Investigation of the strain induced optical transition energy shift of the GaN nanorod light

emitting diode arrays

Liang-Yi Chen,1 Hung-Hsun Huang,

1 Chun-Hsiang Chang,

1 Ying-Yuan Huang,

1 Yuh-

Renn Wu1,2

and JianJang Huang1,2,*

1Graduate Institute of Photonics and Optoelectronics, Taiwan

2 Department of Electrical Engineering, National Taiwan University, 1, Roosevelt Road, Section 4, Taipei, 106, Taiwan

*jjhuang@cc.ee.ntu.edu.tw

Abstract: Strain in the semiconductor light emitting layers has profound effect on the energy band structure and the optical properties of the light emitting diodes (LEDs). Here, we report the fabrication and characterization of GaN nanorod LED arrays. We found that the choice of nanorod passivation materials results in the variation of strain in the InGaN/GaN quantum wells, and thus the corresponding change of light emission properties. The results were further investigated by performing Raman measurement to understand the strain of nanorods with different passivation materials and by calculating the optical transition energy of the devices under the influence of strain-induced deformation potential and the piezoelectric polarization field.

©2011 Optical Society of America

OCIS codes: (220.4241) Nanostructure fabrication; (230.3670) Light emitting diodes.

References and links

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#143761 - $15.00 USD Received 7 Mar 2011; revised 3 Jun 2011; accepted 3 Jun 2011; published 1 Jul 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. S4 / OPTICS EXPRESS A900

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1. Introduction

Recently, GaN based nanorod light emitting diode(LED) arrays have been studied [1–4] to understand the material and device characteristics of the nanostructures. The increased sidewall area of nanorods, as compared with the planar structure, has the advantage of improving the external extraction efficiency. And the vertical guided modes along the nanorods may affect the radiation profile of the LED array [5,6]. For GaN based LEDs, lattice mismatch between the InGaN and GaN layers in the active region induces strain, which creates the internal electric field and results in the separation of electrons and hole and the corresponding reduction of internal quantum efficiency. The phenomenon is called quantum confined stark effect (QCSE) [7] and is considered as one of the reasons for efficiency droop in LEDs [8]. As the planar LED epi-structure is etched to form p-i-n nanorods, the strain between InGaN and GaN was reported to be relieved and thus the QCSE is mitigated [9,10]. Furthermore, for some of the surface roughening processes that removed part of the p-type GaN material, the underneath InGaN/GaN strain was found to be partially relaxed [11]. From the studies above, the variation of strain in the GaN epi-structure implies the delicate change of the energy band profile [12]. Since the strain of the GaN nanostructure varies with the fabrication condition, it becomes intriguing to study the strain-induced bandedge shift and QCSE related light emission wavelength change of such devices.

We previously demonstrated GaN nanorod LED arrays with a nearly constant peak EL(electroluminescent) wavelength under a certain range of injection currents [13] and later indicated that the sidewall leakage current can be significantly decreased using a CMP (chemical mechanical polishing) process [14]. The reduced sidewall leakage enables us to study the effect of strain relaxation based on the EL spectra without worrying about device self-heating under current injection. In this work, by investigating the optical properties of the GaN nanorod LED arrays, we found that the choice of nanorod passivation materials affects EL emission spectra. Raman measurement was then performed to understand the strain of the

#143761 - $15.00 USD Received 7 Mar 2011; revised 3 Jun 2011; accepted 3 Jun 2011; published 1 Jul 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. S4 / OPTICS EXPRESS A901

nanorods with different passivation materials. And the influence of strain-induced deformation potential and the piezoelectric polarization field to the EL spectra of the devices is analyzed.

2. Experiments

The material structure and the device fabrication steps are very similar to our previous work [14]. The LED epi-structure was grown on the c-plane sapphire substrate using MOCVD(Metal-organic chemical vapor deposition). The material structure consists of a 25nm GaN buffer layer, a 2μm Si doped n-type GaN layer, 5 periods of In0.2Ga0.8N/GaN multiple quantum well (MQW) and a 160nm p-type layer. The device fabrication starts from defining a 300x300μm

2 mesa area by ICP-RIE(Inductively coupled plasma reactive ion

etching). In the next step, we employed nanosphere lithography [6] to define nanorods. A monolayer of silica nanospheres as the etching hard mask with the diameter of 100nm was coated on the sample and followed by ICP-RIE etching to define nanorods. The etching depth is around 300nm to ensure the expose of p-i(MQW)-n layers of the nanorods to the air. Then, the space layer was coated to prevent the p-type GaN from shorting to the n-type and meanwhile to passivate the nanorod sidewalls. To understand the effect of the space layer on the device performance, either the SiO2 thin film grown by PECVD (Plasma-enhanced chemical vapor deposition) or the SOG(spin-on-glass) layer is deposited. In this experiment, the Siloxanes family of SOG was used. The SOG was spin-coated, reflowed at 72°C for 15mins and was then put into 400°C oven for 1hour. Following the steps of nanorod definition and space layer insertion, a CMP (chemical mechanical polishing) process was carried out to expose p-GaN tip surface for the subsequent metallization. The Au (5nm) / Ni (5nm) current spreading contact was first deposited on the light emitting mesa area. And finally, the n- and p-type contact pads composed of Au(120nm)/Ti(12nm) were evaporated. A schematic diagram of the nanorod LED array is shown in Fig. 1. The nomenclature of the nanorod LED array with SiO2 and SOG is “Nanorod LED with SiO2” and “Nanorod LED with SOG”, respectively, in this work. In addition, for comparison purpose, we also prepared a planar LED with the same mesa area and metal stack composition but without nanorod definition.

Fig. 1. Schematic diagram of the nanorod LED array. The passivation layer is either spin-coated SOG or PECVD-grown SiO2.

3. Results and disscussion

A. Analysis of the electroluminescent spectra

We first analyze the optical properties of the devices at room temperature. In Fig. 2(a), the EL spectra of the planar LED shows a 51meV peak energy shift from 2.696eV to 2.747eV as the current increases from 2mA to 20mA. The effect of the energy shift is attributed to the quantum confined stark effect (QCSE) which is mainly resulted from strain induced piezoelectric field in the InGaN/GaN epi-structure. The internal electric field tilts the band-gap of quantum well (QW), which not only causes the separation of electrons and holes but also shrinks the optical transition energy. As we increase the injection current, the increased number of carriers screens the internal electric field, leading to the blue shift of light emission.

On the other hand, the nanorod LED arrays show mitigated QCSE. The peak energy shift of “Nanorod LED with SiO2” is 35meV as the injection current is increased from 2mA to

#143761 - $15.00 USD Received 7 Mar 2011; revised 3 Jun 2011; accepted 3 Jun 2011; published 1 Jul 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. S4 / OPTICS EXPRESS A902

20mA (see Fig. 2(b)). Furthermore, as suggested from Fig. 2(c), the peak energy shift of the “Nanorod LED with SOG” is only 6meV, much smaller than those of the previous two samples. The results suggest that even with the relaxed strain after the formation of nanorods [14], the degree of strain relaxation relies not only on the etching condition but also on the choice of the passivation materials. That is, the EL spectra are influenced by the passivation of the GaN nanorod sidewalls. The peak position of the EL spectra and the energy shift are plotted in Fig. 2(d) and (e), respectively. The peak energy of the EL spectra of those devices under various injection currents will be further investigated. In this work, the correlation between the peak energy shift and strain relaxation will be verified by Raman spectroscopic measurement, while the variation of the peak energy position, especially at the low injection current where carrier screening doesn’t prevail, of those devices will be discussed by considering the influence of strain and QCSE.

Fig. 2. EL spectra of the planar LED (a) “Nanorod LED with SiO2“ (b) “Nanorod LED with SOG” (c) at the injection current between 2mA and 20mA. The peak energy position (d) and the peak energy shift (e) of the devices are also plotted.

B. Analysis of the Raman spectra

To understand the strain in InGaN/GaN MQW layers with various passivation materials, Raman spectroscopic measurement was conducted. Samples with either the planar structure or the nanorod strucutre were prepared. The nanorods were defined and passivated using the same process steps as described above. Nanorods with SOG and SiO2 are defined as “nanorod with SOG” and “nanorod with SiO2”, respectively, so that the device results in the previous sub-section won’t be confused with the material characterizations. As shown in Fig. 3, a

close-up view near InGaN E2H mode(around 560cm

1) is taken at the shoulder of the GaN

mode(around 570 cm1

). By applying the Lorentzian curve fitting, the close-up views of the InGaN E2

H modes of three samples are shown in Fig. 3. The peak position of InGaN E2

H

mode was 559.61cm1

, 559.17cm1

and 558.11cm1

for planar structure, “nanorod with SiO2“ and “nanorod with SOG”, respectively. As the Raman shift toward a lower wave function is associated with the strain relieve in the InGaN/GaN layers, the nanostructure shows a relaxed

#143761 - $15.00 USD Received 7 Mar 2011; revised 3 Jun 2011; accepted 3 Jun 2011; published 1 Jul 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. S4 / OPTICS EXPRESS A903

strain as compared to the planar structure. Furthermore, the choice of passivation materials also affects the strain in the semiconductor layers. It is suggested that nanorods passivated with SOG have further strain relaxation.

Figure 4 illustrates the idea of external induced strain, which the material of the space layer exerts vertical force on the nanorod sidewalls. We suspect that since the PECVD grown SiO2 layer has a sturdier atomic bindings than the SOG, leading to less strain relaxation.

Fig. 3. Close-up views of the InGaN E2H phonon mode of the planar structure, nanorod-SiO2

and nanorod-SOG.

n-GaN

p-GaN

Buffer layer

Sapphire

MQWs

Passivation layer

Passivation layer induced strain

Fig. 4. Illustration of the vertical force exerted on the sidewall of the nanorods by the passivation material.

C. Strain relaxation and its correlation with optical transition in the band structure

In order to understand the correlation between the induced strain and the optical properties of the nanorod LED arrays, we next calculated the biaxial strain based on the Raman spectral shift. With the biaxial strain, the band-edge changes of the devices as well as the peak energy shift can be obtained.

#143761 - $15.00 USD Received 7 Mar 2011; revised 3 Jun 2011; accepted 3 Jun 2011; published 1 Jul 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. S4 / OPTICS EXPRESS A904

The wave-number shift of the phonon mode in Raman spectra can be correlated to the biaxial strain ε// following the equation below [15].

13

0 ||

33

2 2c

a bc

(1)

Where the ω is the InGaN E2H mode wave number of the samples, ω0 is the wave number of

the strain free InGaN layer, aλ and bλ are phonon deformation potentials, and C13 and C33 are elastic constants. In our case, Δω ( = ω–ω0) can be obtained from Raman measurement. The parameters aλ, bλ, C13 and C33 of the InxGa1-xN are obtained by linearly interpolating the values of InN and GaN assuming x = 0.2 in our epi-structure(see Table 1). From Eq. (1), the biaxial strain ε// of the planar structure, nanorod with SiO2 and nanorod with SOG are

calculated to be 1.37%, 1.33% and 1.22%, respectively. With the information of the biaxial strain, the band-edge energy and the QCSE induced

wavelength shift due to the InGaN/GaN strain can be calculated. At the first thought, the above two mechanisms have opposite effect on the energy band profile. The relaxed strain of the nanorod structure causes the shrinkage of band-edge while the mitigated QCSE results in less tilt of the band structure. The optical transition energy is reduced by the first phenomenon but increased by the second one. As a result, without considering the effect of carrier screening, light emission energy depends delicately on the strain of InGaN/GaN at the low injection current.

To investigate the effect of passivation material on the EL spectrum, we first calculated the band-edge of these three samples and followed by considering QCSE induced optical transition energy shift, both are based on the strain obtained from Raman measurement.

(a) Band-edge calculation

To calculate the band-edge, the 6 × 6 k•p method [16,17] is applied for obtaining the valence band and the effective mass approximation method [18] is employed for the conduction band. The effective mass of GaN and InGaN is listed in Table 1 [19]. In this case, we assume that there is no QCSE and the energy band profile is a flat band case. The bandgap is only affected by the strain induced deformation potential and quantum confined effect. The band gap energy Eg of the bulk InGaN is calculated by linearly interpolating the bandgap of GaN (Eg, GaN) and InN(Eg,InN) following the equation by assuming X = 0.2

, ,1g GaN g InNE X E X (2)

The optical transition energy is next calculated by employing the Schrödinger solver to obtain the confined energy states within the quantum wells. The optical transition energies between Ec1(first state in the quantum well of the conduction band) and Ev1(first state in the quantum well of the valence band) in the planar structure, nanorod with SiO2, nanorod with SOG are calculated to be 3.073eV, 3.071eV and 3.065eV, respectively (see Fig. 5). The planar structure possesses the largest optical transition energy due to the greatest strain in the material structure, while nanorod with SOG has the smallest one. It suggests the release of compressive strain causes the shrinkage of the QW band gap. However, the results contradict the experimental data (see Fig. 2), especially at the low injection current. It implies that the QCSE needs to be considered.

#143761 - $15.00 USD Received 7 Mar 2011; revised 3 Jun 2011; accepted 3 Jun 2011; published 1 Jul 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. S4 / OPTICS EXPRESS A905

Fig. 5. Calculated band gap profiles and the optical transition energy between first states in the QW of (a) the planar structure, (b) Nanorod with SiO2 (c) Nanorod with SOG. Note only strain relaxation induced band shrinkage is considered here.

(b) Calculation of the strain induced piezoelectric field

The effect of stain induced piezoelectric field is next considered. The piezoelectric field Epz of the wurzite structure is obtained from the in-plane strain εxx following the equation [20].

13

33 31

0 33

2pz xx

r

cE e e

c

(3)

Where єxx carries the same value as the biaxial strain ε// in (1), and the εr, ε0, and eij are the dielectric constants of the material, the permittivity of the free space, and the piezoelectric constants, respectively.

After obtaining the piezoelectric polarization from strain and meanwhile considering the spontaneous polarization, we can calculate the total charge density from the total polarization. The potential affected by the polarization charges is solved with Schrödinger equation and Poisson equation. Following the Schrödinger equation, the confined charge can be obtained and is then plugged in to the Poisson equation. Once again, the potential determined by Poisson will feedback to the Schrödinger equation until the solution reaches convergence [21].

The potential energy in the QW was obtained from the above self-consistently Poisson equation. Again, we applied the 6 × 6 k•p method to calculate the valence band and the effective mass approximation to calculate the conduction band. Finally, the Schrödinger solver was employed to obtain the confined energy state within the tilted QW. The calculated results, by considering both the deformation potential and piezoelectric field, are shown in Fig. 6. The optical transition energy of the nanorod with SOG sample is the highest while the planar one is the lowest.

Fig. 6. Calculated band gap profiles and the optical transition energy between first energy states within the quantum well of (a) Planar structure (b) Nanorod with SiO2 (c) Nanorod with SOG. The results are obtained by considering both the strain relaxation induced band shrinkage and QCSE.

#143761 - $15.00 USD Received 7 Mar 2011; revised 3 Jun 2011; accepted 3 Jun 2011; published 1 Jul 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. S4 / OPTICS EXPRESS A906

(c) Correlation between strain and optical transition energy

The calculated optical transition energy of the nanorod with SiO2 and nanorod with SOG is 7meV and 22meV higher than the planar one, respectively, which is in compared with the experimental EL peak energy position shift of 2.7meV and 29meV in Fig. 2. Although the calculated results are not exactly the same as the experimental ones, they both show the same trend of energy shift. The difference is related to some uncertain factors, such as the Raman E2

H phonon mode of the strain free In0.2Ga0.8N and the uniformity of the epi-structure. Also,

it may be associated with carrier screening. The calculation was conducted without considering the carrier screening, while the EL spectra were obtained with current injection, despite at a low current such as at 2mA.

Table 1. Parameters employed in the simulation

Symbol GaN InN

Stiffness constants 2C13/C33

0.6[15] 0.9[15]

Phonon deformation Potentials (cm-1)

aλ(E2H)

bλ(E2H)

850[15]

920[15]

610[15]

857[15]

Piezoelectric constants (C/m2)

e31

e33

0.33[22]

0.65[22] 0.57[23]

0.97[23]

Dielectric constant (E┴c) εr

9.5[24] 13.1[25]

Effective mass┴ (m0) me mhh mlh

0.18[19] 1.65[19] 0.15[19]

0.1[19] 1.68[19] 0.11[19]

Reference [15,19,22–25]

4.Conclusion

We observed passivation material dependent strain relaxation in the GaN based nanorod structure. For the planar structure, the peak energy shifts 51meV as the injection current increases from 2mA to 20mA, which is in compared to 35meV and 6meV shift for the “nanorod LED with SiO2“ and “nanorod LED with SOG” cases. The difference of peak energy shift and strain relaxation was also verified from the Raman measurement. The external induced strain change is mainly related to vertical force exerted on the nanorod sidewalls by the passivation material. Since the PECVD grown SiO2 layer has a better atomic arrangement than the SOG, stronger bondings on the rod sidewalls can be observed. To understand the effect of strain on the optical transition, the strain induced band-edge shrinkage as well as the piezoelectric field related energy tilt were calculated. The calculated optical transition energy of the nanorod with SiO2 and nanorod with SOG is 7meV and 22meV higher than the planar one, respectively. Although the results are not exactly the same as the experimental ones, they show the same trend of energy shift.

Acknowledgement

This work was supported by the National Science Council in Taiwan under Grant NSC 97-2221-E-002-054-MY3.

#143761 - $15.00 USD Received 7 Mar 2011; revised 3 Jun 2011; accepted 3 Jun 2011; published 1 Jul 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. S4 / OPTICS EXPRESS A907