非極性氮化銦薄膜之兆赫波輻射研究

國 立 交 通 大 學

光 電 工 程 研 究 所

碩 士 論 文

非極性氮化銦薄膜之兆赫波輻射研究

Terahertz Emission Properties of

Nonpolar Indium Nitride Film

研 究 生：何介暐

指導教授：潘犀靈 教授

安惠榮 教授

非極性氮化銦薄膜之兆赫波輻射研究

Terahertz Emission Properties of

Nonpolar Indium Nitride Film

研 究 生：何介暐 Student：Chieh-Wei He

指導教授：潘犀靈 教授 Advisors：Prof. Ci-Ling Pan

安惠榮 教授 Prof. Hyeyoung Ahn

國立交通大學

光電工程研究所

碩士論文

A Thesis

Submitted to Department of Photonics and

Institute of Electro-Optical Engineering

College of Electrical Engineering

National Chiao Tung University

In partial Fulfillment of the Requirements

for the Degree of

Master of Science

in

Electro-Optical Engineering

July 2008

Hsinchu, Taiwan, Republic of China

非極性氮化銦薄膜之兆赫波輻射研究

學生：何介暐 指導教授：潘犀靈教授 安惠榮教授 國立交通大學光電工程研究所 摘 摘摘 摘 要 要要 要 在這篇論文中，我們研究有關 c 軸平面氮化銦薄膜與 a 軸平面氮化銦薄膜之 光激發產生兆赫波輻射研究。我們的團隊曾報導過源自於奈米柱狀結構的兆赫波 輻射強度增強現象，相較於 c 軸平面氮化銦薄膜所展生者在兆赫波輻射電場上大 上十倍，並且我們認為這兩種結構的氮化銦薄膜都是以 photo-Dember effect 作為 輻射兆赫波的主要機制。對於沿著 a 軸 1120 成長的平面而言，極化導致的電場 平行於表面介面，我們並且發現其兆赫波放射能量上遠遠比 c 軸平面氮化銦薄膜 大上兩個級數，且與目前所知最好的兆赫波放射源：砷化銦擁有相同級數的輻射 強度。我們認為 a 軸平面氮化銦薄膜主要的兆赫波輻射機制是來自於受激發載子 在極化感應電場下有著較為有效率輻射出半導體介面的幾何耦合輻射效應。 在高能量雷射的激發之下，放射出的兆赫波顯示出與方位角有關的分量疊加 於與方位角無關的分量上。與激發光線的線性偏振和方位角有關的兆赫波輻射特 性可能是來自於兆赫波的非線性輻射，例如光整流效應，此與 a 軸平面氮化銦薄 膜的電納系數有著密切關係。

Terahertz Emission Properties of Nonpolar Indium Nitride Film

Student：Chieh-Wei He Advisors：Prof. Ci-Ling Pan Prof. Hyeyoung Ahn

Department of Photonics and Institute of Electro-Optic Engineering, College of Electrical Engineering National Chiao Tung University

Abstract

In this thesis, we report the terahertz emission measurement from c-plane and

a-plane indium nitride (InN) films. Our group already has reported the enhancement of terahertz (THz) radiation (greater than ten times in intensity) from InN nanorod arrays compared to the InN films grown along the c-axis and the dominant emission mechanism was proposed to be the photo-Dember effect. For the layers grown along

a-( 1120 ), polarization-induced electric field is parallel to the layer interface and THz emission from it is found to be at least two orders of magnitude stronger than that from

c-plane InN film, which is the same order of InAs, the best semiconductor THz emitter so far. We propose that the primary radiation mechanism of the a-plane InN film is due to the acceleration of photoexcited carriers under the polarization-induced in-plane electric field perpendicular to the a-axis, which effectively enhances the geometrical coupling of the radiation out of semiconductor.

At high photoexcitation, emitted THz wave shows the obvious azimuthal angle dependence superimposed with a strong angle-independent component. Pump polarization and azimuthal angle dependence of emitted THz wave may be due to the nonlinear THz emission mechanism, such as optical rectification, which is depending on the characteristic susceptibility tensor of a-plane InN.

Acknowledgement

這本論文能夠完成首先要感謝我的指導老師潘犀靈教授與安惠榮教授無私 的指導，他們教導我擁有正確的實驗方法與態度，經由討論分析實驗數據釐清許 多實驗上的疑難雜症，使我從大學時代僅埋首書本而無實作經驗的學生轉變成能 夠對於一套實驗系統鉅細靡遺描述與闡論的研究生。此外，也要感謝清大果尚志 老師實驗室提供實驗所需的樣品，並在製程與量測上給予我很大的幫助。 另外，還要感謝王怡超學長在雷射系統的架設與維護上竭盡所能的指導與幫 忙，並教導我許多雷射系統上的知識，讓我能夠在專心實驗之餘沒有後顧之憂。 再者，還要感謝和我一起努力的實驗室伙伴，除了在研究領域上的討論與辨析讓 我對實驗理論有更深層的認知外，平時生活相處的點滴更讓人銘記心頭。 最後，感謝我的家人從小到大對我的栽培，即便在這兩年的研究生涯中共同 經歷了許多人生無法避免的無常與創傷，他們仍舊給予我一美好的家庭環境與親 情，於我情緒低落時提供最強大的精神後盾，在生活無虞的前提下讓我能專心致 志於攻讀碩士學位。還有，我最親愛的爺爺奶奶，您們永遠是我在人生道路上的 楷模。雖然這本論文不是什麼驚天動地的非凡研究，然而記錄刻印這兩年間的實 驗歷程與成果，希望它能夠讓您們引以為傲。 平安有愛 Peace

Contents

Abstract(C)………. i

Abstract(E) ……… ii

Acknowledgement………

iii

Contents……….. iv

List of Figures……… vi

List of Tables……….. x

Chapter 1 Introduction ...1

1-1 Terahertz Radiation...1

1-2 III-Nitride Compound Semiconductors : InN...5

1-3 Organization of Thesis...7

Chapter 2 Experimental Theories ...8

2-1 Terahertz Generation...8

2-1-1 Surge-Current Model...8

2-1-2 Surface Depletion Field...10

2-1-3 Photo-Dember Effect...12

2-1-4 Optical Rectification...16

2-1-5 THz Enhancement by External Magnetic Field ...19

Electro-Optic Sampling (FS-EOS) ...21

Chapter 3 Experimental Setups ...25

3-1 Introduction of Femtosecond Laser System ...25

3-2 Electro-Optic THz System...27

Chapter 4 Sample Properties...31

4-1 InN Film (c-plane InN)...33

4-2 Nonpolar InN Film (a-plane InN)...34

Chapter 5 Experimental Results and Discussion...37

5-1 Terahertz Emission from InN Surface ...37

5-2 Azimuthal Angle dependence of InN...45

5-3 Pump Polarization Dependence of Semiconductors...51

Chapter 6 Conclusion and Future Work ...55

6-1 Conclusion ...55

List of Figures

Fig 1-1 The spectrum range of electromagnetic waves………..….1 Fig 1-2 The energy band gaps of Group-III nitride semiconductors. The ternary system InGaN can match the solar spectral irradiance as shown at the right side….... ….... ….... ….... ….... ….... ….... ….... ….... ….... ….... ….... …..6 Fig 2-1. Band diagram and the schematic flow of drift current in a typical n-type semiconductor. ...12

Fig 2-2 Schematic flow of diffusion current by photo-excited carriers...15

Fig 2-3 Optical geometry of THz radiation from a semiconductor surface...18

Fig 2-4 Azimuthal angle dependence of THz radiation amplitude from semi-conductors with (a) n-InAs (111) and (b) n-InSb. ...18

Fig 2-5. Schematic diagram of the experimental geometry and coordinate system. ...21

Fig 2-6 Schematic figure of Electro-optic sampling...24

Fig 3-1. Femtosecond laser system includes Tsunami, Spitfire and two pump laser (Millennia V and Empower). ...26

Fig 3-2. Electro-Optic THz system...29

Fig 3-3. THz time-domain (a) waveform and (b) its corresponding spectrum generated by the electro-optic THz system using a-plane InN as emitter under the

Fig 3-4. THz time-domain (a) waveform and (b) its corresponding spectrum generated by the electro-optic THz system using a-plane InN as emitter under the humidity of 5% ...30

Fig 4-1 Simplified view of the band edge structure of InN. ...32

Fig 4-2. Crystal structure of InN...33

Fig 4-3 The SEM pictures of c-plane InN film. [This picture is taken from the Prof. S. Gwo’s group, The Department of Physics, National Tsing Hua University.] ...34

Fig 4-4. RT Hall mobility and carrier concentration of a-plane InN films as a function of film thickness. The inset shows the corresponding data of the c-plane InN films. ...35

Fig 4-5. The SEM pictures of a-plane InN film. [This picture is taken from the Prof. S. Gwo’s group, The Department of Physics, National Tsing Hua University.] ...36

Fig 5-1 The amplitude of the terahertz emission from a-plane InN film (red solid line) compare to that from c-plane InN film. The excitation is 0.24 mJ/cm2. Inset: comparison between a-plane InN , c-plane InN measure under identical experimental condition...40

Fig 5-2 Schematic diagram of the experimental geometry and coordinate system.[30] ...42

Fig 5-3 Calculated polar radiation patterns for GaAs at (a) 0 and (b) 8 T. In each part the horizontal line is a schematic representation of the surface of the semiconductor. The bow-tie pattern below the surface line is calculated for radiation within the semiconductor, whereas the pattern above the surface shows the radiation emitted into free-space. The vector B indicates the magnetic-field direction. ...42

Fig 5-4 Ball-and-stick model of the a-plane surface. Large balls are In, small balls are N. ...44

Fig 5-5 Optical reflectivities in InN-epilayer and nonpolar InN as a function of excitation energy. Optical absorption in InN film is about 80%, while that in nonpolar InN is about 76%. ...44

Fig 5-6. Peak amplitude of terahertz emission for c-plane InN film (red points) and a-plane InN film (black points) as a function of laser pump power...45

Fig 5-7. Azimuthal-angle dependence of THz-emission amplitude from n-InAs...46

Fig 5-8. Peak amplitude of the p-terahertz fields as function of azimuthal angel rotation of (a) c-plane InN film and (b) a-plane InN excited at 20mW...49

Fig 5-9. Peak amplitude of the p-terahertz fields as function of azimuthal angel rotation of a-plane InN film excited at different fluence (a) 20mW (b) 50mW (c) 75mW (d) 100 mW by p-polarized pump beam. ...49

Fig 5-10 The amplitude of the p-polarized THz emission field vs pump fluence at the different azimuthal angle.θ_{1 is the angle with minimum azimuthal modulation} andθ_{2 is the angle with maximum azimuthal modulation . ...50}

Fig 5-11. Azimuthal-angle dependence of the a-plane InN film with the pump power 50mW and p-polarized pump beam. ...50

Fig 5-12. Azimuthal-angle dependence of the a-plane InN film with the pump power 50mW and s-polarized pump beam. ...50

Fig5-13 Pump polarization angle dependence of THz peak amplitude of c-plane InN. The pump polarization is p-polarization when angles are at 0°, 180°, 360° and s-polarization when angles are at 90°, 270°. The maximum peak is at the p-pump and the minimum peak amplitude at the s-pump...51 Fig 5-14 .Pump polarization angle dependence of THz peak amplitude of n-type InAs. ...51 Fig 5-15. Peak amplitude of the p-polarized terahertz fields as function of pump

polarization of a-plane InN excited at 20mW. The pump polarization is p-polarization when angles are at 0°, 180°, 360° and s-polarization when angles are at 90°, 270°. ...53

List of Tables

Table 2-1. Band structure parameters of InN and InAs. ...15

Table 3-1. Properties of Tsunami laser and Ti:Sapphire regenerative amplifier. ...26

Table 4-1. The bandgap energies of some semiconductors. ...31

Chapter 1

Introduction

1-1 Terahertz Radiation

In the past years, a significant development of ultrafast terahertz (THz) technique

has been observed. The application of the THz technique has made significant

contribution not only to ultrafast phenomena but also to a wide variety of applications,

including ultrahigh speed optoelectronics, tomographic imaging in biomedical fields.

Terahertz (THz) radiation, lies in the frequency gap between the infrared and

microwaves(see Fig. 1-1), is typically referred to as the frequencies from 100 GHz to

30 THz which are between microwaves and visible light. 1 THz is equivalent to 33.33

cm- 1(wave numbers), 4.1 meV photon energy, or 300 µm wavelength, so THz waves

are also called sub-millimeter wave.

Fig. 1-1 The spectrum range of electromagnetic waves (http://www.rpi.edu/terahertz/about_us.html)

At lower frequencies compared to THz wave, microwaves can be easily generated

light can be generated by “optical” devices, such as a semiconductor laser diode, in

which electrons jump across the energy band gap and then emit light. Until 1980’s, the

spectral range of THz has been inaccessible in both electronic and optical methods.

Until then, Fourier transform spectroscopy is perhaps the most common technique to

study sub-THz phenomena.

The appearance of ultrashort pulse laser of ~100 fs pulse duration made it possible

to generate THz waves covering the whole THz spectral range. In 1981, Mourou and

Auston first demonstrated generation and detection of pulsed THz radiation by a

photo-conducting switch with advantages of time resolution of picosecond and high

sensitivity enhanced by phase-lock technique[ 1][ 2]. In 1988, Grischkowsky used the

photoconductor dipole antenna as the THz sensor, furthering the spectrum into the

order of terahertz frequency [ 3]. Afterward a variety of antennas was appeared, like

typical dipole antenna, large aperture photoconductor dipole antenna [ 4] and also

another method using semiconductor surface electric field [ 5] to generate THz pulses

by the ultrashort pulse laser. In 1996, X. C. Zhang et al. developed free-space

electro-optic sampling (FS-EOS) technique to enhance signal to noise ratio (S/N ratio)

up to 105 and to achieve much large dynamic range [ 6].

medical sciences [ 7]. Image and tomography [ 8] of THz have also been studied and

can be applied to homeland security.

For semiconductors measurement, conventional four point probe and Hall

effect measurement can measure the characteristics including mobility, carrier

concentration and resistivity of the semiconductor materials by direct sample contact.

All these electrical measurements measure only DC value of the sample but some

characteristics like refractive index and conductivity are frequency-dependent. For

some semiconductors with high resistivity and low concentration, the electrical

properties are difficult to be measured by simple direct contact because the Schottky

barrier may disturb the measurement value at the metal-semiconductors interface.

Therefore, THz-TDS is desirable for semiconductors characterization due to the

advantages of non-contact and frequency-dependant measure. In 1990 D.

Grischkowsky et al. [ 9] successfully measured optical properties including

refractive index and conductivity of GaAs wafer and the results fit well with the

Drude model. Besides GaAs, other semiconductors such as silicon [ 10] have also

been widely studied. Recently, many nanostructured semiconductors like

InP-nanoparticle[ 11], ZnO-nanowire[ 12], Si-nanoparticle[ 13] have been studied

using THz-TDS technology and the particular conduction behavior have been

a coherent technology that could obtain both amplitude and phase information

simultaneously. Both absorption coefficient and refractive index could be extracted

without use of Kramers-Kronig relation, therefore, it simplifies the analysis process.

Recently, the spectroscopic technique using pulsed THz radiation,

called ”terahertz time-domain spectroscopy (THz-TDS)”, has been developed, by

taking advantage of short pulses of broadband THz radiation. THz-TDS has the time

resolution of sub-picosecond level and the spectral resolution of 50 GHz and THz-TDS

is a non-destructive method to the carrier concentration and mobility of doped

semiconductors. Many researches have been performed on a variety of gases, liquids,

dielectric materials and semiconductors by THz-TDS. For example, in 1990, D.

Grischkowsky et al.[9] studied the THz-TDS with the dielectric materials, such as

quartz and sapphire, and semiconductors, like silicon and GaAs. They discovered

different carrier concentrations affect the absorption characteristics of the samples in

1-2 III-Nitride Compound Semiconductors: InN

Group-III nitride semiconductors and their alloys have attracted a lot of attention

due to their unique properties for fundamental research and potential applications.

Recent research has shown that the bandgap of InN is actually 0.7 eV [13]. Alloyed

with GaN, the ternary system InGaN has been shown to cover a wide, continuous

spectral range from the near infrared for InN to the near ultraviolet for GaN. Currently

there is research into developing solar cells using the nitride based semiconductors.

Using the alloy indium gallium nitride, an optical match to the solar spectrum is

obtained (see Fig. 1-2). Thus, in this work, we focus on the properties of InN.

Indium nitride, as an essential component of the Ⅲ-nitride system, has received

much attention about ultrafast terahertz pulses emission generated by Indium nitride

film layers in recent years. Indium nitride is an interesting and potentially important

semiconductor material due to the low bandgap, the high electron mobility. In the other

hand, the intervalley scattering is the main reason to increase the effective mass of the

photo-generated electrons, and accordingly reduce the Photo-Dember field in the case

of InAs. Therefore, the absence of any intervalley scattering is another advantage to

use InN as the THz emitter. There have been some several reports on THz emission

from InN films [ 14][ 15][ 16]. The THz radiation emitted from InN films is typically

mechanism of both materials is the Photo-Dember effect.

In the past researches, we had shown the enhancement of terahertz radiation (>10

times in intensity) from InN nanorod arrays compared to the InN films grown along the

c-axis (c-plane InN). Because electron accumulation layer at the surface of c-plane InN

is very thin (< 10nm) and its contribution to terahertz generation is assumed to be

negligibly small, the dominant emission mechanism is proposed to be the

photo-Dember effect.

In this research, we want to study the whole emission mechanism of the a-plane InN

film. The a-plane InN film grown along the a-axis (a-plane InN) were rarely reported

mainly due to the technical difficulty in growing high crystalline quality a-plane InN

films and none were reported for their terahertz emission properties. We find that the

THz emission from the InN film grown along the a-axis (a-plane InN) is stronger than

that from the InN film grown along the c-axis (c-plane InN) about one order and

suppose this enhancement due to the terahertz dipole formed in the favorable in-plane

direction for a-plane InN. In the other hand, the azimuthal angle dependence and

pump polarization dependence of a-plane InN is also different to the c-plane one.

These results may demonstrate there are quite different mechanism for THz emission

Fig. 1-2 The energy band gaps of Group-III nitride semiconductors. The ternary system InGaN can match the solar spectral irradiance as shown at the right side.

1-3 Organization of Thesis

In chapter 1, an overview of THz radiation and the Ⅲ-Nitride compound

semiconductors: InN are presented. In chapter 2, the experimental theories including

THz radiation and detection are interpreted. In chapter 3, the basic characteristics

including growth method and Hall measurement results of the semiconductor samples

studied in this thesis are described. In chapter 4, the experimental setups including the

laser system and the THz-TDS systems are introduced. The experimental results and

discussion will be presented in chapter 5. Finally, our conclusions and future work are

Chapter 2

Experimental Theories

2-1 Terahertz Generation

The THz pulse has been generated by different methods, such as irradiation of

photo-conductive antenna, semiconductor surfaces, or quantum structures with

femtosecond optical pulses. The most common emission mechanisms are surge current

and transient polarization which acts as broadband terahertz sources. As the sample is

illuminated by an ultrashort laser pulse, electron-hole pairs are created in

semiconductors, and then the carriers are accelerated by the external or internal

electrical field to form a transient current which radiate THz waves. In this work, the

THz waves are generated via surge-current model, which will be described in detail in

the next section.

2-1-1 Surge-Current Model

From Maxwell’s equation, we have two inhomogeneous wave equations in terms

of electric potential V and magnetic potential A

r [ 17]: J -t A -A ₂ 2 2 r r r

µ

εµ

= ∂ ∂ ∇ (2-1-1.1)

ε

ρ

εµ

-t V -V ₂ 2 2 = ∂ ∂ ∇ (2-1-1.2)

where J r

is the current density and ρ is the charge density. These equations describe the propagation of the electromagnetic disturbances. In terms of these potential, the electric field E r is expressed as t A -V -E ∂ ∂ ∇ = r r (2-1-1.3)

The continuity equation of free carriers which is generated in the emitter after the absorption of an optical pulse is obtained directly from Maxwell’s equation:

( )

t

J

t

D

J

H

∂

∂

+

⋅

∇

=













∂

∂

+

⋅

∇

=

⋅

∇

⋅

∇

r

ρ

r

r

r

(2-1-1.4)

The current is a transverse current which is perpendicular to the direction of propagation, so that we have J

r ⋅

∇ =0. Eq (2-1-1.1) and Eq (2-1-1.4)(all the vector

arrows should be corrected) imply that the charge density is constant in time and will not contribute to the time dependent radiated electric field. Therefore, from Eq (2.3) we have (t) A t -(t) E_rad r r ∂ ∂ = (2-1-1.5)

The solution to the wave equation (2-1-1.1) and hence for the vector potential A

r

leads to the expression for the time-dependent radiated electric field Erad(t)

r

at a

displacement r

da'

'

r

-r

c

'

r

-r

-t

,

'

r

J

t

c

4

1

-t)

,

r

(

E

s 2 0 rad

∫

⋅

















∂

∂

=

r

r

r

r

r

r

r

r

πε

(2-1-1.6)

where

ε

₀ is the permittivity of free space, c is speed of light in vacuum, Js

r

is the surface current in emitter evaluated at the retarded time, and da' is the increment of surface area at a displacement 'rr from the center of the emitter. In the far field and assuming Js

r

is a constant at all points in the emitter, the radiated field can be written as

J

(t)

dt

d

r

b

t)

,

r

(

E

_{rad s}

r

r

r

=

(2-1-1.7)

where b is a constant, and the radiated field is proportional to the time derivative of photo-current.

2-1-2 Surface Depletion Field

In semiconductors with wide bandgap, such as GaAs (1.43 eV) and InP (1.34 eV), there may exist surface states in the forbidden gaps between valance and conduction bands due to the discontinuous structures in the surface. These states with occupied or vacant would affect the equilibrium concentration of electrons and holes in the surface. Because the Fermi-level is position independent, the energy bands must bend to form a depletion region where the surface built-in field exists. The strength of

surface-depletion field is a function of Schottky [ 18] barrier potential and dopant concentration Eq (2.1.2-1) ( ) ( ) d eN E x W x ε = − (2-1-2.1)

Where N is dopant concentration,

ε

is semiconductor permittivity, and W is depletion

width and has the form of Eq (2.1.2-2)

2 [ kT] W V eN e ε = − (2-1-2.2)

Where V is the potential barrier and kT e is the thermal energy. The direction and / magnitude of the surface depletion field depend on the dopant or impurity species and the position of the surface states relative to the bulk Fermi level. In general, the energy band is bent upward and downward for n-type and p-type semiconductors, respectively. After optical excitation, the electrons and holes are accelerated in opposite directions under the surface-depletion field, forming a surge current in the direction normal to the surface as shown in Fig. 2-1. Therefore, when the depletion surface field is the dominant mechanism for the surge current, the polarity of the emitted THz radiation waveform is opposite between that of the n-type and that of the p-type semiconductor. Contrarily, if the dominant mechanism is Photo-Dember effect, the emitted THz radiation waveform will be same direction either the n-type semiconductor or the p-type semiconductor, as explained in Section 2.1.3. Thus, by comparing the polarity of

the THz waveforms emitted from an n-type semiconductor and that of the p-type semiconductor, we can determine which mechanism is dominant in the semiconductor.

Fig 2-1. Band diagram and the schematic flow of drift current in a typical n-type semiconductor.

2-1-3 Photo-Dember Effect

The role of main band structure parameters such as carrier effective mass and

V

W

+

-

E

c

E

v

E

f

Surface states

E

_surface

-

+

-

J

Drift

-

-

+

-

surfaces. Some semiconductors such as InAs and InN with small band gap and small effective electron mass (Table 2-1) would radiate THz via Photo-Dember effect. With NIR light, the absorption depth is very small(≈100nm) and the excess energy of photo-excited carriers is very large for the excitation of narrow-bandgap semiconductors. All these conditions in the narrow-bandgap semiconductors enhance the photo-Dember effect, which is known to generate current or voltage in semiconductors due to the difference diffusion velocities of the electron and hole.

The band bending in this kind of semiconductors is not obvious resulting in a relative small surface depletion field because of comparatively small bandgap. The high absorption coefficient due to a small bandgap causes a large gradient carrier concentration after excitation by ultrafast laser pulse. The excited electrons and holes diffuse in the same direction but with different velocities, and therefore the Photo-Dember effect dominant (). Because the electron mobility is always larger than hole mobility, the photo-current is always in the same direction either n-type or p-type semiconductors. The fast photo-current rise and decay time due to semiconductors with the small electron mass and high mobility often possess fast photo-current rise and decay time that is helpful for efficient THz generation. In this mechanism the need of photon energy is comparably small; therefore, the free carriers have large excess energy. The photo-Dember voltage can be expressed by [ 19]:

0 0

(

) 1

(

1)

ln(1

)

1

B e h D

k T b T

b

n

V

e

b

n b

p

−

+ ∆

=

+

+

+

(2-1-3.1)

Where n0 and p0 are the intrinsic concentration of the electrons and holes, b is the

mobility ratio e

p

b

µ

µ

= , and Te and Th are the temperature of photo-excited electrons and

holes, respectively. From Eq (2-1-3.1) several properties can be concluded: The conditions to enhance the Photo-Dember voltage are high electron temperature, mobility ratio b and low intrinsic carrier concentration. The corresponding electric field (ED=VD/d, d is absorption length) is enhanced by decreasing absorption length. Thus,

the Photo-Dember effect is much stronger in narrow bandgap materials (InAs) than in wide bandgap materials (GaAs). Recently, InAs has been reported as a strong THz emitter with intensity at least one order of magnitude higher than other unbiased semiconductor emitters such as InP and GaAs. Therefore, high conversion efficiency has made InAs received much attention and be one of the most widely used THz emitters. InN has also been considered to generate THz waves via Photo-Dember effect [ 15].In this thesis, we would focus on the properties of terahertz emission from InN with different lattice structure.

The other band structure parameter we need to concern is the valley energy separations. If the excited carriers have excess energy higher than valley energy

separation, intervally scatterings will happen. Because of the reduction of the transient mobility in the L-valley, where the electron mobility is expected to be extremely low,

the terahertz radiation from Photo-Dember effect became relatively small.

Table 2-1. Band structure parameters of InN and InAs. The effective mass m0* at the bottom of the valley and nonparabolicity factor α are given for the central valley. △E1 (△E 2) is the energy separation

between the central valley and first (second) satellite valley. The parameters for InN and InAs are taken from [ 20] [ 21], respectively.

Semiconductor Eg (eV) m0*(me) α (eV-1) △E1 (eV) △E2 (eV) InN 0.78 0.04 1.43 1.775 2.709 InAs 0.354 0.023 1.4 0.73. 1.02 Air + Semiconductor

-

-

-

-

+ + + + Surface

J

Diffusion current

2-1-4 Optical Rectification

The nonlinear optical process was first suggested by Chuang et al.[ 22][ 23][ 24].

THz radiation field generated by the optical rectification, ETHz(t), is proportional to the

second-order nonlinear polarization in the near field. In the far field, the observed THz field amplitude, ETHz(ob), is proportional to the projection of the second time derivative

of the nonlinear polarization to the polarization direction of detection, n (a unit vector normal to the observation direction), at the observation point:

)

(t

E

_THzob = nnnn˙ETHz ∝ nnnn˙ 2 2

)

(

t

t

P

∂

∂

(2-1-4.1) 2

)

(

Ω

∝

Ω

ob THz

E

nnnn˙

P(Ω)

(2-1-4.2)

The strong dependence of the emitted THz radiation intensity on the crystal orientation to the pump polarization is the most unambiguous evidence for the contribution of the χ(2) process. By rotating a sample about its surface normal, the relative contribution of the azimuthal-angle-dependent component to the total THz radiation can be estimated.

Taking the surface normal as the X-axis and the reflection plane as the XY-plane

(2-1-4.4), respectively [ 25]: For (111) surfaces,                   − + Ω =           =

θ

φ

φ

φ

θ

φ

φ

φ

ε

3 sin cos 6 2 sin cos 6 2 3 cos cos 6 2 sin 6 2 cos 3 1 -) ( E d 2 ) ( ) ( ) ( 2 2 2 2 2 14 0 t Pz t Py t P P x (2-1-4.3) For (100) surfaces,





















Ω

=





















=

θ

φ

θ

φ

θ

φ

ε

2

cos

2

sin

2

sin

2

sin

2

sin

cos

)

(

E

d

2

)

(

)

(

)

(

2 2 14 0

t

Pz

t

Py

t

P

P

x (2-1-4.4)

Here, φ is the angle between the pump-laser beam and the surface normal refracted inside the sample, θ is the azimuthal angle of the sample orientation around the X-axis(See Fig 2-2.) and d14 =χ14(2)/2 is the nonlinear susceptibility coefficient for the difference frequency, Ω , in the contracted notation, and E(Ω) is the autocorrelation function of E(ω). Using (2-1-4.1) and considering the refraction at the interface between the semiconductor/air interfaces, the p-polarized THz field

amplitude observed in the direction of optical reflection is given by the following equation:

(

)

THz Y THz X

sin

P

cos

-P

0

,

cos

,

sin

ˆ

φ

φ

φ

φ

+

=





















−

=

•

∝

Pz

P

P

P

n

E

_Y X THz THz ob THz (2-1-4.6)

The refraction angles for the optical and THz beams are determined by the generalized Snell’s law as :

THz THz

opt

o _{n sin n sin}

45

sin =

φ

=

φ

, where nopt and nTHz is the

refractive index for the pump laser and THz radiation in the semiconductor, respectively. The azimuthal angle dependence of THz radiation amplitude from semiconductors with n-InAs (111) and n-InSb (100) are shown on Fig 2-3.

Fig 2-2 Optical geometry of THz radiation from a semiconductor surface [ 25]

Fig 2-3 Azimuthal angle dependence of THz radiation amplitude from semi-conductors with (a) n-InAs (111) and (b) n-InSb. [ 25]

2-1-5 THz Enhancement by External Magnetic Field

In past years, several groups have observed a large magnetic field induced the enhancement in surface–field THz emission from a variety of semiconducting materials (GaAs, InAs, InP, GaSb and InSb). In the paper published by M. B. Johnston et. al.[ 30], they build up a Monte Carlo dynamics model to explain the phenomenon of magnetic-field enhancement of THz emission and the schematic diagram of the experiment geometry is shown on Fig 2-4. The carrier motion is:

]

B

(t)

v

t)

,

r

(

E

[

m

q

(t)

a

_{* i i} i i i

r

r

r

r

r

×

+

=

(2-1-5.1)

∑

=

∂

∂

i i i

a

q

t

J

r

r

(2-1-5.2) where

r

_i

r

is the position of the carrier, with charge qi and effective mass

* i

m

, in an electric field E(

r

_i

r

,t) and applied magnetic field B. In the absence of any magnetic field there are no x or y components of the average current, because the system has

rotational symmetry about the z axis. Hence, a simple linear THz dipole is formed in

the z direction. The magnetic field rotates the dipole, producing x and y components

of similar magnitude to the z component.

The THz radiation emitted by the dipole is transmitted through the semiconductor surface, and the enhanced power recorded in the experiments is a

result of a dramatic increase in transmission when the dipole is rotated. The TE and TM fields inside the semiconductor are obtained from J(t), and the external fields

computed using the Fresnel transmission coefficients for the two polarizations :













∂

∂

+

∝

t

J

)

sin(

cos

2sin

t)

,

(

E

y i e i e e TE

θ

θ

θ

θ

θ

(2-1-5.3)









∂

∂

∂

∂

+

∝

i x i z i e i e e TM

cos

t

J

-sin

t

J

sin2

sin2

cos

4sin

t)

,

(

E

θ

θ

θ

θ

θ

θ

θ

(2-1-5.4)

where θi is the corresponding internal angle, given by Snell’s law, ne sinθe=ni sin θi ,

with ne , ni the external and internal refractive indices, respectively. At B=0T, there is

a strong suppression of the TM polarized bow-tie dipole pattern due to the index of semiconductor (GaAs: ni=3.5). It is less than 17° of the internal angle, so, only few

fraction of the emission close to the dipole axis (z-axis) can pass through the surface. For B=8T, the dipole is rotated by the magnetic field , thus, the magnetic field enhancement can be seen to be in reality a reduction of the suppression of the emission from the z polarized dipole. The theory predicts a TM power enhancement

of ~10-fold, and a total enhancement (TE+TM) of ~15-fold. The corresponding experimental enhancements are ~20 and 30 times.

Fig 2-4. Schematic diagram of the experimental geometry and coordinate system.[ 30]

2-2 Terahertz Detection: Electro-Optical Crystal and Free Space

Electro-Optic Sampling (FS-EOS)

The coherent detection of a THz-pulse beam with EO crystals is based on the linear Electro-Optical effect (Pockels effect). It is a phase-sensitive detection of electromagnetic (EM) radiation based on a birefringence in an EO crystal induced by the incident EM radiation. Under the external field, the refractive index of a certain material can be changed with the field intensity. In 1996, X. C. Zhang found that THz

pulse can be detected by electro-optic sampling methods [ 6]. The THz electric field would modulate the birefringence of the EO crystals and then change the polarization ellipticity of the optical probe beam passing through the crystal with the time delay. The refractive-index-ellipsoid modulation of the optical beam can then be analyzed to provide the information of the amplitude and phase of the applied electric field.

space electro-optic sampling rather than photoconductive antenna, because the need of focused beam is not necessary that decrease the potential for damaging the material. It is a non-resonant method and is suitable for broadband detection [ 26]. The THz beam is focused onto an EO crystal and modify the index ellipsoid transiently via Pockels effect. The linearly polarized laser probe beam propagate inside the crystal combined with the THz beam, and its phase is modulated by the refractive index change induced by the electric field of the THz pulse as shown in Fig 2-5. The signal difference is proportional to the phase change Γ induced by THz field, for EO crystal, the phase retardation induced in the EO crystal is given by the following equation change term

Γ can be expressed by 3 4 1 d n E

π

γ

λ

Γ = (2-2.1)

Where d is the thickness of the crystal, n is the refractive index of the crystal at the

wavelength of the near-infrared (NIR) probe beam, λ is the probe beam wavelength,

41

γ is the Electric-Optic coefficient, and E is the electric field of the THz wave. Thus,

we can obtain the entire THz time-domain waveform by measuring the signal difference via a balance detector as a function of delay time between the THz pulse and the probe pulse. The total frequency response of the EO sampling technique is given by the product of (2-2.1) and the following equation:

)

(

i2

1

-)]

(

exp[i2

)

T(

dt

t)

exp(i2

)

(

)

T(

)

G(

( ) 0

πωδ

ω

ω

πωδ

ω

πω

ω

δ

ω

ω

=

_∫

δ ω

⋅

=

d c ) n( -) ( n ) (ω g λ0 ω δ = _(2-2.2)

where ng(λ0) is the group refractive index at the wavelength of the probe beam, and

n(ω) is the refractive index at the frequency of the incident THz radiation.

T (ω) = 2/[nTHz(ω)+1], is the Fresnel transmission coefficient with the refractive index

of the EO crystal nTHz(ω) in the range of the target THz frequency. Therefore, a

thicker crystal produces a greater interaction length, but on the other hand it reduces the detection bandwidth due to group-velocity mismatch.

For the time being, there are many different materials for EO sampling such as ZnTe, GaP, GaSe and InP. In addition, ZnTe and GaP are the most commonly used material for EO detection from sub-THz to several tens of THz, because of their relative large EO coefficient and they are transparent at the wavelength of the incident THz radiation. Furthermore, for high chopping frequency, EO sampling has a high SNR as well as photoconductive sampling, but it is more sensitive to laser noise.

Fig 2-5 Schematic figure of Electro-optic sampling

EO Crystal Wollaston

Balance Detector

Chapter 3

Experimental Setups

In this chapter, we will briefly describe our femto-second laser system in section 3.1 and introduce the THz time-domain spectroscopy (THz-TDS) systems in section 3.2.

3-1 Introduction of Femtosecond Laser System

Our femtosecond later system is shown in Fig 3-1. We use the Ti:Sapphire laser as the seeding laser which is then directed into the Ti:Sapphire regenerative amplifier (Spitfire, Spectra-Physics) for amplification. The pump laser of Spectra Physics Tsunami laser is a 5W frequency doubled diode-pumped Nd:YLF laser (Millennia V, Spectra-Physics) with a wavelength λ=532 nm. The Ti:Sapphire laser provides an output trace of intense 35fs pulses with wavelengths ranging from 750nm to 850nm. The pulse repetition rate is ~82 MHz and the output power can up to 0.4W. The properties of these two laser systems are shown in Table 3-1. Properties of Tsunami laser and Ti:Sapphire regenerative amplifier..

The pump laser for the amplification process in Spitfire is Q-switched Nd:YLF laser which delivers a high power output of 20W at 527 nm. The Spitfire amplifies the seeding pulses by a million times from 6 nJ of energy per pulse to 2 mJ per pulse. The pulse repetition rate is 1 kHz and the output power is about 2W.

Fig 3-1. Femtosecond laser system includes Tsunami, Spitfire and two pump laser (Millennia V and Empower).

Tsunami laser Ti:Sapphire regenerative amplifier

Wavelength 800 nm 800nm Pulse width 35 fs 50fs Repetition rate 82 MHz 1kHz Energy 0.6 nJ 2mJ

Polarization Vertical, linear Horizontal, linear

Table 3-1. Properties of Tsunami laser and Ti:Sapphire regenerative amplifier. Ti:Sapphire regenerative amplifier

Ti:Sapphire laser for seed beam (Tsunami, Spectra-Physics) Millennia V Empower 35fs ,82 MHz 200mW,λ= 800nm 50fs ,1 KHz 2W, λ= 800nm 20W , λ= 527 nm

3-2 Electro-Optic THz System

The optical setup of the Electro-Optic THz system is shown in Fig 3-2. An amplified Ti:Sapphire laser providing 50fs, 800nm, 2mJ pulsed at repetition rate of 1kHz is used to drive this system. The linearly s-polarized incident beam is divided into two separated beams by a beam splitter. The transmitted beam from the beam splitter is used as pump beam to excite carrier in our samples and generate terahertz pulse. The other beam, reflected beam, is used as the probe beam to detect terahertz pulse signal. There is a half-wave plate in order to rotate the polarization of the pump beam to linearly p-polarized. Therefore, we could generate linearly p-polarized THz pulsed in a semiconductor surface emitter such as InAs at the incident angle of 70 degrees to the surface normal which is close to the Brewster angle. We use a teflon sheet which has a high transmissive characteristic in the terahertz region to block any reflected laser beam from the emitter.

The generated THz radiation is collimated and focused onto the sample by a pair of gold-coated off-axis parabolic mirrors with focal lengths of 3 and 6 inches respectively. The transmitted THz radiation is again collimated and focused onto a 2-mm-thick (110) ZnTe crystal for free space electro-optic sampling by another pair of parabolic mirrors with the same focal lengths with previous pair. A pellicle beam splitter which is transparent to the THz beam and has a reflectivity of 5% for 800nm

light is used to make the probe beam collinear with the THz beam in the ZnTe crystal. The time delay of the probe beam, which can be tuned by the motor stage, is guided to the ZnTe crystal and the terahertz pulse collinearly impinged on it. The linear polarization of the probe beam is perpendicular to the polarization of the THz beam and we adjust the azimuth angle of the ZnTe crystal to achieve the highest modulation efficiency.

Polarization of the probe beam modulated by the THz radiation is converted to ellipsoid polarization by a quarter-wave plate. The transmitted laser pulse with polarization changed by electro-optical effect is separated into two beams with orthogonal polarizations by Wollaston beam splitter. These two beams are coupled to a balanced detector with two silicon photodiodes which is used to detect the differential signal between two individual probe beams and the signal is proportional to the THz electric field. A motor stage within the probe beam path is used to scan the delay time between the probe pulse and the THz pulse imposing on the ZnTe crystal to obtain the entire THz time-domain waveform. Connecting signal from the balance detector to a lock-in amplifier, the signal can be easily analyzed by a computer.

In order to reduce the water vapor absorption and increase the signal to noise ratio, an optical chopper and a lock-in amplifier are used. Otherwise, the entire THz

terahertz pulse with its corresponding spectrum under humidity of 55% and 5% generated by this setup is shown in Fig 3-3 and Fig 3-4

Fig 3-2. Electro-Optic THz system

Emitter ZnTe λ_{/4 Plate} Wollaston Prism Pellicle Balanced Detector Motor λ_{/2 Plate} Chopper 50fs ,1 KHz ,2W λ= 800nm Nd Filter Nd Filter

0 2 4 6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 (a) T H z F iel d (a .u .) Delay Times(ps) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.00 0.02 0.04 0.06 0.08 0.10 (b) Frequency (Hz) T H z F ie ld (a .u .)

Fig 3-3. THz time-domain (a) waveform and (b) its corresponding spectrum generated by the electro-optic THz system using a-plane InN as emitter under the humidity of 55% 0 2 4 6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 (a) T H z F ie ld (a .u .) Delay Times(ps) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.00 0.02 0.04 0.06 0.08 0.10 (b) purged Frequency (Hz) T H z F ie ld (a .u .)

Fig 3-4. THz time-domain (a) waveform and (b) its corresponding spectrum generated by the electro-optic THz system using a-plane InN as emitter under the humidity of 5%

Chapter 4

Sample Properties

Indium nitride (InN) is an interesting and potentially important semiconductor material with superior electronic transport properties. Compared to all other group-III nitrides, InN possesses the lowest effective mass, the highest mobility, and the highest saturation velocity. Therefore, it is very suitable for high speed and high frequency electronic device applications.

The important properties of InN are lowest effective mass(high mobility), highest saturation speed in III-Nitrides, and the energy bandgap ~0.65eV founded in 2002. Furthermore, the energy gap to the next peak of InN is 2.8eV. This property could prevent the intervalley scatterings of the electrons.

Material Bandgap Distance to next peak InAs 0.35Ev 0.73eV

InSb 0.17eV 0.51eV Gasb 0.73eV 0.08eV InP 1.34eV 0.49eV GaAs 1.42eV 0.29eV

InN 0.69eV 2.8eV

Fig 4-1 Simplified view of the band edge structure of InN.

Properties GaN AlN InN

Effective electron mass 0.2m0 0.48m0 0.07m0

300k mobility (cm2/Vs) 1000 300 4000 Saturation speed (107cm/s) 2.9 1.7 4.2

Table 4-2. Properties of the III-Nitride compound semiconductors

Due to poor sample quality, about few years ago, no band-edge photoluminescence (PL) spectra were reported. In fact, the previous band gap value of ~1.9 eV was determined in the early studies mainly by interband absorption measurements performed on InN polycrystalline films deposited by sputtering techniques, in which oxygen incorporation is a severe problem. The epitaxial growth of InN films is very difficult because of the extremely low dissociation temperature (causing instability in stoichiometry at high temperatures) of InN and the lack of suitable matched substrates

E

g

in terms of lattice constants and thermal expansion coefficients. Recent progress in epitaxial growth techniques (most notably molecular-beam epitaxy (MBE) using highly active nitrogen plasma) [ 36][ 37][ 38][ 39][ 40] has led to significantly improved InN samples, which show PL as well as a clear absorption edge at ~0.7–0.9 eV[ 36][ 38][ 41].

In this thesis report, the two different samples we used are c-plane InN epilayer and a-plane InN epilayer. We describe the growth method and electric properties of these two samples in the next sections.

Fig 4-2. Crystal structure of InN

4-1 InN Film (c-plane InN)

For this work, one of the samples, the InN film(c-plane InN), was grown on the Si (111) substrate using a double-buffer technique by plasma-assisted molecular-beam epitaxy (PA-MBE). The InN epilayers were grown on Si(111) using the epitaxial AlN/β-Si3N4 double-buffer layer technique. Details of the growth procedure can be

because of the smaller lattice mismatch of ~8% for InN(0001)/Si(111) compared to ~25% for InN(0001)/Al2O3(0001).

This c-plane InN film was not intentionally doped, the typically display residual n-type conductivity. The thickness of the c-plane InN film is about 1.05µm. By room-temperature Hall effect measurement, the free electron concentration and mobility which have been determined are 3.1×1018 cm-3 and 1036 cm2/Vs, respectively.

Fig 4-3 The SEM pictures of c-plane InN film. [This picture is taken from the Prof. S. Gwo’s group, The Department of Physics, National Tsing Hua University.]

4-2 Nonpolar InN Film (a-plane InN)

From the letter published by Hai Lu.[ 42], the comparison of the electrical properties of a-plane and c-plane InN films were reported [ 42]. Fig 4-4 shows the RT

is found that under current growth conditions, increasing film thickness does not lead to an apparent improvement on electrical properties of the a-plane InN. In the thickness

range between 0.5 and 3 mm, its Hall mobility and carrier concentration fluctuate around 250 cm2/Vs and 6×1018 cm-3, respectively. This behavior is quite different from that of c-plane InN. As shown in the inset, with increasing film thickness, the Hall

mobility of c-plane InN will continuously increase while carrier concentration

decreases.

Fig 4-4. RT Hall mobility and carrier concentration of a-plane InN films as a

function of film thickness. The inset shows the corresponding data of the c-plane

Fig 4-5. The SEM pictures of a-plane InN film. [This picture is taken from the Prof. S. Gwo’s group, The Department of Physics, National Tsing Hua University.]

Chapter 5

Experimental Results and Discussion

In this chapter, we first discuss the results of a significant enhancement in terahertz emission form the indium nitride (InN) films grown along the a-axis (a-plane InN), relative to the InN films grown along the c-axis. Afterward we discuss the azimuthal- and polarization angle dependence of emitted terahertz wave.

For this work, THz emission from InN was measured by electro-optic THz system describe in chapter 3. The photo-exciting beam is collimated on the samples with a spot size of ~ 2 mm diameter at the angle of incidence of 70˚, which is near the Brewster angle. The emitted THz pulses were detected by free-space electro-optic sampling in a 2-mm-thick ZnTe crystal as a function of delay time with respect to the optical pump pulse.

5-1 Terahertz Emission from InN Surface

In the past years, due to the narrow directive bandgap and large energy gap to the next peak, InN becomes a potential emitter for THz emission. There have been several reports on terahertz emission from InN films[ 14][ 15][ 16]. From our group past research, the terahertz emission from InN film grown by molecular-beam epitaxy on Si(111) substrates has been investigated[ 27].

its contribution to terahertz generation is negligibly small, therefore, the main mechanism emitted the terahertz radiation for c-plane InN film is supposed to the Photo-Dember effect introduced in the section 2-1-3. From the Eq (2-1-3.1):

0 0 ( ) 1 ( 1) ln(1 ) 1 B e h D k T b T b n V e b n b p − + ∆ = + + + ,b=

µ µ

e / p (2-1-3.1)

This equation tell us that the Photo-Dember effect is enhanced by larger electron mobility (

µ

_e ∝b), and higher electron excess energy (∝Te). In other words, the

narrow-bandgap semiconductors have the preferred conditions necessary to create a large photo-Dember field, that is, the very large electron mobility and large excess carrier energy. Moreover, the photo-Dember field (VD/d, d: absorption depth) in

narrow-bandgap semiconductors is further enhanced by the small absorption depth. On the other hand, the surface-depletion field is expected to be small because of the small bandgap energy, in contrast to the wide bandgap semiconductors.

Because the electron accumulation layer at the surface of n-type InAs and c-plane InN is very thin, its contribution to terahertz generation is negligibly small. It is concluded that the terahertz emission mechanism of both materials is the photo-Dember effect, however, the terahertz radiation emitted from c-plane InN films is typically one order of magnitude weaker than that from InAs.(The emission amplitude from n-type InAs is larger than c-plane InN film at least 30 times.) Through

the explanation of the mechanism for photo-Dember effect, we have known that this enormous difference in terahertz radiation amplitude ought to result from the dissimilarity of electron mobility and direct bandgap with these semiconductors: The electron mobility(µ_e) of n-type InAs is about 30000 cm2/Vs, but that of c-plane is

only 1036 cm2/Vs. Furthermore, from the pump source of our experiments with λ= 800nm(photon energy =1.55eV), the excess energy(ΔΕ) of these samples are

1.19 eV for InAs and 0.76 eV for c-plane InN, respectively.

In the other hand, we find that the THz emission from the InN film grown along the a-axis (a-plane InN) is stronger than that from the InN film grown along the c-axis (c-plane InN) about one order (Fig 5-1). The photo-excited carriers generated close to the surface of semiconductors can be accelerated by an appropriate electric field and the resultant transient electric dipole can lead to generation of terahertz pulses. It is well known that the contribution of electron accumulation field to terahertz emission would be very small for both c- and a-plane InN due to the narrow thickness of the electron accumulation layer. For the photo-Dember effect, which is proportional to electron mobility and is independent to the crystal growth direction, its contribution to the radiation from a-plane InN ( µ = 298 cm2 /V) is even smaller than that from c-plane InN(µ = 1036 cm2 /V). Therefore, the drastic power enhancement observed for a-plane InN cannot be explained by either the electron accumulation field or the photo-Dember

fields.

0

2

4

6

8

10

12

14

16

-0.5

0.0

0.5

1.0

1.5

7.6 7.8 8.0 8.2 0.1 1 c-plane a-plane A m p li tu d e (a .u . ) Delay Times(ps)

A

m

p

li

tu

d

e(

a

.u

.)

Delay Times(ps)

c-plane

a-plane

Fig 5-1 The amplitude of the terahertz emission from a-plane InN film (red square) compare to that from c-plane InN film(black circle). The excitation is 0.24 mJ/cm2. Inset: comparison between a-plane InN , c-plane InN measure under identical experimental condition.

From the past investigations, the most familiar method to improve the THz radiation is using an external magnetic field[ 28][ 29]. In past years, several groups have observed a large magnetic field induced enhancement in surface–field THz emission from a variety of semiconducting materials (GaAs, InAs, InP, and InSb)[ 44][ 45][ 46]. In the paper published by M. B. Johnston et. al.[ 30], they build up a Monte Carlo dynamics model to explain the phenomenon of magnetic-field

is shown on Fig 5-2. Because of the rotational symmetry about the z axis, there are no

x or y components of the average current in the absence of any magnetic field. Hence,

a simple linear THz dipole is formed in the z direction like Fig 5-3(a). The magnetic field rotates the dipole, producing x and y components of similar magnitude to the z component (see Fig 5-3(b)).

The THz radiation emitted by the dipole is transmitted through the semiconductor surface, and the enhanced power recorded in the experiments is a result of a dramatic increase in transmission when the dipole is rotated. Using the Fresnel transmission coefficients for the two polarizations, the external fields are:













∂

∂

+

∝

t

J

)

sin(

cos

2sin

t)

,

(

E

y i e i e e TE

θ

θ

θ

θ

θ

(2-1-5.3)









∂

∂

∂

∂

+

∝

i x i z i e i e e TM

cos

t

J

-sin

t

J

sin2

sin2

cos

4sin

t)

,

(

E

θ

θ

θ

θ

θ

θ

θ

(2-1-5.4)

where θi is the corresponding internal angle, given by Snell’s law, ne sinθe=ni sin θi ,

with ne , ni the external and internal refractive indices. At B=0T, there is a strong

suppression of the TM polarized bow-tie dipole pattern due to the index of semiconductor, for example, GaAs (ni=3.5), it is less than 17° of the internal angle, so,

only few fraction of the emission close to the dipole axis (z-axis) can pass through the surface. For B=8T, the dipole is rotated by the magnetic field , thus, the magnetic

field enhancement can be seen to be in reality a reduction of the suppression of the emission from the z polarized dipole. This theory predicts the corresponding experimental enhancements are ~20 and 30 times. Therefore, we could use this similar mechanism for improving light extraction efficiency to explain the THz enhancement on a-plane InN.

Fig 5-2 Schematic diagram of the experimental geometry and coordinate system.[ 30]

Fig 5-3 Calculated polar radiation patterns for GaAs at (a) 0 and (b) 8 T. In each part the horizontal line is a schematic representation of the surface of the semiconductor. The bow-tie pattern below the surface line is calculated for radiation within the semiconductor, whereas the pattern above the surface shows the radiation emitted into free-space. The vector B indicates the magnetic-field direction. [ 30]

In the c-plane InN film, the stacking series of its wurtzite structure is ABABAB…along the c-axis direction so that there are either In- or N-terminated polar surfaces in the surface layers of c-plane InN. This structure results in a electric field generated by these In-N layers directly perpendicular to the surface. For this reason, the out-of-surface radiation would be significantly limited by the geometrical structure which be mentioned before. There would be only few percentages of the radiated terahertz power from this dipole able to escape the surface due to the small emission cone derived from the total reflection within a material of high refractive index. From the other point of view, the layers of a-plane InN have the same amount of In and N atoms in a plane and the in-plane In-N dimers form an in-plane intrinsic electric field perpendicular to the a-axis(see Fig 5-4). Due to the terahertz dipole formed in the favorable in-plane direction, we could expect that the a-plane InN could create the enhancement of terahertz radiation as much as the method with external magnetic field. In spite of the same order of the THz power enhancement, with the magnetic-field-assisted method, it needs to use an awkward experimental setup. In comparison, the power enhancement from a-plane InN just depend on the growth direction so that it can be a general phenomenon for semiconductors grown in the nonpolar direction.

Fig 5-4 Ball-and-stick model of the a-plane surface. Large balls are In, small balls are N. [ 47]

We measured the reflectivity of these samples and the result is shown in Fig 5-5. The reflectivity of a-plane InN is bigger than that of c-plane one a little bit. Furthermore, pump fluence dependence in Fig 5-6 shows that when the pump fluence is increased 10 times, the amplitude of THz emission from a-plane InN film is enhanced by 2.5 times, but that of c-plane InN film is by1.8 times.

200 400 600 800 1000 1200 1400 0.10 0.15 0.20 0.25 0.30 0.35 R ef le ct iv it y Pump Fluence (µµµµJ/cm2) c-plane a-plane

Fig 5-5 Optical reflectivities in InN-epilayer and nonpolar InN as a function of excitation energy. Optical absorption in InN film is about 80%, while that in nonpolar InN is about 76%.

In In