國
立
交
通
大
學
光電工程研究所
碩
士
論
文
氧離子佈植與低溫成長砷化鎵光導天線在連續
波與脈衝波激發下產生兆赫波的研究
A comparative study of continuous-wave and pulsed terahertz
radiation generated by oxygen ion-implanted and
low-temperature-grown GaAs THz photoconductive antennas
研 究 生：楊孟桓
指導教授：潘犀靈 教授
鄒志偉 教授
氧離子佈植與低溫成長砷化鎵光導天線在連續波與脈衝波激發下
產生兆赫波的研究
A comparative study of continuous-wave and pulsed terahertz
radiation generated by oxygen ion-implanted and
low-temperature-grown GaAs THz photoconductive antennas
研 究 生：楊孟桓 Student：Mong-Huan Yang
指導教授： 潘犀靈 教授 Advisors：Prof. Ci-Ling Pan
鄒志偉 教授 Prof. Chi-Wai Chow
國 立 交 通 大 學
光電工程研究所
碩 士 論 文
A Thesis
Submitted to Institute of Electro-Optical Engineering College of Electrical Engineering and Computer Science
National Chiao Tung University In Partial Fulfillment of the Requirements
For the Degree of Master of Engineering
In
Electro-Optical Engineering July 2008
Hsinchu, Taiwan, Republic of China
氧離子佈植與低溫成長砷化鎵光導天線在連續
波與脈衝波激發下產生兆赫波的研究
研究生：楊孟桓 指導教授：潘犀靈、鄒志偉 教授
國立交通大學光電工程研究所
摘 要
本 論 文 討 論 在 多 重 氧 離 子 佈 植 砷 化 鎵 ( 13 22.5 10 ions/cm× (500 keV &
800keV), 13 2 4 10 ions/cm× (1200keV) 薄膜材料及低溫成長之砷化鎵在脈衝波與連續波 的激發下比較其兆赫波的特性。 多重氧離子佈值砷化鎵偶極天線在脈衝雷射與連續波雷射激發下都具有較高的兆 赫波輻射功率，以 180mW 連續波雷射激發時多重氧離子佈植砷化鎵天線輻射功率 (2.27μW)大約比同結構的低溫成長砷化鎵（1.27μW）高。以 30mW 的脈衝光雷射激發時， 多重氧離子佈植砷化鎵天線輻射功率(5.2mW)大約比同樣結構的低溫成長砷化鎵天線產 生（3.6mW）高。另外多重氧離子佈值砷化鎵與低溫成長砷化鎵偶極天線在連續波與脈 衝波激發下測量其頻寬皆可達 1THz。然而，低溫成長砷化鎵光導天線在連續波的激發下 產生飽和的現象，多重氧離子佈值砷化鎵光導天線仍然沒有，因此多重氧離子佈值砷化 鎵光導天線具有較好的兆赫波輸出功率。
A comparative study of continuous-wave and
pulsed terahertz radiation generated by oxygen
ion-implanted and low-temperature-grown
GaAs THz photoconductive antennas
Student: Mong-Huan Yang Advisors: Prof. Ci-Ling Pan
Prof. Chi-Wai Chow
Institute of Electro-Optical Engineering
College of Electrical Engineering and Computer Science
National Chiao Tung University
Abstract
THz wave was generated from dipole antenna-type devices made by using oxygen-ion implanted GaAs (GaAs:O) and low-temperature-grown GaAs (LT-GaAs). We compared the emission properties of LT-GaAs photoconductive (PC) antennas with GaAs:O fabricated condition (2.5 10 ions/cm× 13 2 (500keV & 800keV ), 13 2
4 10 ions/cm× (1200keV ) in the pulse and CW mode. The absolute power of THz wave was also measured by a bolometer for comparison of the relative radiation power.
Compared GaAs:O with LT-GaAs at same structure of PC antennas. The material GaAs:O can generate higher THz power than LT-GaAs both in pulsed mode and CW mode. The THz power of GaAs:O (2.27μW) is higher than that of LT-GaAs(1.27μW) in CW mode, and in pulse mode, the THz peak amplitude of GaAs:O (5.2mW) is higher than that of LT-GaAs (3.6mW). The bandwidth of GaAs:O and LT-GaAs are measured about 1THz both under pulse (TDS) and CW (photomixing) pumping. However, the THz power of LT-GaAs is saturated on CW mode, while GaAs:O doesn’t. The result shows that GaAs:O is a proper THz emitter compare with LT-GaAs which is hardly to reproduce.
Acknowledgement
致謝
本論文得以順利的完成，首先要感謝指導老師潘犀靈教授及鄒志偉教授的悉心教 導，提供良好的研究資源和實驗環境，讓我可以順利完成實驗。在這兩年研究生活中， 我真的很感謝黎宇泰學長在實驗上的協助及理論的指導，使我獲益良多。也很感謝香港 中文大學陳錦泰教授實驗室的陳克堅學長幫忙製作的光導天線和提供許多寶貴的意見 及經驗。此外，也謝謝實驗室的王怡超、陳晉瑋學長們，及同學們：介暐、松輝、育賢 因為有你們的陪伴，我的研究生生活才如此多采多姿，可以在枯燥的研究生活中帶來一 些歡樂和喜悅，還有也謝謝學弟們：俞良、晏徵、承山、維駿、為弘幫忙處理實驗室的 事務及在實驗器材的協助，也因為有你們的鼓勵及幫助，我才能順利畢業。 最後，我要感謝我最親愛的家人：爸爸、媽媽和妹妹，在我求學過程中，一路上 給予我最大的關懷與支持；陪伴我這幾年一路走來，給我的支持及鼓勵，讓我無後顧 之憂，順利完成碩士學位！謝謝。 于新竹 交大 2008/08/22Table of Contents
2008/08/22
Table of Contents
Abstract
...i.
Acknowledgements
...iii.
Table of Contents
...iv.
List of Figures
...vi.
List of Tables
...vii.
Chapter 1 Introduction
...1.
1.1 Background
...1.
1.2 Method of generating THz radiation
...2.
1.2-1 Optical rectification
...2.
1.2-2 Photoconductive switch
...4.
1.2-3 Down-conversion from optical regime
...5.
1.3 Method of detecting THz radiation
...5.
1.3-1 Liquid-helium cooled bolometer
...6.
1.3-2 Photoconductive antenna
...6.
1.3-3 Electro-Optical sampling
...6.
1.4 Material of Photoconductor antenna
...7.
1.4-1 Material of Low-temperature (LT) grown GaAs
...7.
1.4-2 Material of ion-implanted GaAs
...8.
1.5 Objective
...9.
1.5-1 Motive
...9.
1.5-2 Organization of this thesis
...9.
Chapter 2 Basic Theory
. ...11.
2.1
The theory of generated THz radiation
...11.
2.1-1 Current-surge model
...12.
2.1-2 Drude-Lorentz model
...17.
2.2 The properties of the material
...24.
2.2-1 Choosing and analysis the material
...24.
2.2-2 Dark current
...26.
2.2-3 Photocurrent
...26.
Chapter 3 Experimental Method and Setup
...30.
3.1 Sample preparation
...30.
3.1-1 Preparation of the PC antenna
...31.
3.1-2 The setup of PC antenna
...32.
3.2 Dual wavelength laser diode system
...34.
3.2-1 Laser diode characteristics
...34.
3.2-2 Dual wavelength system
...40.
3.3 Experimental setup of generation and detection of THz
...43.
3.3-1 Experiment setup
...43.
3.3-2 The calibration of the Si bolometer
...44.
3.3-3 Semiconductor laser amplifier (MOPA)
...45.
3.4 The time & frequency domain of THz pulse
...46.
3.4-1 Terahertz Time-Domain Spectroscopy (THz-TDS)
46.
Chapter 4 Result and Analysis
...48.
4.1 The result of pulse measurement
...48.
4.1-1 Current-voltage (I-V) curve
...48.
4.1-2 THz power-voltage curve
...50.
4.1-3 THz-TDS measurement
...51.
4.1-4 Analysis and Discussion
...54.
4.2 The result of CW measurement
...57.
4.2-1 Current-voltage (I-V) curve
...57.
4.2-2 THz power-voltage curve
...58.
4.2-3 Analysis and Discussion
...59.
Chapter 5 Conclusion
...65.
5.1 Summary
...65.
5.2 Future work
...66.
List of Figures
1.1-1 Electromagnetic spectrum
...1.
1.2-1
Optical rectification
...3.
1.2-2
Photoconductive switch
...4.
2.1-1
Energy band structure of GaAs
...11.
2.1-2
The simulation of two curves with slightly different frequency
.17.
2.1-3
The plot of Sinc function
...19.
2.1-4
The beating intensity with angular frequency
Ω...20.
3.1-1
Schematic diagram of the PC antenna
...26.
3.1-2
The measurement of carrier life time with both materials
...33.
3.1-3
The measurement of conductivity of GaAs:O and LT-GaAs 34.
3.1-4
Schematic of focused the pump laser on the gap of dipole
a n t e n n a s
. . .35.
3.2-1
L-I curve of laser diode 1 (LD1)
...36.
3.2-2
L-I curve of laser diode 2 (LD2)
...36.
3.2-3
Linewidth of laser diode 1 measured by Fabry-Perot
...37.
3.2-4
Linewidth of laser diode 2 measured by Fabry-Perot
...37.
3.2-5
Temperature control at current 190mA for LD1
...38.
3.2-6
Temperature control at current 190mA for LD2
...38.
3.2-7
Current control at 23
℃for LD1
...39.
3.2-8
Current control at 23
℃for LD2
...39.
3.2-9
Frequency fluctuation of LD1 in 20 minutes
...40.
3.2-10 Frequency fluctuation of LD2 in 20 minutes
...40.
3.2-11 schematic of dual-wavelength system
...42.
3.2-12 The spectrum of 2 laser diodes system
...42.
3.2-13 The beating signal of the PC antenna
...43.
3.3-1
Schematic of experimental setup for measured the electric
characteristics of PC antenna
...44.
3.3-2
Frequency dependence of amplifier gain
...46.
3.4-1
Terahertz Time-Domain Spectroscopy system
...47.
4.1
The structure of PC antenna fabricated on GaAs:O and LT-GaAs
material
...48.
4.1-1
I-V curve of oxygen ion-implant GaAs antennas and Low grown
temperature GaAs antennas with the same antenna structure
source under pulse laser pumping
...49.
4.1-2
(a) Photocurrent-bias (b)THz power-bias curve of GaAs:O and
LT-GaAs antenna with the same antenna structure
...51.
4.1-3
THz time domain waveform of (a) GaAs:O and (b) LT-GaAs at
constant pump power 30mW
...52.
4.1-4
THz spectrum of (a) GaAs:O and (b) LT-GaAs at constant pump
power 30mW
...53.
4.1-5
(a) Time domain waveform (b) Spectrum for both materials
....54.
4.1-6
(a) The amplitude-pump power curve at bias voltage 80V (b)
The THz power-electric field curve at 30mW
...55.
4.1-7
(a) GaAs:O (c) LT-GaAs time domain waveform under different
bias voltage. The inset figure is relative shift (b) GaAs:O (d)
LT-GaAs peak shift- bias voltage curve
...56.
4.2-1
I-V curve of GaAs:O antennas and LT-GaAs antennas with the
same antenna structure source under CW laser pumping
....58.
4.2-2
photocurrent-bias voltage curve (b) THz power-bias voltage
curve of GaAs:O and LT-GaAs fabricated with the same dipole
a n t e n n a
. . .59.
4.2-3
(a) photocurrent-bias voltage curve of both materials (b) the
photocurrent ratio of GaAs:O divide to LT-GaAs
...60.
4.2-4
(a) Different dosage density of GaAs:N and LT-GaAs[48](c)
GaAs:O and LT-GaAs DC photocurrent-electric field curve (b)
Different dosage density of GaAs:N and LT-GaAs (d) GaAs:O
and LT-GaAs THz power-DC photocurrent curve
...61.
4.2-5
CW THz power-optical pump power for both materials
...62.
4.2-6
(a) photocurrent-electric field curve (b) THz power-electric field
curve
...63.
4.2-7
THz spectrum of both materials measured by CW heterodyne
system
...64.
List of Tables
Chapter 1 Introduction
1.1 Background
Terahertz range (wavelengths between 1000μm~300μm or frequencies between 300GHz~10THz) bridges the gap between microwave (mm-wave region) and infra-red frequencies, being until recently one of the least explored regions of the electromagnetic spectrum, which the frequency is near one trillion hertz (10 Hz) 12
as shown in Figure 1.1-1. Although terahertz radiation has already been researched in many fields in the past twenty years, wireless transmissions and computer clock speed are now at frequencies far below 1THz. THz radiation has been primarily developed for physicists and astronomers [01]. Based on heterodyne and Fourier transform techniques, these methods offered astronomers, chemists and space scientists a tool for investigating the thermal emission lines of
a wide diversity of light-weight molecules. The imaging technology and spectroscopic technology are studied in the Terahertz range [02]. Besides, it can be
Figure 1.1-1 Electromagnetic spectrum.
applied not only to medical but also materials inspection. There is a great potential for its application in many other scientific fields as well. In order to generate THz radiation, femto-second pulse laser is the usual optical source, such as Ti-sapphire laser, which is expensive and bulky. Using semiconductor laser diode can also generate the continuous wave THz radiation. Coherent, tunable continuous-wave (CW) THz sources are strongly needed in many applications such as high-resolution spectroscopy, heterodyne receiver systems, local area networks and so on.[03]
1.2 Method of generating THz radiation
Because of the resent development of pico-second and femto-second laser system, there are various ways to generate the ultrashort pulsed millimeter and submillimeter radiation [06], such as optical rectification and resonant THz radiation in photoconductor generated by a pulse laser or optical heterodyne downconversion occurs by illuminating the photomixer with two mode CW laser beam.
1.2-1 Optical rectification
Using second ordered nonlinear effect of nonlinear crystal is one of methods to generation THz. In this electro-optic medium, the low frequency electric field is produced under intense optical illumination. The nonlinear optical process was first suggested by Chung. [05] Optical rectification in a non-absorbing medium is
a process in which a laser pulse creates a time-dependent polarization that radiates an electric field which can be written as
2 2 P E (t) t ∂ ∝ ∂ JK JK
in the far field, where the polarization P follows the pulse intensity envelope. It is called rectification because the rapid oscillations of the electric field of the pulse laser are “rectified” and only the envelope of the oscillations remains. The schematic of the THz generation using optical rectification is shown in Figure 1.2-1. Since the medium is nonabsorbing, the polarization instantaneously follows the pulse envelope, and there is practically no limit on the speed at which the polarization can be switched on and off. The incident of polarization wave radiates a transient electric field which consists of one or one-and-a-half oscillation and therefore has a broadband THz frequency bandwidth. Bandwidth as large as 30 THz has been obtained using this generation mechanism.
1.2-2 Photoconductive switch
Biased PC switch can be used to generate THz radiation. It is generally based on the “current surge model” [06] which will be discussed in detail in the
Nonlinear crystal
Laser pulse
THz radiation
next chapter. According to this model, as the energy of the input laser is higher than the energy of bandgap of photoconductor, then electron-hole pairs are excited and the mechanism to generated THz radiation can occur. Semiconductor such as GaAs (Eg=1.43eV), with the surface bands of a semiconductor lie within the energy produced by input photon and thus Fermi-level pinning occurs, leading to band bending and formation of a depletion region.
In briefly, the electromagnetic field of THz radiation is generated from a transient current which is generated on the surface of the photoconductor. Carriers are generated by the pulse laser instantaneously. In order to accelerate the carriers we add bias across the PC antenna. Then, the resultant transient current, or called current surge, produces an electric field on the surface of the photoconductor. This surface electric field is regarded as the source of the THz radiation. Figure 1.2-2 shows the setup for this method.
1.2-3 Down-conversion from optical regime
Recently, CW Terahertz wave generation techniques have significant
GaAs wafer with antenna structure
Laser pulse
bias
THz radiation
developed. Using offset-frequency-locked CW lasers focused onto a small area of an appropriate photoconductor can generate the carriers. The laser induced photocarriers and shorted the gap producing a photocurrent which is modulated at the laser difference frequency. This current is coupled to an RF circuit or antenna that couples out or radiates the terahertz energy. The resulting power is narrow-band, phase lockable, and readily tuned over the full terahertz band by slightly shifting the optical frequency of one of the two lasers.
Different methods can be used to generation the CW THz wave, such as using one laser to generate two wavelengths by photomixing.[07-09], or using two independent lasers [10-11]. The advantages of using one laser include good spatial mode matching and high common-mode rejection ratio.
1.3 Method of detecting THz radiation
THz radiation is usually detected by liquid-helium cooled bolometer. There are different ways which are developed in recent years to detect THz radiation, such as photoconductive antenna and electro-optic sampling (EO sampling).
1.3-1 Liquid-helium cooled bolometer
Far-infrared (FIR), submillimeter wave and millimeter wave can be detected by Bolometer. A hot electron bolometer is a device, which absorbs the incident radiation to change the electron’s temperature. Its resistance will respond for it
correspondingly. A traditional bolometer consists of a heat-sensitive detection element mounted inside a heat sink and physically supported by a thermally conductive physical supporter. The most common systems are helium-cooled Si, Ge and InSb bolometer. It can measure the radiation power lower in nanowatt region, but it losses the information of phase and frequency. Because of this, using bolometer to detect the power of THz radiation usually accompanies Martin-Puplett interferometer [12]. By using combined system, we can obtain the interferogram of THz radiation [13].
1.3-2 Photoconductive antenna
Using PC antenna as the detector is one of detecting THz radiation ways [14]. When the incident THz radiation illuminates the PC antenna, it induces transient current and then accelerate electron by probe beam. There are two factors determine the spectral bandwidth in this detector. One of them is the photocurrent response (i.e. carrier lifetime) and the other one is the frequency dependence of the antenna structure [15-16]. In general, the low frequency cutoff of the detectors results from the collection efficiency of the dipole, while the upper frequency limit is determined by the photocarrier response. The photocurrent response is the convolution of the optical pulse duration and the impulse current of the photoswitch across the photoconductive antenna on pulse mode.
There are two advantages of Electro-Optical (EO) sampling, one is broad bandwidth spectrum and the other is easy to implement. Recently, technique of EO sampling has become an alternative to photoconductive (PC) detection [17]. The Zinc-Blende crystal was used to measure THz radiation based on the Pockels effect [17]. When we vary the temporal delay between pump and probe beam, the synchronous probe beam will probe the transient change of refractive index result from THz radiation changing the refractive index. There is a trade-off in this method, thick crystal will introduce longer interaction length but reduce the frequency response.
1.4 Material of Photoconductor antenna
1.4-1 Material of Low-temperature (LT) grown GaAs
We often use LT-GaAs as the PC substrate. We use it for generation and detection of THz radiation because of the high resistivity (107
cm
Ω ) [25] and good mobility (100-300 2/
cm Vs ) [19-20], and short carrier lifetime (<1ps) [21-22].
But LT-GaAs has some drawback. One of them is the consistency of reproducing the sample. The quality of the material depends critically on both the growth temperature and the post growth thermal annealing conditions. An alternative material was reported to be promising as the substrate material of PC antennas, which is the arsenic ion-implanted GaAs [23]. These materials exhibit good structural and electrical properties and show ultrafast optoelectronic response. It is
possible to improve the carrier mobility of these ion-bombarded materials using post implantation thermal annealing process. Good control over the overall fabrication process allows studies of the influence of parameters such as the ion-implantation dose, the ion energy, and the thermal annealing conditions on the PC antenna characteristics.
1.4-2 Material of ion-implanted GaAs
Many studies show that the arsenic (As) ion implanted GaAs PC antennas has better THz performance than those made on semi-insulating (SI) GaAs substrates [24-27]. It has been demonstrated that the terahertz emission property of arsenic ion-implanted GaAs has almost the same characteristics with the LT-GaAs. Such enhancement results from ultrafast carrier recombination associated with the presence of the implantation-induced defects. On the other hand, several groups have shown good characteristics of THz emitters when these devices are photoexcited near the anode with the use of PC antennas made on GaAs substrates grown by the Czochralski method. Although defects seem to play a crucial role in the characteristics of THz PC antenna emitters, there are very few studies that investigate the role of defects on these characteristics. Ion-implantation using other types of ions has already been used successfully to reduce the carrier lifetime in GaAs. For example, subpico-second lifetime can be obtained in GaAs:H GaAs:N and GaAs:O [28-33].
1.5 Objective
1.5-1 Motive
In this thesis, we used two different pumping source (pulse and CW) to measure the characteristics of the terahertz emitter fabricated on the substrates of GaAs:O and LT-GaAs. We compared the emission properties of GaAs:O PC antennas with LT-GaAs under different bias and pump power conditions. We also compare their spectra under different conditions.
1.5-2 Organization of this thesis
There are five chapters in the thesis, consisting of introduction (Ch.1), basic theory (Ch.2), experiment setup and method (Ch.3) result and analysis (Ch.4) and conclusion (Ch.5).
In chapter 1, we introduce the background of THz radiation and describe the motivation of the researching work. The basic theories about THz radiation generated from dipole antenna are mentioned in chapter 2 both on pulse and CW mode. The experiment setup and sample preparation are described in chapter 3. And in chapter 4, the results are analyzed and discussed. Finally, we will give a summary of the research work and list some future work in chapter 5.
Chapter 2 Basic Theory
In this chapter, we will explain the basic theory of using PC antenna to generate and detect THz radiation. And then, we will introduce the properties of material which is the substrates of the PC antennas.
2.1 The theory of generated THz radiation
When the small PC gap is irradiated by a femtosecond laser pulse with energy excess above the band gap of the semiconductor, the carriers will be created in the conduction band and valence band. The energy band structure of GaAs has is shown in Figural 2.1-1. The instantaneous concentration of the electron and hole pairs is high enough to “short-out” the gap. Then, by biasing the
Figure 2.1-1 Energy band structure of GaAs
electrode of the PC antenna; the carriers generated by the incident wave can be accelerated. This process can be found and expressed in the current-surge model.
2.1-1 Current-surge model
The first step, there are some time-average parameters which we need to define the THz radiation [29].
Charge density⇒ρ(x,y,z,t) Current density⇒J(x,y,z,t)K
Electric field intensity⇒E(x,y,z,t)JK Magnetic flux density⇒B(x,y,z,t)JK
Then, it is necessary to construct Maxwell’s equation for current-surge model. According to Maxwell’s equation [28]:
B E=-t ∂ ∇× ∂ JK JK (Faraday’s Law) (2.1-1) E=ρ ε ∇ •JK (Gauss Law) (2.1-2) D H=J+ t ∂ ∇× ∂ JK JK K (Ampere’s Law) (2.1-3) B=0 ∇ •JK (2.1-4) And we know B=JK ∇×AJK (2.1-5) From Equation (2.1-1) and (2.1-5), we can obtain:
(
)
B A A E=- =- A = - E+ =0 t t t t ⎛ ⎞ ⎛ ⎞ ∂ ∂ ⎜ ∂ ⎟⎟ ⎜ ∂ ⎟⎟ ∇× ∇× ∇×⎜⎜ ⎟⎟ ⇒ ∇×⎜⎜ ⎟⎟ ⎜ ⎜ ∂ ∂ ⎝ ∂ ⎠ ⎝ ∂ ⎠ JK JK JK JK JK JK (2.1-6)Equation (2.1-6). A - V=E+ t ∂ ∇ ∂ JK JK A E=- V-t ∂ ⇒ ∇ ∂ JK JK (2.1-7)
From Equation (2.1-3)、(2.1-5) and H=B
μ JK JK 、D= EJK εJK,we obtain B E =J+ t ε μ ∇× ∂ ∂ JK JK K
(
A = J+)
E t μ⎛⎜ ε∂ ⎟⎞⎟ ⇒ ∇× ∇× ⎜⎜ ⎟⎟ ⎜ ∂ ⎝ ⎠ JK JK K (2.1-8)Substitute Equation (2.1-7) into Equation (2.1-8)
(
)
(
)
2 2 2 A A = J+ - V-t t V A A - A= J- -t t μ ε μ με με ⎡ ∂⎛⎜ ∂ ⎟⎞⎤ ⎢ ⎥⎟ ∇× ∇× ⎢ ⎜⎜ ∇ ⎟⎟⎥ ⎜ ∂ ⎝ ∂ ⎠ ⎢ ⎥ ⎣ ⎦ ∂ ∂ ∇ ∇• ∇ ∇ ∂ ∂ JK JK K JK JK JK K 2 2 2 A V A- =- J+ A+ t t με∂ μ ⎛⎜ με∂ ⎟⎞ ⇒ ∇ ∂ ∇ ∇•⎜⎜⎝ ∂ ⎟⎟⎠ JK JK K JK (2.1-9) From Equation (2.1-2) and D= EJK εJK( )
E =- V+ A = t ε ⎡⎢ε⎛⎜ ∂ ⎟⎞⎤⎥⎟ ρ ∇• ∇•⎢ ⎜⎜∇ ⎟⎟⎥ ⎜ ∂ ⎝ ⎠ ⎢ ⎥ ⎣ ⎦ JK JK(
)
2V+ A =-t ρ ε ∂ ⇒ ∇ ∇• ∂ JK (2.1-10)Due to Lorentz gauge assumption A+ V=0 t εμ ∂ ∇• ∂ JK , Equation (2.1-9) becomes as 2 2 2 A A- =- J t με∂ μ ∇ ∂ JK JK K (2.1-11)
And, Equation (2.1-10) can be written as
2 2 2 V V- =-t ρ με ε ∂ ∇ ∂ (2.1-12) Equation (2.1-11) and (2.1-12) are the two inhomogeneous wave equations written in terms of AJKand V. The two wave equations are used to determine a functional and time dependent of the radiated electric field in the far field.
From Equation (2.1-3), the continuity equation of the free carriers is obtained.
(
H =)
J+ D = J+ =0 t t ρ ⎛ ∂ ⎞⎟ ∂ ⎜ ⎟ ∇• ∇× ∇•⎜⎜ ⎟⎟ ∇• ⎜ ∂ ∂ ⎝ ⎠ JK JK K K (2.1-13)In the fact, the current density of the photoconductor antenna which adds the bias is the transverse current, parallel the surface of the PC antenna and perpendicular the direction of propagation. So that
J=0
∇•K (2.1-14) From Equation (2.1-13) and (2.1-14), we can deduce that the charge density does not vary with time and not contribute the time dependent radiated electric field. As the result, Equation (2.1-7) becomes
( )
E r,t =- A(t) t ∂ ∂ JK K JK (2.1-15) The solution of the vector potential AJK in Equation (2.1-11) leads into the Equation (2.1-15) to express the time dependent radiated electric field E (r,t)radJK K at the displacement rKfrom the center of the PC antenna.
s rad 2 0 r-r' J r',t-c 1 E (r,t)=- da' 4πεc t r-r' ⎛ ⎞⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ∂ ⎝ ⎠ ∂
∫
K K K K JK K K K (2.1-16)where ε is the permittivity of free space, c is the speed of light in vacuum, 0 Js
K
is the surface current of the PC antenna in the retarded time, and da' is the increment of surface area at the displacement r'K from the center of the PC antenna. The integration is covered with whole the optically illuminated area of the PC antenna. In the far field,
n r' r-r' =r 1- r r ⎛ • ⎟⎞ ⎜ ⎟ ⎜ ⎟≈ ⎜ ⎟⎟ ⎜⎝ ⎠ K K K (2.1-17)
The gap between the electrodes of the PC antenna is assumed to be uniformly illuminated by the optical source. Therefore, the surface current Js
K
can be set as a constant in space. Then, the radiated electric field in Equation (2.1-16) can be written as rad 2 s 0 1 A r E (r,t)=- J t-4πεc r t c ⎛ ⎞ ∂ ⎜ ⎟ ⎟ ⎜ ⎟ ⎜⎝ ⎠ ∂ JK K K (2.1-18)
where A is the illuminated area of the PC antenna and r= x +y +z .We 2 2 2
considered that the THz radiation is generated on Z axis (i.e. x = y = 0 ), and let z
t t-c ⎛ ⎞⎟ ⎜
→ ⎜ ⎟⎜⎝ ⎠⎟. Thus, The Equation (2.1-18) can be written as
( )
rad 2 s 0 1 A E (r,t)=- J t 4πεc z t ∂ ∂ JK K K (2.1-19)If we want to know the CW radiation power of the antenna, we can use a simpler equivalent circuit of the antenna shown in figure2.1-2. The equivalent circuit equation can be written as:
( ) ( ) b V v dv t C G t dt Z − = − (2.1-20) Where ( )G t is the conductance,C is the capacitance, Z is the radiation impedance. Solve the equation (2.1-20), we can get:
2 1 2 1 1 2 2( ) 2 2 2 [1 ( ) ][1 ( ) ] P P R e P hc RC η λη λ τ = + Ω + Ω (2.1-21) whereλ1andλ2are the wavelength of the two pump lasers,P and1 P are the 2
respective pump power, η1 and η2 are the external quantum efficiencies, Ω is the difference frequency, τ is the photocarrier lifetime, R is the resistance of the THz load circuit, C is the photomixer capacitance, and e ,h ,c are
well-known physical constants.
Beside, we can know the equation (2.1-22) from surface current [29].
0 ( ) J ( ) ( ) 1 1 s b s s t E t t n σ σ η = + + K K (2.1-22)
where n is the refractive index of photoconductor antenna under the wavelength of
m
μ . η is the impedance in free space, and 0 σs( )t is the surface conductivity which is shown in the equation (2.1-23).
(1 ) ( ') ( ) t ' ( , ') ( ') exp[ ] s opt car e R t t t dt m t t I t w σ τ −∞ − − − ≡
∫
= (2.1-23)where e is the electric charge, R is the reflectivity of photoconductor antenna, =w is the photon energy, m t t is the time-dependent carrier mobility at time t from ( , ') created carrier at time t', Iopt is the time-dependent of optical intensity, and
car
τ is the carrier lifetime of excited carriers. For the present derivation, we
assume that carrier mobility is a constant. ( , ')
m t t = (2.1-24) m
And assume that the carrier lifetime is long enough, τcar → ∞ . A Gaussian
intensity profile of the optical beam is assumed:
2 0 2 ' ( ') exp( ) opt t I t I τ − = (2.1-25) From these assumptions, the surface conductivity becomes
2 0 2 (1 ) ' ( ) t ' exp( ) s e R t t I dt m w σ τ −∞ − − ≡
∫
= (2.1-26) From the equation (2.1-20) and (2.1-24) lead to the equation (2.1-19).2 2 2 0 0 rad 2 0 2 0 (1 ) 1 A (1 ) E (r,t)=- exp( ) 1 exp( ) 4 c z ( 1) t e R I m e R t I m x dx w n w τ η τ πε τ − −∞ ⎡ − ⎤ − − ⎢ ⎥ × +⎢ − ⎥ + ⎣
∫
⎦ JK K = = (2.1-27)equation (2.1-25) in term of the experimental parameters E which is the bias b
electric field applied across the photoconductor, and F which is the incident opt
optical intensity. 2 0exp( 2 ) 0 opt opt E t F I dt I A π τ τ ∞ −∞ − =
∫
= ≡ (2.1-28) Where Eopt is the average optical energy and A is the area of the incident opticalbeam. Then we define the parameter B and D to simplify the equation.
2 0 (1 ) 4 Ae R m B c z w πε π − = = (2.1-29) 0 (1 ) ( 1) e R m D n w η π − = + = (2.1-30) And then, the electric field in the far field can be written as
2 2
2 2
( ) opt exp( ) 1 t exp( )
rad b opt F t E t BE DF τ x dx τ τ − −∞ − ⎡ ⎤ = − × +⎢⎢ − ⎥⎥ ⎣
∫
⎦ (2.1-31)Beside of current surge model, we can also discuss on the point of the carrier dynamics in semiconductor to analyze the THz generation by Drude-Lorentz model when we need to discuss the factor of material in PC antenna [30-31].
2.1-2 Drude-Lorentz model
For the calculation of carrier transport and THz radiation in a biased semiconductor, the one-dimensional Drude-Lorentz model is used. When a biased semiconductor is pumped by a laser pulse with photon energies greater than the band gap of the semiconductor, electrons and holes will be created in the conduction band and valence band, respectively. The carrier pumped by ultrashort laser pulse is trapped in the mid-gap states with the time constant of the carrier
trapping time. The time-dependence of carrier density is given by the following equation. c (t) (t) (t) dn n G dt = − τ + (2.1-32)
Where n(t) is the density of the carrier, G(t) is the generation rate of the carrier by the laser pulse, and τ is the carrier trapping time. The generated carriers will be c
accelerated by the bias electric field. The acceleration of electrons (holes) in the electric field is given by
, , , , (t) (t) e h e h e h s e h d q E dt m ν ν τ = − + (2.1-33) Where νe h, (t) is the average velocity of the carrier, qe h, is the charge of an
electron (a hole), m is the effective mass of the electron (hole), e h, τ is the e h,
momentum relaxation time, and E is the local electric field. The subscript e and h represent electron and hole, respectively. The local electric field E is smaller than the applied bias electric field E due to the screening effects of the space b
charges, b P E E αε = − (2.1 -34) Where P is the polarization induced by the spatial separation of the electron and hole, ε is the dielectric constant of the substrate and α is the geometrical factor of the PC material. The geometrical factor α is equal to three for an isotropic dielectric material. It is noted that both, the free and trapped carriers contribute to the screening of the electric field. The time dependence of polarization P can be written as dP dt P J τ − + ＝ (2.1-35)
Where τ is the recombination time between an electron and hole. In the r
equation (2.1-33), J is the density of the current contributed by an electron and hole,
h e
J=enν −enν (2.1-36) Where e is the charge of a proton. The change of electric currents leads to electromagnetic radiation according to Maxwell’s equations. In a simple Hertzian dipole theory, the far-field of the radiation ETHz is given by
THz J E t ∂ ∝ ∂ (2.1-37) To simplify the following calculations, we introduce a relative speed ν between an electron and hole,
h e
=
ν ν − (2.1-38) ν
Then the electric field of THz radiation can be expressed as
THz n E e +en t t ν ν∂ ∂ ∝ ∂ ∂ (2.1-39) The first term on the right hand side of the equation (2.1-37) represents the electromagnetic radiation due to the carrier density change, and the second term represents the electromagnetic radiation which is proportional the acceleration of the carrier under the electric field.
2.1-3 Photomixing
CW THz wave can be generated through photomixing which produces optical intensity beating at THz frequencies by mixing two single-mode lasers or mode beating within a single laser. The combination of two waves with slightly
different frequencies is equivalent to a wave which envelope is modulated by the difference frequency. The intensity-modulated beam will excite the electron-hole pairs in PC antennas then accelerated by the bias voltage applied to the PC antennas. The generated THz frequency is as the same as the optical beating frequency.
When two electric fields with slightly different frequencies propagate collinearly into biased PC antennas, beating signal will be radiated. Set two parallel, scalar electric fields as:
1 10 1 1 2 20 2 2 ( ) ( ) ( ) ( ) ( ) ( ) E t E t Cos w t E t E t Cos w t φ φ = + = + (2.1-40) Where E ,10 E ,20 w ,1 w ,2 φ and1 φ are the amplitude, angular frequency and 2
constant phases of wave 1 and wave 2, respectively. And the total electric filed is the superposition of the two waves:
1 2 1 1 1 2 2 2
( ) ( ) ( ) ( ) ( )
E t =E t +E t =E Cos w t+φ +E Cos w t+φ (2.1-41)
From the simulated curves of figure 2-1-2, we can see that the total electric field has the waveform with a slowly various envelope and a fast carrier frequency inside.
-100 -50 0 50 100 -2 -1 0 1 2
Because the PC antenna has photocarrier lifetime about 1 ps, so it can’t response the faster frequencies. The beating intensity needs to be time averaged:
2 2 2 beat 0 0 1 2 2 2 2 2 2 2 0 1 1 1 2 2 2 1 2 1 1 2 2 2 2 2 2 0 1 1 2 2 1 2 2 1 2 1 1 2 I ( ) ( ') ( ( ') ( ')) ' [ ( ' ) ( ' ) 2 ( ' ) ( ' )] ' 1 2( ' ) 1 ( ' ) { 2 2 [( ' ) ( T T T T T T T t c E t c E t E t dt
c E Cos w t E Cos w t E E Cos w t Cos w t dt
c Cos w t Cos w t E E T E E Cos w t w ε ε ε φ φ φ φ ε φ φ φ − − − = < > = + = + + + + + + + + + + = + + + +
∫
∫
∫
2 1 2 1 1 2 2 2 2 0 1 1 2 2 1 2 1 2 2 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 1 2 2 1 2 2 ' )] [( ' ) ( ' )]} ' 2( ' ) 2( ' ) { [ ] [ ] 2 2 2 2 [( ) ' ( )] [( ) ' ( )] } T T t t T T t t T T t t T T t t t E E Cos w t w t dt c T Sin w t T Sin w t E E T Sin w w t Sin w w t E E E E w w w w φ φ φ ε φ φ φ φ φ φ + + − − + + − − + + + + + + + = + + + + + + + − + − + + − (2.1-42) where c is the speed of light in vacuum, ε0 is the permittivity of free space, TFigure 2.1-2 The simulated curves of two wave with slightly different frequencies. The thin curve is the sum of the two waves. The thick
is the detector response time. We know that 2 2 [ ( ) ] [ ( ) ] 2 ( ) ( ) ( ' ) 2 2 2 ( ) ( ) 2 T t T t T T wT
Sin w t Sin w t Cos wt Sin Sin wt wT wT wT wT Cos wt Sinc φ φ φ φ φ + − + + − − + + + = = = + (2.1-43) Where ( ) 2 ( ) 2 2 wT Sin wT Sinc wT = .
Substituing (2.1-25) into (2.1-24), the formula will become simpler:
2 2 1 0 1 1 1 1 2 2 2 2 2 2 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 ( ) { (2 ) ( ) 2 (2 ) ( ) 2 ( ) [( ) ( )] [ ] 2 ( ) [( ) ( )] [ ]} 2 beat E I t c E Cos w t Sinc w t E E Cos w t Sinc w t w w T E E Cos w w t Sinc w w T E E Cos w w t Sinc ε φ φ φ φ φ φ = + + + + + + + + + + − + − + − (2.1-44) The Sinc-function Sin x( ) plots in figure2.1-3. As x values increase, y values will decrease rapidly.
0 5 10 15 20 25 30 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
When x values larger thenπ(3.1415), the y values are small enough to ignore it. The laser frequency is about 1015
Hz, but the fast detector response time T is just about 10-12
s. We can ignore these faster terms in equation (2.1-26), so the equation can be written as: 2 2 0 1 0 2 1 2 0 1 2 1 2 1 2 1 2 1 2 ( ) ( ) [( ) ( )] [ ] 2 2 2 2 [ ] beat c E c E w w T I t c E E Cos w w t Sinc I I I I Cos t ε ε ε φ φ φ − = + + − + − = + + Ω + (2.1-45) The first two terms are the average intensities of wave 1 and wave 2, respectively.Ω is the difference of angular frequency between two waves. φ is the phase different of the two waves (figure2.1-4).
-200 -100 0 100 200 0 1 2 3 4
2.2 The properties of the material
2.2-1 Choosing and analysis the material
In order to generate high power THz radiation, two properties are necessary for the material. One of properties is long carrier lifetime, and the other is high carrier mobility. Because of them, PC antenna could be generated more current flow which will also increase THz radiation power. Therefore, we can give consideration to two conditions. When we create the more recombination centers in semiconductor, it can trap carriers by using recombination centers to decrease the carrier lifetime. To create the more recombination centers, we implant the more defect in substrate and from deep level recombination. However, implanting
Figure 2.1-4 The beating intensity with an angular frequency of Ω. In the simulation, we set I1 equals I2
the more defect, the structure of the crystal will be destroyed and decrease the carrier mobility. 1 c t c th N τ σ ν = < > (2.2-1) 22 0 0 * t m 1.4 10 N m ε μ ε × ≈ (2.2-2) 0
m : the original mass of carrier
*
m : the effective mass of carrier
0
ε : quasi-static dielectric constant
r
ε : relative dielectric constant
0 = r ε ε ε t N : defect density μ : carrier mobility c τ : carrier lifetime c
σ : capture cross section
th
<ν > : mean thermal velocity
According to the Equation (2.1-1) and (2.1-2), we can know that the longer carrier lifetime the more carrier mobility. It means that we decreasing the carrier lifetime by implanting defects and the carrier mobility also decrease at the same time. Because of it, we use the way which is thermal annealing process to improve it. The thermal annealing processes can rearrangement the crystal of material which implanted defects. It can increase some of the carrier mobility. However, the carrier lifetime also increase.
2.2-2 Dark current
In theory, there is no current generated from PC antenna when we applied voltage across antenna, when it does not illuminate laser beam yet. However, we can measure a few current in PC antenna, which we call dark current. In general, the theory of current transport of the metal-semiconductor junction potential barrier is mainly drift, diffusion, and tunneling effect. It’s contribution is in relation to intrinsic potential barrierqΦ , built-in electric potential B V and bi
applied voltage. In order to avoid generating rectification effect and junction resistance on the metal-semiconductor junction, it is usually using the process of implant high concentration of defect in semiconductor to increase built-in electric potential and decrease the width of depletion region. So the carrier can easily through the junction potential as applying voltage. It is the process of Ohm contact.
2.2-3 Photocurrent
Comparing with dark current, photocurrent means that CW THz is generated from photoconductive antenna which applies voltage, when it illuminates laser beam. We use the two modes laser to incident into the gap on the photoconductor antenna, we define the optical generation rate g as the number of absorbed 0
incident photons per second, i.e photon flux (P0
hv) per unit volume, multiplied by
the optical quantum efficiency ηopt , which accounts for reflections at the air-semiconductor interface, as well as for the finite thickness of the
photoconductive layer. Accordingly, we define the optical quantum efficiency as (1 tLT)
opt e
α
η = Τ − − , where T is the transmission coefficient at the
air-semiconductor interface and tLT is the thickness of the sample layer. Hence,
the generation rate becomes:
0 1 o opt P g hv V η = (2.2-3) Where V is the elementary volume associated with the elementary photocurrent
ph
I .If we consider n and p the densities of free photogenerated electrons and holes
(assumed spatially homogeneous), we can write the current continuity equation:
0 0 e dn n g R g dt = − = −τ (2.2-4) where e n R τ
= is the electron recombination rate. In fact, in case of LT-GaAs and
GaAs:O photoconductor one should replace the recombination rate with the trapping rate. The same equation holds for holes. For an uniformly illuminated photoconductor, the electron and hole current densities are given only by the drift components, since there is no diffusion due to the lack of spatial dependence (∂/ ∂x ≣ 0): ( ) ( ) n e p p J env E J env E = = (2.2-5) wherev,e,h is the field-dependent electron (hole) drift velocity. The total current density is J =Jn +Jp , where, at this point the holes contribution to the
photocurrent is discarded due to their low mobility in material. Moreover, the low mobility of holes produces a small displacement of the hole population in the external applied field, whereas due to their much higher mobility a significant
number of electrons are displaced into the cathode (+); hence, for maintaining the space-charge neutrality in the illuminated gap and current continuity at the electrodes. A replenishment of electrons at the anode is necessary (i.e. electron injection). The DC photocurrent flowing into the external circuit is given by:
( )
DC
ph e
I = Aenv E (2.2-6) where A is the total contact area. With g independent of time, that is ∂/∂t ≣ 0
0 at steady state, from Eq. 2.2-4, the density of photogenerated electrons becomes:
0 ( ) opt e P n V hv η τ = (2.2-7) and by substituting it into Eq. 2.2-6 we obtain:
0 ( ) ( ) opt DC ph e e P I e v E d hv η τ = (2.2-8) We can regroup the terms in Equation 2.2-8, by denoting the primary photocurrent
0 ( ) p ph opt P I e hv η
= and introducing the photoconductive gain
( ) e tr g t E τ = where ( ) ( ) tr e d t E v E
= is the photocarrier transit time. In other words, the
photoconductive gain is determined by how fast the electrons can transit across the electrodes and contribute to the photocurrent in the circuit before they recombine with the holes, or as in the case of material, they become trapped. In most of the existing designs of photomixers, the carrier transit time is neglected since the transittime for an electrode spacing of ∼1 µm is much larger than the carrier lifetime. Forexample, assuming a trapping time of ∼1 ps and a drift velocity of ∼4.4×106cm/s,this yields a transit time of ∼25 ps and a gain of about 0.04 (<<1), hence the low quantum efficiency of photoswitches. This large
difference between the carrier transit and lifetime means that the photomixer is a carrier lifetime dominated device.
In Eq. 2.2-8, the electron drift velocity is a ected by the saturation effects and has the general form:
( ) 1 e e e sat E v E E v μ μ = + (2.2-9)
where μe is the carrier mobility and vsat the saturation velocity. At low electric
fields one can assume a field-independent mobility, such that v Ee( ) eE eV d
μ μ
Replacing in Eq. 2.2-8, we obtain:
opt 0 I=e ( ) ( ) d e e P v E hv η τ (2.2-10)
If we now consider the photocurrent modulated at a THz frequency, we can write:
0 2 2 ( ) ( ) 1 ( ) 1 ( ) DC ph opt THz e e ph e e I P v E I e d hv w w η τ τ τ = = + + (2.2-11)
We can also use the ultra-pulse laser to incident into the gap on the photoconductor antenna, and generate the transient photocurrent to radiate THz electromagnetic pulse. The value of photocurrent is in relation to the bias value and the power of the laser beam. It can express as:
0 V V V I= ( ) ( ) ( ) gap bias bias R +R t =R t ≈ R t (2.2-12) 0
R is time-independence value of resistance. It can divide into two parts, one is
contact resistance and the other is load resistance. R(t) is time-dependence value of resistance which photoconductor illuminates laser beam. We set that there is an
incident beam on the photoconductor and using the photon energy generate the electron-hole pair. And then, the photoconductor parameter σ can be expressed as:
n p
=q( + ) n
σ μ μ Δ (2.2-13) where q is the charge of electron, μ and n μ are the mobility of electron and hole. p
n
Δ is the density of carrier. If the average power of incident optical pulse is
avg
P and photon energy is hν . The carrier generation rate G per unit volume can express as: avg pw 0 P G= h QV η ντ (2.2-14)
where η is the quantum effect, τ is the bandwidth of laser pulse, Q is the pw
repetition rate of laser pulse and V is the total volume of activity region. 0 Under the steady state, the carrier generation rate G is:
pw n G= τ Δ (2.2-15) n p n p pw =q( + ) n=q( + )G σ μ μ μ μ τ ∴ Δ (2.2-16) From Equation (2.2-16), we can get the optical resistanceR . p
2 p n p avg L h QL R = = A q ( + )P ν σ η μ μ (2.2-17)
where A is the cross-section area of activity region and L is the length of activity region.
From Equation (2.2-12) and Equation (2.2-17), we can express the photocurrent as: n p bias avg bias 2 p q ( + )V P V I= = R h QL η μ μ ν (2.2-18)
Chapter 3 Experiment Method and Setup
In this chapter, we introduce the samples which are fabricated for our PC antenna. And then, we introduce the experiment methods and setups to measure the emission properties of the THz radiation.
3.1 Sample preparation
We used the dipole antenna as the antenna structure in our experiment. Large signal and high bandwidth can be obtained from this kind of structure [38]. The photoconductive antenna structure is shown in Figure 3.1-1. Knon et al. proved that the spectral response of the PC antenna for broadband detection is mainly determined by the temporal behavior of the number of photo-excited carriers [22].
Antenna width
Gap
Antenna length
Transmission line width
Recently, Salem et al. [32] improved the characteristics of GaAs substrate and generated THz waves by implanting oxygen ion. Normally, oxygen ion is considered as dust (a disadvantage) for electrical devices fabrication during the process, as its existence will make the contacts to be not Ohmic-contact. But, in the THz generation, it can become advantages. As the electrical level formed by oxygen ion in GaAs is close the Femi-level, it makes the oxygen ion implanted GaAs close to electrically neutral and has comparative high resistance. This kind of material also have high breakdown voltage; and short carrier lifetime by implanted under certain high dosage and annealed under suitable annealing temperature.
3.1-1 Preparation of the PC antenna
By using multi-implanted GaAs:O as the substrate and then fabricated dipole antenna on it. And our sample is fabricated by KeJian Chen who studies in CUHK. From some groups [29-30, 32], the GaAs:O is further studied. They demonstrated that this kind of material really has some advantages for THz waves generation, and can generate higher power and higher frequency if we can optimize the implant dosage, annealing temperature and introduce some antenna design for high frequency purpose.
By optimize the dosage and the implanted energy to match the requirements. Considering the cost of time for RBS facility, we prepared two kinds of materials which have different carrier life times and mobilities as the same dipole antenna
structure. In implanting process, multi-implants dosage concentrations is
13 2
2.5 10 ions/cm× (500Kev & 800Kev) and 13 2
4 10 ions/cm× (1200kev). After implantation process, we performed the thermal annealing by RTA (Rapid Thermal Annealing) under N2 gas environment and use a GaAs cap to prevent As ion absorption. In our experiment, we performed annealing at 500℃ for 60s. (For reference, under 500℃ for 60s annealing, the resistance of this GaAs:O substrate is close to 1.26 10 (7 )
sq
× Ω ) and we also measured the carrier life time of both materials by optical-pump probe measurement. The carrier life time of GaAs:O is 550fs and LT-GaAs is 700fs. The fitting curve are shown in figure 3.1-2
We also calculated the conductivity of GaAs:O and LT-GaAs. The conductivity of GaAs:O is 3.8x10 -2 Ω-1 cm-1 and LT-GaAs is 1.7x10-4 Ω-1 cm-1 , the measurement are shown in figure 3.1-3.
500 1000 1500 2000 2500 3000 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 500 1000 1500 2000 2500 3000 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 No rm ali z ed Δ R/R ( a .u.) Time (fs) LT-GaAs (No140) GaAs:O (No121)
550fs
700fs
3.1-2 The setup of PC antenna
After preparing the PC antenna, we put the PC antenna on the mount which we designed. We used objective lens to focus pump laser on the dipole antenna. And then, we used the silicon lens to decrease the angle of the THz radiation outgoing the substrate. The type of our silicon lens is hyper-hemispherical lens, the radius is 6.75mm and the total thickness is 8.35mm. In order to make sure the right position of laser beam, we used two steps. For the first step, we used a thin glass and put it before the objective lens. Then, we can see the image on the screen reflected from the dipole antenna and check the location of focused laser beam on the sample. The detail experiment method is shown in the Figure 3.1-4. After checking the correct location the next step was to contact the multi-meter to the dipole antenna for measuring the resistance, and then optimized the objective lens Figure 3.1-3 The measurement of dark current and conductivity of GaAs:O and
LT-GaAs 0 20 40 60 80 0.0 1.0x10-2 2.0x10-2 3.0x10-2 -1 0 1 2 3 4 5 6 7 8 Dark current ( μ A) Bias Voltage (V) LT-GaAs GaAs:O 1 10 10-3 10-2 10-1 100 LT-GaAs σ=1.72x10-4 Ω−1cm-1 C u rrent Densit y (A/ c m 2 ) Electric Field (kV/cm) σ=3.835x10-2Ω−1cm-1 GaAs:O J=σE
and incident pump beam until search the minimum value of resistance was found.
3.2 Dual wavelength laser diode system
3.2-1 Laser diode characteristics
In order to measuring the better THz radiation power, we directly excited our PC antenna by using two frequency-independent circular laser diodes (SANYO DL-8032-001) with output power 57mW and wavelength around 830nm. The L-I curve of the laser diodes are showing in Fig. 3.2-1 and Fig 3.2-2
PC Antenna
Afterimage
Thin glass
0
50
100
150
200
0
10
20
30
40
50
60
Pow
er (m
W)
Current (mA)
LD1
0
50
100
150
200
0
10
20
30
40
50
60
Pow
er (m
W)
Current (mA)
LD2
The linewidth of LD1 and LD2 measured by Fabry-Perot interferometer are shown in Fig 3.2-3 and Fig 3.2-4, where their linewidth are 22MHz and 21MHz, respectively.
Figure 3.2-2 L-I curve of laser diode 2 (LD2), Ith=50mA
0.02
0.04
0.06
0
2
Ampli
tude (a.u.
)
scan time (s)
FSR=2GHz
(0.006264s) (0.00068s)21.7MHz
0.04
0.06
0.08
0
1
Ampli
tude (a.u.
)
scan time (s)
(0.00066s)21.0MHz
FSR:2GHz
(0.06284s)In our experiment, we can get CW the THz radiation with different central frequency by tuning the wavelength of each LD. Therefore, by controlling the operation current and temperature, we can tune the wavelength difference between
Figure 3.2-3 Linewidth of LD1 measured by Fabry-Perot
the two laser diodes. The accuracy of the current driver (New port 505B) and the temperature controller (New port 325B) are ± 0.004mA and ± 0.1 ℃ respectively. 0.035 0.042 0.0 0.3 0.6 a m pl itude (V ) Time (second) 0.036 0.045 0.054 0.0 0.6 1.2 am pl it ude (a. u. ) Time(s)
Figure 3.2-5 Temperature control at current 190mA for LD1. The inset picture is Fabry-Perot interferogram of the laser diode 1.
Figure 3.2-6 Temperature control at current 190mA for LD2.
The inset picture is Fabry-Perot interferogram of the two laser diodes.
10 15 20 25 30 359.5 360.0 360.5 361.0 361.5 Frequency (THz) Temperature (0C) 10 15 20 25 30 358.8 359.2 359.6 360.0 360.4 Frequency (THz) Temperature (oC)
In figures 3.2-5 and fig 3.2-6, the wavelength shift caused by changing temperature are 11.6GHz/℃(LD1) and 13.2GHz/℃(LD2) ; the shift caused by shifting current are 2.3GHz/mA(LD1) and 2.1GHz/mA(LD2).
0.04 0.05 0.06 0.0 0.2 0.4 0.6 A m p lit ud e (a. u. ) Time (s) 0.04 0.05 0.06 0.0 0.2 0.4 0.6 A m p lit ud e (a. u. ) Time (s)
Figure 3.2-7 Current control at 23℃ for LD1.
The inset picture is Fabry-Perot interferogram of the laser1.
Figure 3.2-8 Current control at 23℃ for LD2.
The inset picture is Fabry-Perot interferogram of the laser2.
100 120 140 160 180 200 360.6 360.8 361.0 361.2 Frequenc y (T Hz) Current (mA) LD1
100
120
140
160
180
200
359.6
359.8
360.0
360.2
360.4
Frequency (TH
z
)
Current (mA)
LD2
We used Fabry-Perot interferometer to measure the frequency stability of the two laser diodes. We recorded the fluctuation of frequency of two laser diodes on the oscilloscope around 20 minutes. The individual frequency shifts of LD1 and LD2 are 416 MHz and 554.MHz, respectively.
Figure 3.2-9 Frequency fluctuation of LD1 in 20 minutes
Table 3-1 is a brief summary of the characteristics of the two laser diodes
3.2-2 Dual-wavelength laser diodes system
LD1 LD2
wavelength ~830nm ~830nm
Power 57mW@190mA 57mW@190mA
linewidth 22 MHz 21 MHz
Current v.s.
frequency 2.3GHz/mA 2.1GHz/mA
Temperature v.s.
freqency 11.6GHz/℃ 13.2GHz/℃
Frequency
fluctuation 416MHz@20mins 554MHz@20mins Figure 3.2-10 Frequency fluctuation of LD2 in 20 minutes
FSR
Our dual-wavelength light source system is presented in figure 3.2-7. It is composed of two frequency-independent laser diodes and some proper optics. The polarization of the LD is S polarization. The 40X objective lens are used to focus the spot size of the two LD, when light passes through the isolator, the polarization of the incident light will rotated to45 to prevent the optical feedback 0
from other optics, when the light passes through the half-wave plate, the polarization will be changed from linear polarization to elliptical polarization.
We measure the output spectrum by optical spectrum analyzer (OSA, MS 9030, resolution 0.01nm) is shown in figure 3.2-8.
λ/2 plate
λ/2 plate polarizer λ/2 plate
isolator
isolator
Laser diode 1
Laser diode 2
To optimize beating efficiency, we need RF spectrum to check it. Because the maximum frequency can be detected from our spectrum analyzer is 3GHz, we must adjust the frequency difference of two laser diodes lower than 3GHz.The low frequency beating signal is shown in figure 3-.2-8
. 0.5 1.0 1.5 2.0 2.5 -70 -60 -50 -40 Relative Power (dBm) Frequency (GHz)
Beating at 2.3GHz
T1=21.2℃
T2=12.3℃
832 833 834 835 -65 -60 -55 -50 power (dBm ) wavelength (nm)λ1=831.82nm
λ2=834.42nm
at 23℃ 190mA
Figure 3.2-11 The beating signal of the PC antenna Figure 3.2-10 The spectrum of 2 laser diodes system
3.3 Experimental setup of generation and detection of THz
3.3-1 Experimental setup
The emitted THz radiation was collimated and focused by a pair of off-axis parabolic mirrors onto the detector. We used a High-Voltage Source Meter (Model2410) to provide bias to the PC antenna and measure the current-voltage curve. To measure total THz power, we used a 4.2 K liquid-helium-cooled Si bolometer as our detector, which was carefully calibrated with a blackbody radiation source. The experiment setup for generation and detection of THz radiation is shown in Figure 3.3-1.
MOPA
Pulse
Figure 3.3-1 Schematic of experimental setup for measure the electric characteristics of PC antenna
