This content has been downloaded from IOPscience. Please scroll down to see the full text.

Download details:

IP Address: 128.82.252.58

This content was downloaded on 23/06/2014 at 12:49

Please note that terms and conditions apply.

Quantitative analysis of carrier activation and redistribution in self-assembled quantum dot

(QD) heterostructures using rate equations

View the table of contents for this issue, or go to the journal homepage for more

2011 Semicond. Sci. Technol. 26 045013

(http://iopscience.iop.org/0268-1242/26/4/045013)

Home Search Collections Journals About Contact us My IOPscience

IOP PUBLISHING SEMICONDUCTOR SCIENCE AND TECHNOLOGY

Semicond. Sci. Technol. 26 (2011) 045013 (6pp) doi:10.1088/0268-1242/26/4/045013

Quantitative analysis of carrier activationand redistribution in self-assembledquantum dot (QD) heterostructuresusing rate equationsXuejun Lu1 and Jarrod Vaillancourt2

1 Department of Electrical and Computer Engineering, University of Massachusetts Lowell,One University Avenue, Lowell, MA 01854, USA2 Applied NanoFemto Technologies, LLC, 181 Stedman St #2, Lowell, MA 01851, USA

E-mail: xuejun_lu@uml.edu

Received 27 September 2010, in final form 17 November 2010Published 25 February 2011Online at stacks.iop.org/SST/26/045013

AbstractIn this paper, we report a temperature-dependent photoluminescence study of the carrierthermal activation and redistribution in the QD heterostructures with different (i.e. InGaAs andGaAs) capping layers. Quantitative analysis of the carrier thermal activation and redistributionprocesses among the QDs with different capping layers was performed using rate equations.The rate equation model agrees well with the experimental observations for temperaturesabove 50 K. Relations between the radiative and nonradiative recombination rate ratio and thephoto-excitation rate for the QDs with different capping layers are also determined.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Self-assembled quantum dots (QDs) grown via the Stanski–Krastanow (SK) growth mode have shown great promise inhigh-performance optoelectronic device development, suchas ultra-low threshold QD lasers [1–3], and high operatingtemperature (HOT) QD infrared photodetectors (QDIP) [4–6].We have reported voltage-tunable multi-spectral QDIP andfocal plane arrays (FPA) based on InAs QD heterostructureswith InGaAs and GaAs capping layers [7, 8]. Voltage-tunable multi-spectral imaging was demonstrated with goodphotoresponsivity and photodetectivity selectivity [8]. Suchtechnology is promising for adaptive multispectral infrared(IR) sensing and imaging with voltage-tunable detection bandselection capabilities. To further understand the mechanism ofthe voltage-tunable multi-spectral photodetection, it is desiredto have detailed knowledge of carrier capture and redistributionin the InAs QD heterostructures with different capping layers.Carrier thermal activation and recapture in self-assembled QDensembles have been studied [9–13]. However, few report onthe quantitative analysis of the carrier activation and recapture

processes. In this paper, we report a temperature-dependentphotoluminescence (PL) study of the carrier thermal activationand recapture in QD heterostructures. Quantitative analysisof the carrier thermal activation and recapture processeswas performed using a rate equation model [14]. Atlow temperatures the photo-excited carriers (electrons andholes) are captured locally independent of the QD energylevels, a significant deviation from the classical Boltzmanndistribution. As the temperature increases, the capturedcarriers are thermally excited and redistributed to the QDs withlow energy levels. The carrier thermal activation and recaptureprocesses can be well explained using the rate equation modelfor temperatures above 50 K. Relations between the radiativeand nonradiative recombination rate ratio and the photo-excitation rate for the QDs with different capping layers arediscussed. We also find that at low temperatures (<50 K),the rate equation model shows a significant deviation fromthe experimental data. Since the rate equation model isbased on the Arrhenius-type thermal activation [14], the lowtemperature deviation suggests that the Arrhenius-type thermalactivation assumption is inappropriate at low temperatures.

0268-1242/11/045013+06$33.00 1 © 2011 IOP Publishing Ltd Printed in the UK & the USA

Semicond. Sci. Technol. 26 (2011) 045013 X Lu and J Vaillancourt

(a)

(b)

Figure 1. Schematic structures of QD samples (a) #2051 and(b) #2050. Sample #2051 contains five layers of QDs with GaAscapping layers. Sample #2050 contains five layers of QDs withIn0.15Ga0.85As capping layers and five layers of QDs with GaAscapping layers.

2. Experiment

Two QD hetero-structure samples were grown for thequantitative PL emission analysis. The schematic structuresof the two samples (i.e. #2051 and #2050) are shown infigures 1(a) and (b), respectively. Sample #2051 was grown tohave five layers of GaAs-capped QDs. Sample #2050 containsfive layers of QDs with In0.15Ga0.85As capping layers and fivelayers of QDs with GaAs capping layers. The QD layersare separated by 62 nm thick GaAs buffer layers. Both ofthe QD samples were grown by a V80H molecular beamexpitaxy (MBE) system. The QD layers and the In0.15Ga0.85Asand GaAs cap layers were grown at 470 ◦C. The growthtemperature for the GaAs buffer layers was 620 ◦C. The growthrates of the InAs QDs, In0.15Ga0.85As cap layers and GaAsspacers were 0.16, 0.8, and 0.9 ML s−1, respectively. ThePL was performed using a continuous wave diode-pumpedsolid-state laser (DPSSL) with an excitation wavelength of532 nm and laser output power of approximately 70 mW. Thelaser spot size was around 0.5 mm2. This gives a pumpingpower density of 14 W cm−2. The PL emission was collectedusing a collimator and analyzed using an Oriel MS257TM

1/4 m monochromator and detected by a liquid-nitrogen (LN2)cooled InGaAs photodetector. The PL was measured at varioussample temperatures from T = 12 to 300 K.

Figure 2. PL spectra of sample #2051 at various temperatures from12 to 300 K. The PL emission peak red shifts from 1.297 eV to alower energy (longer wavelength) of 1.211 eV as temperatureincreases from 12 to 300 K. The PL intensity decreases as thesample temperature increases.

3. Results and discussion

Figure 2 shows the PL spectra of sample #2051 at varioustemperatures from 12 to 300 K. Assuming all photo-excitedelectron–hole pairs are effectively captured in the QDs andthe lifetime of the photo-excited electron–hole pairs is 1 ns[15, 16], the laser excitation power density of 14 W cm−2

gives an excitation density of 3.7 × 1010 cm−2. Since thetypical QD density is ∼2–3 × 1010 cm−2 for each QD layer[5–7], the photo-excitation density is much lower than theQD densities for all the multi-layer QD samples. At thislow excitation density, the average population of the photo-excited electron–hole pairs in a QD is much smaller than1. The PL emission profiles and wavelengths are consistentwith reported QD PL emissions in InAs/GaAs heterostructures[9]. At low temperatures (<90 K), the PL emission spectrashow Gaussian-type profiles with a standard deviation (σ ) ofapproximately 30 meV, indicating that the PL emissions aremostly coming from QDs with negligible contribution fromthe wetting layers of the QDs. The low standard deviation (σ )value indicates good uniformity of the QDs.

As shown in figure 2, as the sample temperature increases,the PL intensity decreases (i.e. thermal quenching of PLemission) and the PL emission profiles show deviation fromthe Gaussian shape. The thermal quenching of PL emissionis attributed to the carrier thermal activation and escape out ofthe QD ground states, which results in less excited carriers inQDs and leads to weaker PL emissions [10–12]. In quantumwells (QW), the thermal activation and reemission process ismodeled using a rate equation [14]. Lambkin et al have shownthat [9] the integrated PL intensity I is related to the activationenergy Ea of the thermal evaporation process by

− Ea

kBT= ln

(R

R′

)+ ln

(P

I− 1 − R′

U

), (1)

2

Semicond. Sci. Technol. 26 (2011) 045013 X Lu and J Vaillancourt

Figure 3. ln( 1I

− 1I0

) versus 1000/T plot for QD sample #2051 at

different temperatures. ln( 1I

− 1I0

) shows a linear dependence with1000/T for temperatures over 50 K (the dashed line shows the linearcurve fitting).

where kB is the Boltzmann constant, P is the photo-excitationrate, U is the carrier capture rate, and R and R′ are the radiativeand nonradiative emission rates, respectively. At T = 0 Kthe thermal reemission from the QWs is negligible, and if oneignores the nonradiative recombination in QWs, the capturerate equals the PL emission rate, i.e.

I0 = Rm = Un, (2)

where I0 is the PL intensity at 0 K, and m and n are the carrierdensities in the QW and the barriers, respectively. The pumprate can thus be written as

P = (U + R′)n. (3)

Equation (1) can therefore be written as

ln

(1

I− 1

I0

)= − Ea

kBT− ln

(R

R′

)− ln P, (4)

where ln represents the natural logarithm operation, and I0 isthe integrated PL intensity at T = 0 K, which can be obtainedby extrapolating the I–T curve to T = 0 K. Note that equation(1) through equation (4) are derived for QWs. Nevertheless,we still find a good agreement with the model for our QDsamples as we plot ln

(1I

− 1I0

)versus 1000/T. Figure 3 shows

the ln(

1I

− 1I0

)versus 1000/T plot for QD sample #2051 at

different temperatures. As one can see from figure 3, thereare two temperature regions. In the low temperature region(T < 50 K or 1000/T > 20 1/K), ln

(1I

− 1I0

)does not change

much with 1000/T. In the high temperature region (T >

50 K or 1000/T < 20 1/K), a linear relationship betweenln

(1I

− 1I0

)and 1000/T is obtained (dashed line in the figure).

This indicates that in the high temperature region, the QDPL emission follows the rate equation model (4), whereasat low temperature (<50 K), the PL intensity shows a largedeviation from the rate equation model (dashed line). Sincethe rate equation model is based on the Arrhenius-type thermalactivation [14], the low temperature deviation indicates that the

Arrhenius-type thermal activation assumption is inappropriateat low temperatures. Note that the 300 K PL intensity pointis above the dashed line, indicating a faster thermal activationrate than the model’s prediction. We attribute the deviation tothe excited state PL emission at 1.285 eV.

Equation (4) also indicates that the relation between theradiative and nonradiative recombination rate ratio R

R′ and thephoto-excitation rate P can be obtained from the interceptionon the y-axis.

Figures 4(a) through (c) show the PL emission spectraof QD sample #2050 at different temperatures. At eachtemperature, the PL spectrum shows two peaks. Comparedwith the PL emission from GaAs-capped QDs (figure 2), thehigher energy peak can be attributed to the PL emission fromthe GaAs-capped QDs. As discussed above, since the photo-excitation density is much lower than the QD densities ofthe QD sample, the photo-excited electron–hole pairs wouldoccupy the ground state of the QDs at low temperature andPL emission is primarily from the ground states of the QDs.The lower energy peak is thus from the In0.15Ga0.85As-cappedQDs [8].

When the sample temperature is less than 90 K(figure 4(a)), the GaAs-capped QDs show a stronger PLemission than the In0.15Ga0.85As-capped QDs, indicating alarger carrier density in the GaAs-capped QDs. Sincethe GaAs-capped QDs have higher energy levels thanIn0.15Ga0.85As-capped QDs, the larger carrier density in theGaAs-capped QDs suggests that the carrier capture intoQDs is localized and independent of energy levels. Similarobservations have been reported by Polimeni et al and Heitzet al [12, 17]. As the temperature increases from 90 to 150 K,the PL intensity of the GaAs-capped QDs keeps decreasing,while the PL intensity of the In0.15Ga0.85As-capped QDs startsincreasing (figure 4(b)). The PL intensity increase is dueto the carrier thermal excitation and redistribution from theGaAs-capped QDs to the In0.15Ga0.85As-capped QDs. Asthe temperature further increases from 170 to 300 K, the PLintensity begins to decrease and the higher energy PL emissionpeak shows up again (figure 4(c)). Since the high energy peakis comparable with the PL peak of sample #2051 (samplewith GaAs-capped QDs only), we attribute this to the carrierthermal occupation of GaAs-capped QDs. Considering the∼5.5 times larger PL intensity of GaAs-capped QDs thanthat of the In0.15Ga0.85As-capped QDs at low temperatures(figure 4(a)), one can calculate that the carrier density ratio ofthe GaAs-capped QDs to the In0.15Ga0.85As-capped QDs with∼50 meV energy difference is 5.5 × e−50 meV (kT)−1

, which is∼1.0 at T = 300 K. This agrees well with the PL intensities ofthe GaAs-capped and the In0.15Ga0.85As-capped QDs in figure4(c). This suggests that the carrier distribution follows theclassic Boltzmann distribution at T = 300 K.

Figure 5 shows the PL intensity from the In0.15Ga0.85As-capped QDs at different temperatures. The triangle pointsindicate the rate equation predicted high temperature PLintensity without the carrier redistribution from the GaAs-capped QDs. As shown in figure 5, without the carrierredistribution from the GaAs-capped QDs, the PL of theIn0.15Ga0.85As-capped QDs is negligible at high temperaturesover 135 K.

3

Semicond. Sci. Technol. 26 (2011) 045013 X Lu and J Vaillancourt

(a)

(b)

(c)

Figure 4. PL emission spectrum of QD sample #2050 at differenttemperatures. At each temperature, the PL spectrum shows twopeaks. The higher energy peak is attributed to the PL emission fromthe GaAs-capped QDs, and the lower energy peak is from theIn0.15Ga0.85As-capped QDs. (a) At low temperature, the PL intensityof the In0.15Ga0.85As-capped QDs decreases with increasingtemperature. (b) As temperature increases from 90 to 150 K, the PLintensity of the GaAs-capped QDs decreases, while the PL intensityof the In0.15Ga0.85As-capped QDs starts to increase. (c) As thetemperature further increases from 170 to 300 K, the PL intensitybegins to decrease and the higher energy PL emission peak showsup again.

Figure 6 shows the ln(

1I

− 1I0

)versus 1000/T plot for the

GaAs-capped QDs (squares) and the In0.15Ga0.85As-capped

Figure 5. PL intensity of the In0.15Ga0.85As-capped QDs at differenttemperatures. The triangle points are the rate equation predictedhigh temperature PL intensity without the carrier redistribution fromthe GaAs-capped QDs. Without the carrier redistribution from theGaAs-capped QDs, the PL of the In0.15Ga0.85As-capped QDs isnegligible at high temperatures over 135 K.

Figure 6. ln( 1I

− 1I0

) versus 1000/T plot for the GaAs-capped QDs(squares) and the In0.15Ga0.85As-capped QDs (triangles) in sample#2050. For the In0.15Ga0.85As-capped QDs (triangles), a linearrelationship between ln( 1

I− 1

I0) and 1000/T is obtained at the

sample temperature range from 33 to 90 K. For the GaAs-cappedQDs (squares), a linear relationship between ln( 1

I− 1

I0) and 1000/T

can also be obtained at the temperature range from 50 to 155 K.

QDs (triangles) in sample #2050. For the In0.15Ga0.85As-capped QDs (triangles), a linear relationship betweenln

(1I

− 1I0

)and 1000/T is obtained at the sample temperature

range from 33 to 90 K. This shows that the rate equation modelis still valid in this temperature range. For the GaAs-cappedQDs (squares), a linear relationship between ln

(1I

− 1I0

)and

1000/T can also be obtained at the temperature range from 50to 155 K. The larger slope of the GaAs-capped QDs is due tothe deeper carrier confinement.

4

Semicond. Sci. Technol. 26 (2011) 045013 X Lu and J Vaillancourt

Note that the two linear fittings have the same interceptat the y-axis: Ycp. Since the PL intensity I at the y-axis, i.e.1000/T = 0 (high temperature), is much smaller than the PLintensity at T = 0 K, I0, one obtains 1

I>> 1

I0. Therefore, the

intercept at the y-axis, Ycp, can be approximately written as

Ycp ≈ ln

(1

IHT

), (5)

where IHT is the PL intensity at the high temperature limit.Thus from the intercept at the y-axis, Ycp, one can obtain IHT.From equation (4), the PL intensity at the high temperaturelimit IHT can be further written as

IHT

P≈ R

R′ . (6)

Equation (6) can be directly derived from the rate equationmodel (4) by setting the carrier densities m and n to be thesame at the high temperature limit (Boltzmann distribution)and R′n � Rm. From equation (6), the ratio of the radiativeand nonradiative recombination rates R

R′ can be obtained fromthe ratio of the IHT and the pump power. Assuming that theexcitation rates for the InGaAs-capped QDs and the GaAs-capped QDs are the same, the same intercepts at the y-axis, Ycp,for both the GaAs-capped and the In0.15Ga0.85As-capped QDsindicates that the radiative and nonradiative recombination rateratio R

R′ is the same for both types of QDs.Note that at low temperatures, GaAs-capped QDs show an

around 5.5 times stronger PL intensity than the In0.15Ga0.85As-capped QDs. It might be due to the combination of higher QDdensity and larger capture rate from the barrier into the QDsas well as higher excitation photon density at top layers.

In the above discussion, we attributed the PL intensityincrease of the In0.15Ga0.85As-capped QDs from T = 90 to150 K (figure 4(b)) to the redistribution of the thermallyactivated carriers from the GaAs-capped QDs to theIn0.15Ga0.85As-capped QDs. We still use the rate equationmodel [9] to quantitatively analyze this effect. Under steadystate, the carrier density in the barriers n can be expressed as

n = P(R + U e−Ea/kT )

RU + R′(R + U e−Ea/kT ). (7)

At T = 0 K, the carrier density in the barriers is

n0 = P

U + R′ . (8)

The total carrier dissipation rate in the barriers at T = 0 Kis thus

R′

Re−Ea/kT = R′

U

[1

R′n0− 1

R′n

][

1R′n − 1

P

] . (9)

Since the pump power P is greater than the carrierdissipation rate in the barriers Rn′, for approximation, equation(9) can be written as

ln

(n

n0− 1

)= −Ea

kT− ln

(R

U

). (10)

At high temperatures n � n0, equation (10) is then

ln (n) = −Ea

kT− ln

(Rn0

U

). (11)

Figure 7. ln (I ) versus 1000/T plot at the temperature range from135 to 160 K for the PL of the In0.15Ga0.85As-capped QDs. A linearrelationship between ln (I ) and 1000/T is obtained, indicating thatPL intensity increase �I due to the carrier redistribution reasonablyagrees with the rate equation model.

Assuming that the redistribution rate to the In0.15Ga0.85As-capped QDs is V, then, the carrier redistribution-induced PLintensity increase of the In0.15Ga0.85As-capped QDs is

ln (�I) = ln (RV n) = −Ea

kT− ln

(Rn0

URV

), (12)

where �I is the PL intensity increase due to the carrierredistribution. Since without the carrier redistribution, the PLof the In0.15Ga0.85As-capped QD is negligible at T > 135 K(figure 5), �I approximately equals the measured PL intensityI. Equation (12) can thus be written as

ln (I ) ≈ ln (�I) = −Ea

kT− ln

(Rn0

URV

). (13)

Figure 7 shows the ln (I ) versus 1000/T plot in the temperaturerange from 135 to 160 K. A linear relationship between ln (I )

and 1000/T is obtained. This suggests that the PL intensityincrease �I due to the carrier redistribution reasonably agreeswith the rate equation model.

4. Conclusions

We have conducted the PL study of the temperature-dependent carrier capture and redistribution process in QDheterostructures with different capping layers. At lowtemperatures the photo-excited carriers (electrons and holes)are captured locally independent of the QD energy levels, asignificant deviation from the classical Boltzmann distribution.As the temperature increases, the captured carriers arethermally excited and redistributed to the QDs with lowenergy levels. The carrier thermal activation and recaptureprocesses can be well explained using the rate equation modelfor temperatures above 50 K. At T = 300 K, the carrierdistribution in the GaAs-capped and the In0.15Ga0.85As-cappedQDs follows the classic Boltzmann distribution.

5

Semicond. Sci. Technol. 26 (2011) 045013 X Lu and J Vaillancourt

Acknowledgments

This research was supported by 2006 and 2008 ASEE summerfaculty research programs, and the Air Force SBIR Phase IIprograms under contract nos FA9453-07-C-0075 and FA8650-09-C-1617. The authors would like to thank Dr AndreasStintz of Center for High Technology Materials (CHTM) ofUniversity of New Mexico for MBE growth and valuablediscussion. The authors appreciate the help and valuablediscussions with Dr Danhong Huang, Dr Dave Cardimona,Dr Thomas Nelson, Mr John Scheihing, Dr Robert Bedford,Mr Wally Rice, and Dr William Ewing and Dr Alvin Drehmanof the Air Force Research Laboratory (AFRL).

References

[1] Huffaker D L, Park G, Zou Z, Shchekin O B and Deppe D G1998 1.3 μm room temperature GaAs-based quantum-dotlaser Appl. Phys. Lett. 73 2564–6

[2] Park G, Huffaker D L, Zou Z, Shchekin O B and Deppe D G1999 Temperature dependence of lasing characteristics forlong-wavelength (1.3-μm) GaAs-based quantum-dot lasersIEEE Photon. Technol. Lett. 11 301–3

[3] Liu G T, Stintz A, Li H, Malloy K J and Lester L F 1999Extremely low room-temperature threshold current densitydiode lasers using InAs dots in In0.15Ga0.85As quantum wellElectron. Lett. 35 1163–5

[4] Bhattacharya P, Su X H, Chakrabarti S, Ariyawansa Gand Perera A G U 2005 Characteristics of a tunnelingquantum-dot infrared photodetector operating at roomtemperature Appl. Phys. Lett. 86 191106-1–3

[5] Stiff A, Krishna S, Bhattacharya P and Kennerly S 2001High-detectivity normal-incidence, midinfrared (4 μm)InAs/GaAs quantum dot detector operating at 150 K Appl.Phys. Lett. 79 421–3

[6] Lu X, Vaillancourt J and Meisner M J 2007Temperature-dependent photoresponsivity andhigh-temperature (190 K) operation of a quantum dotinfrared photodetector Appl. Phys. Lett. 91 051115

[7] Vaillancourt J et al 2009 A voltage-tunable multi-spectral320×256 InAs/GaAs quantum-dot infrared focal planearray (FPA) Semicond. Sci. Technol. 24 045008

[8] Meisner M J, Vaillancourt J and Lu X 2008 Voltage-tunabledual-band InAs quantum-dot infrared photodetectors basedon InAs quantum dots with different capping layersSemicond. Sci. Technol. 23 095016

[9] Popescu D P, Eliseev P G, Stintz A and Malloy K J 2004Temperature dependence of the photoluminescenceemission from InAs quantum dots in a strainedGa0.85In0.15As quantum well Semicond. Sci. Technol.19 33–8

[10] Sanguinetti S, Henini M, Alessi M G, Capizzi M, Friferi Pand Franchi S 1999 Carrier thermal escape and retrappingin self-assembled quantum dots Phys. Rev. B 60 8276–83

[11] Ortner G, Schwab M, Bayer M, Passler R, Fafard S,Wasilewski Z, Hawrylak P and Forchel A 2005 Temperaturedependence of the excitonic band gap in InGaAs/GaAsself-assembled quantum dots Phys. Rev. B 72 085328

[12] Polimeni A, Patane A, Henini M, Eaves L and Main P C 1999Temperature dependence of the optical properties ofInGaAs/AlyGa1−yAs self-organized quantum dots Phys.Rev. B 59 5064–8

[13] Seravalli L, Trevisi G, Frigeri P, Franchi S, Geddo Mand Guizzetti G 2009 The role of wetting layer states on theemission efficiency of InAs/InGaAs metamorphic quantumdot nanostructures Nanotechnology 20 275703

[14] Lambkin J D, Dunstan D J, Homewood K P and Howard L K1990 Thermal quenching of the photoluminescence ofInGaAs/GaAs and InGaAs/AlGaAs strained-layerquantum wells Appl. Phys. Lett. 57 1986–8

[15] Dawson P, Rubel O, Baranovskii S D, Pierz K, Thomas Pand Gobel E O 2005 Temperature-dependent opticalproperties of InAs/GaAs quantum dots: independentcarrier versus exciton relaxation Phys. Rev. B 72 235301

[16] Xu Z Y, Lu Z D, Yang X P, Yuan Z L, Zheng B Z, Xu J Z,Ge W K, Wang Y, Wang J and Chang L L 1996 Carrierrelaxation and the thermal activation of the localizedexcitons in self-organized InAs multi-layers grown onGaAs substrates Phys. Rev. B 54 11528–31

[17] Heitz R et al 1996 Multiphonon-relaxation processes inself-organized InAs/GaAs quantum dots Appl. Phys. Lett.68 361

6