.1, and its peak value and peak wavelength for each structure is specified.

empty.


Table 1. QD-SOA structures studied.

160 Selected Topics on Optical Amplifiers in Present Scenario

Quasi-thermal equilibrium is assumed between states. To ensure this convergence, the

12 0( /) *E E kT ES GS B d GS ES*

2 0( /) *E E kT wl ES B*

 

 

, ( /) ( /) *E kT SCH wl B*

 

layers and *Hb* is the total thickness of the SCH. *SCH wl* , *<sup>E</sup>* is the energy difference between SCH

from the WL to the ES and from the ES to the GS with the hypothesis that the nal state is

Sb-based QD semiconductors suffer from the difficulty of QD growth methods, like the selfassembled growth method, due to kinetic effects. Sb-based QD crystals growth hinders due to large mismatch (>7 or 8%) with GaAs semiconductors. Now it is possible to grow GaSb QDs on GaAs substrate [18]. In addition, an interfacial misfit array method can be used now to grow Sb-based layers on a GaAs platform although the (8%) lattice mismatch between

Accordingly, we choose a large number of structures, it is classified here in a five types, as in Table 1. In these structures, we change the composition of QD ( structure Nos. 1, 4 and 5), WL (No. 2) or barrier layer (No. 3). This is to examine the effect of these layers on the QD-SOA and also to specify the possible spectral ranges in the Sb-based QD structures. In all of these structures there is a lattice mismatch between layers (dot and WL or WL and barrier) not exceeds (6%) and in some cases its value is very small. This is to intend these structures to the ease of QD growing. QD energy levels are calculated using parabolic band quantumdisc model [20] where the dots are assumed to be in the form of a disc with radius (14 ) *nm* and height (2) *h nm* , unless states otherwise. Quantum well WL thickness is taken as (9 nm). The accuracy of the quantum disc model is checked by a comparison with the experimental data and numerical methods [20, 21]. The parameters used in the calculations of Sb-based structures are stated in Tables 2 and 3. Thus, it is adequate to calculate energy levels without time consumption. An example of QD energy levels calculated using parabolic band model is shown in Fig. 3 for InAs0.1Sb0.9 /GaAs.1Sb.9/Al.1Ga.9As QD-SOA. In the calculation of quasi-Fermi energy Eqs. (3) and (4) are used. Gain is then calculated, using

Eq.1, and its peak value and peak wavelength for each structure is specified.

  ([ ]/ )

([ ]/ )

*we s weff QD SCH b N He* (17)

*SCH* is the density of states per unit volume in the SCH. They are given

 and *<sup>d</sup>*<sup>0</sup> 

*w c ES Q weff N e* (16)

*<sup>e</sup>* (15)

*SCH eSCH B m kT* . *NQD* is the number of QD

*weff* is the density of states per unit

are the average capture time

carrier escape times are related to the carrier capture times as follows [17]

 

 

 

 *weff ewl B m kT* and 2 3/2 2(2 / ) 

 

**6. Sb-based QD-SOA structures** 

area in the WL and

empty.

by <sup>2</sup> ( /)

GaAs and GaSb [19].

GS and ES QD energy levels are denoted by , *E E GS ES* .

and WL band edge energies. The capture times *c*<sup>0</sup>


Table 2. Binary structure parameters [22].


Table 3. The relation used to calculate structure parameters (bandgap *Eg* and effective mass *mi*). Note that the subscript (i) with *mi* refers to conduction or valence band effective masses [22, 23].

The Composition Effect on the Dynamics of Electrons in Sb-Based QD-SOAs 163

**Parameter Symbol Value Unit** 

0.4 *ns* <sup>1</sup>*<sup>R</sup>* Spontaneous radiative lifetime in QDs

1 *ns wR* Spontaneous radiative lifetime in WL

1 *ps <sup>c</sup>*<sup>0</sup> Carrier escapes time from ES to WL

3 *ps <sup>w</sup>*<sup>2</sup> Carrier relaxation time from the two-

1.2 *ps* <sup>12</sup> Carrier relaxation time from GS to ES

7 *ps <sup>d</sup>*<sup>0</sup> Carrier relaxation time from ES to GS

6 *ns <sup>s</sup>* Diffusion time in the barrier layer

4.5 *ns sr* SCH recombination time

*m* The effective thickness of the active layer *Lw*

1.335 kA/cm2 Injection current density *J* 

int Internal loss

Table 4. Parameters used in the calculations [11, 17].

Optical confinement factor 0.007

Laser length *L* 2000

Strip . width *D* 10

dimensional WL to the ES

*cm-1* 2

0.1

*m*

*m*

Fig. 3. Energy band diagram of an InAs0.1Sb0.9/GaAs0.1Sb0.9/Al0.1Ga0.9As QD-SOA structure.
