Thermal annealing effects on the optical gain of InGaN/GaN quantum well structures

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Thermal annealing eﬀects on the optical gain

of InGaN/GaN quantum well structures

Chii-Chang Chen

a,*

, Tao-Hung Hsueh

b

, Yi-Sheng Ting

c

, Gou-Chung Chi

c

,

Chin-An Chang

d

, S.C. Wang

b

a

Institute of Optical Sciences, National Central University, 32054 Chung-Li, Taiwan, ROC

b_{Institute of Electro-Optical Engineering, National Chiao Tung University, Hsinchu 300, Taiwan, ROC} c_{Department of Physics, National Central University, 32054 Chung-Li, Taiwan, ROC}

d_{Opto-Electronics and Systems Laboratories, Industrial Technology Research Institute, Chutung, Hsinchu 310, Taiwan, ROC}

Abstract

In this work, the variation of the optical gain in the InGaN/GaN quantum well after thermal annealing is simulated. The potential profile change of the quantum well resulting from the interdiffusion of Ga and In atoms across the in-terface of the well and the barrier during the thermal treatments is assumed to follow FickÕs law. The results show that the thermal annealing can induce an increase of the optical gain in the InGaN/GaN quantum well. The maximum optical gain can be obtained at a diffusion length of 0.4 nm of In and Ga atoms. However, an excessive annealing may result in decreasing the optical gain. There is a good agreement between the experimental data in literature and the optimized diffusion length studied in this work.

Keywords: GaN; InGaN; Annealing; Quantum well; Interdiﬀusion; Gain

1. Introduction

GaN is a promising material for light emitting devices in the violet–blue–green region. Quantum well (QW) structures are often used for GaN-based light-emitting diodes and lasers. Up to now, most of the commercial GaN epitaxial layers are grown by metalorganic chemi-cal vapor deposition. The typichemi-cal growth temperatures of InGaN, GaN and AlGaN layers are 800, 1020 and 1020 °C, respectively [1]. After the growth of the epitaxial

layers, a thermal annealing at 700 °C is employed to

convert the as-grown p-type GaN layer into a uniform highly p-type GaN layer [1]. To obtain high hole con-centrations in the p-layer, ion implantation and diﬀusion

techniques are also considered. A thermal activation at

1000 °C for 5 min after Mg or Zn ion implantation is

employed [2–4]. Diﬀusion with Mg at 1000°C for 60 min

can also be used for the same intention [5]. To realize the ohmic contacts between metals and semiconductors,

thermal annealing at 450–950°C for 60 min is performed

[4,6–8]. During the expitaxial growth of InGaN/GaN MQW structure and the fabrication of devices, InGaN layers undergo several high-temperature treatments. The distribution of the indium composition and the strain in the QW may be changed due to the In and Ga interdif-fusion across the interface of the QW and the barrier after these thermal treatments. This leads to a change of the optical properties of the QW [9–13]. After the sample was annealed, a blue shift of the PL peak has been ob-served [11–13] and the photoluminescence (PL) intensity is increased [13]. In this work, we investigate theoretically the variation of the optical properties in InGaN/GaN QW resulting from the interdiﬀusion of In and Ga atoms across the interface of the QW and the barrier.

*

Corresponding author. Tel.: +886-3-4227151x5257; fax: +886-3-425-2897.

E-mail address:[email protected](C.-C. Chen).

Solid-State Electronics 47 (2003) 575–578

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2. Calculation procedures

The thermal treatments can induce an In and Ga interdiffusion across the interface of barrier and well. In general, the diffusion mechanism of the atoms is de-scribed by FickÕs law. After thermal treatment, the step-like potential profile of the quantum well is transformed into a gradient one. In this calculation, we assume that the electrical potential variation of the quantum well in the direction of the crystal growth (direction z) follows FickÕs law. The potential profile can be described as [10] VðzÞ ¼wdp 2 erf Lwþ 2z 2Ld þ erf Lw 2z 2Ld ð1Þ where z denotes the coordinate along the crystal growth direction. wdpis the potential difference between the well

and barrier for conduction or valence band which is de-ﬁned by the indium composition of the QW and VegardÕs law, i.e. wdp¼ ðEgbarrier Ewellg Þ ðband offset parameterÞ.

Ebarrier

g and E

well

g are the band-gap of the barrier and well,

respectively. Lw is the well width before the diﬀusion

process, Ldis the diﬀusion length which is 2

ffiffiffiffiffi Dt p

, D is the diffusion coefficient, and t is the time of diffusion.

The variation of the optical properties due to the In

and Ga interdiﬀusion were calculated for In0:1Ga0:9N

and In0:2Ga0:8N single quantum well (SQW) structures.

The strong built-in piezoelectric field is considered in this calculation. However, the value of the piezoelectric field in the InGaN/GaN QW depends not only on the indium composition but also on the heterojunction structure [14]. For simplifying the calculation, we as-sume that the piezoelectric field is proportional to the indium composition in the QW and that the piezoelectric field in the InN/GaN heterostructure is 0.55 V/nm in [0 0 0 1]-direction [14]. Therefore, the piezoelectric field in In0:1Ga0:9N and In0:2Ga0:8N QW is 0.055 and 0.11 V/

nm, respectively. The gradient potential profile in QW calculated by Eq. (1) is inclined due to the piezoelectric field. The potential profile with consideration of the in-terdiffusion and piezoelectric effects is used in the time-independent Schr€oodinger equation to obtain the distri-bution of electrons or holes in the region of the quantum well by the finite-difference method [15]. The optical gain spectra were obtained by the standard calculation pro-cedure [15]. The effective mass of electron and hole is 0.2m0and 1.56m0, respectively [16], m0being the electron

mass. The value of the band oﬀset parameter used in this study is 38:62 that we reported recently, as deduced from the optical pumping spectra of the high-indium com-position InGaN/GaN quantum well [17].

3. Results and discussion

Fig. 1 shows the potential proﬁle of the conduction

band for the 3 nm-wide In0:1Ga0:9N/GaN QW with the 0

and 0.6 nm diﬀusion length (Ld), respectively. For the

QW without interdiﬀusion eﬀect (Ld¼ 0 nm), the

step-like potential profile is inclined due to the strong pi-ezoelectric field. With the interdiffusion effect, the QW potential profile is transformed into a gradient one at increasing diffusion length.

Fig. 2 shows the optical gain as a function of the In diﬀusion length for the 3 nm-wide QW with 10% and 20% indium composition. The current density in the

calculation is 1600 and 800 A/cm2 _{for the In}

0:1Ga0:9N

Fig. 1. Conduction band diagram for 3 nm-wide In0:1Ga0:9N

QW under 5:5 102_{V/nm piezoelectric ﬁeld with L} d¼ 0 and

0.6 nm.

Fig. 2. Variation of the optical gain for (a) In0:1Ga0:9N and (b)

In0:2Ga0:9N QW with diﬀerent diﬀusion length under the

cur-rent density of 1600 and 800 A/cm2_{, respectively.}

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and In0:2Ga0:8N QW, respectively. The result shows that

for both QWs with 10% and 20% indium composition, the optical gain increases as the diffusion length in-creases from 0 to 0.4 nm. The maximum optical gain is obtained for a diffusion length of 0.4 nm. As the diffu-sion length is greater than 0.4 nm, the optical gain de-creases severely as the diffusion length inde-creases. The increase of the optical gain originates principally from the fact that as the diffusion length increases to 0.4 nm, the ‘‘effective’’ well width decreases leading to the in-crease of the overlap of the electron and hole distribu-tions (transition probability). At a diffusion length larger than 0.4 nm, the decrease of the optical gain originates from the flattening of the quantum well. This indicates that the quantized energy of the conduction band be-comes close to the energy difference between the barrier and the well leading to decrease of the confinement of the electrons in QW. This results in a decrease of the electron–hole transition probability. These results pro-vide a theoretical analysis to the increase of the PL in-tensity of the InGaN/GaN quantum structures due to the thermal annealing [13].

In Ref. [12], the thermal annealing was performed to the InGaN/GaN quantum well structures from 900 to

1050°C for 10 min. The diﬀusion coeﬃcients have been

reported to be 2 106 _{and 1}₁₀4 _nm2_{/s for the}

an-nealing at 900 and 1050°C, respectively [12]. By

follow-ing the Arrhenius expression, the diﬀusion coeﬃcient can

be described as D¼ 1:93 109_{expð40473=T Þ nm}2_{/s. T}

is the annealing temperature in Kelvin. In Ref. [14], the PL intensity increases as the annealing temperature

in-creases from 900 to 1000 °C. However, the annealed

sample at 1050°C shows a severe decrease of PL

inten-sity. The maximum PL intensity occurred after the

an-nealing treatment between 1000 and 1050°C for 10 min.

The corresponding diffusion lengths can be obtained by the Arrhenius expression to be 0.27 and 0.48 nm, re-spectively. There is an agreement between these experi-mental data and the calculated diffusion length in this work for the maximum optical gain at 0.4 nm. These results reveal quantitatively that there may be a maxi-mum optical gain of the QW with the diffusion length around 0.4 nm. Thermal treatments at high temperature for about 10 min are often performed during the fabri-cation of the laser. Therefore, the result of this study shows that the thermal treatments during the fabrication of the laser can significantly influence the performance of the devices. An additional thermal treatment after the growth of the epitaxial layers could help determine whether the optical gain can be improved.

4. Summary

In this work, we investigate the optical gain variation of InGaN/GaN QW for diﬀerent diﬀusion conditions.

The maximum optical gain can be obtained as the dif-fusion length of the indium is 0.4 nm. The result shows a good agreement with the experimental results in litera-ture. The results can help to increase the optical gain of InGaN/GaN QW laser and LED.

Acknowledgements

The work was supported by the grants from Opto-Electronics and Systems Laboratories, Industrial Tech-nology Research Institute, Taiwan and MOE Program for Promoting Academic Excellence of Universities un-der the grant number 91-E-FA06-1-4.

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