Manuscript accepted for publication in Semiconductor Science and Technology 27 (2012)

1

Effect of active QW population on optical characteristics of

polar, semipolar and nonpolar III-nitride light emitters

Mikhail V. Kisin*, Chih-Li Chuang, and Hussein S. El-Ghoroury

Ostendo Technologies, Inc., 6185 Paseo del Norte, Ste. 200, Carlsbad, CA 92011, USA

*E-mail: mikhail@ostendo.com

Abstract. QW population effects are compared in III-nitride light-emitters with different levels of

polarity. We show that wider nonpolar active QWs are characterized by increased QW transparency

current and reduced differential optical gain which consequently increases the laser threshold. We

also show that high intra-QW recombination rates in nonpolar/semipolar structures make the QW

populations strongly non-equilibrium and vulnerable to inhomogeneous QW injection. In LED

regime, structures with different polarity level reveal different mechanisms of the efficiency droop.

In polar structures, the droop is dominated by the electron leakage and is noticeably affected by the

active region ballistic overshoot. Efficiency droop in semipolar/nonpolar structures is dominated by

combined effect of radiative time saturation and nonradiative Auger recombination.

Keywords: III-nitrides, laser diodes, light emitting diodes, injection efficiency, radiative efficiency,

carrier leakage.

PACS: 42.55.Px, 42.72.Bj, 78.67.De, 85.60.Bt

This is an author-created, un-copyedited version of an article accepted for publication/published in

Semiconductor Science and Technology. IOP Publishing Ltd is not responsible for any errors or

omissions in this version of the manuscript or any version derived from it. The Version of Record is

available online at DOI 10.1088/0268-1242/27/2/024012.

1. Introduction

Optical characteristics of III-nitride light emitters are expected to be superior in QW structures grown in

nonpolar or semipolar orientations (Waltereit et al., 2000). Reduced intra-QW polarization fields and

enhanced overlap between electron and hole states participating in optical transitions improves the QW

radiative recombination rate and increases the optical output of nonpolar/semipolar structures. QW structures

designed for laser applications also benefit from the possible use of wider field-free active QWs which

provide for better optical mode confinement, higher modal optical gain, and as a result, allow simplified

design of laser structure (Feezell et al., 2007). Lower rate of indium incorporation during the nonpolar growth

(Strittmatter et al., 2011) gives additional motivation for using wider QW layers to curb the effect of carrier

quantum confinement, especially in longer-wavelength emitters.

Large carrier effective masses in III-nitride semiconductors result in higher subband density of states (DOS)

entailing higher level of QW transparency injection, typically above 4x1012

/cm2

(Hader et al., 2007).

Corresponding increase in laser threshold discourages multi-QW (MQW) active region designs and supports

using a smaller number of active QWs optimized for efficient emission at higher injection levels (Kisin et al.,

2009a). Using wide QWs can become inappropriate at this point (Kisin et al., 2009b). Additional

complications come from uneven and imbalanced populations of different QWs and strong disparity of

Manuscript accepted for publication in Semiconductor Science and Technology 27 (2012)

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electron and hole injection in MQW III-nitride structures (Kisin and El-Ghoroury, 2010a). In an ideal active

region design, in order to prevent some of the active QWs from under-pumping, different QWs should be

optimized differently.

In this work, we compare optical gain and efficiency characteristics of polar, semipolar, and nonpolar three-

QW diode structures with active QWs designed for the same emission wavelength at the highest injection

level of 5x1013

/cm2. We show that in wide nonpolar QWs the thermal carrier redistribution among closely

separated subbands outweighs the benefits of enhanced dipole matrix elements and can increase the lasing

threshold, especially in laser diodes with Auger-dominated threshold currents. We also show that high intra-

QW recombination rates make the populations of active QWs strongly non-equilibrium. Due to asymmetrical

carrier injection, even in nonpolar MQW structures the QW populations remain unbalanced and

inhomogeneous. In our 3-QW illustrative example, the best performance was demonstrated by semipolar

structure with optimized 4 nm QW width.

2. Active QWs

For laser active region simulation we employed COMSOL-based Ostendo’s Optoelectronic Device Modeling

Software (ODMS) described in details elsewhere (Kisin and El-Ghoroury, 2010b). Special attention was paid

to thorough microscopic modeling of carrier confinement and radiative characteristics of active QWs.

Valence subband spectrum was calculated using the Rashba-Sheka-Pikus 6x6 matrix Hamiltonian for strained

wurtzite semiconductors in arbitrary crystallographic configuration (Kisin et al., 2009a). The resulting multi-

band equation system for QW eigenstates was solved self-consistently with Poisson’s equation taking into

account effects of intra-QW polarization field screening and thermal carrier redistribution between the QW

subbands and contiguous extended bulk-like states. QW radiative characteristics have been then obtained by

k-space and spectral integrations of interband optical transitions for each pair of QW subband. This

automatically includes into our simulations the radiative time saturation effect due to phase-space filling at

high QW population levels (David and Grundmann, 2010). On the other hand, to uniquely identify the QW

population effects and allow direct comparison between different structures, the carrier kinetic and non-

radiative recombination parameters have been treated phenomenologically and assumed to be the same for all

modeled structures; see table 1. These values are close to typical experimental estimates (Zhang et al., 2009).

One order of magnitude increase of SRH lifetimes in QW layers has been also adopted to simulate the

enhancement of radiative efficiency in III-nitride QWs due to indium compositional fluctuations (Chichibu et

al., 1996). To further facilitate comparison, we also assume the same small homogeneous optical transition

broadening of 10 meV for all QWs. Microscopic band structure parameters have been mostly adopted from a

single source (Vurgaftman and Meyer, 2007); the valence to conduction band offsets ratio was kept as 3:7 for

all interfaces.

Table 1. Assumed material parameters

QW electron (hole) capture time 5 (1) ps

QW (bulk) carrier SRH lifetime 10 (1) ns

QW (bulk) Auger coefficient 10-17

cm4/s (10

-30 cm

6/s)

Bulk radiative constant 0.2x10-10

cm3/s

Electron (hole) mobility 200 (10) cm2/V·s

Electron ballistic velocity 2x107 cm/s

Manuscript accepted for publication in Semiconductor Science and Technology 27 (2012)

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Table 2 compares the calculated nominal characteristics of active QWs at low and high injection. Low

injection level corresponds to QW transparency; low-injection optical gain characteristics have been

evaluated at doubled transparency concentration value. Our choice of QW widths and compositions is aimed

to illustrate the adverse effect of thermal carrier redistribution between the closely separated subbands in

wider quantum wells with nominally the same emission. It also reflects lower indium intake currently

characteristic for the nonpolar structure growth. The barrier materials contain 2% indium and all layers are

assumed to be strained to GaN template lattice. QW strain components and components of peak gain

coefficient are presented in the coordinate system with z-axis taken along the structure growth direction and

x-axis parallel to [11-20] crystallographic direction. The x-axis is contained within the growth plane for each

crystallographic template. In nonpolar and semipolar structures x-axis thus represents the inclination axis of

the crystallographic coordinate system. For laser waveguide strips oriented along the c-axis projection, the x-

component of the gain coefficient corresponds to the TE gain, which is the only component shown for

differential gain characteristics in table 2. Modal gain coefficients have been estimated using nominal optical

mode confinement factor equal to the ratio of QW width to the QW emission wavelength. This simplified

estimation allows for comparison of the active QWs independently on any particular waveguide designs.

Structure injection characteristics which depend on detailed layout will be addressed in the next section. All

radiative characteristics in table 2 take into account only the optical output originating from the transitions

between the lowest conduction subband and two upper valence subbands dominating the optical gain

spectrum; the related effective radiative parameters have been calculated with respect to the total carrier

concentration in QW layer. Efficiency of the lowest (lasing) subband population is indicated in table 2 as a

percentage of this total.

Table 2. Comparative QW characteristics at transparency and high-injection levels

Template orientation (0001) (11-22) (11-20)

QW width, nm 2.5 4.0 8.0

QW composition Ga0.75In0.25N Ga0.80In0.20N Ga0.82In0.18N

QW strain, % a -2.72/-2.72/1.57/0.0 -2.18/-2.02/1.66/-0.07 -1.97/-1.77/1.27/0.0

QW bandgap (strained), eV 2.568 2.626 2.693

Carrier injection, 1012

/cm2 3.38 30 3.75 30 5.37 30

QW internal field, MV/cm -2.37 -1.20 0.09 0.05 0.0 0.0

Spontaneous emission , nm 488 455 454 447 452 449

Subband population, c1 (hh1), % 100 (85) 89 (74) 100 (61) 76 (52) 83 (33) 54 (30)

Radiative lifetime, ns 24.1 1.79 6.25 1.97 9.94 4.11

Radiative constant, 10-5

cm2/s 1.22 1.88 4.25 1.69 1.87 0.81

Radiative efficiency, % 20.3 5.87 45.6 5.31 22.9 2.62

Peak modal gain G, cm-1

b 10/10/0.08 123/123/1.1 55/1.6/3.1 188/16/42 40/0.12/5.6 123/0.39/41

∂GTE/∂N , 10-9

cm 4.1 4.3 12 3.1 6.7 2.6

∂GTE/∂Jrad (∂GTE/∂Jtot), cm/A 166 (24) 23 (0.87) 274 (85) 28 (0.50) 267 (31) 49 (0.45)

a xx/yy/zz/yz components

b x/y/z components

Manuscript accepted for publication in Semiconductor Science and Technology 27 (2012)

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From table 2 it is readily seen that decreased population efficiency of the lasing states in the widest nonpolar

QW outweighs the benefits of enhanced dipole matrix elements; thermal carrier redistribution between the

closely separated and less optically active subbands deteriorates the radiative and gain characteristics. Figures

1-4 illustrate this effect in more details.

Figure 1 compares the structure of valence band subbands accounting for hole redistribution. Subband

dispersions along the x- and y-axes are indicated, correspondingly, by solid and dashed lines; for the polar

QW with hexagonal in-plane symmetry these dispersions coincide. In narrow polar QW the overall DOS

distribution is more favorable for efficient optical emission than the crowded subband structure of the wider

nonpolar QW. It is also important that due to hexagonal c-plane symmetry two upper hole subbands in polar

QW include a nearly equal mix of x- and y-polarized Bloch functions and, therefore, are both TE optically

active. Thermal hole redistribution between these subbands does not deteriorate TE gain with increased

injection. On the contrary, in semipolar and nonpolar QWs the states of uppermost hole subband h1 are

predominantly x-polarized. This strain split-off subband accounts for optical anisotropy of nonpolar and

semipolar QWs (Feneberg et al., 2007) and provides strong TE gain enhancement (Scheibenzuber et al.,

2009); see calculated gain components in table 2. With the increased injection, however, the gain in wider

QWs becomes susceptible to thermal hole redistribution into the next subbands with much smaller optical

matrix elements.

Figure 1. Upper valence subbands of polar (0001), semipolar (11-22), and nonpolar (11-20) QWs at the same

injection level of 3x1013

cm-2

. Subband energy is counted from the valence band top at the QW center.

Figure 2 compares the resulting spectra of spontaneous and stimulated radiative recombination rates

calculated at the same high injection level of 3x1013

cm-2

. Presented rates are originated from optical

transitions between the lowest conduction subband and two upper valence subbands, i.e. in laser structures

they recount the main states contributing to the lasing action. At such a high carrier concentration, the intra-

QW screening in the polar QW allows for sufficiently large electron-hole overlap and assures radiative rates

comparable with rates in nonpolar and semipolar structures. Stimulated emission spectra of semipolar and

nonpolar QWs both demonstrate strong rate enhancement for TE polarized emission. The rates, however,

notably decline in the widest (nonpolar) 8 nm QW. Rate reduction between lasing subbands in the widest QW

Manuscript accepted for publication in Semiconductor Science and Technology 27 (2012)

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is directly related to the carrier redistribution into the upper subbands which concerns not only holes but

electrons as well; see subband population data in table 2. The table presents the relative population of c1 and

h1 subbands with respect to the total QW layer population including the extended bulk-like states. Bulk states

are responsible for sharp decline of c1 relative population in narrow polar QW at high injection level. In

widest (nonpolar) QW, the electron redistribution manifests itself in the reduced spectral width of the c1

subband emission rate essentially determined by electron Fermi level position.

Figure 2. Spectral rates of spontaneous radiative recombination (solid lines) and stimulated recombination per

single photon for TE (dashed lines) and TM (dash-dotted lines) transitions at high QW injection of

3x1013

cm-2

for different template orientations and QW widths: 2.5 nm polar (0001), 4 nm semipolar (11-22),

and 8 nm nonpolar (11-20). Only rates for transitions between the lowest electron and two upper hole

subbands are shown.

Figure 3 compares the TE-gain characteristics of three modeled structures and illustrates optical gain

deterioration in the wide nonpolar QW at high injection levels. Data presented in table 2 also shows the

corresponding increase of the QW transparency concentration. The inset in figure 3 demonstrates strong

impact of the QW width on the gain-current characteristics calculated for our representative choice of non-

radiative recombination parameters from table 1. For low-loss structures, the lasing threshold of the wide

nonpolar QW falls behind the polar structure threshold and, due to the increased QW transparency

concentration, the threshold cannot be recovered by appealing to MQW active region design. In polar QWs,

on the contrary, the threshold current can be lowered by the reduced spatial electron-hole overlap and

decreased radiative losses. Emission characteristics of polar QW also demonstrate some increase at higher

injection levels, above 1013

cm-2

, which is attributed to the onset of strong intra-QW free-carrier screening

and corresponding raise in electron-hole overlap. In addition we note that the Auger coefficient, assumed in

our illustrative simulations to be the same for all modeled structures, can in fact be higher in wide nonpolar

QWs because of wider range of available final states for different indirect Auger transitions, while in polar

QW with reduced spatial electron-hole overlap the Auger recombination can be even suppressed, in analogy

with type-II QW structures (Meyer et al., 1998).

Manuscript accepted for publication in Semiconductor Science and Technology 27 (2012)

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Figure 3. Nominal TE-gain characteristics for QWs grown in different orientations: squares - polar (0001),

triangles - semipolar (11-22), and circles - nonpolar (11-20). The inset shows gain-current relations near the

QW transparency injection level calculated using the nonradiative recombination parameters of table 1.

3. Inhomogeneous injection in MQW structures

In polar diode structures, polarization charges at the structure interfaces induce high potential barriers for

carrier transport which reduce the injection efficiency of MQW active regions. The total internal efficiency

of the light emitter also suffers a loss if some of the active QWs are under- or over-pumped with either one or

both types of carriers. MQW injection conditions are affected by the highly non-equilibrium character of

active QW populations and large residual QW charges, - even in nonpolar structures. For carrier injection

simulation, ODMS utilizes a drift-diffusive model of carrier transport through extended bulk states coupled

with rate equation systems for each QW (Tessler and Eisenstein, 1993). Strong electrical inhomogeneity of

the polar active regions provides the necessary conditions for the onset of the electronic ballistic transport

effects. To take them into account, we have additionally incorporated a phenomenological model for active

region ballistic overshoot (Kisin and El-Ghoroury, 2011).

Figure 4 clarifies the extent of the non-equilibrium effects in QW population process. The set of curves on the

left panel shows the non-equilibrium electron population in polar QW as a function of the equilibrium value

of QW hole concentration; level of electron injection serves as a curve set parameter. The equilibrium hole

concentration is used as the plot argument only for clarity of presentation in order to characterize the hole

injection level in an unambiguous way. In actual simulations, ODMS uses quasi-Fermi levels of mobile

electron and hole subsystems as independent variables; equilibrium QW carrier populations are calculated

with respect to corresponding quasi-Fermi levels. Non-equilibrium electron and hole QW populations are

obtained as a solution of rate equation system for corresponding QWs. They are self-consistently determined

by the resulting intra-QW recombination rates. In the presented set of curves, the equilibrium electron

concentration can be traced as a starting value of each curve at low hole injection. The curve crowding at the

Manuscript accepted for publication in Semiconductor Science and Technology 27 (2012)

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highest levels of electron injection 4x1013

/cm2 represents the finite capacity of the electron QW. The hole

QW with higher DOS allows much higher population. At higher level of electron injection (upper curves),

higher hole injection is required for non-equilibrium effects to step in. It is readily seen that for all realistic

injection levels the actual non-equilibrium electron QW populations notably deviate from their equilibrium

values; same effect holds for holes and becomes more pronounced in nonpolar/semipolar QWs with higher

recombination rates. In MQW structures, the non-equilibrium QW populations also depend on the QW

injection conditions for both types of carriers. Residual QW charges modify the carrier transport in diode

structure and provide the feedback for QW injection conditions. Modeling shows that residual QW charges

remain quite high even in nonpolar MQW structures with otherwise electrically uniform active regions. These

charges can be attributed to dissimilar electron-hole transport in III-nitride heterostructures and strong carrier

confinement in deep QWs. The right panel of figure 4 compares QW residual charges in 3-QW polar and

nonpolar diodes of the same design. Each diode structure includes a 15 nm wide electron blocking layer

(EBL) with 15% aluminum content and incorporates 2% indium concentration in QW barriers and n-side

waveguide layer to improve uniformity of QW injection (Kisin and El-Ghoroury, 2010b). Charges of

opposite QWs in the same MQW structure are reversed, with the middle QW practically neutral. Charges of

extreme left or right QWs in polar and nonpolar MQW structures are also reversed which reflects their

different origin. In nonpolar structure, QW charges are determined by carrier injection asymmetry, with n-

side QW1 charged negatively and p-side QW3 charged positively, while in polar structure the positive

polarization charge at the active region side of EBL induces excessive electron accumulation and negative

charge in p-side QW3 (Kisin and El-Ghoroury, 2010b). Note, that in our illustrative simulations, to facilitate

comparison between polar and nonpolar structures, we did not attempt to optimize the EBL, for instance by

polarization matching.

Figure 4. Left: non-equilibrium electron population of 2.5 nm polar QW for different levels of electron and

hole injection. Right: residual QW charges in 3-QW polar (squares) and nonpolar (circles) diode structures

vs. the injection current density: QW1 – solid, QW2 – dash-dot, QW3 – dashed lines; QWs are numbered

from n-side to p-side of the diode.

Inhomogeneous QW injection and non-equilibrium population effects result in different optical output of

active MQWs. Figure 5 compares QW radiative currents in our modeled 3-QW structures of different

polarity. Noticeably, the best uniformity of the radiative current distribution among all three active QWs was

achieved not in the nonpolar diode with wide QWs but in semipolar emitter with optimum 4 nm QW width.

Manuscript accepted for publication in Semiconductor Science and Technology 27 (2012)

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Figure 5. QW radiative currents in 3-QW diode structures grown on different templates vs. diode injection

current. QWs are numbered from n-side to p-side of the diode and presented by solid (QW1), dash-dot

(QW2), and dashed (QW3) lines.

Strong electrical inhomogeneity of polar MQW structure triggers the onset of the electronic ballistic transport

across the active region (Ni et al., 2010) which additionally contributes to the dominance of the p-side QW in

optical emission. In nonpolar and semipolar structures with indium-enriched separate confinement layers, the

active region is much more uniform and in our simulations ballistic overshoot of the active region was not

seen in these structures at any bias. Active region overshoot also increases the electron leakage from the polar

active region. Figure 6 shows the spatial distribution of injected current components across the active regions

of polar and nonpolar 3-QW emitters at a moderate injection level of 1 kA/cm2. In nonpolar and semipolar

diodes, the leakage is of pure drift-diffusive nature and starts at much higher levels of the current injection.

Left panel of figure 7 compares the total injection efficiencies of the modeled diode structures. Electrical

inhomogeneity of the polar active region reduces the three-QW structure injection efficiency comparing to

single-QW diodes. Radiative efficiencies are compared in figure 7 on the right panel. With our choice of

nonradiative recombination parameters presented in table 1, the decrease of radiative efficiency at high

injection is attributed to the onset of Auger recombination. Once again, we emphasize that employing the

same provisional value of the Auger coefficient for all modeled structures is an illustrative simplification

used here to compare on the same footing structures of different polarity with inherently different radiative

recombination rates and different levels of active region uniformity. While radiative recombination rates have

been explicitly calculated in our model, the nonradiative processes are described phenomenologically, so that

the corresponding coefficients should be treated as fitting parameters and in more elaborate model can

depend on the injection level and QW structure design (Ozgur et al., 2010). Our simulation, however, allows

separate analysis of the injection and radiative efficiencies of the modeled QW structures. In the polar

structure, the efficiency decline at high injection is cushioned to some extent by radiative recombination

enhancement due to more efficient intra-QW screening. Contrarily, in nonpolar and semipolar structures,

phase-space filling in lowest subbands saturates the radiative time for corresponding optical transitions

(David and Grundmann, 2010) and decreases the radiative efficiency with injection. This exacerbates the

detrimental effect of Auger recombination. As expected, the radiative efficiency in each 3-QW diode peaks at

a higher injection current than in the corresponding single-QW structure. In total external efficiency of the

polar structure, however, this shift is concealed by a strong decrease of the structure injection efficiency. As a

result, the efficiency droop in polar and nonpolar diodes have different natures. In polar structures, droop is

dominated by the electron leakage with the strong effect of the active region ballistic overshoot, whilst in

Manuscript accepted for publication in Semiconductor Science and Technology 27 (2012)

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nonpolar structure the droop is mostly determined by combined effect of radiative time saturation and,

possibly, nonradiative Auger recombination.

Figure 6. Upper panel: electrical inhomogeneity of 3-QW active regions in polar and semipolar diodes.

Thinner lines indicate electronic quasi-Fermi level position. Lower panel: spatial distribution of the injection

current components. Solid lines – polar (0001) structure, dashed lines – semipolar (11-22) structure. Injection

current density is 1 kA/cm2.

Figure 7. Efficiency characteristics of 3-QW (solid lines) and 1-QW (dashed lines) light-emitting diode

structures of different polarity. Inset compares I-V characteristics of polar (lower curves) and semipolar

structures (upper curves) and illustrates stronger electrical inhomogeneity of polar MQW active region.

Manuscript accepted for publication in Semiconductor Science and Technology 27 (2012)

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4. Conclusions

Optical properties of III-nitride QW structures grown on semipolar and nonpolar crystallographic planes

benefit from reduced QW internal fields and enhanced electron-hole overlap. As a result, wider active QWs

can be used in laser design providing for the higher modal optical gain. Detailed modeling shows, however,

that in wider QWs smaller subband separation and related thermal carrier redistribution overweighs the TE-

gain enhancement, consequently reducing the QW differential optical gain and increasing the laser threshold

in nonpolar structures. We also show that active QW populations in nonpolar/semipolar structures with

inherently high intra-QW recombination rates are strongly non-equilibrium. As a result, even in nonpolar

structures the multi-OW active regions suffer from inhomogeneous QW injection which reduces the total

radiative efficiency of the emitter. Modeling shows that efficiency droops in polar and nonpolar structures

have different origins. In polar structures, the droop is dominated by the electron leakage and is noticeably

affected by the active region ballistic overshoot. Efficiency droop in semipolar and nonpolar structures is

determined by combined effect of radiative time saturation due to lowest subband state filling and, possibly,

nonradiative Auger recombination.

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