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A comparative study of InAs quantum dot lasers with barriers of direct and indirect band gaps
Microelectronics Journal 36 (2005) 183–185 www.elsevier.com/locate/mejo
A comparative study of InAs quantum dot lasers with barriers of direct and indirect band gaps G. Suna,*, Richard A. Sorefb, Jacob B. Khurginc a Department of Physics, University of Massachusetts at Boston, Boston, MA 02125, USA Sensors Directorate, Air Force Research Laboratory, Hanscom Air Force Base, MA 01731, USA c Department of Electrical and Computer Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA b
Available online 16 March 2005
Abstract We propose the idea of making quantum dot (QD) lasers by embedding direct-bandgap QDs in a short-period superlattice whose bandgap is indirect. In comparison with similar QD lasers with barriers of direct band gap, this technique not only reduces the temperature dependence of threshold current, but also leads to extremely small linewidth enhancement factor, making low-temperature sensitivity, low chirp, and narrow linewidth semiconductor lasers feasible. q 2005 Elsevier Ltd. All rights reserved. Keywords: Quantum dot laser; Linewidth enhancement factor; Indirect short-period superlattice; Indium arsenide
1. Introduction QD lasers were expected to exhibit all the advantages of semiconductor lasers (small size, high efficiency, tunability, high speed, etc.), yet to be free of all the drawbacks associated with the semiconductor gain medium—hightemperature sensitivity, chirp, broad linewidth and so on. Years of intensive research have yielded a number of significant achievements, but some of the potential benefits such as temperature stability and narrow linewidth have not been fully realized to date. The main reason for this lack of progress is that substantial fraction of carriers resides not in QDs but in the surrounding barriers at higher temperatures since the QD density of states (DOS) is significantly less than that of barriers [1]. As a result, the lasing threshold increases with temperature as the carrier recombination in the barriers becomes more significant, and the shape of the gain becomes strongly asymmetric, with the tail extending towards shorter wavelengths. This shape, typical of 2D and 3D semiconductor lasers, is responsible for the broad linewidth and chirp in these lasers that are characterized by the linewidth enhancement factor (a). A number of schemes * Corresponding author. Tel.: C1 617 287 6432; fax: C1 617 287 6053. E-mail address: [email protected] (G. Sun).
0026-2692/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2005.02.001
had been put forward to reduce the recombination in barriers with the tunneling injection of electrons and holes into the QDs from opposite sides [2–4]. Such a tunneling scheme, however, relies upon a resonant (with or without phonon) process that makes the performance vulnerable to inhomogeneous broadening and charging effect. We propose a new type of QD laser with a (GaAs)6(AlAs)6 short-period superlattice (SL) as barriers of indirect bandgap for obtaining low-temperature sensitivity, low chirp, narrowlinewidth semiconductor lasers.
2. Laser structures For comparative purpose, we have investigated two laser structures of InAs QDs: one embedded in direct-bandgap GaAs barriers with cladding layers of Al0.4Ga0.6As (Fig. 1(a)) and the other in indirect-bandgap (GaAs)6(AlAs)6 shortperiod SL barriers with cladding layers of Al0.7Ga0.3As (Fig. 1(b)). The choice of (GaAs)6(AlAs)6 SL as indirect barriers instead of a simple indirect AlxGa1KxAs (xO0.42) alloy is made with the consideration of a waveguide that can effectively confine both carriers and photons. A more detailed description of the proposed waveguide is given in Ref. [5]. The indirect character of the (GaAs)6(AlAs)6 SL in both real space and k-space confines electrons primarily in the X-states of AlAs layers, while the holes in the G-states of GaAs layers, yielding very long recombination times
G. Sun et al. / Microelectronics Journal 36 (2005) 183–185
Threshold Current Density (A/cm2)
184
1000
Direct GaAs 100
Indirect SL
10 0
50
100
150
200
250
300
Temperature (K) Fig. 2. Threshold current density as a function of temperature to maintain threshold gain of 8 cm for InAs QDs in direct GaAs and indirect SL barriers.
Fig. 1. Illustration of QD band structure formed on thin wetting layers in waveguides of (a) direct GaAs barriers with Al0.4Ga0.6As cladding and (b) indirect (GaAs)6(AlAs)6 short-period SL barriers with Al0.7Ga0.3As cladding.
(up to a few hundred ns to ms range according to [6,7]). Such a QD structure can produce not only a lower threshold current and higher characteristic temperature, but also much smaller a-factor because of the very small modulation in the index of refraction induced by the carriers with indirect localization in the short-period SL.
3. Threshold temperature dependence The temperature dependence of the threshold current is better illustrated with the assumption of a fixed value of optical gain that is required to compensate the typical losses (2–10 cm) found within QD laser cavities. Taking the value of threshold gain as gthZ8 cm, we have calculated the threshold current density Jth as a function of temperature for both structures (Fig. 2). Fig. 2 reveals that the QD laser with indirect SL barriers has a slightly larger threshold current at lower temperatures (T!130 K) because higher number of QDs are needed in the laser structure with
indirect SL barriers for obtaining the same optical confinement factor. As a result, a higher pumping current is required to populate them in order to achieve population inversion for optical gain. We also notice that in the lowtemperature region T!100 K, the threshold current stayed almost constant for both structures since the carrier population in the barrier regions is very small, and practically all carriers injected by the pumping current went to the QD states. At higher temperatures, however, the QD laser with direct barriers requires more pumping current to reach the threshold. A rather significant difference in J th between the two cases at higher temperatures is the direct result of the lifetime difference between the two types of barriers where there is an inevitable carrier buildup at elevated temperatures. We have obtained a characteristic temperature T0Z50 K for the QD laser structure with direct GaAs barriers in the temperature range of TO100 K and T0Z216 K for the indirect SL barriers in TO150 K—a significant improvement on the temperature characteristics of threshold.
4. Linewidth enhancement a-factor The a-factor that connects real (cr) and imaginary (ci) parts of optical susceptibility consisting of contributions from QD (cd) and barrier layers (cb) by cZGdcdCGbcb is defined as aZ
vcr =vn vci =vn
(1)
where the total carrier density (n) is distributed between QDs, barriers, and WL. A more detailed calculation procedure is given in Ref. [8]. The calculated results of a-factor and the modal gain g are shown in Fig. 3 for both structures at room temperature. Comparing Fig. 3(a) and (b), it can be seen that QDs with
G. Sun et al. / Microelectronics Journal 36 (2005) 183–185
1.0
10
0.8
8
6
10 α 5
4 2
γ
6
0.6
4
0.4 0.2
α
2
3
Direct
Gth=8/cm
LWEF α
10 8
15
LWEF α
12
LWEF α
γ
4
1.2
Modal Gain γ [1/cm]
20
(b) Indirect barrier 12
Modal Gain γ [1/cm]
(a) Direct barrier 25
185
2
1 Indirect
0 0
T=300K 0
0 1 2 3 Current Density J (kA/cm2)
0.0
0
T=300K
-2 0 50 100 150 200 250 Current Density J (A/cm2)
50
100
150
200
250
300
350
Temperature (K) Fig. 3. a and g versus pumping current density J at 300 K for InAs QD lasers with (a) direct GaAs barriers and (b) indirect (GaAs)6(AlAs)6 SL barriers.
indirect SL barriers can not only reduce the requirement of pumping current J, but also lower a. At lower J, the majority of the carrier population change takes place within the QDs instead of in the barriers. As a result, the modulation of gain is relatively larger and a is smaller. At high J, especially when g is approaching saturation, the majority of the carrier population builds up in the barriers and a becomes larger. But this increase of a for the direct GaAs barriers is much more rapid than that of indirect (GaAs)6(AlAs)6 SL barriers as shown comparatively with two very different scales of a and J between Fig. 3(a) and (b). Taking the value of threshold gain at 8 cm, we have calculated a for direct and indirect barriers as a function of temperature (Fig. 4). For T!125 K, there is little carrier buildup in the barriers, and a remains practically zero for both structures at threshold. As temperature increases, it requires more pumping current to reach the same threshold, and there is inevitable carrier accumulation in the barriers. For the direct barriers, this leads to significant change in real part of the barrier susceptibility (cr,b) and large a. For the indirect barriers, however, the carrier buildup in the barriers does not translate to large change in cr,b because electrons and holes are located indirectly in both k-space and real space where the direct optical transitions are far detuned from the lasing transition; as a result, a for indirect barriers can be significantly smaller. Fig. 4 shows that a for InAs QDs embedded in indirect barriers at room temperature can be as small as 0.1, which is significantly less than the 1.9-value for the direct GaAs barriers at the same lasing threshold.
Fig. 4. a as a function of temperature for InAs QD lasers with direct and indirect barriers reaching threshold gain of 8 cm.
5. Conclusion We have investigated the idea of incorporating directband gap InAs QDs in indirect-band gap short-period (GaAs)6(AlAs)6 SL barriers. In comparison with a similar QD laser with direct-band gap GaAs barriers, we have shown that the temperature-sensitivity can be significantly improved as demonstrated by our result of a much higher characteristic temperature (T0Z216 K). Such a structure can also produce a very small linewidth enhancement factor (az0.1) at room temperature as compared to aZ1.9 for a similar QD laser with GaAs barriers. The linewidth of a semiconductor laser is known to be proportional to 1Ca2, the reduction of a-factor from 1.9 to 0.1 yields a nearly fivefold narrowing of linewidth. The chirp during modulation (proportional to a) on the other hand can be reduced by a factor of 20.
References [1] [2] [3] [4] [5] [6] [7] [8]
L.V. Asryan, S. Luryi, IEEE J. Quantum Electron. 37 (2001) 905. L.V. Asryan, S. Luryi, Solid State Electron. 47 (2003) 205. S.L. Chuang, N. Holonyak, Appl. Phys. Lett. 80 (2002) 1270. P.K. Kondratko, S.-L. Chuang, G. Walter, T. Chung, N. Holonyak, Appl. Phys. Lett. 83 (2003) 4818. G. Sun, R.A. Soref, J.B. Khurgin, Appl. Phys. Lett. 84 (2004) 3861. E. Finkman, M.D. Sturge, M.C. Tamargo, Appl. Phys. Lett. 49 (1986) 1299. M.-H. Meynadier, R.E. Nahory, J.M. Worlock, M.C. Tamargo, J.L. de Miguel, M.D. Sturge, Phys. Rev. Lett. 60 (1988) 1338. G. Sun, J.B. Khurgin, R.A. Soref, IEEE Photon. Technol. Lett. 16 (2004) 2203.
A comparative study of InAs quantum dot lasers with barriers of direct and indirect band gaps G. Suna,*, Richard A. Sorefb, Jacob B. Khurginc a Department of Physics, University of Massachusetts at Boston, Boston, MA 02125, USA Sensors Directorate, Air Force Research Laboratory, Hanscom Air Force Base, MA 01731, USA c Department of Electrical and Computer Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA b
Available online 16 March 2005
Abstract We propose the idea of making quantum dot (QD) lasers by embedding direct-bandgap QDs in a short-period superlattice whose bandgap is indirect. In comparison with similar QD lasers with barriers of direct band gap, this technique not only reduces the temperature dependence of threshold current, but also leads to extremely small linewidth enhancement factor, making low-temperature sensitivity, low chirp, and narrow linewidth semiconductor lasers feasible. q 2005 Elsevier Ltd. All rights reserved. Keywords: Quantum dot laser; Linewidth enhancement factor; Indirect short-period superlattice; Indium arsenide
1. Introduction QD lasers were expected to exhibit all the advantages of semiconductor lasers (small size, high efficiency, tunability, high speed, etc.), yet to be free of all the drawbacks associated with the semiconductor gain medium—hightemperature sensitivity, chirp, broad linewidth and so on. Years of intensive research have yielded a number of significant achievements, but some of the potential benefits such as temperature stability and narrow linewidth have not been fully realized to date. The main reason for this lack of progress is that substantial fraction of carriers resides not in QDs but in the surrounding barriers at higher temperatures since the QD density of states (DOS) is significantly less than that of barriers [1]. As a result, the lasing threshold increases with temperature as the carrier recombination in the barriers becomes more significant, and the shape of the gain becomes strongly asymmetric, with the tail extending towards shorter wavelengths. This shape, typical of 2D and 3D semiconductor lasers, is responsible for the broad linewidth and chirp in these lasers that are characterized by the linewidth enhancement factor (a). A number of schemes * Corresponding author. Tel.: C1 617 287 6432; fax: C1 617 287 6053. E-mail address: [email protected] (G. Sun).
0026-2692/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2005.02.001
had been put forward to reduce the recombination in barriers with the tunneling injection of electrons and holes into the QDs from opposite sides [2–4]. Such a tunneling scheme, however, relies upon a resonant (with or without phonon) process that makes the performance vulnerable to inhomogeneous broadening and charging effect. We propose a new type of QD laser with a (GaAs)6(AlAs)6 short-period superlattice (SL) as barriers of indirect bandgap for obtaining low-temperature sensitivity, low chirp, narrowlinewidth semiconductor lasers.
2. Laser structures For comparative purpose, we have investigated two laser structures of InAs QDs: one embedded in direct-bandgap GaAs barriers with cladding layers of Al0.4Ga0.6As (Fig. 1(a)) and the other in indirect-bandgap (GaAs)6(AlAs)6 shortperiod SL barriers with cladding layers of Al0.7Ga0.3As (Fig. 1(b)). The choice of (GaAs)6(AlAs)6 SL as indirect barriers instead of a simple indirect AlxGa1KxAs (xO0.42) alloy is made with the consideration of a waveguide that can effectively confine both carriers and photons. A more detailed description of the proposed waveguide is given in Ref. [5]. The indirect character of the (GaAs)6(AlAs)6 SL in both real space and k-space confines electrons primarily in the X-states of AlAs layers, while the holes in the G-states of GaAs layers, yielding very long recombination times
G. Sun et al. / Microelectronics Journal 36 (2005) 183–185
Threshold Current Density (A/cm2)
184
1000
Direct GaAs 100
Indirect SL
10 0
50
100
150
200
250
300
Temperature (K) Fig. 2. Threshold current density as a function of temperature to maintain threshold gain of 8 cm for InAs QDs in direct GaAs and indirect SL barriers.
Fig. 1. Illustration of QD band structure formed on thin wetting layers in waveguides of (a) direct GaAs barriers with Al0.4Ga0.6As cladding and (b) indirect (GaAs)6(AlAs)6 short-period SL barriers with Al0.7Ga0.3As cladding.
(up to a few hundred ns to ms range according to [6,7]). Such a QD structure can produce not only a lower threshold current and higher characteristic temperature, but also much smaller a-factor because of the very small modulation in the index of refraction induced by the carriers with indirect localization in the short-period SL.
3. Threshold temperature dependence The temperature dependence of the threshold current is better illustrated with the assumption of a fixed value of optical gain that is required to compensate the typical losses (2–10 cm) found within QD laser cavities. Taking the value of threshold gain as gthZ8 cm, we have calculated the threshold current density Jth as a function of temperature for both structures (Fig. 2). Fig. 2 reveals that the QD laser with indirect SL barriers has a slightly larger threshold current at lower temperatures (T!130 K) because higher number of QDs are needed in the laser structure with
indirect SL barriers for obtaining the same optical confinement factor. As a result, a higher pumping current is required to populate them in order to achieve population inversion for optical gain. We also notice that in the lowtemperature region T!100 K, the threshold current stayed almost constant for both structures since the carrier population in the barrier regions is very small, and practically all carriers injected by the pumping current went to the QD states. At higher temperatures, however, the QD laser with direct barriers requires more pumping current to reach the threshold. A rather significant difference in J th between the two cases at higher temperatures is the direct result of the lifetime difference between the two types of barriers where there is an inevitable carrier buildup at elevated temperatures. We have obtained a characteristic temperature T0Z50 K for the QD laser structure with direct GaAs barriers in the temperature range of TO100 K and T0Z216 K for the indirect SL barriers in TO150 K—a significant improvement on the temperature characteristics of threshold.
4. Linewidth enhancement a-factor The a-factor that connects real (cr) and imaginary (ci) parts of optical susceptibility consisting of contributions from QD (cd) and barrier layers (cb) by cZGdcdCGbcb is defined as aZ
vcr =vn vci =vn
(1)
where the total carrier density (n) is distributed between QDs, barriers, and WL. A more detailed calculation procedure is given in Ref. [8]. The calculated results of a-factor and the modal gain g are shown in Fig. 3 for both structures at room temperature. Comparing Fig. 3(a) and (b), it can be seen that QDs with
G. Sun et al. / Microelectronics Journal 36 (2005) 183–185
1.0
10
0.8
8
6
10 α 5
4 2
γ
6
0.6
4
0.4 0.2
α
2
3
Direct
Gth=8/cm
LWEF α
10 8
15
LWEF α
12
LWEF α
γ
4
1.2
Modal Gain γ [1/cm]
20
(b) Indirect barrier 12
Modal Gain γ [1/cm]
(a) Direct barrier 25
185
2
1 Indirect
0 0
T=300K 0
0 1 2 3 Current Density J (kA/cm2)
0.0
0
T=300K
-2 0 50 100 150 200 250 Current Density J (A/cm2)
50
100
150
200
250
300
350
Temperature (K) Fig. 3. a and g versus pumping current density J at 300 K for InAs QD lasers with (a) direct GaAs barriers and (b) indirect (GaAs)6(AlAs)6 SL barriers.
indirect SL barriers can not only reduce the requirement of pumping current J, but also lower a. At lower J, the majority of the carrier population change takes place within the QDs instead of in the barriers. As a result, the modulation of gain is relatively larger and a is smaller. At high J, especially when g is approaching saturation, the majority of the carrier population builds up in the barriers and a becomes larger. But this increase of a for the direct GaAs barriers is much more rapid than that of indirect (GaAs)6(AlAs)6 SL barriers as shown comparatively with two very different scales of a and J between Fig. 3(a) and (b). Taking the value of threshold gain at 8 cm, we have calculated a for direct and indirect barriers as a function of temperature (Fig. 4). For T!125 K, there is little carrier buildup in the barriers, and a remains practically zero for both structures at threshold. As temperature increases, it requires more pumping current to reach the same threshold, and there is inevitable carrier accumulation in the barriers. For the direct barriers, this leads to significant change in real part of the barrier susceptibility (cr,b) and large a. For the indirect barriers, however, the carrier buildup in the barriers does not translate to large change in cr,b because electrons and holes are located indirectly in both k-space and real space where the direct optical transitions are far detuned from the lasing transition; as a result, a for indirect barriers can be significantly smaller. Fig. 4 shows that a for InAs QDs embedded in indirect barriers at room temperature can be as small as 0.1, which is significantly less than the 1.9-value for the direct GaAs barriers at the same lasing threshold.
Fig. 4. a as a function of temperature for InAs QD lasers with direct and indirect barriers reaching threshold gain of 8 cm.
5. Conclusion We have investigated the idea of incorporating directband gap InAs QDs in indirect-band gap short-period (GaAs)6(AlAs)6 SL barriers. In comparison with a similar QD laser with direct-band gap GaAs barriers, we have shown that the temperature-sensitivity can be significantly improved as demonstrated by our result of a much higher characteristic temperature (T0Z216 K). Such a structure can also produce a very small linewidth enhancement factor (az0.1) at room temperature as compared to aZ1.9 for a similar QD laser with GaAs barriers. The linewidth of a semiconductor laser is known to be proportional to 1Ca2, the reduction of a-factor from 1.9 to 0.1 yields a nearly fivefold narrowing of linewidth. The chirp during modulation (proportional to a) on the other hand can be reduced by a factor of 20.
References [1] [2] [3] [4] [5] [6] [7] [8]
L.V. Asryan, S. Luryi, IEEE J. Quantum Electron. 37 (2001) 905. L.V. Asryan, S. Luryi, Solid State Electron. 47 (2003) 205. S.L. Chuang, N. Holonyak, Appl. Phys. Lett. 80 (2002) 1270. P.K. Kondratko, S.-L. Chuang, G. Walter, T. Chung, N. Holonyak, Appl. Phys. Lett. 83 (2003) 4818. G. Sun, R.A. Soref, J.B. Khurgin, Appl. Phys. Lett. 84 (2004) 3861. E. Finkman, M.D. Sturge, M.C. Tamargo, Appl. Phys. Lett. 49 (1986) 1299. M.-H. Meynadier, R.E. Nahory, J.M. Worlock, M.C. Tamargo, J.L. de Miguel, M.D. Sturge, Phys. Rev. Lett. 60 (1988) 1338. G. Sun, J.B. Khurgin, R.A. Soref, IEEE Photon. Technol. Lett. 16 (2004) 2203.