photonics and nanotechnology, 2008, p.116

This paper presents comparison of second harmonic generation schemes using a nonlinear optic crystal and two types of laser diode, which are a 440 nm single mode blue laser diode and a 4

Photonics

Nanotechnology

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PHOTONICS AND NANOTECHNOLOGY Proceedings of the International Workshop and Conference on ICPN 2007

v

PREFACE

Nonlinear optical physics has been to optical engineers and scientists a very interesting subject, especially, when

the nonlinear behaviors of light in optical devices generate benefits in some cases This book is entitled ‘Photonics

and Nanotechnology’, where the papers were selected by the International Conference on Photonics and

Nanotechnology (ICPN) committees during the conference in the year 2007, which was held in Pattaya, Thailand,

from December 16 –18, 2007 The conference was organized by the Department of Applied Physics, Faculty of

Science, King Mongkut’s Institute of Technology Ladkrabang (KMITL), Thailand Twelve papers out of sixty were

selected, and the extended versions were slightly different from the conference versions All papers concern optical devices and materials, especially, the nonlinear behaviors and their benefits The conference was partially supported

by the Department of Applied Physics, Faculty of Science, KMITL, Optical Society of America (OSA), The Institute of Optical Engineering Society (SPIE), IEEE-LEOS (Thailand), National Electronics and Computer Technology Center (NECTEC), Thailand and Ch Karnchang (Thailand) There were some keynote and invited talks involved from the United States of America, Europe and Japan Professor Yupapin from KMITL was the

general chair of the conference He had pushed a lot of effort and contributions to make the conference a success Finally, we expect that the proceedings volume will be useful to the optical researchers and society

Preecha P Yupapin

CONTENTS

Capacitance-Voltage Characteristics of InN Quantum Dots in AlGaN/GaN Heterostructure 1

A Asgari and M Afshari Bavili

A Comparison of Different Coherent Deep Ultraviolet Generations Using Second Harmonic Generation 7 with the Blue Laser Diode Excitation

C Tangtrongbenjasil and K Konaka

X He, D.N Wang, D Huang and Y Yu

Temperature-Dependent Photoluminescence Investigation of Narrow Well-Width InGaAs/InP Single 24 Quantum Well

W Pecharapa, W Techitdheera, P Thanomngam and J Nukeaw

Shooting Method Calculation of Temperature Dependence of Transition Energy for Quantum 31 Well Structure

B Jukgoljun, W Pecharapa and W Techitdheera

P Saeung and P.P Yupapin

Chaotic Signal Filtering Device Using the Series Waveguide Micro Ring Resonator 42

P.P Yupapin, W Suwancharoen, S Chaiyasoonthorn and S Thongmee

An Alternative Optical Switch Using Mach Zehnder Interferometer and Two Ring Resonators 48

P.P Yupapin, P Saeung and P Chunpang

Entangled Photons Generation and Regeneration Using a Nonlinear Fiber Ring Resonator 52

S Suchat, W Khunnam and P.P Yupapin

Nonlinear Effects in Fiber Grating to Nano-Scale Measurement Resolution 60

P Phipithirankarn, P Yabosdee and P.P Yupapin

C Sripakdee, W Suwancharoen and P.P Yupapin

M.M.A Fadhali

A Soliton Pulse in a Nonlinear Micro Ring Resonator System: Unexpected Results and Applications 81

P.P Yupapin, S Pipatsart and N Pornsuwancharoen

CAPACITANCE-VOLTAGE CHARACTERISTICS OF InN QUANTUM DOTS IN

AlGaN/GaN HETEROSTRUCTURE

Tabriz 51665-163, Iran

Crawley, WA 6009, Australia E-mail: asgari@tabrizu.ac.ir

In this paper the capacitance-voltage characteristics of InN quantum dots embedded in AlGaN/GaN heterostructure has been studied This work has been done for the InN quantum dots with different quantum dot size, and energy dispersion and for the AlGaN/GaN heterostructures with different Al mole fraction and number of quantum wells in different temperatures The presence of InN quantum dot will cause Gaussian shape in capacitance-voltage charac- teristics approximately, where the peak of curves can evidence the position of quantum dots in the structures Our calculation results show the Gaussian shape (or negative differential capacitance) is much higher at low temperature and for quantum dots with low energy and higher size dispersion.

Keywords: AlGaN/GaN Heterostructures; InN Quantum Dots; capacitance.

1 Introduction

The progress of epitaxial growth technology has been responsible for many new structures based on dimensional system where quantum effects were clearly observed Self assembled systems like the quantumdots (QDs) are very important examples of this advance Recently, considerable interest has been focused onelectronic devices based on semiconductor heterostructures containing quantum dots, in which the motion ofquasi-particles is quantized along all three coordinates In order to develop the application of these devices,

low-it is necessary to investigate the influence of quantum dot on electronic properties of these semiconductorstructures.1

Capacitance spectroscopy is a highly efficient method for studying of electrical properties of thesestructures Recently, several research groups reported some results about AlGaAs/GaAs heterostructurescontaining a layer of self-organized InAs QDs.2

But Nitride based nanostructures have significantly differentproperties as compared to GaAs based quantum wells and QDs GaAs has zinc blend crystal structure, butIII-V nitrides are available in both zinc blend and wurtzite crystal structure which leads to strong built inpiezoelectric fields in heterostructures This can induce red shift in GaN/AlN self-organized QDs.3

In thispaper we present the results of capacitance-voltage studies of the AlGaN/GaN heterostructures containing

a layer of InN QDs

2 Model Description

Consider the modeled sample structure as Fig 1 The capacitance of the structure is the sum of the bulkcapacitance and QDs capacitance In order to determine the capacitance, one has to know the conductionband profile and all quantized state to calculate the electron density function and Fermi energy level usingself consistent solution of Schrdinger and Poisson equations It has been done in this article using numericalNumerov’s method.4–6

To calculate the charge density in the structure, it has been assumed that the planecontaining the QDs acts like an equipotential surface and also only the ground state of quantum dots hasbeen occupied Also, we consider the plane containing QDs and the highly doped buffer layer are near theelectrostatic equilibrium.7

The capacitance in devices as Schottky device is directly related with the chargeinside the depletion region and can be expressed by C = ∂Q∂V where

And S is the Schottky contact area, ND is the bulk doping density, W is the width of depletion region andequal to in the Fig 1 Solving Poisson equation for the different applied voltage the capacitance can beobtained as:7

Cbulk = S

dSL+ S

Z ∞

0D(E, V )f (E, V )dE



(3)where

EQD is the electron level within the QDs To calculate the QD energy levels, it has beenassumed the QDs have spherical shape and the Fermi level in the dots was the same as in highly dopedsubstrate.8

To find the CQD, the integral in Eq (2.3) has been solved numerically

3 Results and Discussion

The device structure as shown in Fig 1 contains an AlGaN/GaN superlattice of N quantum wells with 1.5 nmthickness of GaN and 3 nm of AlxGa1−xN barrier width, a layer containing InN QDs, a 10 nm GaN layerbetween QDs layer and superlattice, and a 20 nm Si-doped GaN layer with doping density of 8 × 104

cm−3.The QDs layer includes a carrier density of 6.5 × 1010

cm−2 The Schottky contact area and barrier high is

2 × 10−7

cm2and φB= 1.3x + 0.84 (eV), respectively, where x is the Al mole fraction in the barrier.The capacitance-voltage characteristics of these structures have been analyzed in different physical sit-uations For the applied voltage range from −1 to +1 V, the dominant behavior of capacitance comes from

temperature The number of quantum well in super lattice is n = 30 and Al mole fraction is x = 0.3.

and Al mole fraction is x = 0.3.

the QD capacitance As one can see from Figs 2, 3, and 4, the total capacitance increases with increasing

of applied voltage from −1 V, due to the filling of the quantum dots, showing a peak at voltage range from

V = −0.25 to 0.25 The peak broadening is due to the fluctuations in the dot sizes If the voltage increases,the total capacitances decreases and for further increases trend to bulk capacitance because the dots arecompletely discharge Figure 2 shows the variation of the capacitance as function of applied voltage at dif-ferent temperature As evident from the figure, the QD capacitance for low temperature is higher than the

and for different quantum dot energy The number of quantum well in super lattice is n = 30 and Al mole fraction is x = 0.3.

high temperatures capacitance Also with the increasing of the temperature, the peak positions shift towardthe low voltages This is caused by the dynamical process involving the capture/emission rate of the dots.The energy dispersion characteristics, ∆E, is 110 meV and EQD is the 80 meV in these calculations.Figure 3 shows the variation of the capacitance as function of applied voltage at different energy dis-persion characteristics, in T = 100 K and for dots with EQD is the 80 meV As evident from the figure,

the QD capacitance for low energy dispersion characteristic is very small and total capacitance behave asbulk capacitance With increasing the energy dispersion characteristic, the QD show a higher negative dif-ferential capacitance In this case there is only a small change in the peak positions which shift toward thehigh voltages Also, as shown in Fig 4, the total capacitance as function of applied voltage at different QDenergy level, in T = 100 K and for the quantum dots with energy dispersion characteristic of 110 meV

is expressed As evident from the figure, the QD capacitance for dots with high energy level is very smalland total capacitance behaves as same as bulk capacitance With decreasing the QD energy level, the QDcapacitance shows a higher negative differential capacitance In this case there is not any change in the peakpositions along the voltage axes To calculate the C-V characteristic in Figs 3, 4, and 5, 30 quantum wellshas been taken into account in super lattice and Al mole fraction in the barriers is x = 0.3 The effects ofAlGaN/GaN heterostructures on C-V characteristics have been analyzed too The variation of Capacitance

as function of applied voltage for the structures with Al mole fraction of 0.1 to 1 in the super lattice barriersare shown in Fig 5 As evident from the figure and Eq (2.2), the capacitance decreases with increasing theSchottky barrier potential which varies linearly with Al mole fraction So, for the structures with higher Almole fraction, the quantum dots show more negative differential capacitance Also the calculation has beendone for the structures with different number of quantum well in the superlattice Figure 6 shows the results

of this calculation for the number of quantum well of n = 5, 10, 20, 30, 40, and 50 It is clearly known thatwith increasing the distance between the capacitor plates, the electrical capacitance decreases So to see thequantum dot capacitance effect, it’s better to have the structures with low bulk capacitance

4 Conclusions

In summary, this paper presented a study of the capacitance-voltage characteristics in the InN quantumdots system embedded in a GaN matrix in AlGaN/GaN heterostructure The proposed is based on theanalysis of the solution of the Poisson and Schrdinger equations and in the well defined relationship betweencapacitance and density of sates The calculation results shoe that the presence of InN quantum dot will cause

a negative differential capacitance which can evidence the position of quantum dots in the structures Also,our calculation results show that the negative differential capacitance is much higher at low temperature andfor quantum dots with low energy and higher size dispersion

References

1 A A J Chiquito, et al., Phys Rev B 61, 5499 (2000)

2 P N Brounkov, et al., Semiconductors 32, 1096 (1998)

3 A Bagga, et al., Phys Rev B 68, 155331 (2003)

4 A Asgari, Study of transport properties of AlGaN/GaN Heterostructure, Physics Faculty, University of Tabriz,Ph.D Thesis , 84 (2003)

5 A Asgari, et al., J Appl Phys 95, 1185 (2004)

6 A Asgari, et al., Materials Science and Engineering C 26, 898 (2006)

7 Ph Lelong, et al., Physica E 2, 678 (2006)

8 C E Pryor, et al., Phys Rev B 72, 205311 (2005)

7

A COMPARISON OF DIFFERENT COHERENT DEEP ULTRAVIOLET GENERATIONS USING SECOND HARMONIC GENERATION WITH BLUE LASER DIODE EXCITATION

C TANGTRONGBENCHASILAND K NONAKA

Department of Electronic and Photonic Systems Engineering, Frontier Engineering Course, Kochi University of Technology, Tosayamada, Kami City, Kochi Prefecture 782-8502, Japan

Nano-focus beam applications of short wavelength approximately 220 nm now play important roles

in engineering and industrial sections At present, light sources at approximately 220 nm are

commercially available but large size, difficult to maintain, and expensive Compact wavelength

tunable and cost effective light sources at approximately 220 nm are required Laser diode with

sum-frequency generation methods are employed to generated the shorter wavelength

approximately 220 nm This paper presents comparison of second harmonic generation schemes

using a nonlinear optic crystal and two types of laser diode, which are a 440 nm single mode blue

laser diode and a 450 nm multimode Fabry-Perot blue laser diode, has potential to generate wide

tunable coherent deep ultraviolet-c at approximately 220 nm Using the blue laser diode with the

sum-frequency technique, a high second harmonic power is hardly observed due to low conversion

efficiency The best performance of second harmonic generation using blue laser diode, nonlinear

optic crystal, and an high-Q external cavity laser diode was observed as 1.1 µW second harmonic

ultraviolet-c power at 224.45 nm ultraviolet-c wavelength and 5.75 nm ultraviolet wavelength

tunability In addition, the improvement of increasing second harmonic power approximately

220 nm and the limitation of wavelength tuning of short wavelength are also theoretically discussed

in this paper

1 Introduction

Coherent short wavelength ultraviolet C (UV-C) approximately 220 nm is very useful for nano-focus beam applications such as beam lithography for very large scale integrated circuit (VLSI) and molecular spectroscopy Excimer lasers and sum-frequency from solid state lasers, which are able to generate very high power1 but these lasers have very large bodies, complex structures, fixed wavelength, high manufacturing costs, and high maintenance costs, are conventional coherent UV sources at the short wavelength approximately 220 nm Due to these disadvantages of excimer UV lasers and solid state UV lasers, compact, simple to fabricate, cost effective, and coherent wavelength tunable flexibility of UV sources are in demanded One of the possible solutions is second harmonic generation (SHG) with nonlinear optic crystal and laser diode (LD) Due to advance technology in opto-electronics, small size LD can generate high optical power as 300 mW for continuous wave at 20ºC2,3 The SHG researches have been reported for 4 decades4-6 Most of SHG researches were implemented with gas laser at wavelength longer than 780 nm resulting fixed wavelength4-6 Only a few researchers reported the SHG for short wavelength approximately 220 nm, due to very low conversion efficiency, a complex setup, insufficient LD power, oscillation quality, and crystal efficiency7-10 External cavity diode laser (ECDL) with nonlinear optic crystal, that is one of the solutions for SHG researches, has been reported7-10

This paper present a performance comparison of SHG using a 440 nm single mode blue LD with a BBO nonlinear optic crystal and a 450 nm multimode Fabry-Perot blue LD with a BBO nonlinear optic crystal The mathematical estimation of SH power and the improvement of SHG conversion efficiency are also discussed

2 Theoretical Background

Dmitriev, et al and Mills published simple SHG mathematical estimations when uniform beam is employed4-5 However, Dmitriev, et al and Mills’ equations are not able to estimate properly the SH power Boyd and Kleinman

8

published a SHG mathematical model including phase mismatch factor, focal position factor, strength of focusing factor, birefringence factor, and absorption factor, that is suitable to estimate the SH power when focusing Gaussian beam is employed6 In this paper, a 440 nm fundamental single mode wavelength blue LD with a BBO nonlinear optic crystal and a 445 nm and fundamental wavelength multimode Fabry-Perot blue LD with a BBO nonlinear optic crystal were implemented to generate tunable coherent deep UV-C The shortest usable wavelength of the BBO crystal is 205 nm, due to phase matching angle limitation of fundamental and SH waves11 Using Sellmeier’s equations4,5, operating refractive index, phase matching angle, walk-off angle, and effective conversion coefficient can be theoretically obtained The SH output power (P2ω) can estimated by6,

= , ρis walk off angle [radian], κ is absorption factor, and σ is phase mismatch When σ = 0, focal position is at the center of the BBO crystal orµ = 0, and no absorption or κ = 0, the optimized SH output power (P2ω) can be calculated as6,

2 2

2 2 [ ( ) ]2

β = 0if and only if ρ = 0 that is invalid at either short fundamental wavelength as 440 nm or 445 nm ρ are equal

to 0.067 radian and 0.073 radian, at 440 nm fundamental wavelength and 445 nm fundamental wavelength, respectively Consequently, β are equal to 13.06 radian and 14.05 radian when 100 mm focal length of focusing lens was employed for 440 nm fundamental wavelength and 445 nm fundamental wavelength, respectively Moreover, effective focal length, which is a very important factor to optimized the SH conversion efficiency, is required to estimate but it is not included in Eq (1) and Eq (2) The effective focal length can be estimated by6,

22

oF eff

c

n f b

L

w

ππ

where f is operating focal length of focusing lenses and w c is beam radius of the collimated input beam The effective focal length is directly proportional to the confocal parameter Equation 3 implies that there is an optimum effective focal length of any arbitrary confocal parameter depending on the focal length of focusing lens By the symmetry of focusing and defocusing with the identical focal lengths of focusing lenses, consequently the optimized

crystal length is equal to 2L eff In addition, the confocal parameter is directly proportional to the operating focal length, so longer focal length requires longer crystal length or longer SH interaction length to optimize the conversion efficiency Figure 1 shows simulations of SH output power vs fundamental input power with various focal lengths and optimum nonlinear optic crystal lengths when confocal parameter = 0.084 Even confocal parameter is fixed; the conversion efficiency can be improved by implementing long focal length and long nonlinear optic crystal length Moreover, it implies that long focal length requires long interaction length or long crystal length

to optimize SH output power Figure 2 shows simulations of SH output power vs fundamental input power with various confocal parameters when focal length of focusing lenses is 100 mm and nonlinear optic crystal length is

10 mm Even focal length of focusing lens and interaction length are fixed; the conversion efficiency can be improved by constructing the higher confocal parameter system However, if the higher value of confocal parameter

is required, the optic size including lens diameter, nonlinear optic crystal length, nonlinear optic crystal sectional area, and optical operating distance must be enlarged

cross-9

Fig 1 Simulations of SH output power vs fundamental input power with various focal length of focusing lenses

and optimum nonlinear optic crystal lengths when confocal parameter = 0.084

Fig 2 Simulations of SH output power vs fundamental input power with various confocal parameters when

focal length of focusing lenses is 100 mm and nonlinear optic crystal length is 10 mm

On the other hand, narrow wavelength tolerance or single longitudinal mode oscillation is one of requirements to realize theoretical SHG efficiency that must be enhanced The wavelength tolerance must be control as narrow as possible by oscillation wavelength selection system e.g grating and feedback mirror, etc12-16 If the fundamental

10

wavelength is single longitudinal mode oscillation, consequently the SH wave is also single longitudinal mode oscillation The SH wavelength tunablility depends on the angle and position of feedback fundamental light passing through grating back to LD The feedback angle of fundamental light must be set as close as possible to the polarization plane of LD, so that narrow single mode fundamental wavelength can be realized To tune fundamental wavelength, the position shift with respect to the orthogonal of polarization plane must be tuned In contrast, narrowing wavelength tolerance can cause phase mismatch To overcome this problem, the nonlinear optic crystal angle must be properly adjusted to matching angle

3 Coherent Deep UV-C Generation Setups and Experimental Results

In this section, 3 experimental setups of coherent deep UV-C generations approximately 220 nm basing on SHG scheme are discussed A single mode blue LD approximately 440 nm and a multimode Fabry-Perot blue LD approximately 450 nm are employed as fundamental wavelength light sources The single mode blue LD 440 nm can provide maximum continuous fundamental wave only 60 mW To enhance higher continuous fundamental power, the multimode Fabry-Perot blue LD 450 nm, which is able to provide up to 300 mW when LD temperature is proper controlled at 25ºC3, was implemented instead of the 440 nm single mode blue LD The detail performance and comparison will be discussed in later section

3.1 SHG with Feedback Grating as a Wavelength Selector Configuration

The simple and compact coherent deep UV-C generation approximately 220 nm is shown in Fig 3 The single mode blue LD approximately 440 nm was employed as fundamental light source that can provide maximum continuous fundamental wave at 60 mW The single mode blue LD was installed in a mount that can control the LD temperature constantly and also provide a quasi-collimating beam LD waveguide rear-end has approximately 90% high reflection (HR) coating but LD waveguide front-end has coating reducing a few percentage of reflectivity decreases the catastrophic optical damage (COD) damaging The LD was controlled at 20ºC The quasi-collimating beam has beam profile of the effective parallel and perpendicular beam axes are 3.5 mm and 1.5 mm, respectively The quasi-collimating beam was focused at the center of 10 mm length BBO crystal by a 100 mm bi-convex lens Consequently, the effective parallel and perpendicular beam waist at the focusing region are 74.68 µm and 32.01 µm, respectively The maximum average power of the fundamental wavelength inside the cavity was 64.83 mW Thus, a 3.45 kW/cm2 excitation is expected at around focus region The output radiation from BBO optic crystal consisting of approximately 440 nm fundamental wavelength and approximately 220 nm SH wavelength were, consequently, collimated and reflected by a 100 mm concave mirror to obtain the similar quasi-collimating beam profile as launching from LD mount Then, the approximately 440 nm fundamental wavelength and the approximately 220 nm SH wavelength were completely separated by prism at Brewster angle for the 440 nm fundamental wave To stabilize and narrow wavelength tolerance, the 440 nm fundamental wave was launched to reflection grating that has 40% transmission and 60% reflection The 40% transmission from the reflection grating was employed to monitor the fundamental wavelength tolerance To enhance the external high-Q ECLD and to narrow the fundamental wave, the 60% reflection from the reflection grating must be fed to the same path back to the LD mount In addition, if the fundamental wave is narrow and single mode, the SH wave would also narrow and single mode Consequently, the conversion efficiency of narrow and single mode wave is better than wide and multimode wave To tune the wavelength, slight adjusting the angle of the reflection grating with respect to LD polarization plane can stabilize and tune fundamental wavelength and SH wavelength Generated UV light was measured by the photomultiplier tube with transimpedance amplifier as shown in Fig 3

Figure 4 shows experimental results of SHG with feedback grating as the wavelength selector and examples of operating fundamental wavelength stabilities 220-nm range deep UV-C is too close to the limiting edge of crystal matching condition and BBO crystal absorption band Consequently, the conversion efficiency is lower than near

UV wavelength The maximum generated SH power was obtained as 0.165 µW at 218.45 nm SH wavelength when

11

Fig 3 SHG experimental setup with internal wavelength separator

Fig 4 Experimental results of SHG with internal wavelength separator and examples of operating fundamental

wavelength stabilities

64.83 mW fundamental power was enhanced The SH tunability is 1.45 nm in range of 218.45 nm – 219.9 nm The 3-dB spectrum widths (∆λ) of 436.9 nm fundamental wave and 439.8 nm fundamental wave are 0.035 nm and 0.039 nm, respectively In addition, the extinction ratio of 436.9 nm fundamental wave and 439.8 nm fundamental wave are 24.10 dB and 29.56 dB, respectively The wavelength separator was located inside the SHG cavity, it caused the difficulty of minimizing phase mismatch When operating fundamental wavelength was changed, the crystal angle must be re-tuned In addition, the position of optical spectrum analyzer (OSA) must be re-tuned to monitor the stability of operating fundamental wavelength Moreover, 1.45-nm narrow SH wavelength tunability wave was observed

12

3.2 SHG with Transmission Grating as a Wavelength Selector Configuration

Due to the difficulty of re-tuning of SHG cavity and OSA position in section 3.1, the wavelength separator (prism) should be located outside the SHG cavity Because of the polarizations of fundamental wavelength and SH wavelength differ by 90º, so a 220 nm dichroic mirror was employed to separate approximately 220 nm wave and approximately 440 nm wave In addition the feedback light in section 3.1 is only 60%, so a transmission grating and

a 440 nm high reflection (HR) flat mirror were implemented as wavelength selector In addition the transmission grating and the 440 nm HR flat mirror were also employed as an external high-Q ECDL enhancement The transmission grating has splitting ratio of 0th order and 1st order by 5% and 95% of incident wave, respectively The

0th order from the transmission grating was employed to monitor the stability of the operating fundamental wave The OSA can be fixedly place to monitor the stability of the operating fundamental wave because the position of 0thorder does not depend on the transmission grating angle Adjust the angle of feedback mirror is able to tune and stabilize the operating wavelength in this setup In addition, employing the transmission grating with the 440 nm HR feedback mirror is able to improve the Q factor of ECLD Figure 5 shows SHG experimental setup with transmission grating as the wavelength selector configuration In practice, the 220 nm dichroic mirror is not able to reflect only 220 nm wave but a few percentages of 440 nm wave is also reflected To separate 220 nm wave out of

440 nm wave completely, the prism must be employed With the similar of beam profile as in section 3.1 and the maximum average power of the fundamental wavelength inside the cavity was 64.36 mW Thus, a 3.43 kW/cm2excitation is expected at around focus region

Fig 5 SHG experimental setup with external wavelength separator

Figure 6 shows experimental results of SHG with external wavelength separator and examples of operating fundamental wavelength stabilities The maximum generated SH power was obtained as 0.194 µW at 218.25 nm

SH wavelength when 64.36 mW fundamental power was enhanced The SH tunability is 1.85 nm in range of 218.25 nm – 220.1 nm The 3-dB ∆λ of 436.6 nm fundamental wave, 438.2 nm fundamental wave, and 440.2 nm fundamental wave are 0.040 nm, 0.039 nm, and 0.042 nm, respectively In addition, the extinction ratio of 436.6 nm fundamental wave, 438.2 nm fundamental wave, and 440.2 nm fundamental wave are 25.73 dB, 23.55 dB, and 29.47 dB, respectively This configuration can be improved by enhancing higher fundamental power Because of high-Q ECDL feed operating fundamental wave back to LD mount with similar beam profile, so SH power can also

be detected in front of LD mount

13

Fig 6 Experimental results of SHG with external wavelength separator and examples of operating fundamental

wavelength stabilities

3.3 Symmetry SH Detection Configuration with Multimode Blue LD

The enhancement of higher fundamental wave power is one of the important factors to generate high SH power, so a

450 nm multimode Fabry-Perot blue LD was employed The 450 nm multimode Fabry-Perot blue LD is able to generate continuous power up to 300 mW when LD temperature is controlled at 25ºC3 However, the number of oscillation mode increases when the injection current increases Multimode oscillation reduces the SHG efficiency due to narrow crystal matching tolerance Moreover, the SHG from section 3.2 can be improved by bi-directional detection; in front of LD mount and before the transmission grating (see Fig 7) However, to simplify the experimental setup of bi-directional detection, symmetry configuration is extremely required Figure 7 shows symmetry SH detection configuration multimode blue LD In this section, two 100 mm plano-convex lenses were employed to focus quasi-collimating fundamental wave from LD mount and defocus to re-collimate and to obtain similar quasi-collimating fundamental wave beam profile as launching from LD mount The polarizations of fundamental wavelength and SH wavelength differ by 90º as mentioned in section 3.2 Two dichroic mirrors were placed before (forward detection) and after (backward detection) plano-convex lenses (see Fig 7) to separate the

225 nm SH wave out of SHG cavity and to maintain the 450 nm fundamental wave in the SHG cavity In practice, the reflected 225 nm wave from the dichroic mirror always contains a few percentage of the 450 nm wave, even the dichroic mirrors are exactly placed at the Brewster angle So the reflected wavelength can be completely separated

by prisms that were set to Brewster angle for the 225 nm SH wavelength transparency to obtain pure 225 nm coherent deep UV-C With the similar of beam profile as in section 3.1 and 3.2, the maximum average power of the fundamental wave inside the cavity of multimode Fabry-Perot blue LD can be obtained 103.30 mW, due to imperfect of temperature controller Thus, a 5.50 kW/cm2 excitation is expected at around focus region

Figure 8 shows experimental results of SHG at 448.9 nm fundamental wavelength and the variation of fundamental power vs fundamental wavelength The maximum generated SH power was obtained as 1.1 µW at 224.45 nm SH wavelength when 103.30 mW fundamental power was enhanced The 1.1 µ W was the total detections of 0.67 µW forward detection and 0.34 µW backward detection Using bi-directional detection technique,

an approximately 50% of SH power was obtained at backward detection, due to surface loss and scattering from

14

Fig 7 Symmetry configuration of SHG with external wavelength separator

Fig 8 Experimental results of SHG at 448.9 nm and the variation of fundamental power vs fundamental

wavelength

fundamental wave, and 455.4 nm fundamental wave were small as 0.040 nm and 0.050 nm, respectively In addition, the average extinction ratio was approximately 25 dB From this setup, the transmission grating was set and fixed at 60º that maximized the splitting ratio of 0th order and 1st order of transmission Only adjusting the angle

of the 440 nm HR flat mirror can tune the operating fundamental wavelength The difference position and angle of feedback fundamental light can cause wavelength tunability and oscillation mode suppression of fundamental light

of multimode Fabry-Perot blue LD Consequently, fundamental power of nearby wavelength is decreased, due to mode suppression In addition, the limitation of wavelength tuning range is gain profile LD waveguide At the shortest wave and longest wave, the operating fundamental power was decreased by 2.1 dB comparing with 448.9 nm fundamental wave that has the maximum fundamental power at 103.30 mW Consequently, the SH power

at the shortest wave and longest wave in this setup were decreased as 0.6 dB comparing with 224.45 nm SH wave

15

that has the maximum generated UV power at 1.1 µW The total SH powers of shortest wave and longest wave in

this system were obtained as 0.101 µW and 0.104 µW, respectively

4 Discussion

The 3 different coherent deep UV-C generation experimental setups and experimental results were explained

Table 1 shows performance comparison of 3 experimental SHG setup The SHG with feedback grating as a

wavelength selector configuration can generate the maximum UV power only 0.165 µ W at 218.45 nm SH

wavelength when 64.83 mW fundamental power was enhanced by the 440 nm single mode blue LD The SH

tunability was only 1.45 nm in range of 218.45 nm – 219.9 nm Because of the SH wavelength tunability was too

narrow as 1.45 nm, the wavelength separator (prism) should be located outside SH cavity by inserting the 220 nm

dichroic mirror to reflect approximately 220 nm wave outside the SH cavity and maintain the fundamental wave

inside the SH cavity In addition, to improve the fundamental feedback power, the transmission grating, which has

the extinction ratio of 5% and 95% of 0th order and 1st order, and the 440 nm HR flat mirror were employed

to reduce feedback loss and to enhance high-Q ECLD From this improvement, the maximum UV power can

be generated as 0.194 µW at 218.25 nm SH wavelength when 64.36 mW fundamental power was enhanced by the

440 nm single mode blue LD The SH tunability was improved by 0.5 nm to be 1.85 nm in range of 218.25 nm –

220.1 nm The UV generation basing on SHG scheme can generate UV in both of forward direction that was

enhanced directly from LD and backward direction that was enhanced indirectly from LD but from feedback

fundamental light from the 440 nm HR flat mirror To assure the experimental high-Q cavity symmetry for

bi-directional UV detection, two of the 220 nm dichroic mirrors were employed to separate the SH wave outside the

SHG cavity and maintain fundamental wave inside the SHG cavity The maximum generated UV power was

SHG with transmission grating as the wavelength selector

Symmetry SH detection with multimode

blue LD Type of LD 440 nm Single mode blue LD 450 nm multimode Fabry-Perot blue LD

1 Too low enhanced fundamental power low

2 Low confocal parameter

1 Difficulty of LD temperature control

2 Low confocal parameter

SH wavelength

tunability

1.45 nm in range of 218.45 nm – 219.9 nm

1.85 nm in range of 218.25 nm – 220.1 nm

5.75 nm in range of 221.95 nm – 227.7 nm Type of wavelength

selection and feedback Only reflection grating Transmission grating and flat mirror

wavelength tuning

technique

Low fundamental feedback light causes difficulty in wavelength tuning

Waveguide characteristic of single mode blue LD limits wavelength tuning

Waveguide characteristic of multimode Fabry-Perot blue LD limits wavelength

tuning

16

obtained as 1.1 µW at 224.45 nm SH wavelength when 103.30 mW fundamental power was enhanced by the

450 nm multimode Fabry-Perot blue LD The 1.1 µW was the total detections of 0.67 µW forward detection and 0.34 µW backward detection Using bi-directional detection technique, an approximately 50% of SH power was obtained at backward detection, due to surface loss and scattering from lenses, BBO crystal, transmission grating, and flat mirror Using the multimode LD, the SH tunability was extremely improved by 3.9 nm to be 5.75 nm in range of 221.95 nm – 227.7 nm

On the other hand, there are 2 possibilities to improve the SHG conversion efficiency; 1) increase the enhanced fundamental power or 2) increase the confocal parameter Increasing the enhanced fundamental power is easy method but it consumes a lot of energy whereas increasing the confocal parameter requires beam expander and beam reducer that causes enlarge optical size To improve the wavelength tunability, the high feedback fundamental power is required to reduce wavelength tolerance and suppress nearby wavelength By this technique, the high performance grating and high refection fundamental power are required

5 Conclusions

In summary, using the single mode blue LD with flexible wavelength tunable and high-Q ECLD can observed similar level of fundamental power at every tuned wavelength resulting similar level of SH generated UV power can also be obtained In contrast, using the multimode Fabry-Perot blue LD with wide wavelength tunability and single mode oscillation high-Q ECLD cannot provide the similar level of fundamental power at every tuned wavelength The maximum fundamental power was observed as 103.30 mW at 448.9 nm whereas the maximum fundamental power of the shortest and the longest wavelength were observed as 55 mW which was approximately 2.1 dB decreasing resulting different levels of SH generated UV power were observed which was approximately 0.6 dB difference The experimental results of our experimental setups were well matched to the Boyd and Kleinmann model estimation To improve the SH conversion efficiency, higher enhanced fundamental power is required but it consumes a lot of energy Moreover, the increasing of confocal parameter and the crystal length are another possible solution However, there is a trade-off between optic size and conversion efficiency If the high conversion efficiency is required, the optical system size must be increased In contrast, if the compactness is required, the conversion efficiency is low On the other hand, the main parameters; phase matching angle, walk-off angle, and effective coefficient must be carefully controlled due to very slightly change of these parameters cause suddenly change of SH efficiency Up to present, the best performance of wavelength tuning is implementation of the multimode Fabry-Perot blue LD with transmission grating and feedback mirror that is able to tune as wide as 5.75 nm The limitation of wavelength tuning of this setup is from the waveguide characteristic and gain profile of the multimode Fabry-Perot blue LD

This paper showed the sufficient of wavelength tunability and compactness comparing with the conventional excimer and YAG laser Moreover, this system has potential to focus and achieve the higher power density than bulk laser at the selected area

Acknowledgment

This research was supported by JST research foundation and NICHIA Corporation foundation

References

1 W L Zhou, Y Mori, T Sasaki, and S Nakai, Optics Communications 123, pp 583-586, 1996

2 NICHIA Corp., “Blue Violet Laser Diode, NDHU110APAE2”

3 NICHIA Corp., “Fabry-Perot Multimode Blue Laser Diode, NDHB220APAT1”

4 V G Dmitriev, G G Gurzadyan, and D.N Nikogosyan, Handbook of Nonlinear Optical Crystals, Springer

Series in Optical Sciences Volume 64

5 D.L Mills, Nonlinear Optics: Basic Concepts, 2nd edition, ed (Springer, New York, 1998)

11 CASIX Co., Ltd., “Product Catalog 2004”

12 T Laurila, T Joutsenoja, R Hernberg, and M Kuittinen, “Tunable external-cavity diode laser at 650 nm based

on a transmission diffraction grating,” Applied Op., Vol 41, No 27, pp 5632–5637, 2002

13 H Patrick and C.E Wieman, “Frequency stabilization of a diode laser using simultaneous optical feedback from a diffraction grating and narrowband Fabry-Perot cavity,” Rev Sci Instrum., Vol 62, No 11, pp 2593–

18

APPLICATION OF REFLECTION SPECTRUM ENVELOP

FOR SAMPLED GRATINGS

XIAOYING HE1,2, D.N.WANG2*, DEXIU HUANG1 AND YONGLIN YU1

1

Wuhan National Laboratory for Optoelectrons, Huazhong University of Science and Technology, Wuhan,

Hubei,430074, P.R.China

2

Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon,

Hong Kong, P.R.China

* Corresponding author email: eednwang@polyu.edu.hk

Analytical expression is proposed for evaluating the performances of sampled gratings Accuracy of this expression has been verified by simulated reflectivity spectrum with the transfer matrix method A new technique of multiplex reflection-spectrum envelope concatenation is introduced to demonstrate a 23-channel grating with uniform characteristics in all channels The proposed technology can densify sampled grating both in spectral channels number and in spatially physical corrugation

1 Introduction

Sampled gratings (SGs) are naturally attractive for wide applications in optical communications and optical sensor systems such as tunable semiconductor reflectors [1, 2], multi-channel dispersion compensators [3, 4], multi-channel multiplexers-demultiplexers [5], repetition rate multiplication [6], etc Particular interests that have been shown in the performances of sampled gratings include the envelope-top flatness and 3dB envelope bandwidth of the reflection spectrum Especially, the multi-channel gratings with broad flat-top spectrum envelopes, as tunable semiconductor reflectors, will significantly improve the performances of laser over a wide tuning range A number of techniques proposed for this purpose, including Sinc-apodization [7], multiple-phase shift technique [8], and interleaved technique [9] Moreover, the transfer matrix method cannot convey the relation of grating parameters and the top-flatness and width of reflection-spectrum envelope (RSE) Simulation employing transfer matrix method is a time-consuming task especially for long gratings Therefore, it is necessary to propose an analytical expression of RSEs for conventional sampled gratings to study the impacts of grating parameters on RSEs

In this paper, an accurate analytical expression of the RSE for sampled grating is proposed and demonstrated Based on this analytical expression, the new multiple reflection-spectrum envelope concatenation (MRSEC) technology is employed to design multi-channel gratings with broad flat-top reflection spectra

2 Analytical Expression of Reflection-spectrum Envelope

grating The rectangular function f (z) is the sampling function of the SG without apodization, and the rectangular function g(z) is the whole grating profile function without apodization The coupling coefficient κ(n) corresponding

to the nth Fourier component in the SG is:

where, Z0/π can be regarded as the diffracted numerical aperture of sampled grating, and the 2n 0,eff π/λ is the wave

number Thus, due to the Fourier theory, the analytic expression for the RSEs is defined by:

,

,

eff g

Fig 1 Reflection spectrum and reflection-spectrum envelope of conventional sample grating

The Sinc function in Eq (6) is related with the Fourier transform component function of the rectangular function

( )

f z From Eq (6), it is clear that the shape of the RSEs is determined by the Sinc function related with

the grating pitch length Zg, the average effective refractive index n0,eff and the grating period Λ Clearly, only using

Eq (6), the basic performances of the RSEs can be analyzed accurately, and the optimal design of parameters for the SGs can be obtained as well This will be helpful to design multi-channel gratings with broad flat-top reflection spectra

20

2.2 Reflection-spectrum Envelope of Conventional Sampled Grating

Fig 2 Conventional sampled grating in real space and spatial frequency β space

Fig 3(a) Reflection-spectrum envelope of conventional sampled grating with different sampling period and

the duty cycle Zg/Z0 = 1/15

Fig 3(b) Reflection spectrum of conventional sampled grating with different sampling period and

the duty cycle Zg/Z0 = 1/15

The RSE of the conventional sampled grating calculated by the analytical expression Eq (6) is plotted with the dashed line in Fig 1 The transfer matrix method is also used to verify the proposed method, simulated the reflection

spectrum with the solid line Parameters are used here as follows: n 0,eff = 1.485, Λ = 521.7 nm, δn eff = 5 × 10-4, and

N = 20 (the number of the sampling period) Simulation with the transfer matrix method is a time-consuming task especially for long gratings Obviously the proposed method provides a simple and fast way to evaluate overall performances of SGs, such as the flatness and 3dB bandwidth of reflection-spectrum envelop As shown in Fig 1, the calculated RSE are well consistent with the reflection-peak values in reflection spectrum obtained by the transfer matrix method

21

Fig 4 Principle of the multiple reflection-spectrum envelope concatenation technology, (a) reflection-spectrum envelopes of conventional sampled gratings, (c) resultant reflection-spectrum envelope, (b) sub-gratings,

(d) new grating structure

The spatial corrugation and reflection frequency spectrum of the conventional sampled grating have a relation analogous to the Fourier transform, which are illustrated in Fig 2 The spatial index profile of the sampled grating

in Fig 2(e) can be composed by the mathematic operation of the four spatial index profile functions in Fig 2(a), Fig 2(b), Fig 2(c), and Fig 2(d) The reflection spectrum corresponding to the spatial frequency β in Fig 2( j) consists of the four parts of Fig 2(f ), Fig 2(g), Fig 2(h), and Fig 2(i) From Fig 2, it is apparent that the every reflection peak and its sidelobes are related with the Fourier transform component function of the rectangular function g z( ) , and the rough shape of the RSEs is determined by the Fourier transform function of the rectangular function f z( ) Assuming that the length of conventional sampled grating is infinite, their sidelobes will be eliminated and the linewidth of every reflectivity peak is quite narrow

The impact of the sampling period on reflection spectrum envelope are calculated by the proposed method and the transfer matrix method respectively, and shown in Fig 3(a) and Fig 3(b) Obviously, Fig 3(a) presents a clear picture of dependence of reflection spectrum envelope on the sampling period

3 Application of Reflection-spectrum Envelope

The analytical expression (Eq (6)) of the RSE for conventional sampled gratings is based on the Fourier theory The broad flat-top RSE can be realized by concatenating or partly overlapping a series of RSEs of conventional sampled gratings, which can be proposed as multiple reflection-spectrum envelope concatenation (MRSEC) technology Concatenation with M = 5 RSEs of conventional sampled gratings in Fig 4 provides an example of application of the multiple reflection-spectrum envelop concatenation technology to present a new grating structure composed by five sub-gratings, which can be called as the digital concatenated grating The digital concatenated grating consists of

a set of nonapodized M conventional sampled gratings As shown in Fig 4(b), the duty cycle of each conventional sampled grating is 1/M (M = 5) From Fig 4(a), the concatenation and overlap of RSEs can supply the gap of the Sinc shape of conventional sampled gratings Based on the Fourier theory the proposed grating structure, as shown in Fig 4(d), can be obtained by inverse Fourier transform of the resultant RSE with a broad flat-top in Fig 4(c) The characteristics of every RSE in Fig 4(a) are basically uniform except the central wavelength The spacing of the central wavelength of adjacent RSE in Fig 4(a) keeps as a constant, which must be lower than the 3dB bandwidth of each RSE In accordance with the RSE of Fig 4(a), the characteristics of sub-gratings, such as sampling period, the effective refractive index and the grating pitch length must be the same except grating period in Fig 4(b) At the interface of each adjacent grating in Fig 4(d) the phase is zero, which is used for eliminating the unwanted phase modulation in the whole grating The channel spacing ∆f of the digital concatenated grating, which is equal to the channel spacing of the sub-gratings, is inversely proportional to the sampling period Z0 as:

,

eff

c f

22

In this proposed scheme, spectrum property of the digital concatenated grating composed of five sub-gratings has

been simulated in Fig 5 The simulation parameters of those gratings are n 0,eff = 1.485, δn eff = 5 × 10-4, N = 10, and

Z0 = 1.043 mm, respectively The reflection-spectrum of the digital concatenated grating simulated with transfer matrix method has been plotted with black line in Fig 5 Obviously, in Fig 5, the reflectivity peak values of the digital concatenated gratings (black line) are consistent well with its RSE (red lines) calculated by analytical expression It can be seen in Fig 5 that twenty-three identical useful channels has been obtained From Fig 5, the envelope top of reflection spectrum has ripples, which can be introduced by sidelobes of Sinc-envelopes of each sub-grating Therefore, it is important for choosing a proper interval of central wavelengths of RSEs to obtain a broad flat-top RSE For well design of the digital concatenated grating with the best broad flat-top envelope, we should ensure the separation between center wavelengths of adjacent conventional sampled grating be the multiple of the spacing between reflectivity peaks

Fig 5 Digital concatenated grating with five sub-gratings

4 Conclusion

The analytical expression of the RSE for conventional sampled grating is deduced by Fourier theory Sidelobes can

be eliminated and the linewidth of each reflectivity peak becomes quite narrow with infinite grating length The accuracy of this expression has been verified by simulated reflectivity spectrum by use of transfer matrix method When compared to the transfer matrix method, our proposed technology provides a simple, clear and fast way to evaluate the performance of the RSEs A new technique of multiple reflection-spectrum envelope concatenation is introduced to increase the channel number with uniform peaks The proposed technology can densify sampled grating both in spectral channels number and in spatially physical corrugation An example of a 23-channel grating with uniform characteristics in all channels is demonstrated

Acknowledgments

The authors undertook this work with the supports of the National Natural Science Foundation of China under Grant

No 60677024, the National High Technology Research Development Program of China under Grant No 2006AA0320427, and Hong Kong Polytechnic University Research Grant G-U321

6 P Petropoulos, M Ibsen, M N Zervas, and D J Richardson, “Generation of a 40 GHZ pulse stream by pulse

multiplication with a sampled fiber Bragg grating,” Opt Lett., Vol 25, No 8, pp 521–523, Apr 2000

7 M Ibsen, M K Durkin, M J Cole, and R I Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation”, IEEE Photon, Technol Lett., Vol 10, No 6, pp 842–845, 1998

8 H Ishii, Y Tohmori, Y Yoshikuni, T Tamamura, and Y Kondo, “Multiple-phase-shift super structure grating DBR lasers for Broad wavelength tuning”, IEEE Photon Technol Lett., Vol 5, No 6, pp 613–615, 1993

9 M Gioannini and I Montrosset, “Novel interleaved sampled grating mirrors for widely tunable DBR laser”, IEE

Proceedings, Vol 148, 13–18, 2001

TEMPERATURE-DEPENDENT PHOTOLUMINESCENCE INVESTIGATION OF

NARROW WELL-WIDTH InGaAs/InP SINGLE QUANTUM WELL

KMITL Nanotechnology Research Center, King Mongkut’s Institute of Technology Ladkrabang,

Bangkok 10520, Thailand

53 Ga 0

Phase Epitaxy is verified by photoluminescence spectroscopy PL spectra exhibit the e(1)-hh(1) transition in the well.

PL measurement was conducted at various temperatures from 15 K to 200 K in order to investigate the important temperature-dependent parameters of this structure Important parameters such as activation energies responsible for the photoluminescence quenching and broadening mechanisms are achieved Because of small thermal activation energy of 15.1 meV in the narrow well, carriers can escape from the well to the barrier states The dependence of

PL width on temperature revealed that Inhomogeneous mechanism is the dominant mechanism for the broadening

of PL peak and homogeneous mechanism is responsible at high temperature due to electron-phonon interaction Keywords: InGaAs/InP; single quantum well; photoluminescence.

1 Introduction

Semiconductor compound materials from group III and V have gained great interest according to suitableproperties for practical optoelectronic devices Most of these devices are fabricated in form of quantumstructures In0.53Ga0.47As lattice-matched to InP has promised for ultrahigh speed devices utilizing thehigh electron mobility and high peak velocity The band gap of 0.75 eV is good for photodetector in opticalcommunication systems Moreover, semiconductor injection lasers using InGaAs/InP quantum well structurescan be shifted into the 1.3–1.55 µm region by change the well thickness Therefore, high-quality interface ofquantum structure device is required Many works have devoted to study the optical properties of relatedstructures Band gap blue shift of InGaAs/InP multiple quantum wells(MQWs) by different dielectric filmcoating and annealing was observed by PL.1The results suggested that the shift depended on the dielectriclayers, annealing conditions and combination between cladding layer and dielectric layer The effect of dopingconcentration variation in the InP donor layer of InGaAs/InP high-electron mobility transistor (HEMT)structures was investigated by mean of PL.2The variation of doping concentration caused different transitions

of the confined states in the wells PL technique and secondary ion mass spectroscopy (SIMS) were conducted

to determine the well widths in InGaAs/InP MQWs.3 Both techniques give good agreement in values ofquantum well widths

In this work, the formation of In0.53Ga0.47As/InP single quantum well with narrow well width grown

by Organometallic Vapor Phase Epitaxy is verified by photoluminescence spectroscopy PL spectra exhibitthe e(1)-hh(1) transition in the well PL measurement was conducted at various temperatures from 15 K to

200 K in order to investigate the important temperature-dependent parameters of this structure

2 Methodology

Few monolayers In0.53Ga0.47As/InP SQWs were grown by Organometallic Vapor Phase Epitaxy (OMVPE)

at low pressure Trimethylgallium (TMGa), Trimethylindium (TMIn), AsH3, and PH3 were used as thesource gases for Ga, In, As and P respectively 100-nm thick InP buffer layer was grown on semi-insulatingInP substrate After the gas source for In and P was suspended, InGaAs well layer was grown with thickness

of 2–4 monolayers (ML) before InP cap layer with 2 nm thick was grown The growth temperature was

600◦C In PL experiment, Argon ion laser with filtered wavelength of 488 nm was used as optical excitationsource The sample was cooled down from room temperature (RT) to 15 K in a cryostat The luminescence

from the sample was dispersed by the monochromator and was carried out by Ge detector The signal wasamplified by a lock-in amplifier and displayed by a computer The stepped motor of the monochromator wasautomatically controlled by a signal from PC via RS-232 port

3 Results and Discussion

In Fig 1, PL spectra of all samples at 15 K exhibit clear peaks, which are attributed to the luminescencefrom quantum well The solid lines represent the fitting curves of each sample The observed PL peak of thesample with the well width of 4 ML, 3 ML, and 2 ML is at 1.079 eV, 1.151 eV, and 1.198 eV respectively.The peaks due to the n=1 excitonic transition (e(1)-hh(1)) are clearly identified PL peak has a dramaticincrease (about 40–60 meV) when the well width is decreased by only one monolayer These features reflectthe formation of the extremely thin well-width single quantum well between lattice-matched InP and InGaAs.The sample with 3 ML-well width shows the strongest intensity, implying the optimization of good formationand uniformity of the sample

Figure 2 shows temperature-dependent PL of the sample with 3 ML well width As temperature increasesfrom 15 K to 200 K, PL spectra are weaker and exhibit the red shift, moving to the lower photon energy.The PL peak position versus measured temperature is illustrated in Fig 3 The PL peak of about 1.152 eV

at 15 K slightly shifts to lower energy of 1.138 eV at 200 K The red shift of about 14 meV from 15 K to

200 K is probably caused by the decrease in the band-gap energy as the temperature increases.4 It can bededuced that the luminescence of the extremely thin or small quantum structure is almost independent ofthe temperature.5 Meanwhile, the PL intensity drop as temperature increases is due to the fact that whentemperature increases, the photocarriers have more probability meet various types of defects and recombinenon-radiatively on them5 and the small binding energy of the exciton At higher temperature, the thermalenergy is significant comparing to the binding energy of the exciton, and the exciton-phonon interaction isconsiderable, reflecting in weaker and broader PL spectra

The calculation of the peak observed in the PL spectra of the particular quantum well transition is done

by estimating the transition energies expected for a quantum well with a given well width The ground stateenergy level in the quantum well is calculated by solving one-dimensional Schr¨odinger equation of a finitesquare well In the calculation, the energy gap of InP and In0.53Ga0.47As are 1.35 eV and 0.73 eV respectively.6The effective mass of electron (m∗

respectively.6 The calculation shows the higher values (about 70–90 meV) than the measured values Theorigin of the difference may come from the imperfection at the interface between the extremely thin layer

of InGaAs and InP barrier.7 The effect of temperature on PL characteristics of the sample is thoroughlyinvestigated The integrated PL intensity shown by closed square and full width at half maximum (FWHM)

of the PL peak shown by closed circle of the sample as a function of temperature is plotted in Fig 4

As the temperature increases from 15 K to 80 K, The PL intensity rapidly decreases Further increase intemperature from 80 K to 150 K causes insignificant decrease of PL intensity Meanwhile, The FWHM of

PL peak increases with increasing temperature, especially after 80 K The temperature dependence of theintegrated PL intensity of an exciton emission peak is expressed as following equation,8,9

IP L(T ) = I0

where I0 is the integrated PL intensity near 0 K, A is a constant, EA is the thermal activation energywhich is responsible for the quenching of PL intensity in the temperature-independent PL spectra, T is thetemperature, and kB is Boltzmann constant Figure 5 presents the integrated PL intensity of the sample.These measured values were fitted using equation (1) and shown by the solid line The fitting curve obviouslyexhibits satisfactory consistence with the experimental data From fitting curve, the thermal activation energy(EA) of this structure of 15.1 meV is obtained

Normally, the temperature-induced quenching of luminescence in quantum well structure is caused bytwo mechanisms: thermal emission of charge carriers out of confined states in the well into barrier states10and thermal dissociation of excitons into free-electron-hole pairs.4 Because of very narrow well width, thesubband energy of electron in conduction band and hole in valence band are closed to the top of the well.The confined carriers can easily escape from the quantum wells Therefore the first quenching mechanismdominates and the small thermal activation energy can be regarded as the delocalization energy of carriers

in the well.4 The temperature-dependent broadening of PL spectra of this structure is also investigated.Typically, the broadening of the PL spectra in quantum well structure can be summarized as the sum oftwo components: a temperature-independent inhomogeneous broadening due to interface roughness, fluctu-ations in binding energies alloy fluctuations (Γin), and the temperature-dependent homogeneous broadeningwhich typically due to electron-optical phonon or exciton-phonon interactions, (Γhom), which is given by thefollowing expression,11

exp ELO

kBT

+ 1

Note that, ΓLOis the electron-phonon or exciton-LO-phonon coupling constant and ELOis the optical phononenergy Therefore the total broadening is the summation of inhomogeneous broadening and homogeneousbroadening due to the electron-phonon interaction

Figure 6 shows the FWHM of PL spectra from the sample with 3-ML well width as a function of perature The solid line is the fitting curve to the measured point using equations (2) It agrees well withthe experimental data The corresponded parameters extracted from the curve fitting are obtained as fol-lows, ΓLO = 32.0 meV, ELO = 24.5 meV, and Γin = 42.7 meV Fitting data reveals that inhomogeneousbroadening mechanism is the dominant mechanism responsible to the broadening of PL spectrum of thisstructure The inhomogeneous broadening which is independent to temperature depends on several mecha-nisms such as well width fluctuation, donor-to-acceptor recombination and local fluctuation in the strain.11For this quantum structure of very narrow well, the well width fluctuation should dominates and the localfluctuation in the strain is neglected due to lattice matching between InP and In0.53Ga0.47As The secondpart of broadening of PL spectrum is homogeneous broadening which is temperature-dependent mechanism.Figure 7 shows the homogeneous broadening of In0.53Ga0.47As/InP SQW as a function of temperature.The homogeneous broadening is negligible at low temperature (<40 K) At higher temperature, its valueincrease drastically from 0 meV to 4 meV with increasing temperature from 40 K to 150 K At low tem-perature, the carriers are trapped in the well resulting in minimum variations of the binding energies of thecarriers and the inhomogeneous broadening mechanism dominates At elevated temperatures, the electron-phonon interaction becomes the dominant broadening mechanism and the FWHM consequently increaseswith increasing temperature

is obtained from the plot of integrated PL intensity versus temperature Due to small thermal activationenergy in the narrow well, carriers can easily escape from the well to the barrier states resulting in the

PL intensity quenching at low temperature The broadening of PL emission peak is analyzed in terms ofhomogeneous and inhomogeneous broadening mechanisms It is revealed that inhomogeneous mechanism isthe dominant mechanism for the broadening of PL peak and homogeneous mechanism has significant role athigh temperature due to electron-phonon interaction

Acknowledgements

The authors would like to acknowledge National Nanotechnology Center for research funds and department

of Applied Physics, King Mongkut’s Institute of Technology Ladkrabang for the research facilities

References

1 J Zhao, J Chen, Z.C Feng, J.L Chen, R Liu, and G Xu, Thin Solid Films 498, 179 (2006)

2 K Radhakrishnan, T.H.K Patrick, H.Q Zheng, P.H Zhang, S.F Yoon, Microelectron Eng 51-52, 441 (2000)

3 D.N Bose, P Banerji, S Bhunia, Y Aparna, M.B Chhetri, and B.R Chakarborty, Appl Surf Sci 158, 16(2000)

4 Y.T Shih, Y.L Tsai, C.T Yuan, C.Y Chen, C.S Yang, and W.C Chou, J Appl Phys 96, 7267 (2004)

5 B lambert, A Le Corre V Drouot, H.L Haridon, and S Loualiche, Semicond Sci Tech 13, 143 (1998)

6 J Nukeaw, R Asaoka, Y Fujiwara, and Y Takeda, Thin Solid Films 334, 44 (1998)

7 J Boherer, A Krost, and D Bimberg, Appl Phys Lett 60, 2258 (1992)

8 M Furis, A.N Cartwright, J Hwang, and W.J Schaff, Proc Material Research Society Symposium 2004 798,(2004)

9 Y.A Chang, J.R Chen, H.C Kuo, Y.K Kuo, and S.C Wang, J Lightwave Technol 24, 536 (2006)

10 S Weber, W Limmer, K Thonke, R Sauer, K Panzlaff, G Bacher, H.P Meier, and P Roentgen, Phys Rev

B 52, 14739 (1995)

11 M Furis, A.N Cartwright, H Wu, and W.J Schaff, Proc Material Research Society Symposium 2004 798,(2004)

31

SHOOTING METHOD CALCULATION OF TEMPERATURE DEPENDENCE OF

TRANSISITION ENERGY FOR QUANTUM WELL STRUCTURE

BUNJONG JUKGOLJUN

Computational Physics Research Laboratory, Applied Physics Department, Faculty of Science,

KMITL, Bangkok, Thailand, 10520

WISANU PECHARAPA

Optical Development Research Laboratory, Applied Physics Department, Faculty of Science,

KMITL, Bangkok, Thailand and KMITL Nanotechnology Research Center, KMITL, Bangkok, Thailand, 10520

WICHARN TECHITDHEERA

Computational Physics Research Laboratory, Applied Physics Department, Faculty of Science,

KMITL, Bangkok, Thailand, 10520 and KMITL Nanotechnology Research Center, KMITL, Bangkok, Thailand, 10520

The ground state transition energy as various temperatures of a single quantum well structure has been calculated The numerical technique called shooting method was developed to get eigen values and eigen functions Pässler’s model and Aspnes’s equation are adopted to calculate the energy gap(Eg) of Al0.3Ga0.7As and GaAs respectively Our calculation has been tested by comparing the results to PL experimental data of Al0.3Ga0.7As/GaAs single quantum well Good agreement has been found in the low temperature range (less than 40 K) and fair result has been obtained in the range of temperature higher than 40 K

1 Introduction

Quantum well devices have been extensively studied in the last decade due to their potential of producing the high performance and low energy consumption devices In the former works [1– 4], our calculations based on an analytical solution of finite quantum well In this work, the full numerical scheme has been developed to calculate the eigen values and eigen functions

2 Quantum Well Structure and Temperature Dependence

The model of quantum well structure we’ve used to calculation, shown below The left and the right hand side materials are symmetric Al0.3Ga0.7As which energy gap depends on temperature through the equation after Pässler[5]

p = 3.5 (for Al0.3Ga0.7As)

32

Fig 1 The model of quantum well structure of Al0.3Ga0.7As/GaAs

In the same way, the inside material, GaAs, changes its energy gap through the equation after Aspne[6],

3 The Ground State Energy Calculation by Shooting Method

We had started our work by dividing the problem into two parts to calculate The first part is in conduction band and the second one is in the valence band The calculation scheme of the two parts are slightly different

3.1 Calculation in Conduction Band

The Schroedinger equation for a single quantum well with a constant potential depth V0 and electron effective mass

hh 1

e 1

E g (Al 0.3 Ga 0.7 As)

E g (GaAs) ∆E c =0.6∆E g

∆E v =0.4∆E g

Al0.3Ga0.7As barrier GaAs Well

x = 0 to x = L/2 due to the symmetry of well The computer code has been developed by using the equation (5)–(7) when V0 is specified, m is known as mention above and ħ is Planck’s constant over 2π

3.2 Calculation in Valence Band and Transition Energy

The calculation in valence band is the same with the calculation in conduction band Only the difference is the effective mass of hole (m = 0.45 m0) and band offset (equal to and 0.4∆Eg) After the calculation, we get the ground state energy in the valence band Ehh1 The transition energy is calculated from

4 Result and Discussion

Our calculation of transition energy as various temperatures range from 12 K to 200 K are compared to the photoluminescence data[8] The PL peaks shown in Fig 2 the small peaks is clearly observed in the low temperatures range from 12 K to 40 K Higher than 40 K small peaks and dominant peaks seem to be merged The important thing is that, the small peaks are the peaks from ground state transition energies of the quantum well So it’s should be careful to use this data, especially in case of the extreme precision is required From the comparison to this PL data, we found that the calculation give the good results in the temperatures range from 12 K to 40 K Higher than 40 K it give the fair results (see Fig 3)

Fig 2 PL peaks as various temperatures

From the testing by above comparison, our calculation is usable to calculate a quantum well transition energy by full numerical scheme called shooting method Only slightly changed some parameters or functions, we would calculate any species of quantum well and predict ground state transition energy at a given temperature