Journal of ELECTRONIC MATERIALS, Vol. 42, No. 5, 2013

DOI: 10.1007/s11664-013-2548-5 Ó 2013 TMS

Room-Temperature Quantum Cascade Laser: ZnO/Zn1xMgxO Versus GaN/AlxGa1xN HUNG CHI CHOU,1 ANAS MAZADY,1 JOHN ZELLER,2 TARIQ MANZUR,3 and MEHDI ANWAR1,4 1.—Department of Electrical and Computer Engineering, University of Connecticut, Storrs, CT 06269-2157, USA. 2.—Magnolia Optical Technologies, 52B Cummings Park, Suite 314, Woburn, MA 01801, USA. 3.—Naval Undersea Warfare Center (NUWC), Newport, RI 02841-1708, USA. 4.—e-mail: [email protected]

A ZnO/Zn1xMgxO-based quantum cascade laser (QCL) is proposed as a candidate for generation of THz radiation at room temperature. The structural and material properties, field dependence of the THz lasing frequency, and generated power are reported for a resonant phonon ZnO/Zn0.95Mg0.05O QCL emitting at 5.27 THz. The theoretical results are compared with those from GaN/AlxGa1xN QCLs of similar geometry. Higher calculated optical output powers [PZnMgO = 2.89 mW (nonpolar) at 5.27 THz and 2.75 mW (polar) at 4.93 THz] are obtained with the ZnO/Zn0.95Mg0.05O structure as compared with GaN/Al0.05Ga0.95N QCLs [PAlGaN = 2.37 mW (nonpolar) at 4.67 THz and 2.29 mW (polar) at 4.52 THz]. Furthermore, a higher wall-plug efficiency (WPE) is obtained for ZnO/ZnMgO QCLs [24.61% (nonpolar) and 23.12% (polar)] when compared with GaN/AlGaN structures [14.11% (nonpolar) and 13.87% (polar)]. These results show that ZnO/ZnMgO material is optimally suited for THz QCLs. Key words: ZnMgO, quantum cascade lasers, terahertz, oxide semiconductors, wall-plug efficiency, THz power

INTRODUCTION ZnO is a direct- and wide-bandgap (3.37 eV) transparent semiconductor.1–3 The LO phonon energy of ZnO is 74 meV,4 which is comparable to the value of 90 meV5 for GaN, allowing QCL operation at room temperature. Krishnamoorthy et al.6 reported resonant tunneling action in a ZnO/ZnMgO doublebarrier structure. By choosing an appropriate Mg mole fraction, ZnMgO/ZnO heterostructures can be designed to have almost perfect lattice match along with a barrier height up to 0.9 eV7 that takes into account polarization effects.8 This is certainly an advantage over III-nitride and III–IV quantum wells (QWs), in which lattice mismatch is significantly greater and thus the electron mobility is lower. All these properties make ZnO-based QW lasers promising candidates for optoelectronic (Received August 16, 2012; accepted February 18, 2013; published online April 4, 2013)

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applications in the visible and the ultraviolet (UV) regions, as well as potentially better THz sources. The development of a high-power solid-state farinfrared laser source could deeply impact the progress of laser-based techniques for applications including homeland security, medical systems, and semiconductor defect detection. Traditional methods for taking measurements in the THz frequency range have typically relied on bulky, optically pumped gas lasers and required complex setups. With the capability for output powers on the order of milliwatts,9 THz QCLs have been considered an ideal solution to replace present optical source technologies. III-nitride semiconductors, which have been investigated for over a decade, offer wide direct bandgaps, large conduction-band discontinuities (2.1 eV in GaN/AlN and GaN/InN; a larger offset possible in InN/AlN), high peak electron velocities, high saturation electron velocities, and high thermal stability.10–12 Research relating to III-nitride-based electronic devices has focused on

Room-Temperature Quantum Cascade Laser: ZnO/Zn1xMgxO Versus GaN/AlxGa1xN

AlGaN/GaN high-electron-concentration and highelectron-mobility transistors for high-power microwave applications. However, material-related issues still present a challenge for the development of III-nitride QCLs. A potentially more advantageous material platform for high-power room-temperature THz QCLs is offered by ionic semiconductors such as ZnO/ZnMgO. As is well known, internal fields resulting from the combination of spontaneous and piezoelectric polarizations play an important role in the optical properties of III-nitride heterostructures, and such polarization effects and resulting built-in electric fields also occur in Zn-based heterostructures. The present study considers wurtzite-phase III-nitrides and ZnO/ZnMgO while taking into account the effect of the polarization-induced electric field on the QWs. Nonpolar orientations such as a-plane or m-plane, proposed to avoid built-in electric-field-induced quantum efficiency degradation,13 are also investigated by setting the net polarization to zero. Nonpolar ZnO/ZnMgO heterostructures have been grown by plasma-assisted molecular beam epitaxy (MBE) by Chauveau et al.,14 while GaN-based nonpolar materials have been epitaxially grown and characterized by Waltereit et al.13 The variation in lattice mismatch between ZnO and ZnMgO is less significant compared with that between GaN and AlGaN,15 resulting in weaker internal fields due to piezoelectric polarizations in ZnO/ZnMgO QWs than in GaN/AlGaN heterostructures.16 However, experimental data reported by Gopal et al.17,18 indicate a significantly higher intrinsic spontaneous polarization in ZnMgO compared with that in AlGaN. In polar ZnO/ZnMgO and GaN/AlGaN structures, polarization-induced internal fields alter the wavefunctions, thereby reducing the optical matrix element. Evidence for this occurring with GaN/AlGaN has been reported by Park et al.19 Research into GaAs as a material for THz QCLs has been developing rapidly. However, limitations associated with GaAs material parameters have the potential to affect QCL performance, limiting output power and high-temperature operation. In recent years, QCLs based on wide-bandgap materials such as GaN/AlGaN have been developed and reported in literature, but thus far ZnO/ZnMgO QCLs have received considerably less attention. Here we examine ZnO/ZnMgO material in comparison with GaN/AlGaN as a potential candidate for realization of high-power, efficient THz-generation QCLs operating at room temperature. To develop ZnO/ZnMgO QCLs, three major challenges that have been associated with GaN/AlGaN THz QCLs must likewise be overcome for ZnO/ ZnMgO. Firstly, the stability of ZnO is greater than that of MgO, which could increase the possibility of unwanted effects during the growth process. Based on the calculation by Andrei et al.,17 at zero temperature the Zn1xMgxO alloy is never stable with respect to phase-separated wurtzite ZnO and rocksalt MgO. Also, Sarver et al.10 point out that at above zero

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temperatures a small solid solubility of Mg in wurtzite ZnO is expected. Secondly, the energy of a THz-range photon is so low that thermal excitations can easily disturb the electron configuration, most importantly population inversion, which is necessary for lasing in a QCL. Thirdly, it is difficult to design a suitable waveguide for frequencies in the THz range. While waveguides are a necessary component of THz QCL designs, the dielectric waveguides of conventional solid-state lasers cannot be used in THz QCLs since THz wavelengths are far longer than the size of their active regions. In this paper we report the theoretical calculation of output power and wall-plug efficiency of polar ZnO/ ZnMgO heterostructures as well as nonpolar heterostructures taking into account the presence of spontaneous and piezoelectric polarizations based upon fundamental device physics. EXPERIMENTAL PROCEDURE A schematic of lasing and cascading in a QCL is shown in Fig. 1. The two periods of the QCL superlattice structure each consist of an injector, injection barrier, and active region. Electrons are guided through the injector region to the upper laser level in the active region, where optical transitions occur between a few discrete levels. Such intersubband transitions, comprising multiple QWs, give rise to radiation emission. Laser action in this Zn1xMgxO multiple quantum well (MQW) structure is based on a three-level system. A population inversion is created between upper and lower states, and the QCL structure is biased by a high static electric field (100 kV/cm) so that the ground state of the active region is aligned with the upper state of the next period. Hao et al.20 have reported characteristics of GaN material showing that a higher critical field (2 MV/cm for GaN versus 0.4 MV/cm for GaAs) can be applied to supply higher output power density. Since nitride-based material is comparable to Zn-based material due to similar material parameters and the presence of piezoelectric fields that offer a number of advantages over GaAs-based THz QCLs,20 similar high fields would likewise be applicable to ZnO-based QCL devices. Finally, the electrons in one active region are injected into and transferred to the next period. The determination of an appropriate THz frequency and the tailoring of the QWs to facilitate transition of the carriers to the ground state assisted by LO phonon scattering requires solving the Schro¨dinger equation to define the eigenstates formed in the conduction band. The time-independent Schro¨dinger equation under the effective-mass approximation can be written as21

2 @2 h wð xÞ þ ½qV ð xÞ þ DEc ð xÞwð xÞ 2mð xÞ @x2 ¼ j Ejwð xÞ ¼ Hwð xÞ;

(1)

where m(x) is the position-dependent effective mass, V(x) is the electrostatic potential, DEc(x) is the

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Fig. 1. (a) Schematic of a Zn0.95Mg0.05O THz QCL device along with conduction-band profile. (b) Wavefunctions for the ZnO/Zn0.95Mg0.05O MQW structure, biased at 100 kV/cm. The layer sequence for one period of the structure beginning from the left in the injector region (in nm) is 4/ 2.5/3.2/1.5/2.3/3.5/2/3.2. Lasing is expected to occur between the upper state (n = 3) and lower state (n = 2), and rapidly depopulate with LO phonon scattering out of the lower state into the ground state (n = 1). The black script denotes the walls and the barriers, respectively.

conduction-band discontinuity, w(x) is the electron wavefunction, and |E| is the energy eigenvalue. The presence of spontaneous PSP and piezoelectric PPE polarizations in polar semiconductors modifies the shape of the QW and the magnitudes of the band offsets, and thus plays a major role in the determination of the eigenenergies and carrier dynamics. It is to be noted that, depending upon the type of substrate (ZnO or MgO) and the composition of the epilayers, the direction of the spontaneous polarization may change.22 In modeling structures with nonpolar crystalline orientation (oriented along a-plane or m-plane), the built-in electric field due to polarization is considered to be zero. The determination of photon population proceeds by assuming the system to be in a state of equilibrium, where the total rate at which electrons transition into a given level equals the total rate at which electrons transition out. The rate equations therefore form a series of coupled equations. The photon populations are solved self-consistently with the electron populations. There is a photon population associated with each possible transition, and a rate equation for each photon population. Determination of the generated THz power and operation of the THz QCL requires finding the photon populations by using the coupled rate equations (Eqs. 2 and 3) as defined by Slingerland et al.23 dni ¼ VWif ni VWfi nf stimulated þ VWfi ni spontaneous dt Vp mif WifPh ¼ 0; ð2Þ where V is the active region volume, Vp is the cavity volume, and ni and nf are the electron population numbers in electron states i and f, respectively. Wfi

represents the absorption rate and Wif the emission rate expressed as Wif ¼ s1if , where sif is the lifetime due to transitions from initial electron state i to final electron state f (due to fast intersubband electron–electron scattering between the closely spaced injection levels). In THz QCLs, the difference between eigenstate energies needs to be smaller than in conventional QCLs, requiring the incorporation of various intersubband scattering mechanisms such as electron–electron, electron–impurity, electron–interface roughness, and photon scattering for lifetime calculation.24 WifPh , the total photon cavity loss rate between states i and f, is a function of the waveguide loss aw, mirror loss aM2 , and group velocity Vg: ðaM2 þ aw ÞVg . mif is the photon population.23 In a three-level system, the determination of photon population follows from dni SP SP SP ¼ m13 W31 n3 Vp ðn1 n3 Þ þ Cn1 W13 m13 W21 ; dt (3) where mif is the photon density between states, i = 1 is the ground state, f = 2 and 3 are the lower and final states, respectively, and WijSP and WjiSP are the total spontaneous transition rates corresponding to the i–j transitions. Here the optical confinement factor C can be treated as the fraction of the optical mode that overlaps with the entire active region, and can be obtained from Eq. 2: C = V/Vp. Optical output power is a useful measure characterizing the performance of a laser. Due to their cascading scheme, this parameter is intrinsically high in QCLs because the electrons that have contributed to generation of photons in one module of the active region are still present in the conduction band and can be reused in subsequent modules of

Room-Temperature Quantum Cascade Laser: ZnO/Zn1xMgxO Versus GaN/AlxGa1xN

the active region. We use the following relationships to calculate the output power:23 Pout ðxÞ ¼ ME ¼ M hx;

(4)

where x is the radiation frequency, E is the photon energy, h is the reduced Planck constant, M is the number of photons at a certain frequency being emitted per unit time from the front surface. Incorporating the mirror loss aM2 , the waveguide confinement equation is written as follows:23 Pout ðxÞ ¼

Vmtot aM2 c hx ; nC

(5)

where n is the modal index and mtot is the total number of photons present at that frequency inside the laser cavity. This defines the power spectrum as a function of frequency. The power is calculated using this equation for all possible transitions to ensure completeness. Wall-plug efficiency (WPE) is defined as the ratio of the emitted peak optical power and the total input electrical power following the treatment outlined by Bai et al.24 The WPE can be expressed as gw ¼ gi go gv ge ;

(6)

where for the QCL structures under consideration the internal quantum efficiency gi is fixed at 70% and the optical efficiency go is fixed at 98%. The voltage efficiency is formulated as24 gv ¼

N hx ; qVth

(7)

where N is the number of QCL periods, q is the elementary electron charge, and Vth is the voltage at threshold current Ith. The electrical efficiency is formulated as24 I Ith i ; ge ¼ h th I 1 þ R II Vth

(8)

where I is the operating current and R is the resistance. It should be noted that the record for high-temperature pulsed operation performance by GaAs-based THz QCL systems has been achieved for resonant phonon designs with two to three QWs per period, but this requires a large number of periods (200 to 250) resulting in high operating voltage.25 To obtain a lower operating voltage, a relatively large number of QWs per period may be utilized,26 allowing Zn- and nitride-based THz QCL structures to potentially achieve THz radiation with comparatively fewer periods.27 RESULTS AND DISCUSSION The energy levels of the wavefunctions can be determined by solving the Schro¨dinger equation. Figure 1a shows the physical device, and Fig. 1b displays two periods of the conduction-band profile and associated wavefunctions for polar and

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nonpolar ZnMgO-based QC structures, showing the energy levels, the superlattice, and the wavefunctions. Each period consists of four QWs: two form the active region, one forms the injector, and the remaining QW forms the collector. The layer sequence for each period, beginning from the left in the injector region, is 4/2.5/3.2/1.5/2.3/3.5/2/3.2 (in nm). An external electric field F = 100 kV/cm is applied. Electrons are injected from the upper state (n = 3) into the lower state (n = 2), and make vertical transitions into the ground state (n = 1). The expected emission frequencies of 5.27 THz (nonpolar case) and 4.93 THz (polar case) correspond to an energy separation DE32 between states 3 and 2 of 21.81 meV (nonpolar case) and 20.41 meV (polar case). Depopulation of level 2 to the ground state (DEZnO = 73 meV) is facilitated by LO phonons scattering with RhxLO = 72 meV. The required condition for population inversion in this case is n3 > n2, where n is the electron population in the specific state calculated using the rate equations (Eqs. 2 and 3). The calculated lifetimes, s32 and s2, were found to be 0.93 ps and 85 fs, respectively. The relative longevity of s32 occurs because the energy spacing between state 3 and state 2 is sufficiently below the LO phonon energy but still large enough to induce photon scattering, while the comparable shortness of s2 implies that population inversion is present in the ZnO/ZnMgO THz QCL device. With the establishment of population inversion in the system, each optical transition leads to a net spontaneous emission into the cavity mode, and correspondingly power is added to the field as it propagates through the system. Figure 2a shows room-temperature THz QCL output power versus injection current for Al0.05Ga0.95N/GaN/Al0.05Ga0.95N and Zn0.95Mg0.05O/ZnO/ Zn0.95Mg0.05O MQW structures consisting of 80 periods with total lengths of 133.2 nm. When the number of periods in the structures is increased from 60 to 130, the THz output powers are found to increase marginally. Higher peak THz QCL output powers are demonstrated in the Zn0.95Mg0.05O/ZnO/ Zn0.95Mg0.05O MQW [PZnMgO = 2.89 mW (nonpolar) and 2.75 mW (polar)] compared with the Al0.05Ga0.95N/GaN/Al0.05Ga0.95N MQW [PAlGaN = 2.37 mW (nonpolar) and 2.29 mW (polar)]. The lower calculated THz frequencies for the Al0.05Ga0.95N/ GaN/Al0.05Ga0.95N MQW structure [xAlGaN = 4.67 THz (nonpolar) and 4.52 THz (polar), compared with xZnMgO = 5.27 THz (nonpolar) and 4.93 THz (polar)] are determined by solving structure eigenenergies to find the difference in energy between eigenstates. The higher THz output power for Zn0.95Mg0.05O/ZnO/Zn0.95Mg0.05O is attributed = 1.65 in part to its lower refractive index nZnMgO r = 2.49, since it is evident compared with nAlGaN r from Eq. 5 that a lower refractive index results in higher peak optical output power. Figure 2b shows the optical output power as a function of number of periods for the Zn0.95Mg0.05O/

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Zn 3.0

Zn

THz Power (mW)

2.5

Al Al

2.0

0.95 0.95 0.05 0.05

Mg Mg Ga Ga

0.05 0.05 0.95 0.95

(b)

O Polar O Nonpolar N Polar

THz Power (mW)

(a)

N Nonpolar

1.5 1.0 0.5 0.0 0

5

10

15

2.95 2.90 2.85 2.80 2.75 2.70 2.65 2.60 2.55 2.50 2.45 2.40 2.35 2.30 2.25

20

Zn 0.95 Mg 0.05 O Polar Zn 0.95 Mg 0.05 O Nonpolar Al 0.05 Ga 0.95 N Polar Al 0.05 Ga 0.95 N Nonpolar

50

60

70

Current (mA)

90

100

110

120 130

140

(d)

5.4

Zn 0.95 Mg 0.05 O Polar

0.27

5.2 5.0

Zn 0.95 Mg 0.05 O Nonpolar

0.26

4.8 0.25

4.6

Al 0.05 Ga 0.95 N Polar

Γ

Radiation Frequency (THz)

(c)

80

Number of Periods

4.4

Zn

4.2

Zn

4.0

Al

3.8

Al

3.6 50

60

0.95 0.95

0.05 0.05

Mg Mg

Ga Ga

70

0.05 0.05

0.95 0.95

80

0.24

O Polar O Nonpolar

Al 0.05 Ga 0.95 N Nonpolar

0.23

N Polar 0.22

N Nonpolar 90

100

110

120

130

140

Number of Periods

50

60

70

80

90

100 110 120 130 140

Number of Periods

Fig. 2. (a) Room-temperature THz QCL output power versus injection current for Al0.05Ga0.95N/GaN/Al0.05Ga0.95N and Zn0.95Mg0.05O/ZnO/ Zn0.95Mg0.05O MQW structures having 80 periods. (b) Optical output power as a function of number of periods for the Zn0.95Mg0.05O/ZnO/ Zn0.95Mg0.05O MQW and Al0.05Ga0.95N/GaN/Al0.05Ga0.95N MQW for polar and nonpolar planes, each biased at 100 kV/cm. (c) Corresponding radiation frequency as a function of number of periods. (d) Corresponding optical confinement factor of the ionic and nitride-based materials with polar and nonpolar orientations.

ZnO/Zn0.95Mg0.05O MQW and Al0.05Ga0.95N/GaN/ Al0.05Ga0.95N MQW for polar and nonpolar planes, each biased at 100 kV/cm. The simulations incorporated fixed total number of photons, charge, external voltage, threshold current, threshold voltage, and injection current of 20 mA. The higher THz optical emission frequency of ZnMgO compared with AlGaN can be attributed to the higher polarization field of the former, which is dependent on its structural properties and will cause a shift in the energy difference between states, thereby increasing the radiation frequency and affecting output power. The total polarization, calculated as the sum of the spontaneous and piezoelectric polarizations, is 0.0785 C/m2 for ZnMgO-based material and 0.0336 C/m2 for the AlGaN-based system assuming the same mole fraction, x = 0.05, for Mg and Al. The higher output power for the nonpolar structure compared with the polar structure can be attributed to the higher radiation frequencies of the latter: 5.27 THz (nonpolar) and 4.93 THz (polar) for Zn0.95Mg0.05O and 4.67 THz (nonpolar) and 4.52 THz (polar) for Al0.05Ga0.95N. In addition, it can be seen that the output power, which is proportional to

the ratio of the radiation frequency and the optical confinement factor, increases only slightly with increasing number of periods. The corresponding radiation frequency as a function of number of periods is plotted in Fig. 2c. The change in radiation frequency with increasing total device length due to the increasing number of periods is the result of variation in the differential eigenstate energies. From the simulation results, a decrease in the energy difference between eigenstate 3 and eigenstate 2 was observed as a function of number of periods. Figure 2d shows the corresponding optical confinement factor of the ionic and nitride-based materials with polar and nonpolar orientations, which due to its frequency dependence is observed to decrease with increasing number of periods according to Eq. 5. Changing the number of periods alters the total length of the structure and causes the difference in energies between eigenstates to be shifted to different levels, thus resulting in a change in the radiation frequency and wavelength. The WPE, defined as the energy conversion efficiency by which the heterostructure device converts

Room-Temperature Quantum Cascade Laser: ZnO/Zn1xMgxO Versus GaN/AlxGa1xN

(b)

Wall Plug Efficiency (%)

25

Zn Zn

20 15

0.95 0.95

Mg Mg

0.05 0.05

O Polar

28 26

O Nonpolar

Wall Plug Efficiency (%)

(a)

887

Al 0.05 Ga 0.95 N Polar Al 0.05 Ga 0.95 N Nonpolar

10 5 0

24 22

Zn 0.95 Mg 0.05 O Polar

20

Zn 0.95 Mg 0.05 O Nonpolar

18

Al 0.05 Ga 0.95 N Polar

16

Al 0.05 Ga 0.95 N Nonpolar

14 12

0

5

10

15

20

Current (mA)

50

60

70

80

90

100

110

120

130

140

Number of Periods

Fig. 3. (a) Calculated WPE of Zn0.95Mg0.05O and Al0.05Ga0.95N with both polar and nonpolar orientations versus injection current over the range of 0 mA to 20 mA. (b) Wall-plug efficiency (WPE) as a function of number of periods for Zn0.95Mg0.05O/ZnO/Zn0.95Mg0.05O and Al0.05Ga0.95N/ GaN/Al0.05Ga0.95N MQWs with polar and nonpolar structures.

electrical power into optical power, was calculated for Zn0.95Mg0.05O and Al0.05Ga0.95N with both polar and nonpolar orientations versus injection current in the range of 0 mA to 20 mA and plotted in Fig. 3a. For a current of 20 mA, maximum WPE values of 24.61% (nonpolar) and 23.12% (polar) were observed for the Zn0.95Mg0.05O/ZnO/Zn0.95Mg0.05O MQW structure, significantly higher than for the Al0.05Ga0.95N/GaN/Al0.05Ga0.95N MQW structure [WPE = 14.11% (nonpolar) and 13.87% (polar)]. The WPE results derived for the ZnMgO/ZnO structure are comparable to those of current state-of-the-art mid-wavelength infrared (MWIR) lasers,28 providing evidence in support of the suitability of this material for practical QCL devices. Figure 3b shows the WPE as a function of number of periods for Zn0.95Mg0.05O/ZnO/Zn0.95Mg0.05O and Al0.05Ga0.95N/GaN/Al0.05Ga0.95N MQWs for polar and nonpolar orientations. The relatively high photon energy of Zn1xMgxO, which is evident from comparison of its emission frequency with that of other materials such as AlxGa1xN (Fig. 2c), results in higher voltage efficiency that leads to a greater overall WPE. In addition, it can be seen that the WPE of Zn0.95Mg0.05O increases slightly with increasing number of periods; this is due to a slight increase in the voltage efficiency resulting from the variation in radiation frequency which decreases with increasing structure length. Similar behavior was observed in the electrical efficiency for the two types of MQW structures. It is to be noted that the III–V structure is similar to the QCL reported by Bai et al., but lacks the additional quantum structure in the barriers. A 3-mm high-reflection coating with waveguide loss of 0.7 cm1 corresponds to an optical efficiency go of 98%, and the internal quantum efficiency gi is assumed to be 70%.24 The voltage efficiency gv for Zn0.95Mg0.05O is primarily dependent on the number of periods, radiation frequency, and threshold voltage. The peak value of electrical efficiency

ge, which is a function of the injection current, is determined to be 65%. Using these go and gi values, the frequency, mole fraction, and period dependence of the other materials may be determined. CONCLUSIONS A theoretical ZnO/Zn0.95Mg0.05O QCL structure emitting at 5.27 THz based upon the fundamental physics of operation has been reported. With input current of 20 mA, a maximum calculated optical output power of 2.89 mW may be achievable at 5.27 THz for nonpolar ZnO/Zn0.95Mg0.5O QW structures compared with an output power of 2.37 mW at 4.67 THz for nonpolar GaN/Al0.05Ga0.95N QW structures. The higher calculated output power of the ZnO/ZnMgO structure is attributed = 1.65 in part to its lower refractive index nZnMgO r = 2.49). In addition, WPE (compared with nAlGaN r values of 24.61% (nonpolar) and 23.12% (polar), which are comparable to those of current MWIR lasers, are obtained for the ZnO/ZnMgO QW structure compared with 14.11% (nonpolar) and 13.87% (polar) for the GaN/AlGaN structure. These results support the conclusion that ZnO/Zn1xMgxO is a promising material system for THz QCLs operating at room temperature.

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888 7. T. Makino, Y. Segawa, M. Kawasaki, and H. Koinuma, Semicond. Sci. Tech. 20, S78–S91 (2005). 8. F. Bernardini, V. Fiorentini, and D. Vanderbilt, Phys. Rev. Lett. 79, 3958 (1997). 9. J.M. Chalmers, H.G.M. Edwards, and M.D. Hargreaves, eds., Infrared and Raman Spectroscopy in Forensic Science (Chichester: Wiley, 2012). 10. S. Strite and H. Morkoc, J. Vac. Sci. Technol., B 10, 1237 (1992). 11. T. Wang, Y.H. Liu, Y.B. Lee, J.P. Ao, J. Bai, and S. Sakai, Appl. Phys. Lett. 81, 2508 (2002). 12. V. Adivarahan, A. Chitnis, J.P. Zhang, M. Shatalov, J.W. Yang, G. Smith, and M.A. Khan, Appl. Phys. Lett. 79, 4240 (2001). 13. P. Waltereit, O. Brandt, S.A. Trampert, H.T. Granhn, J. Menninger, M. Ramsteiner, M. Reiche, and K.H. Ploog, Nature 406, 865 (2000). 14. J.M. Chauveau, M. Laugt, P. Vennegues, M. Teisseire, B. Lo, C. Deparis, C. Morhain, and B. Vinter, Semicond. Sci. Tech. 23, 035005 (2008). 15. S. Amoruso, M. Armenante, R. Bruzzese, N. Spinelli, R. Velotta, and X. Wang, Appl. Phys. Lett. 75, 7 (1999). 16. S.H. Park, K.J. Kim, S.N. Yi, D. Ahn, and S.J. Lee, J. Korean Phys. Soc. 47, 448 (2005). 17. P. Gopal and N.A. Spaldin, J. Electron. Mater. 35, 538 (2006).

Chou, Mazady, Zeller, Manzur, and Anwar 18. M. Brandt, M. Lange, M. Stolzel, A. Muller, G. Benndorf, J. Zippel, J. Lenzer, M. Lorenz, and M. Grundmann, Appl. Phys. Lett. 97, 052101 (2010). 19. S.H. Park and S.L. Chuang, Appl. Phys. Lett. 76, 1981 (2000). 20. Y. Hao, L. A. Yang, and J. C. Zhang, Terahertz Sci. Tech. 1, p. 51 (2008). 21. A.F.J. Levi, Applied Quantum Mechanics (Cambridge: Cambridge University Press, 2003). 22. T. Makino, A. Ohtomo, C.H. Chia, Y. Segawa, H. Koinuma, and M. Kawasaki, Physica E (Amsterdam) 21, 671 (2004). 23. P. Slingerland (Ph.D. Thesis, University of Massachusetts, 2011). 24. Y. Bai, N. Bandyopadhyay, S. Tsao, S. Slivken, and M. Razeghi, Appl. Phys. Lett. 98, 181102 (2011). 25. K. Sushil (Ph.D. Thesis, Massachusetts Institute of Technology, 2009). 26. M. Wienold (Ph.D. Thesis, Paul Drude Institut fu¨r Festko¨rperelektronik, 2012). 27. G.S. Huang, T.C. Lu, H.H. Yao, H.C. Kuo, S.C. Wang, G. Sun, C.W. Lin, L. Chang, and R.A. Soref, J. Cryst. Growth 298, 687 (2007). 28. T.M. Fitzgerald, M.A. Marciniak, and S.E. Nauyok, Proc. SPIE Reflection, Scattering, and Diffraction from Surface II 7792, 779209 (2010).

DOI: 10.1007/s11664-013-2548-5 Ó 2013 TMS

Room-Temperature Quantum Cascade Laser: ZnO/Zn1xMgxO Versus GaN/AlxGa1xN HUNG CHI CHOU,1 ANAS MAZADY,1 JOHN ZELLER,2 TARIQ MANZUR,3 and MEHDI ANWAR1,4 1.—Department of Electrical and Computer Engineering, University of Connecticut, Storrs, CT 06269-2157, USA. 2.—Magnolia Optical Technologies, 52B Cummings Park, Suite 314, Woburn, MA 01801, USA. 3.—Naval Undersea Warfare Center (NUWC), Newport, RI 02841-1708, USA. 4.—e-mail: [email protected]

A ZnO/Zn1xMgxO-based quantum cascade laser (QCL) is proposed as a candidate for generation of THz radiation at room temperature. The structural and material properties, field dependence of the THz lasing frequency, and generated power are reported for a resonant phonon ZnO/Zn0.95Mg0.05O QCL emitting at 5.27 THz. The theoretical results are compared with those from GaN/AlxGa1xN QCLs of similar geometry. Higher calculated optical output powers [PZnMgO = 2.89 mW (nonpolar) at 5.27 THz and 2.75 mW (polar) at 4.93 THz] are obtained with the ZnO/Zn0.95Mg0.05O structure as compared with GaN/Al0.05Ga0.95N QCLs [PAlGaN = 2.37 mW (nonpolar) at 4.67 THz and 2.29 mW (polar) at 4.52 THz]. Furthermore, a higher wall-plug efficiency (WPE) is obtained for ZnO/ZnMgO QCLs [24.61% (nonpolar) and 23.12% (polar)] when compared with GaN/AlGaN structures [14.11% (nonpolar) and 13.87% (polar)]. These results show that ZnO/ZnMgO material is optimally suited for THz QCLs. Key words: ZnMgO, quantum cascade lasers, terahertz, oxide semiconductors, wall-plug efficiency, THz power

INTRODUCTION ZnO is a direct- and wide-bandgap (3.37 eV) transparent semiconductor.1–3 The LO phonon energy of ZnO is 74 meV,4 which is comparable to the value of 90 meV5 for GaN, allowing QCL operation at room temperature. Krishnamoorthy et al.6 reported resonant tunneling action in a ZnO/ZnMgO doublebarrier structure. By choosing an appropriate Mg mole fraction, ZnMgO/ZnO heterostructures can be designed to have almost perfect lattice match along with a barrier height up to 0.9 eV7 that takes into account polarization effects.8 This is certainly an advantage over III-nitride and III–IV quantum wells (QWs), in which lattice mismatch is significantly greater and thus the electron mobility is lower. All these properties make ZnO-based QW lasers promising candidates for optoelectronic (Received August 16, 2012; accepted February 18, 2013; published online April 4, 2013)

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applications in the visible and the ultraviolet (UV) regions, as well as potentially better THz sources. The development of a high-power solid-state farinfrared laser source could deeply impact the progress of laser-based techniques for applications including homeland security, medical systems, and semiconductor defect detection. Traditional methods for taking measurements in the THz frequency range have typically relied on bulky, optically pumped gas lasers and required complex setups. With the capability for output powers on the order of milliwatts,9 THz QCLs have been considered an ideal solution to replace present optical source technologies. III-nitride semiconductors, which have been investigated for over a decade, offer wide direct bandgaps, large conduction-band discontinuities (2.1 eV in GaN/AlN and GaN/InN; a larger offset possible in InN/AlN), high peak electron velocities, high saturation electron velocities, and high thermal stability.10–12 Research relating to III-nitride-based electronic devices has focused on

Room-Temperature Quantum Cascade Laser: ZnO/Zn1xMgxO Versus GaN/AlxGa1xN

AlGaN/GaN high-electron-concentration and highelectron-mobility transistors for high-power microwave applications. However, material-related issues still present a challenge for the development of III-nitride QCLs. A potentially more advantageous material platform for high-power room-temperature THz QCLs is offered by ionic semiconductors such as ZnO/ZnMgO. As is well known, internal fields resulting from the combination of spontaneous and piezoelectric polarizations play an important role in the optical properties of III-nitride heterostructures, and such polarization effects and resulting built-in electric fields also occur in Zn-based heterostructures. The present study considers wurtzite-phase III-nitrides and ZnO/ZnMgO while taking into account the effect of the polarization-induced electric field on the QWs. Nonpolar orientations such as a-plane or m-plane, proposed to avoid built-in electric-field-induced quantum efficiency degradation,13 are also investigated by setting the net polarization to zero. Nonpolar ZnO/ZnMgO heterostructures have been grown by plasma-assisted molecular beam epitaxy (MBE) by Chauveau et al.,14 while GaN-based nonpolar materials have been epitaxially grown and characterized by Waltereit et al.13 The variation in lattice mismatch between ZnO and ZnMgO is less significant compared with that between GaN and AlGaN,15 resulting in weaker internal fields due to piezoelectric polarizations in ZnO/ZnMgO QWs than in GaN/AlGaN heterostructures.16 However, experimental data reported by Gopal et al.17,18 indicate a significantly higher intrinsic spontaneous polarization in ZnMgO compared with that in AlGaN. In polar ZnO/ZnMgO and GaN/AlGaN structures, polarization-induced internal fields alter the wavefunctions, thereby reducing the optical matrix element. Evidence for this occurring with GaN/AlGaN has been reported by Park et al.19 Research into GaAs as a material for THz QCLs has been developing rapidly. However, limitations associated with GaAs material parameters have the potential to affect QCL performance, limiting output power and high-temperature operation. In recent years, QCLs based on wide-bandgap materials such as GaN/AlGaN have been developed and reported in literature, but thus far ZnO/ZnMgO QCLs have received considerably less attention. Here we examine ZnO/ZnMgO material in comparison with GaN/AlGaN as a potential candidate for realization of high-power, efficient THz-generation QCLs operating at room temperature. To develop ZnO/ZnMgO QCLs, three major challenges that have been associated with GaN/AlGaN THz QCLs must likewise be overcome for ZnO/ ZnMgO. Firstly, the stability of ZnO is greater than that of MgO, which could increase the possibility of unwanted effects during the growth process. Based on the calculation by Andrei et al.,17 at zero temperature the Zn1xMgxO alloy is never stable with respect to phase-separated wurtzite ZnO and rocksalt MgO. Also, Sarver et al.10 point out that at above zero

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temperatures a small solid solubility of Mg in wurtzite ZnO is expected. Secondly, the energy of a THz-range photon is so low that thermal excitations can easily disturb the electron configuration, most importantly population inversion, which is necessary for lasing in a QCL. Thirdly, it is difficult to design a suitable waveguide for frequencies in the THz range. While waveguides are a necessary component of THz QCL designs, the dielectric waveguides of conventional solid-state lasers cannot be used in THz QCLs since THz wavelengths are far longer than the size of their active regions. In this paper we report the theoretical calculation of output power and wall-plug efficiency of polar ZnO/ ZnMgO heterostructures as well as nonpolar heterostructures taking into account the presence of spontaneous and piezoelectric polarizations based upon fundamental device physics. EXPERIMENTAL PROCEDURE A schematic of lasing and cascading in a QCL is shown in Fig. 1. The two periods of the QCL superlattice structure each consist of an injector, injection barrier, and active region. Electrons are guided through the injector region to the upper laser level in the active region, where optical transitions occur between a few discrete levels. Such intersubband transitions, comprising multiple QWs, give rise to radiation emission. Laser action in this Zn1xMgxO multiple quantum well (MQW) structure is based on a three-level system. A population inversion is created between upper and lower states, and the QCL structure is biased by a high static electric field (100 kV/cm) so that the ground state of the active region is aligned with the upper state of the next period. Hao et al.20 have reported characteristics of GaN material showing that a higher critical field (2 MV/cm for GaN versus 0.4 MV/cm for GaAs) can be applied to supply higher output power density. Since nitride-based material is comparable to Zn-based material due to similar material parameters and the presence of piezoelectric fields that offer a number of advantages over GaAs-based THz QCLs,20 similar high fields would likewise be applicable to ZnO-based QCL devices. Finally, the electrons in one active region are injected into and transferred to the next period. The determination of an appropriate THz frequency and the tailoring of the QWs to facilitate transition of the carriers to the ground state assisted by LO phonon scattering requires solving the Schro¨dinger equation to define the eigenstates formed in the conduction band. The time-independent Schro¨dinger equation under the effective-mass approximation can be written as21

2 @2 h wð xÞ þ ½qV ð xÞ þ DEc ð xÞwð xÞ 2mð xÞ @x2 ¼ j Ejwð xÞ ¼ Hwð xÞ;

(1)

where m(x) is the position-dependent effective mass, V(x) is the electrostatic potential, DEc(x) is the

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Fig. 1. (a) Schematic of a Zn0.95Mg0.05O THz QCL device along with conduction-band profile. (b) Wavefunctions for the ZnO/Zn0.95Mg0.05O MQW structure, biased at 100 kV/cm. The layer sequence for one period of the structure beginning from the left in the injector region (in nm) is 4/ 2.5/3.2/1.5/2.3/3.5/2/3.2. Lasing is expected to occur between the upper state (n = 3) and lower state (n = 2), and rapidly depopulate with LO phonon scattering out of the lower state into the ground state (n = 1). The black script denotes the walls and the barriers, respectively.

conduction-band discontinuity, w(x) is the electron wavefunction, and |E| is the energy eigenvalue. The presence of spontaneous PSP and piezoelectric PPE polarizations in polar semiconductors modifies the shape of the QW and the magnitudes of the band offsets, and thus plays a major role in the determination of the eigenenergies and carrier dynamics. It is to be noted that, depending upon the type of substrate (ZnO or MgO) and the composition of the epilayers, the direction of the spontaneous polarization may change.22 In modeling structures with nonpolar crystalline orientation (oriented along a-plane or m-plane), the built-in electric field due to polarization is considered to be zero. The determination of photon population proceeds by assuming the system to be in a state of equilibrium, where the total rate at which electrons transition into a given level equals the total rate at which electrons transition out. The rate equations therefore form a series of coupled equations. The photon populations are solved self-consistently with the electron populations. There is a photon population associated with each possible transition, and a rate equation for each photon population. Determination of the generated THz power and operation of the THz QCL requires finding the photon populations by using the coupled rate equations (Eqs. 2 and 3) as defined by Slingerland et al.23 dni ¼ VWif ni VWfi nf stimulated þ VWfi ni spontaneous dt Vp mif WifPh ¼ 0; ð2Þ where V is the active region volume, Vp is the cavity volume, and ni and nf are the electron population numbers in electron states i and f, respectively. Wfi

represents the absorption rate and Wif the emission rate expressed as Wif ¼ s1if , where sif is the lifetime due to transitions from initial electron state i to final electron state f (due to fast intersubband electron–electron scattering between the closely spaced injection levels). In THz QCLs, the difference between eigenstate energies needs to be smaller than in conventional QCLs, requiring the incorporation of various intersubband scattering mechanisms such as electron–electron, electron–impurity, electron–interface roughness, and photon scattering for lifetime calculation.24 WifPh , the total photon cavity loss rate between states i and f, is a function of the waveguide loss aw, mirror loss aM2 , and group velocity Vg: ðaM2 þ aw ÞVg . mif is the photon population.23 In a three-level system, the determination of photon population follows from dni SP SP SP ¼ m13 W31 n3 Vp ðn1 n3 Þ þ Cn1 W13 m13 W21 ; dt (3) where mif is the photon density between states, i = 1 is the ground state, f = 2 and 3 are the lower and final states, respectively, and WijSP and WjiSP are the total spontaneous transition rates corresponding to the i–j transitions. Here the optical confinement factor C can be treated as the fraction of the optical mode that overlaps with the entire active region, and can be obtained from Eq. 2: C = V/Vp. Optical output power is a useful measure characterizing the performance of a laser. Due to their cascading scheme, this parameter is intrinsically high in QCLs because the electrons that have contributed to generation of photons in one module of the active region are still present in the conduction band and can be reused in subsequent modules of

Room-Temperature Quantum Cascade Laser: ZnO/Zn1xMgxO Versus GaN/AlxGa1xN

the active region. We use the following relationships to calculate the output power:23 Pout ðxÞ ¼ ME ¼ M hx;

(4)

where x is the radiation frequency, E is the photon energy, h is the reduced Planck constant, M is the number of photons at a certain frequency being emitted per unit time from the front surface. Incorporating the mirror loss aM2 , the waveguide confinement equation is written as follows:23 Pout ðxÞ ¼

Vmtot aM2 c hx ; nC

(5)

where n is the modal index and mtot is the total number of photons present at that frequency inside the laser cavity. This defines the power spectrum as a function of frequency. The power is calculated using this equation for all possible transitions to ensure completeness. Wall-plug efficiency (WPE) is defined as the ratio of the emitted peak optical power and the total input electrical power following the treatment outlined by Bai et al.24 The WPE can be expressed as gw ¼ gi go gv ge ;

(6)

where for the QCL structures under consideration the internal quantum efficiency gi is fixed at 70% and the optical efficiency go is fixed at 98%. The voltage efficiency is formulated as24 gv ¼

N hx ; qVth

(7)

where N is the number of QCL periods, q is the elementary electron charge, and Vth is the voltage at threshold current Ith. The electrical efficiency is formulated as24 I Ith i ; ge ¼ h th I 1 þ R II Vth

(8)

where I is the operating current and R is the resistance. It should be noted that the record for high-temperature pulsed operation performance by GaAs-based THz QCL systems has been achieved for resonant phonon designs with two to three QWs per period, but this requires a large number of periods (200 to 250) resulting in high operating voltage.25 To obtain a lower operating voltage, a relatively large number of QWs per period may be utilized,26 allowing Zn- and nitride-based THz QCL structures to potentially achieve THz radiation with comparatively fewer periods.27 RESULTS AND DISCUSSION The energy levels of the wavefunctions can be determined by solving the Schro¨dinger equation. Figure 1a shows the physical device, and Fig. 1b displays two periods of the conduction-band profile and associated wavefunctions for polar and

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nonpolar ZnMgO-based QC structures, showing the energy levels, the superlattice, and the wavefunctions. Each period consists of four QWs: two form the active region, one forms the injector, and the remaining QW forms the collector. The layer sequence for each period, beginning from the left in the injector region, is 4/2.5/3.2/1.5/2.3/3.5/2/3.2 (in nm). An external electric field F = 100 kV/cm is applied. Electrons are injected from the upper state (n = 3) into the lower state (n = 2), and make vertical transitions into the ground state (n = 1). The expected emission frequencies of 5.27 THz (nonpolar case) and 4.93 THz (polar case) correspond to an energy separation DE32 between states 3 and 2 of 21.81 meV (nonpolar case) and 20.41 meV (polar case). Depopulation of level 2 to the ground state (DEZnO = 73 meV) is facilitated by LO phonons scattering with RhxLO = 72 meV. The required condition for population inversion in this case is n3 > n2, where n is the electron population in the specific state calculated using the rate equations (Eqs. 2 and 3). The calculated lifetimes, s32 and s2, were found to be 0.93 ps and 85 fs, respectively. The relative longevity of s32 occurs because the energy spacing between state 3 and state 2 is sufficiently below the LO phonon energy but still large enough to induce photon scattering, while the comparable shortness of s2 implies that population inversion is present in the ZnO/ZnMgO THz QCL device. With the establishment of population inversion in the system, each optical transition leads to a net spontaneous emission into the cavity mode, and correspondingly power is added to the field as it propagates through the system. Figure 2a shows room-temperature THz QCL output power versus injection current for Al0.05Ga0.95N/GaN/Al0.05Ga0.95N and Zn0.95Mg0.05O/ZnO/ Zn0.95Mg0.05O MQW structures consisting of 80 periods with total lengths of 133.2 nm. When the number of periods in the structures is increased from 60 to 130, the THz output powers are found to increase marginally. Higher peak THz QCL output powers are demonstrated in the Zn0.95Mg0.05O/ZnO/ Zn0.95Mg0.05O MQW [PZnMgO = 2.89 mW (nonpolar) and 2.75 mW (polar)] compared with the Al0.05Ga0.95N/GaN/Al0.05Ga0.95N MQW [PAlGaN = 2.37 mW (nonpolar) and 2.29 mW (polar)]. The lower calculated THz frequencies for the Al0.05Ga0.95N/ GaN/Al0.05Ga0.95N MQW structure [xAlGaN = 4.67 THz (nonpolar) and 4.52 THz (polar), compared with xZnMgO = 5.27 THz (nonpolar) and 4.93 THz (polar)] are determined by solving structure eigenenergies to find the difference in energy between eigenstates. The higher THz output power for Zn0.95Mg0.05O/ZnO/Zn0.95Mg0.05O is attributed = 1.65 in part to its lower refractive index nZnMgO r = 2.49, since it is evident compared with nAlGaN r from Eq. 5 that a lower refractive index results in higher peak optical output power. Figure 2b shows the optical output power as a function of number of periods for the Zn0.95Mg0.05O/

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Zn 3.0

Zn

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0.05 0.05 0.95 0.95

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(a)

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1.5 1.0 0.5 0.0 0

5

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15

2.95 2.90 2.85 2.80 2.75 2.70 2.65 2.60 2.55 2.50 2.45 2.40 2.35 2.30 2.25

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Zn 0.95 Mg 0.05 O Polar Zn 0.95 Mg 0.05 O Nonpolar Al 0.05 Ga 0.95 N Polar Al 0.05 Ga 0.95 N Nonpolar

50

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Current (mA)

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(d)

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0.27

5.2 5.0

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0.26

4.8 0.25

4.6

Al 0.05 Ga 0.95 N Polar

Γ

Radiation Frequency (THz)

(c)

80

Number of Periods

4.4

Zn

4.2

Zn

4.0

Al

3.8

Al

3.6 50

60

0.95 0.95

0.05 0.05

Mg Mg

Ga Ga

70

0.05 0.05

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80

0.24

O Polar O Nonpolar

Al 0.05 Ga 0.95 N Nonpolar

0.23

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Number of Periods

Fig. 2. (a) Room-temperature THz QCL output power versus injection current for Al0.05Ga0.95N/GaN/Al0.05Ga0.95N and Zn0.95Mg0.05O/ZnO/ Zn0.95Mg0.05O MQW structures having 80 periods. (b) Optical output power as a function of number of periods for the Zn0.95Mg0.05O/ZnO/ Zn0.95Mg0.05O MQW and Al0.05Ga0.95N/GaN/Al0.05Ga0.95N MQW for polar and nonpolar planes, each biased at 100 kV/cm. (c) Corresponding radiation frequency as a function of number of periods. (d) Corresponding optical confinement factor of the ionic and nitride-based materials with polar and nonpolar orientations.

ZnO/Zn0.95Mg0.05O MQW and Al0.05Ga0.95N/GaN/ Al0.05Ga0.95N MQW for polar and nonpolar planes, each biased at 100 kV/cm. The simulations incorporated fixed total number of photons, charge, external voltage, threshold current, threshold voltage, and injection current of 20 mA. The higher THz optical emission frequency of ZnMgO compared with AlGaN can be attributed to the higher polarization field of the former, which is dependent on its structural properties and will cause a shift in the energy difference between states, thereby increasing the radiation frequency and affecting output power. The total polarization, calculated as the sum of the spontaneous and piezoelectric polarizations, is 0.0785 C/m2 for ZnMgO-based material and 0.0336 C/m2 for the AlGaN-based system assuming the same mole fraction, x = 0.05, for Mg and Al. The higher output power for the nonpolar structure compared with the polar structure can be attributed to the higher radiation frequencies of the latter: 5.27 THz (nonpolar) and 4.93 THz (polar) for Zn0.95Mg0.05O and 4.67 THz (nonpolar) and 4.52 THz (polar) for Al0.05Ga0.95N. In addition, it can be seen that the output power, which is proportional to

the ratio of the radiation frequency and the optical confinement factor, increases only slightly with increasing number of periods. The corresponding radiation frequency as a function of number of periods is plotted in Fig. 2c. The change in radiation frequency with increasing total device length due to the increasing number of periods is the result of variation in the differential eigenstate energies. From the simulation results, a decrease in the energy difference between eigenstate 3 and eigenstate 2 was observed as a function of number of periods. Figure 2d shows the corresponding optical confinement factor of the ionic and nitride-based materials with polar and nonpolar orientations, which due to its frequency dependence is observed to decrease with increasing number of periods according to Eq. 5. Changing the number of periods alters the total length of the structure and causes the difference in energies between eigenstates to be shifted to different levels, thus resulting in a change in the radiation frequency and wavelength. The WPE, defined as the energy conversion efficiency by which the heterostructure device converts

Room-Temperature Quantum Cascade Laser: ZnO/Zn1xMgxO Versus GaN/AlxGa1xN

(b)

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28 26

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Fig. 3. (a) Calculated WPE of Zn0.95Mg0.05O and Al0.05Ga0.95N with both polar and nonpolar orientations versus injection current over the range of 0 mA to 20 mA. (b) Wall-plug efficiency (WPE) as a function of number of periods for Zn0.95Mg0.05O/ZnO/Zn0.95Mg0.05O and Al0.05Ga0.95N/ GaN/Al0.05Ga0.95N MQWs with polar and nonpolar structures.

electrical power into optical power, was calculated for Zn0.95Mg0.05O and Al0.05Ga0.95N with both polar and nonpolar orientations versus injection current in the range of 0 mA to 20 mA and plotted in Fig. 3a. For a current of 20 mA, maximum WPE values of 24.61% (nonpolar) and 23.12% (polar) were observed for the Zn0.95Mg0.05O/ZnO/Zn0.95Mg0.05O MQW structure, significantly higher than for the Al0.05Ga0.95N/GaN/Al0.05Ga0.95N MQW structure [WPE = 14.11% (nonpolar) and 13.87% (polar)]. The WPE results derived for the ZnMgO/ZnO structure are comparable to those of current state-of-the-art mid-wavelength infrared (MWIR) lasers,28 providing evidence in support of the suitability of this material for practical QCL devices. Figure 3b shows the WPE as a function of number of periods for Zn0.95Mg0.05O/ZnO/Zn0.95Mg0.05O and Al0.05Ga0.95N/GaN/Al0.05Ga0.95N MQWs for polar and nonpolar orientations. The relatively high photon energy of Zn1xMgxO, which is evident from comparison of its emission frequency with that of other materials such as AlxGa1xN (Fig. 2c), results in higher voltage efficiency that leads to a greater overall WPE. In addition, it can be seen that the WPE of Zn0.95Mg0.05O increases slightly with increasing number of periods; this is due to a slight increase in the voltage efficiency resulting from the variation in radiation frequency which decreases with increasing structure length. Similar behavior was observed in the electrical efficiency for the two types of MQW structures. It is to be noted that the III–V structure is similar to the QCL reported by Bai et al., but lacks the additional quantum structure in the barriers. A 3-mm high-reflection coating with waveguide loss of 0.7 cm1 corresponds to an optical efficiency go of 98%, and the internal quantum efficiency gi is assumed to be 70%.24 The voltage efficiency gv for Zn0.95Mg0.05O is primarily dependent on the number of periods, radiation frequency, and threshold voltage. The peak value of electrical efficiency

ge, which is a function of the injection current, is determined to be 65%. Using these go and gi values, the frequency, mole fraction, and period dependence of the other materials may be determined. CONCLUSIONS A theoretical ZnO/Zn0.95Mg0.05O QCL structure emitting at 5.27 THz based upon the fundamental physics of operation has been reported. With input current of 20 mA, a maximum calculated optical output power of 2.89 mW may be achievable at 5.27 THz for nonpolar ZnO/Zn0.95Mg0.5O QW structures compared with an output power of 2.37 mW at 4.67 THz for nonpolar GaN/Al0.05Ga0.95N QW structures. The higher calculated output power of the ZnO/ZnMgO structure is attributed = 1.65 in part to its lower refractive index nZnMgO r = 2.49). In addition, WPE (compared with nAlGaN r values of 24.61% (nonpolar) and 23.12% (polar), which are comparable to those of current MWIR lasers, are obtained for the ZnO/ZnMgO QW structure compared with 14.11% (nonpolar) and 13.87% (polar) for the GaN/AlGaN structure. These results support the conclusion that ZnO/Zn1xMgxO is a promising material system for THz QCLs operating at room temperature.

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