DTIC ADA471348: Strain-free Ge/GeSiSn Quantum Cascade Lasers Based on L-Valley Intersubband Transitions

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21-08-2007 Journal Article 30 June 2007
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Strain-free Ge/GeSiSn quantum cascade lasers based on L-valley intersubband 5b. GRANT NUMBER

transitions
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6. AUTHOR(S) 5d. PROJECT NUMBER
2305
R. A. Soref, G. Sun, H. Cheng, J. Menendez, and J. Khurgin 5e. TASK NUMBER
HC
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Published in Applied Physics Letters 90, 251105 (2007). CLEARANCE ESC-07-0560
Cleared for public release by ESC/PA: ESC-07-0560, dated 14 May 07
14. ABSTRACT

The authors propose a Ge/Ge0.76Si0.19Sn0.05 quantum cascade laser using intersubband transitions at
L valleys of the conduction band which has a “clean” offset of 150 meV situated below other energy
valleys Gamma and X. The entire structure is strain-free because the lattice-matched Ge and Ge0.76Si0.19Sn0.05
layers are to be grown on a relaxed Ge buffer layer on a Si substrate. Longer lifetimes due to the weaker scattering of
nonpolar optical phonons reduce the threshold current and potentially lead to room temperature operation.
15. SUBJECT TERMS

Quantum cascade laser, terahertz, silicon, germanium, tin, optoelectronics
16. SECURITY CLASSIFICATION OF: 17.LIMITATION 18.NUMBER 19a. NAME OF RESPONSIBLE PERSON
OF ABSTRACT OF PAGES Richard Soref
a. REPORT b. ABSTRACT c.THIS PAGE 19b. TELEPHONE NUMBER (include area code)
Unclassified Unclassified Unclassified SAR 5 N/A
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Prescribed by ANSI Std. Z39.18
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APPLIEDPHYSICSLETTERS90,251105(cid:1)2007(cid:2)
Strain-free Ge/GeSiSn quantum cascade lasers based on L-valley
intersubband transitions
G. Sun
DepartmentofPhysics,UniversityofMassachusettsBoston,Massachusetts02125
H. H. Chenga(cid:1)
CenterforCondensedMatterSciences,NationalTaiwanUniversity,Taipei,106,
TaiwanandGraduateInstituteofElectronicsEngineering,NationalTaiwanUniversity,Taipei106,Taiwan
J. Menéndez
DepartmentofPhysicsandAstronomy,ArizonaStateUniversity,Tempe,Arizona85287
J. B. Khurgin
DepartmentofElectricalandComputerEngineering,JohnsHopkinsUniversity,Baltimore,
Maryland21218
R. A. Soref
SensorsDirectorate,AirForceResearchLaboratory,HanscomAFB,Massachusetts01731
(cid:1)Received 11April 2007; accepted 24 May 2007; published online 20 June 2007(cid:2)
TheauthorsproposeaGe/Ge Si Sn quantumcascadelaserusingintersubbandtransitionsat
0.76 0.19 0.05
Lvalleysoftheconductionbandwhichhasa“clean”offsetof150 meVsituatedbelowotherenergy
valleys (cid:1)(cid:1),X(cid:2). The entire structure is strain-free because the lattice-matched Ge and
Ge Si Sn layers are to be grown on a relaxed Ge buffer layer on a Si substrate. Longer
0.76 0.19 0.05
lifetimesduetotheweakerscatteringofnonpolaropticalphononsreducethethresholdcurrentand
potentially lead to room temperature operation. © 2007 American Institute of Physics.
(cid:3)DOI:10.1063/1.2749844(cid:4)
Electrically pumped Si-based lasers have long been the two (cid:2) valleys along the (cid:1)001(cid:2) growth direction are still
2
sought because they serve as light sources for monolithic entangled with the L valleys in the conduction band, leading
integration of Si electronics with photonic components on todesigncomplexityandpotentiallycreatingadditionalnon-
the same Si wafer. Unfortunately, Si has not been a material radiative decay channels for the upper laser state.
of choice for luminescence applications owing to its indirect In this letter, we propose to employ Ge/Ge Si Sn
1−x−y x y
bandgap.Ithasbeenproposedthatlasersbasedonintersub- heterostructurestodevelopL-valleyQCLs.Ge Si Sn al-
1−x−y x y
band transitions (cid:1)ISTs(cid:2) in SiGe quantum wells (cid:1)QWs(cid:2) could loys have been studied for the possibility of forming direct
circumvent the issue of band gap indirectness.1 In addition, band gap semiconductors.6–9 Since the initial growth of this
SiGe QWs, being a nonpolar material, are expected to have alloy,10 device-quality epilayers with a wide range of alloy
longer intersubband lifetimes that reduce the threshold cur- contents have been achieved. Incorporation of Sn provides
rentandtobefreefromthereststrahlabsorptionthatisfound the opportunity to engineer separately the strain and band
in III-V quantum cascade lasers (cid:1)QCLs(cid:2). Various groups structure since we can vary the Si (cid:1)x(cid:2) and Sn (cid:1)y(cid:2) composi-
have obtained electroluminescence from Si-rich Si/SiGe tionsindependently.Certainalloycompositionsofthismate-
quantum cascade structures,2–4 but lasing has eluded re- rial system offer three advantages: (cid:1)1(cid:2) the possibility of a
searchers up to now. Those efforts all have one scheme in “cleaner” conduction band lineup in which the L valleys in
common:holesinsteadofelectronsareusedforISTbecause both well and barrier sit below other valleys (cid:1)(cid:1),X(cid:2), (cid:1)2(cid:2) an
most of the band offset between the Si-rich SiGe QWs and electroneffectivemassalongthe(cid:1)001(cid:2)growthdirectionthat
the Si barriers is in the valence band.There are a number of is much lower than the prior heavy-hole mass, and (cid:1)3(cid:2) a
difficulties associated with valence band Si/SiGe QCLs. lattice-matched structure that is entirely strain-free. In addi-
First, the strong mixing of heavy-hole, light-hole, and split-
tion, recent advances in the direct growth of Ge layer on Si
off bands makes the QCL design exceedingly cumbersome
provide a relaxed matching buffer layer on a Si substrate
and adds a great degree of uncertainty. Second, the large uponwhichthestrain-freeQCLisgrown,11althoughprecise
effective mass of heavy holes hinders carrier injection effi-
control of the layer thickness and interface sharpness is
ciency and leads to small IST oscillator strength between
yet to be accomplished before the proposed QCL can be
laser states. Third, for any significant band offset needed to
implemented.
implement QCLs, lattice-mismatch-induced strain in SiGe
Since band offsets between ternary Sn-containing alloys
QWs is likely to limit total structural thickness in order to
and Si or Ge are not known experimentally, we have calcu-
avoidgenerationofstructuraldefects.Recently,aconduction
lated the conduction band minima for a lattice-matched het-
intersubbandapproachwasproposedtoconstructaGe/SiGe
erostructure consisting of Ge and a ternary Ge Si Sn
QCL using strained Ge QWs and SiGe alloy barriers.5 That basedonJaros’bandoffsettheory,12whichising1o−ox−dyagxreey-
structureeffectivelyavoidsthevalencebandcomplexity,but
ment with experiment for many heterojunction systems. For
example,thistheorypredictsanaveragevalencebandoffset,
a(cid:2)Electronicmail:[email protected] (cid:2)Ev,av=0.48 eV for a Ge/Si heterostructure (cid:1)higher energy
0003-6951/2007/90(cid:2)25(cid:1)/251105/3/$23.00 90,251105-1 ©2007AmericanInstituteofPhysics
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251105-2 Sunetal. Appl.Phys.Lett.90,251105(cid:2)2007(cid:1)
FIG.1. ConductionbandminimaatL,(cid:1),X pointsofGe SiSn thatis
1−x-y x y FIG.2. (cid:1)Coloronline(cid:2)L-valleyconductionbandprofileandsquaredenve-
latticematchedtoGe.
lope functions under an electric field of 10kV/cm. Layer thicknesses in
angstromaremarkedwithboldnumbersforGeQWsandregularforGe-
on the Ge side(cid:2), close to the accepted value of (cid:2)E SiSnbarriers.Arraymarkstheinjectionbarrier.
v,av
=0.5 eV. The basic ingredients of our calculation are the
average (cid:1)between heavy, light, and split-off hole bands(cid:2) va- edge of the Ge Si Sn barrier. This band alignment
0.76 0.19 0.05
lence band offset between the two materials and the compo- presents a desirable alloy composition from which a QCL
sitionaldependenceofthebandstructureoftheternaryalloy. operatingatL valleyscanbedesignedusingGeasQWsand
F=o0r.69aeVGe/(cid:1)(cid:3)h-iSghnerinteenrefargcey Joanros’thetheSorny spirdeed(cid:2)i.ctsFo(cid:2)rEvth,aev Gfroe0m.76oStih0e.1r9Senn0e.0rg5yasvablaleryrise.rs without the complexity arising
Ge1−x−ySixSny/Ge interface we have used the customary ap- Figue 2 shows the QCL structure based upon
proach for alloy semiconductors, interpolating the average Ge/Ge Si Sn QWs. Only L-valley conduction band
0.76 0.19 0.05
valence band offsets for the elementary heterojunctions lineups are shown in the potential diagram under an applied
Ge/Si and Ge/(cid:3)-Sn. Thus we used (cid:2)Ev,av(cid:1)x,y(cid:2) electricfieldof10 kV/cm.InordertosolvetheSchrödinger
=E (cid:1)GeSiSn(cid:2)−E (cid:1)Ge(cid:2)=−0.48x+0.69y (cid:1)ineV(cid:2).Oncethe equation to yield subbands and their associated envelope
v,av v,av
average valence band offset is determined, the energies of functions, it is necessary to determine the effective mass m
z
individual conduction band edges in the Ge Si Sn alloy along the (cid:1)001(cid:2) growth direction (cid:1)z(cid:2) within the constant-
1−x−y x y
can be calculated relative to those in Ge from the composi- energy ellipsoids at the L valleys along the (cid:1)111(cid:2) direction
tional dependence of the spin-orbit splitting of the top va- whichistiltedwithrespectto(cid:1)001(cid:2).UsingtheL-valleyprin-
lence band states and the compositional dependence of the cipal transverse effective mass m =0.08m and the longitu-
t o
energyseparationsbetweenthoseconductionbandedgesand dinal effective mass m =1.60m , we obtain m =(cid:1)2/3m
l o z t
the top of the valence band in the alloy.13 We have assumed +1/3m(cid:2)−1=0.12m where m is the free electron mass. The
l o o
that all required alloy energies can be interpolated between squared magnitudes of all envelope functions are plotted at
the known values for Si, Ge, and (cid:3)-Sn as energy positions of their associated subbands. As shown in
E (cid:1)x,y(cid:2)=E (cid:1)1−x−y(cid:2)+E x Fig.2,eachperiodoftheQCLhasanactiveregionforlasing
GeSiSn Ge Si emission and an injector region for carrier transport. These
+E y−b (cid:1)1−x−y(cid:2)x two regions are separated by a 30 Å barrier. The active re-
Sn GeSi
−b (cid:1)1−x−y(cid:2)y−b xy. (cid:1)1(cid:2) gionisconstructedwiththreecoupledGeQWsthatgiverise
GeSn SiSn tothreesubbandsmarked1,2,and3.Thelasingtransitionat
Thebowingparametersb ,b ,andb havebeendis- the wavelength of 49 (cid:5)m is between the upper laser state 3
GeSi GeSn SiSn
cussed in Refs. 14 and 15. Finally, for the indirect conduc- and the lower laser state 2. The injector region consists of
tionbandminimumneartheX point,WeberandAlonsofind four Ge QWs of decreasing well widths all separated by
E =0.931+0.018x+0.206x2 (cid:1)in eV(cid:2) for Ge Si alloys.16 20 Å Ge Si Sn barriers. The depopulation of lower
X 1−x x 0.76 0.19 0.05
Ontheotherhand,theempiricalpseudopotentialcalculations state 2 is through scattering to state 1 and to the miniband
ofCohenandBergstresserplacethisminimumat0.90 eVin downstream formed in the injector region. These scattering
(cid:3)-Sn, virtually the same as its value in pure Ge.17 We thus processes are rather fast because of the strong overlap be-
assume that the position of this minimum in ternary tween the involved states. Another miniband in the injector
Ge Si Sn alloys is independent of the Sn concentration regionformedofquasiboundstatesissituated45 meVabove
1−x−y x y
y. This is qualitatively in agreement with the virtual-crystal theupperlaserstate3,effectivelypreventingescapeofelec-
calculations of Jenkins and Dow,7 which find that the trons from upper laser state 3 into the injector region.
X-related minima have the weakest compositional depen- The nonradiative transition rates between different sub-
dence. The conduction band minima results are shown in bands in such a low-doped nonpolar material system with
Fig.1forSnconcentrations0(cid:4)y(cid:4)0.1.TheSiconcentration low injection current should be dominated by deformation-
x was calculated using Vegard’s law in such a way that the potential scattering of nonpolar optical and acoustic
ternary Ge Si Sn is exactly lattice matched with Ge. phonons. Because of the large energy separation between L
1−x−y x y
It can be seen from Fig. 1 that a conduction band offset and(cid:1)valleys,andbetweenLandXvalleys,theL-(cid:1)andL-X
of 150 meV at L valleys can be obtained between lattice- intervalley scattering processes are negligible. Between the
matched Ge and Ge Si Sn alloy while all other con- fourequivalentLvalleys,itcanbearguedthroughthematrix
0.76 0.19 0.05
duction band valleys (cid:1)(cid:1),X, etc(cid:2) are above the L-valley band element for electron-phonon interaction that the inter
Downloaded 30 Jul 2007 to 146.153.144.35. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
251105-3 Sunetal. Appl.Phys.Lett.90,251105(cid:2)2007(cid:1)
We have simulated the TM-polarized mode in a QCL
structure of 40 periods that is confined by double-Au-
plasmon waveguide and obtained near unity optical confine-
ment (cid:1)(cid:14)1.0 and waveguide loss (cid:3) =110/cm. Assuming a
w
mirror loss (cid:3) =10/cm for a typical cavity length of 1 mm,
m
the threshold current density J can be calculated from the
th
balancing relationship, (cid:1)g =(cid:3) +(cid:3).The result is shown in
th w m
Fig. 3 for J that ranges from 22 A/cm2 at
th
5 K to 550 A/cm2 at 300 K. These threshold values are
lower than those of III-V QCLs as a result of the longer
scattering times due to nonpolar optical phonons.
In summary, we propose a Ge/Ge Si Sn QCL
0.76 0.19 0.05
that operates at L valleys of the conduction band.According
FIG.3. Lifetimesandthresholdcurrentdensityasafunctionofoperating to our estimation of the band lineup, this particular alloy
temperature.
composition gives a clean conduction band offset of
150 meV at L valleys with all other energy valleys conve-
L-valley scattering, an umklapp process, is much weaker
nientlyoutoftheway.AllQCLlayersarelatticematchedto
than the intra-L-valley scattering.The lifetimes are therefore
a Ge buffer layer on a Si substrate and the entire structure is
determined by the intra-L-valley scattering. For this Ge-rich
therefore strain-free. The electron effective mass along the
structure, we have used bulk-Ge phonons for calculation of
growth direction is much lighter than that of heavy holes
the scattering rate to yield lifetimes for the upper laser state
bringing a significant improvement in tunneling rates and
(cid:6) andthelowerlaserstate(cid:6),aswellasthe3→2scattering
3 2 oscillator strengths. The lasing wavelength of this device is
time (cid:6) .18They are shown in Fig. 3 as a function of operat-
32 49 (cid:5)m. With different GeSiSn alloy compositions that are
ing temperature. These lifetimes are at least one order of
lattice matched to Ge, QCLs can be tuned to lase at other
magnitude longer than those of III-V QCLs owing to the
desired wavelengths. Lifetimes determined from the
nonpolar nature of GeSiSn alloys. The necessary condition
for population inversion (cid:6) (cid:7)(cid:6) is satisfied throughout the deformation-potential scattering of nonpolar optical and
32 2 acoustic phonons are at least an order of magnitude longer
temperature range. Using these predetermined lifetimes in
thanthoseinIII-VQCLswithpolaropticalphonons,leading
the population rate equation under current injection:
(cid:5) (cid:6) toareductioninthresholdcurrentdensityandthepossibility
(cid:3)N (cid:8)J N −N¯ of room temperature operation.
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