Electronic and optical properties of

ZnO quantum well structures

Hee Chang Jean, Tae Won Kang, and Seung Joo Lee*

Quantum-functional Semiconductor Research Center Dongguk University

Seoul, Korea Email: leesj@dongguk.edu

Abstract-This study investigates optical properties as a function of internal and external fields in the quantum well (QW). Optical

properties of CdZnO/MgZnO QW structures, considering

various applied electric fields are evaluated by using many-body

effects. The strain-induced piezoelectric polarization and the

spontaneous polarization can be reduced effectively by applied

electric field in CdZnO/ZnMgO quantum well (QW) structures with high Cd composition. That is, optical properties as a

function of internal and external fields in the CdZnO/ZnMgO QW with various applied electric field result in the increased optical gain due to the fact that the QW potential profile is

flattened as a result of the compensation of the internal field by

the reverse field as confirmed by Stark shifts. These results demonstrate that a high-performance optical device operation can be realized in CdZnO/MgZnO QW structures by reducing the droop phenomenon.

Keywords- laser diode efficiency; ZnO; quantum well

I. INTRODUCTION

Wide band-gap wurtzite semiconductors have attracted much attention due to their potential applications for optoelectronic devices in the photonic devices such as light­emitting devices and solar cells. ZnO materials have great potential for highly-efficient and novel photonic device applications due to their high crystallinity, wide and direct band gap, peculiar physical properties such as large exciton binding energy [1]. In principle, a lower pumping threshold can be expected if an exciton-related recombination, rather than an electron-hole plasma recombination, is used. Recently, the quantum Hall effect and fractional quantum Hall effect were observed in very high purity ZnO/ZnMgO heterostructures with high mobility of �200,OOO(cm2/Vsec)[2,3], which is close to that of a pure sample of GaAs. ZnO-related semiconductor photonic devices can be realized by tuning structural, electrical, and optical properties of these semiconducting materials.

Seoung Hwan Park

Department of Electronics Engineering Catholic University of Daegu

Daegu, Korea

Experimentally, several groups reported the successful growth of CdZnO/MgZnO multiple QWs and showed that these systems are promising for optical applications and solar cell. However, many fundamental properties of CdZnOIMgZnO QW structures are not yet well understood because these studies are in an early developmental stage. In particular, key issues remain for high-performance photonic device applications, such as the droop phenomenon [4], wherein the efficiency of a light-emitting diode (LED) or laser diode tends to decrease for increasing current. As the current increases, the LED emission power fIrst tends to maintain a constant value and then starts to decrease. The origin of the droop phenomenon, i.e., the decrease in effIciency with increasing current to the nominal value, is attributed to the leakage of carriers in the QW interfaces or their tunneling by internal fields and their non-radiative recombination with holes at semiconductor hetero-interfaces [5]. The droop in an LED creates large difficulties. Several efforts have been undertaken to overcome this, but so far unsuccessful [6, 7].

In this work, we try to recognize and reduce the droop phenomenon by engineering the internal and external applied electric fields in a CdolZno90/Mgo2ZnosO QW structure with varying the applied electric fIeld. On the theoretical side, an understanding of the roles of applied electric fields in wurtzite CdZnO-based QW structures is very important in order to give guidelines on sample growth and a device design. Optical properties of CdZnO/ZnMgO QW structures were investigated numerically with various applied electric fields by using the many-body effect method [8,9]. We consider a QW structure with a ZnMgO buffer layer, which is used as the substrate for the growth ofQWs[lO]. Thus, a CdZnO quantum well is under a compressive strain and a ZnMgO barrier is lattice-matched to the substrate. The self-consistent (SC) band structures and wave functions for the QW structures are obtained by solving the Schroedinger equation for electrons and the 3x3 Hamiltonian for holes[ll, 12].

978-1-4673-6374-7/13/$31.00 ©2013 IEEE

We assume that a CdZnO/MgZnO QW structure is grown on a thick ZnO substrate with a fixed Mg composition of 0.2 in the barrier.

5 .-----_-, (a ) E.=O MV/cm 4 Cl

(c) E.= 2 MV/cm

Cl

:> 3 �

J :�llE'�4 ��'� � m W 0 m W 0 m W Length (A) Length (A) Length (A)

Figure 1. Potential profiles and the wave functions (CI and HHI) at the zone center for the self-consistent model of 30 A CdlllZno90IMg02ZnO,0 QW

structures at (a) En = 0.0, (b) En = 1 MV/cm, and (c) En = 2 MY/cm. Here, the barrier width is set to be 50 A.

CdZnO-based QWs are expected to have a larger spontaneous polarization constant comparable to that of ZnO­based QWs. This may be attributed to the fact that the sum of spontaneous (SP) polarization and piezoelectric (PZ) polarization in the well, where the internal field in the well is determined from the difference of the sum of SP and PZ polarizations in the well and the barrier. Internal electric fields due to piezoelectric effects or ionized dopants are present. Thus, it is important that the internal field due to SP polarization and PZ polarization in the well and the barrier in the CdZnO-based

QWs is reduced due to the additional polarization by ionized dopants. Here, we also investigate the electronic and optical properties of CdZnO/ZnMgO QWs structures with external fields. The results are compared with those of CdZnO/ZnMgO

QWs structures with SP and PZ polarization. Optical gain is expected to be enhanced because the internal field is canceled due to external fields in CdZnO/MgZnO QWs structure.

IT. RESULTS

Figure I shows the potential profiles and the wave functions (CI and HHI) at the zone center for the SC model with the spontaneous polarization(SP) and piezoelectric polarization(PZ) for 30 A CdxZnl_xO/Mgo2ZnOgO QW structures with x = 0.1.

It was noted that the energy band structures show significant shifts with external bias. The energy band shows a Stark type shift with increasing the bias voltage. However, in the case of external field with increasing forward bias, the internal field increases and reaches a maximum around 2MY/cm, as shown in Fig. I.

These results indicate that the optical efficiency is significantly influenced by the interplay of internal and external field effects in the QW.

(a) E,=O MVlcm 4 C1

(b) E,= -1 MV/cm C1

(c) E, = -2 MVlcm

C1

Figure 2. Potential profiles and the wave functions at the zone center for the self:consistent model of 30 A Cd(llZno90IMg(12ZnOgO QW structures at (a) En

= 0.0, (b) En = -I MY/cm, and (c) En = -2 MY/cm. Here, the barrier width is set to be 50 A.

In this paper, the barrier width is set to 50 A. The SC solutions are obtained at the sheet carrier density of NZD =

Ix1013/cm2 and the dashed line corresponds to the wave function for the flat-band model with various applied electric field. The MgZnO barrier and the CdZnO well are under a compressive strain and it is assumed that the layers have a zinc plane. For the Zn face, SP polarization is directed towards the substrate and the alignment of SP and PZ polarizations is antiparallel in the case of compressive strain. If the barrier is under tensile strain, the alignment of SP and PZ polarizations becomes parallel. In the case of ZnO/MgZnO QW structures with x = 0.0, the potential profile shows that the internal field caused by SP and PZ polarizations is relatively small compared to those with high Cd compositions. The internal field is determined by the difference between the sum of the SP and PZ polarization in the barrier and in the well.

On the other hand, in Fig. I (c), with increasing positive applied electric field, a significant change of the internal field is observed, and the bottom of the potential well in the conduction band is shown to exist on the left side in the well. This is due to the fact that the positive applied electric field in the well overcomes the original polarizations existed in the well. That is, QW potential is flattened, as shown in Fig. 1 (b), as a result of the compensation of the strain-induced piezoelectric polarization and the spontaneous polarization by the reverse bias, as confirmed by Stark type shifts.

Figure 2 shows the potential profiles and the wave functions (CI and HHI energy levels) at the zone center for the SC model with the spontaneous and piezoelectric polarizations for 30 A CdolZno90/Mgo2ZnOgO QW structures with (a) E. =

0.0, (b) E. = -1.0 MY/cm, and (c) E. = -2.0 MY/cm. CdZnO/MgZnO QW structure shows that the bottom of the potential well in the conduction band exists on the right side in the well because the barrier is under compressive strain and the PZ polarization is antiparallel to the SP polarization.

3.3

3.1

3'C:2 -1 0 1 2 Applied electric field (MV/cm)

Figure 3. Interband transition energy between Eel and EHHl at kll=O for several applied electric field in CdZnO/MgZnO QWs structures.

In the case of Figs 2 (b) and (c), the potential profile shows that the internal field is shown to be increased due to several negative applied electric fields in CdolZno90/Mgo2ZnOgO QW structure. The potential profile shows that the internal field caused by the negative applied electric field is relatively large as compared to those with zero applied electric field, because negative applied electric field is parallel to the SP+PZ polarization in this case. This is because of the additional field caused by the increase of the applied electric field in the well. The sum of SP and PZ polarizations are increased due to additional field of same direction by negative applied electric field in CdZnO/ZnMgO QW structure.

Figure 3 shows the interband transition energy between Eel and EHHI at kll=O for several applied electric fields in CdZnOIMgZnO QWs structures. The transition energy is shown to increase with applied electric field relatively. This is mainly attributed to the fact that the band edge is flattened due to the increase with increasing positive applied electric field. In the case of CdZnOIMgZnO QW structures with several applied electric fields, the transition energy is dependent on the applied electric field. The transition energy is gradually shifted to a short wavelength because the internal field is screened by charged carriers.

This unique dependence on the optical intensity variation at different injection levels originates from the difference in the bias voltage (external field effect). The changes of the optical efficiency with bias support this interpretation by internal field. These results imply that the usual evolution of the optical gain with bias can be due to variations of the actual potential field distribution (due to both internal and external fields), which significantly influence the optical efficiency within the QW structure. and the droop phenomenon can be reduced also.

Ill. CONCLUSION

The energy band structure and the optical gain of CdZnOIMgZnO QW structures were studied theoretically. Optical gain is expected to be increased because internal field is canceled due to positive applied electric field In

CdolZno90/Mg02ZnOgO QW structures. These results demonstrate that a high-perfonnance optical devices operation can be realized in CdZnO/MgZnO QW structures by eliminating the droop phenomenon in a LED.

ACKNOWLEDGMENT

This work was supported by the Korea Science and Engineering Foundation through the Quantum-functional Semiconductor Research Center at Dongguk University, and this work was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (No.2012-00109, No.2012-0000217, No.2012RIA lA2005772)

REFERENCES

[ 1] T. Makino, K. Tamura, C. H. Chia, Y. Segawa, M. Kawasaki, A. Ohtomo, and H. Koinuma, "Radiative recombination of electron-hole pairs spatially separated due to quantum-confined Stark and Franz­Keldish effects in ZnO/Mgo27Zn07J0 quantum wells", Appl. Phys. Lett., vol. 8 1, pp. 2355-2357, 2002.

[2] A. Tsukazaki, A. Ohtomo, T. Kita, Y. Ohno, H. Ohno, and M. Kawasaki, "Quantum Hall Effect in Polar Oxide Heterostructures", Science, vol. 3 15,pp. 1388-139 1,2007.

[3] A. Tsukazaki, S. Akasaka, K. Nakahara, Y. Ohno, H. Ohno, D. Maryenko, A. Ohtomo, and M. Kawasaki, "Observation of the fractional quantum Hall eflect in an oxide.", Nature Materials, vol. 9, pp. 889-893, 20 10.

[4] A. A Efremov., N. I. Bochkareva, R. I. Gorbunov, D. A. Larinovich, Yu. T. Rebane, D. V. Tarkhin, and Yu. G. Shreter, "Quantum efficiency and choice of thermal conditions for high-power blue InGaN/GaN LEDs", Semiconductors, vol. 40, pp. 605-610, 2006.

[5] Y. C. Shen, G. O. Mueller, S. Watanabe, N. F. Gardner, A. Munkholm, and M. R. Krames, "Auger recombination in InGaN measured by photoluminescence", Appl. Phys. Lett., vol. 9 1, pp. 14 1 10 1- 14 1 104 2007.

[6] 1. A. Pope, P. M. Smowton, P. Blood, 1. D. Thomson, M. 1. Kappers, and C. J. Humphreys, "Carrier leakage in InGaN quantum well Iight­emitting diodes emitting at 480 nm", Appl. Phys. Lett. vol. 82, pp. 2755-2758,2003.

[7] I. V. Rozhansky and D. A. Zakheim "Analysis of processes limiting quantum efliciency of AlGaInN LEDs at high pumping", Phys. Status Solidi A, vol. 204, pp. 227-230,2007.

[8] D. Ahn, "Theory of non-Markovian optical gain in quantum-well lasers", Prog. Quantum Electron, vol. 2 1, pp. 249-287, 1997.

[9] S. H. Park, S. L. Chuang, 1. Minch, and D. Ahn, "Intraband relaxation time effects on non-Markovian gain with many-body effects and comparison with experiment.", Semicond. Sci. Technol., vol. 15, pp. 203-208,2000.

[ 10] H. C. Jeon, S. H. Park, S. J. Lee, T. W. Kang, and T. F. George, "Electronic and optical properties of CdZnO quantum well structures with electric field and polarization effects.", Appl. Phys. Lett., vol. 96, pp. 10 1 1 13- 10 1 1 16,2010.

[ 1 1] S. L. Chuang and C .S. Chang, "k'p method for strained wurtzite semiconductors.", Phys.Rev. B, vol. 54, pp. 249 1-2504, 1996.

[ 12] S. H. Park and S. L. Chuang, "Comparison of zinc-blende and wurtzite GaN semiconductors with spontaneous polarization and piezoelectric field eflects.", 1. Appl. Phys., vol. 87, pp. 353-365, 2000.