**7.1 QD-SOA gain**

The REs system are solved numerically to see the gain change with input power *Pin*, and to examine the dynamic effects. The parameters used in the numerical calculations are listed in Table 4. Fig. 4 shows input power-gain curves for Sb-based QD-SOAs studied. Fig. 4 (a) shows the effect of changing Sb mole fraction in the QD layer. The effect of WL, barrier and QD layers composition on gain is shown in Fig. 4 (b), (c), (d). Curve arrangement in these figures coincides with that in [12]. While both QD and WL composition are shown to give a respected changes in gain, the contribution due to changing Sb-composition in the barrier layer is minor as in Fig. 4 (c). The overall behavior of Fig. 4 is the same, gain saturates at low input power, then it declines at high input powers. This can be attributed to the carrier depletion in the QDs where the output power begins to increase. In Fig. 4 (d), InSb QD-SOA gives a higher gain than that obtained from GaSb QD-SOA. Comparing Fig. 4 (a) and (d) shows the effect of QD composition. To deal with composition effect, we must refer to the material confinement effect: the difference between bandgap in the dot and WL. The higher difference gives more carrier confinement in the QD layer. InSb is known as a lower band

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

The REs system are solved numerically to see the gain change with input power *Pin*, and to examine the dynamic effects. The parameters used in the numerical calculations are listed in Table 4. Fig. 4 shows input power-gain curves for Sb-based QD-SOAs studied. Fig. 4 (a) shows the effect of changing Sb mole fraction in the QD layer. The effect of WL, barrier and QD layers composition on gain is shown in Fig. 4 (b), (c), (d). Curve arrangement in these figures coincides with that in [12]. While both QD and WL composition are shown to give a respected changes in gain, the contribution due to changing Sb-composition in the barrier layer is minor as in Fig. 4 (c). The overall behavior of Fig. 4 is the same, gain saturates at low input power, then it declines at high input powers. This can be attributed to the carrier depletion in the QDs where the output power begins to increase. In Fig. 4 (d), InSb QD-SOA gives a higher gain than that obtained from GaSb QD-SOA. Comparing Fig. 4 (a) and (d) shows the effect of QD composition. To deal with composition effect, we must refer to the material confinement effect: the difference between bandgap in the dot and WL. The higher difference gives more carrier confinement in the QD layer. InSb is known as a lower band

**7. Simulation results and discussion** 

**7.1 QD-SOA gain** 


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

The Composition Effect on the Dynamics of Electrons in Sb-Based QD-SOAs 165


Sb mole fraction=0.7

Sb1-x/Al0.1Ga0.9As

Ga1-xAs

0.5 0.3

(b)

(c)

InAs0.1Sb0.9/GaAsx

Input Power (dBm)

x=0.2 0.4

InAs0.1Sb0.9/GaAs0.1Sb0.9/Alx


Input Power (dBm)

0.2

0.8

Fig. 4. (Continued)

1

1.2

1.4

Gain (dB)

1.6

1.8

2

2.2

0.3

0.4

0.5

0.6

Gain (dB)

0.7

0.8

0.9

1

gap semiconductor. Thus, a higher gain is obtained from InSb than GaSb QD-SOAs due to the higher material confinement of the former (GaSb bandgap differ from InSb by ~0.56 eV). This reason is not enough to explain curves arrangement in Fig. 4 (a). Here gain curves are not arranged due to QD band gap where only very small differences result from varying Sb mole fraction in the QD region. Thus, in addition to material confinement, one must refer to the quantum confinement. Curves are arranged due to the gap (Ec1+Eg+Ev1) where Ec1, Ev1 are the 1st conduction and valence subbands and Eg is the QD band gap. From Figs. 4 (a) and (d), the structure InSb/GaAs0.7Sb0.3/GaAs, is more appropriate for inline static amplification applications due to its maximum gain obtained and higher saturation power than InAsxSb1 x/GaAs0.1Sb0.9/Al0.1Ga0.9As and GaSb QD-SOAs. The effect of QD size is shown in Fig. 4 (e) and (f). In Fig. 4 (e), it is shown that QDs with shorter height gives a higher gain. In Fig. 4 (f), QDs with longer radius gives higher gain.

Fig. 4. (Continued)

gap semiconductor. Thus, a higher gain is obtained from InSb than GaSb QD-SOAs due to the higher material confinement of the former (GaSb bandgap differ from InSb by ~0.56 eV). This reason is not enough to explain curves arrangement in Fig. 4 (a). Here gain curves are not arranged due to QD band gap where only very small differences result from varying Sb mole fraction in the QD region. Thus, in addition to material confinement, one must refer to the quantum confinement. Curves are arranged due to the gap (Ec1+Eg+Ev1) where Ec1, Ev1 are the 1st conduction and valence subbands and Eg is the QD band gap. From Figs. 4 (a) and (d), the structure InSb/GaAs0.7Sb0.3/GaAs, is more appropriate for inline static amplification applications due to its maximum gain obtained and higher saturation power than InAsxSb1 x/GaAs0.1Sb0.9/Al0.1Ga0.9As and GaSb QD-SOAs. The effect of QD size is shown in Fig. 4 (e) and (f). In Fig. 4 (e), it is shown that QDs with shorter height gives a higher gain. In Fig. 4 (f),


Sb mole fraction=0.3

Sb1-x/GaAs0.1Sb0.9/Al0.1Ga0.9As

0.7 0.9

(a)

InAsx

Input Power (dBm)

QDs with longer radius gives higher gain.

0.8

Fig. 4. (Continued)

1

1.2

1.4

Gain (dB)

1.6

1.8

2

2.2

Fig. 4. (Continued)

The Composition Effect on the Dynamics of Electrons in Sb-Based QD-SOAs 167

R=9nm 11nm 13nm


InAs0.1Sb1-9/GaAs0.1Sb0.9/Al0.1Ga0.9As

InAs0.1Sb0.9/GaAs0.1Sb0.9/ AlxGa1-xAs, (d) GaSb and InSb. (e) The disc height and (f) the disc

Figure 5 (a) shows the carrier density dynamics in the barrier layer *Ns* of InAsxSb1 x/GaAs.1Sb.9/Al.1Ga.9As QD-SOAs at three x-mole fraction values (x=0.3, 0.7 and 0.9 Sbfraction). The energy subbands of the QD at each mole fraction are included through relaxation times (see Eqs. 15-17), thus a difference appears between curves. The carrier density in the barrier layer obtained here is in the range of (1015cm-3) which is near to the value of WL carrier density in [11] which assumes that carriers are injected directly to WL. *Ns* curves are arranged according to the shallower Fermi energy level in the barrier layer of the QD SOA structure. According to this, the barrier layer in the structure with (0.9) Sb mole fraction filled earlier, since its quasi-Fermi energy is shallower, then the structure with (0.3) and finally, the structure with (0.7) Sb mole fraction. Fig. 5 (b) shows the carrier density in the WL (*NW*). While *NW* obtained here is in the range of (1012cm-3), a (1014 - 1015 cm-3) WL carrier density is obtained in [11] due to the neglect of barrier layer in that work. Here, *NW* curves are arranged according to the quasi-Fermi energy in their wetting layers. Fig. 5 (c) and (d) shows ES and GS occupation probabilities for the structures InAsxSb1 x/GaAs.1Sb.9/Al.1Ga.9As at Sb mole fractions (0.3, 0.7 and 0.9) where the same probability is obtained in these structures for each ES and GS. This is due to very small differences between their relaxation times, i.e. the inclusion of QD subbands energies, not so much effects, see Eqs. (15-17). In Fig. 6 (a), the effect of changing mole-fraction in the WL of InAs.1Sb.9/GaAsxSb1-x/Al.1Ga.9As QD structure is studied. WL is shown to be saturated at

Fig. 4. Gain-input power relation at J=1.335 kA/cm2 for the QD-SOAs: (a) InAsxSb1-

x/GaAs0.1Sb0.9/Al0.1Ga0.9, (b) InAs0.1Sb0.9/GaAsxSb1-x/Al0.1Ga0.9As, (c)

radius for InAs.1Sb.9/GaAs.1Sb.9/Al.1Ga.9As QD-SOA is shown.

(f)

Input Power (dBm)

0.8

**7.2 Dynamical effects** 

1

1.2

Gain (dB)

1.4

1.6

1.8

2

Fig. 4. (Continued)

Fig. 4. Gain-input power relation at J=1.335 kA/cm2 for the QD-SOAs: (a) InAsxSb1 x/GaAs0.1Sb0.9/Al0.1Ga0.9, (b) InAs0.1Sb0.9/GaAsxSb1-x/Al0.1Ga0.9As, (c) InAs0.1Sb0.9/GaAs0.1Sb0.9/ AlxGa1-xAs, (d) GaSb and InSb. (e) The disc height and (f) the disc radius for InAs.1Sb.9/GaAs.1Sb.9/Al.1Ga.9As QD-SOA is shown.

### **7.2 Dynamical effects**

166 Selected Topics on Optical Amplifiers in Present Scenario

GaSb/GaAs0.7Sb0.3/GaAs InSb/GaAs0.7Sb0.3/GaAs

(d)

(e)


Input Power (dBm)


h=1nm h=3nm h=5nm

InAs0.1Sb1-9/GaAs0.1Sb0.9/Al0.1Ga0.9As

Input Power (dBm)

0.8

2

0.5

Fig. 4. (Continued)

1

1.5

Gain (dB)

1

1.2

1.4

1.6

Gain (dB)

1.8

2

2.2

2.4

2.6

Figure 5 (a) shows the carrier density dynamics in the barrier layer *Ns* of InAsxSb1 x/GaAs.1Sb.9/Al.1Ga.9As QD-SOAs at three x-mole fraction values (x=0.3, 0.7 and 0.9 Sbfraction). The energy subbands of the QD at each mole fraction are included through relaxation times (see Eqs. 15-17), thus a difference appears between curves. The carrier density in the barrier layer obtained here is in the range of (1015cm-3) which is near to the value of WL carrier density in [11] which assumes that carriers are injected directly to WL. *Ns* curves are arranged according to the shallower Fermi energy level in the barrier layer of the QD SOA structure. According to this, the barrier layer in the structure with (0.9) Sb mole fraction filled earlier, since its quasi-Fermi energy is shallower, then the structure with (0.3) and finally, the structure with (0.7) Sb mole fraction. Fig. 5 (b) shows the carrier density in the WL (*NW*). While *NW* obtained here is in the range of (1012cm-3), a (1014 - 1015 cm-3) WL carrier density is obtained in [11] due to the neglect of barrier layer in that work. Here, *NW* curves are arranged according to the quasi-Fermi energy in their wetting layers. Fig. 5 (c) and (d) shows ES and GS occupation probabilities for the structures InAsxSb1 x/GaAs.1Sb.9/Al.1Ga.9As at Sb mole fractions (0.3, 0.7 and 0.9) where the same probability is obtained in these structures for each ES and GS. This is due to very small differences between their relaxation times, i.e. the inclusion of QD subbands energies, not so much effects, see Eqs. (15-17). In Fig. 6 (a), the effect of changing mole-fraction in the WL of InAs.1Sb.9/GaAsxSb1-x/Al.1Ga.9As QD structure is studied. WL is shown to be saturated at

The Composition Effect on the Dynamics of Electrons in Sb-Based QD-SOAs 169

0.7 0.9

InAsx

(c)

Sb mole fraction=0.3

Sb1-x/GaAs0.1Sb0.9/Al0.1Ga0.9As

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (s)

Sb mole fraction=0.3

Sb1-x/GaAs0.1Sb0.9/Al0.1Ga0.9As

0.7 0.9

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

InAsx

Time (s)

Fig. 5. Carrier density for (a) barrier and (b) WL. Then occupation probability for (c) ES, and

0

0

(d) ES for InAsxSb1-x/GaAs0.1Sb0.9/Al0.1Ga0.9As QD-SOAs.

0.1

0.2

0.3

Carrier Occupation Probability of GS

0.4

(d)

0.5

0.02

0.04

0.06

0.08

Carrier Occupation Probability of ES

0.1

0.12

0.14

0.16

x 10-10

x 10-10

Fig. 5. (Continued)

Sb1-x/GaAs0.1Sb0.9/Al0.1Ga0.9As

4 5 6 7 8 9 10

0.7 0.9

Sb mole fraction=0.3

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.7 0.9

InAsx

(b)

Sb mole fraction=0.3

Sb1-x/GaAs0.1Sb0.9/Al0.1Ga0.9As

Time (s)

x 10-11

x 10-10

Carrier Density of Barrier (x1015cm-3)

1.8702

0

Fig. 5. (Continued)

1

2

3

Carrier Density of WL (cm-3)

4

5

6

7 x 1010

1.870205

1.87021

1.870215

1.87022

1.870225

1.87023

1.870235

1.87024

InAsx

(a)

1.870245

1.87035

Fig. 5. Carrier density for (a) barrier and (b) WL. Then occupation probability for (c) ES, and (d) ES for InAsxSb1-x/GaAs0.1Sb0.9/Al0.1Ga0.9As QD-SOAs.

The Composition Effect on the Dynamics of Electrons in Sb-Based QD-SOAs 171

0.5 0.3

InAs0.1Sb0.9/GaAsx

(b)

Sb mole fraction=0.7

Sb1-x/Al0.1Ga0.9As

Sb1-x/Al0.1Ga0.9As

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (s)

Sb mole fraction=0.7

InAs0.1Sb0.9/GaAsx

0.5 0.3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (s)

Fig. 6. (a) Carrier density for WL. Then occupation probability for: (b) ES and (c) GS for

0

0

InAs0.1Sb0.9/GaAsxSb1-x/ Al0.1Ga0.9As QD-SOAs

(c)

0.1

0.2

0.3

Carrier Occupation Probability of GS

0.4

0.5

0.02

0.04

0.06

0.08

Carrier Occupation Probability of ES

0.1

0.12

0.14

0.16

x 10-10

x 10-10

higher carrier density for the structures with Sb mole fraction in WL (0.3 and 0.5). Here curves arrangement is appear according to shallower quasi-Fermi energy levels in the WL, where the effect of WL band gap energy is obvious in this arrangement. Fig. 6 (b) and (c) shows the dynamics of ES and GS occupation probabilities, respectively. Checking the parameters that arrange these curves shows that although the escape times to ES ( <sup>12</sup> and 2*w* ) are very short for the structure No. 2 with Sb mole fraction (0.7), it saturates after other mole fractions (0.3 and 0.5) in these structures. This can be explained if one follows the energy difference between QD ES and WL energy level where this difference is greater for the structure with (0.7) Sb mole fraction in the WL. Also for GS one must refer to the difference between QD GS subband and WL energy level. In Fig. 7, the WL dynamics are shown for In0.1AsSb0.9/GaAs0.1.Sb0.9/AlxGa1-xAs QD-SOAs. WL carrier density saturates at a higher value for the structure with (x=0.2) Al mole fraction in the barrier layer. Also the same reason for shallower quasi-Fermi energy in the WL can explain this arrangement. One can refer to effect of the main difference between structures here (energy gap of barrier layer Egb) where a higher separation between NW curves is compared to the effect of WL energy gap (Egw) as shown in Fig. 6 (a). Occupation probabilities in GS and ES coincides for both (x=0.2 and 0.4) structures and thus they are not drown. In Figs. (5)-(6), although the faster rate of transition between ES and GS, but they are not always the faster one reaching steady state. Both SCH barrier and WL get steady state faster although there is a longer rate of transition between the barrier and WL. This is because of the limited dynamics for these layers so they are in the steady state earlier. At all cases, the GS reaches steady state faster

Fig. 6. (Continued)

higher carrier density for the structures with Sb mole fraction in WL (0.3 and 0.5). Here curves arrangement is appear according to shallower quasi-Fermi energy levels in the WL, where the effect of WL band gap energy is obvious in this arrangement. Fig. 6 (b) and (c) shows the dynamics of ES and GS occupation probabilities, respectively. Checking the parameters that arrange these curves shows that although the escape times to ES ( <sup>12</sup>

 ) are very short for the structure No. 2 with Sb mole fraction (0.7), it saturates after other mole fractions (0.3 and 0.5) in these structures. This can be explained if one follows the energy difference between QD ES and WL energy level where this difference is greater for the structure with (0.7) Sb mole fraction in the WL. Also for GS one must refer to the difference between QD GS subband and WL energy level. In Fig. 7, the WL dynamics are shown for In0.1AsSb0.9/GaAs0.1.Sb0.9/AlxGa1-xAs QD-SOAs. WL carrier density saturates at a higher value for the structure with (x=0.2) Al mole fraction in the barrier layer. Also the same reason for shallower quasi-Fermi energy in the WL can explain this arrangement. One can refer to effect of the main difference between structures here (energy gap of barrier layer Egb) where a higher separation between NW curves is compared to the effect of WL energy gap (Egw) as shown in Fig. 6 (a). Occupation probabilities in GS and ES coincides for both (x=0.2 and 0.4) structures and thus they are not drown. In Figs. (5)-(6), although the faster rate of transition between ES and GS, but they are not always the faster one reaching steady state. Both SCH barrier and WL get steady state faster although there is a longer rate of transition between the barrier and WL. This is because of the limited dynamics for these layers so they are in the steady state earlier. At all cases, the GS reaches steady state faster

Carrier Density of WL (cm-3)

Sb mole fraction=0.7

Sb1-x/Al0.1Ga0.9As

0.5 0.3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

InAs0.1Sb0.9/GaAsx

Time (s)

2*w* 

5

Fig. 6. (Continued)

5.5

6

6.5

7

7.5

x 1010

(a)

x 10-10

and

Fig. 6. (a) Carrier density for WL. Then occupation probability for: (b) ES and (c) GS for InAs0.1Sb0.9/GaAsxSb1-x/ Al0.1Ga0.9As QD-SOAs

The Composition Effect on the Dynamics of Electrons in Sb-Based QD-SOAs 173

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

InAs.1Sb.9/GaAs.1Sb.9/Al.2Ga.8As

(b)

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

InAs0.1Sb0.9/GaAs0.1Sb0.9/Al0.1Ga0.9As

Time (s)

108

0

Fig. 8. (Continued)

0.05

0.1

0.15

Carrier Occupation Probability of ES

0.2

0.25

0.3

0.35

109

1010

1011

1012

Carrier Density of WL (cm-3)

1013

1014

(a)

1015

1016

x 10-10

x 10-10

4REs 3REs

4REs 3REs

than ES since the relaxation between ES to GS is very fast. Finally, a comparison is done between three and four REs system for QD-SOA as shown in Fig. 8 (a), (b) and (c) for WL, ES and GS respectively, where a three REs system is shown to be an overestimates the dynamics due to neglecting the effect of barrier layer. So, this layer must be included in the REs system used to study QD systems.

Fig. 7. Carrier density for WL for InAs0.1Sb0.9/GaAs0.1Sb0.9/AlxGa1-xAs QD-SOAs.

than ES since the relaxation between ES to GS is very fast. Finally, a comparison is done between three and four REs system for QD-SOA as shown in Fig. 8 (a), (b) and (c) for WL, ES and GS respectively, where a three REs system is shown to be an overestimates the dynamics due to neglecting the effect of barrier layer. So, this layer must be included in the

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

InAs0.1Sb0.9/GaAs0.1Sb0.9/Alx

Fig. 7. Carrier density for WL for InAs0.1Sb0.9/GaAs0.1Sb0.9/AlxGa1-xAs QD-SOAs.

x=0.2 x=0.4

Ga1-xAs

Time (s)

x 10-10

REs system used to study QD systems.

0

1

2

3

Carrier Density of WL (cm-3)

4

5

6 x 1010

Fig. 8. (Continued)

The Composition Effect on the Dynamics of Electrons in Sb-Based QD-SOAs 175

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Noise Figure, and Carrier Distribution for Quantum-Dot Semiconductor-

Fig. 8. A comparison between three- and four-REs system for (a) WL carrier density, (b) ES and (c) GS occupation probabilities for InAs.1Sb.9/GaAs.1Sb.9/Al.1Ga.9As QD-SOA.
