Chapter 1. Introduction
1.5 Organization of this thesis
We organize our thesis below:
Chapter 1 gives the fundamental principle involving with THz radiation, and reviews some terahertz radiation sources and their operation principles. The motivation and our contribution are also contained in this chapter.
In the Chapter 2 we describe photoconductive antennas with different types of designs and three kinds of materials.
In the Chapter 3 we review four theoretical models involving with carrier and field dynamics. The numerical algorithm is also provided for each model. We will also suggest several softwares to use in numerical simulation.
In the Chapter 4 we conduct a comparison between the characteristics of terahertz radiation pulses generated using biased semi-insulating and
arsenic-ion-implanted GaAs photoconductive antennas with 1.5-cm aperture size under various pump fluences and bias fields. We use fullwave model to explain the distinct terahertz radiation characteristics between both types of materials.
In the Chapter 5 we investigate the gap-dependent THz pulses from mid-size-gap multi-energy arsenic-ion-implanted GaAs photoconductive antennas in terahertz time-domain spectroscopy experiments. We demonstrate the carrier and field dynamics within the antennas. An explanation for the gap-dependent phenomenon is provided in this Chapter.
Chapter 6 summarizes the results obtained during this work, and provides an outlook on future prospects of the numerical simulation of THz radiation mechanism.
References
[1] A. S. Krishnagopal and V. Kumar, Radiat. Phys. Chem. 70, 559 (2004).
[2] H. P. Freund and G. R. Neil, Proceedings of IEEE 87, 782 (1999).
[3] R. Kompfner and N. T.Williams, Proc. IRE, 41, 1602 (1953).
[4] T. Y. Chang and T. J. Bridges, Opt. Commun. 1, 423 (1970).
[5] M. Inguscio, G. Moruzzi, K. M. Evenson, and D. A. Jennings, J. Appl. Phys. 60, 161 (1986).
[6] D. D. Bicanic, B. F. J. Zuidberg, and A. Dymanus, Appl. Phys. Lett. 32, 367 (1978).
[7] G. A. Blake, K. B. Laughlin, R. C. Cohen, K. L. Busarow, D-H. Gwo, C. A.
Schmuttenmaer, D. W. Steyert, and R. J. Saykally, Rev. Sci. Instrum. 62, 1693 (1991).
[8] M. C. Gaidis, H. M. Pickett, C. D. Smith, S. C. Martin, P. R. Smith, and P. H.
Siegel, J. Appl. Phys. 60, 161 (1986).
[9] R. F. Kazarinov and R. A. Suris, Fiz. Tekh. Poluprov. 5, 797 (1971) [Sov. Phys.
Semicond. 5, 707 (1971)]
[10] J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, Science 264, 553 (1994).
[11] M. Bass, Phys. Rev. Lett. 9, 446 (1962).
[12] A. Bonvalet, Appl. Phys. Lett. 67, 2907 (1995).
[13] O. S. Heavens and R. W. Ditchburn - Insight into Optics (1987)
[14] D. R. Grischkowsky, IEEE J. Sel. Top. Quantum Electron. 6, 1122 (2000).
[15] M. Nagel, C. Meyer, H.-M. Heiliger, T. Dekorsy, H. Kurz, R. Hey, and K. Ploog, Appl. Phys. Lett. 72, 1018 (1998).
[16] B. B. Hu and M. C. Nuss, Opt. Lett. 20, 1716 (1995).
[17] G. Zhao, R. N. Schouten, N. van der Valk, W. T. Wenckebach, and P. C. M.
Planken, Rev. Sci. Instrum.73, 1715 (2002).
[18] A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, App. Phys. Lett. 86, 121114 (2005).
Fig. 1.1: THz radiation spectrum.*
Fig. 1.2: Schematic of a THz-TDS system.*
Chapter 2
Photoconductive antennas
Besides of FEL, QCL, and FSEOS, THz radiation also can be generated by employing femtosecond laser pulses to excite biased photoconductive (PC) antennas.
These devices were first proposed by Auston et al. [1] and subsequently studied by many groups [2-4]. Typical PC antennas have two parallel metallic contacts deposited on the surface of a semiconductor as shown in Fig. 2.1. THz pulses are typically produced by conduction between two electrodes patterned on a semi-insulating GaAs (SI-GaAs), low temperature gallium arsenide (LT-GaAs), or other ion-implanted materials substrate. To generate THz radiation, a femtosecond laser pulse (often a titanium sapphire laser (Ti-Sapphire laser)) has to be focused onto the gap of the photoconductive antennas with a DC bias across the gap. Absorption of the laser pulse whose center frequency exceeds the bandgap of the semiconductor substrate generates free carriers there between the electrodes. The mechanism underlying the THz radiation is to quickly create photoexcited carriers between the externally biased contacts using an ultrafast laser pulse. The charge carriers are then quickly accelerated to the opposite electrodes by the bias field and lead to the formation of an electrical dipole due to the difference of mobility between electrons and holes. This acceleration
of the charge carriers by the external electric field generates an electromagnetic transient. That is, the bias–laser pulse combination allows these charge carriers to rapidly jump the gap, and the resulting fast temporal change in a transient current can generate a pulse of electromagnetic radiation in the THz frequency range. The performance of THz generation depends on the temporal shape of photo-induced current from charge acceleration. The far-field radiation E t from the current r
( )
distribution J (t) (s ∝ v, v is the drift velocity of the carriers) on the propagating axis
of the radiation can be expressed by [5]
( ) ( )
2 0
4 ,
s r
A dJ t
E t a
c r dt
≅ − πε ∝ (2.1)
where A is the area of the emitter carrying the current distribution and a is acceleration of the carriers. Since the THz radiation in the far field is proportional to the time derivative of the current density, the emitted THz transient depends crucially on the carrier drift velocity. As a result, the THz radiation field has a field shape proportional to the acceleration of the photo-excited carriers. Very short THz pulses (typically ~2 ps) are produced due to the rapid rise of the photo-induced current in the gap and in short lifetime materials such as LT-GaAs. This current may persist for only a few hundred femtoseconds or up to several nanoseconds, depending on the material of which the substrate is composed. This photoconductive antenna puts out a train of pulses, whose repetition frequency is the same as that of the femtosecond pump laser.
Pulse widths are on the order of 100 fs, with average powers below a few hundred nW and a frequency spread of > 500 GHz. The pulse bandwidth is typically centered at about 1 to 2 THz. The details of the spectrum can vary significantly, however, depending on the design of the antenna and pump-laser power, pulse width and shape, and configuration.
2.1 Antenna types
The features of the pump pulses will significantly affect the generated THz radiation. Besides, the characteristics of THz radiation also depend on the designs of photoconductive antennas. Several designs of antennas includes the dipoles, bow tie, and coplanar strip line as shown in Fig. 2.1, or interdigitated structures, logarithmic spiral antennas, and more sophisticated designs derived from microwave theory. The most commonly used are the Hertzian dipole antenna which has been reported to have an emission spectral distribution as high as 2 or 3 THz. The bow-tie antenna possesses a wide frequency bandwidth, and is also used as a photoconductive antenna. For the bow-tie antenna, increased radiation power was observed, although its emission spectrum distributed at frequencies lower than dipole antennas. A unique photoconductive source is the biased coplanar strip line, the metal and semiconductor interface of which was excited with femtosecond laser pulses. The biased strip line
showed a very wideband emission spectrum (< 5 THz).
In 1997, M. Tani et. al. report a quantitative and systematic comparison of the emission properties of the photoconductive antennas [6]. In their experiments, they investigated the characteristics of THz radiation from several photoconductive antennas with three different designs (the three dipoles, bow tie, and coplanar strip line) and two different materials (semi-insulating GaAs (SI-GaAs) and low-temperature grown GaAs (LT-GaAs)). They found that the radiation spectra showed no significant difference for both materials under the same design. In addition, the pump-power dependencies of the radiation power showed saturation for higher pump intensities, which was more serious in SI-GaAs-based antennas than in LT-GaAs-based antennas.
2.2 Photoconductive materials
One of the essential device factors determining the efficiency of THz antennas is the photoconductive materials fabricated on the antenna. To generate high THz power, the photoconductive materials should have large carrier mobility. In addition, a high resistivity is desired for the materials so that the PC antennas can endure high bias field and thus obtain high THz radiation power. To fulfill these conditions, some approaches like doped and ion-implantation are applied to the PC materials. In the
following, we introduce three materials which are commonly fabricated on PC antennas.
2.2.1 Semi-insulating GaAs
One typical material fabricated on biased PC antennas is known as semi-insulating GaAs (SI-GaAs) [7]. By a variety of techniques one may produce SI-GaAs [8-10] with carrier lifetimeτ of several picoseconds as a whole. The c
electrostatic property of SI-GaAs exhibits greatly reduced parasitic capacitance suitable for fast devices, and allows for integration and the implementation of monolithic microwave integrated circuits. SI-GaAs provides semiconductor qualities including thermal stability during epitaxial growth or anneal of ion-implanted active layer, absence of undesirable substrate active layer interface effects, no degradation of active layer properties by outdiffusion of impurities from substrate during thermal processing, and lowest possible density of crystalline defects. Undoped GaAs can be made semi-insulating by the addition of either oxygen or chromium to the melt. For our study, the SI-GaAs grown by the liquid encapsulated Czochralski method.
Through a compensation of shallow acceptors by the intrinsic type of deep donor defect, EL2, the resistivity of SI-GaAs antenna is able to reach a value as high as the order of 1017Ωicm.This high resistivity is about six orders of magnitude greater than
that of silicon and provides excellent isolation and substrate insulation. The resistivity of the semiconductor can be controlled by counter doping with a deep-level impurity that has a conductivity type opposite to that of the impurities introduced during growth.
Hurd et al. [11] found that if pump light is incident upon SI-GaAs, the deep traps within SI-GaAs lead to the photo-induced space charge at the electrode, and therefore produce a space-charge field that screen the bias field and alter the transient response of a PC antenna. The influence of space-charge field depends on the ratio of the deep trap and shallow concentrations.
A particularly appealing phenomenon is provided by SI-GaAs when a DC external bias is applied to the electrodes of a SI-GaAs antenna: an enhanced bias field will form near the edge of the anode leading to an enhanced THz radiation when femtosecond laser pump pulses are incident upon the edge of the anode [12].
2.2.2 Low-temperature grown GaAs
One usually makes use of molecular beam epitaxy method to grow GaAs thin films on certain device. If the growth temperature during the film deposition is reduced to about 200 - 300 under arsenic overpressure an incorporation of excess group V-atoms (As) occurs. Post annealing at temperatures above 600o leads to the
oC
C
nucleation of the excess arsenic in crystalline As precipitates of several nanometer size [13]. These As clusters act as burried Schottky barriers, form localized mid-gap states and are responsible for trapping of electrons and holes [14]. Other types of trapping centers are point defects, which are incorporated during the growth process.
They are double donors, which consist of neutral and positively charged arsenic antisites. Energetically the antisite states are localized close to the center of the band gap [15]. The charged antisites as well as the precipitates are believed to influence the electrical properties of the material and the carrier relaxation after optical excitation [16]. Due to the fast carrier trapping the carrier lifetime of such low-temperature grown GaAs (LT-GaAs) is only about 250 ~ 500 fs [17] and depends critically on the growth temperature.
The trapping states may consist of Urbach tail states, which are located energetically close to the conduction band edge and the mid-gap states, mentioned above. The Urbach tail states are caused by disorder in the material, while the mid-gap states formed by the arsenic precipitates and the defects. In LT-GaAs the mid-gap state concentration can be as high as 10 cm20 −3after growth [18], but decreases while the subsequent annealing to values of about to
depending on growth and annealing temperature [19].
17 3
5 10 cm× −
18 3
5 10 cm× −
At high injected carrier densities a saturation of the trapping can occur and
therefore the slow recombination of the trapped carriers acts as a bottleneck for the depopulation of the bands via the point defects. High epitaxial GaAs crystals, grown under standard conditions (not LT-GaAs), exhibit a typical electron-hole recombination time of about 100 ~ 500 ps [18]. Therefore it is obvious that localized states in the energy gap due to defects or impurities (trapping states) can act as recombination centers for non-radiative processes, which change the recombination time substantially. If the density of trapped states is sufficiently high, carriers can tunnel through these centers to valence band. Because the trapping of carriers due to these localized states occurs very fast, the recombination time is reduced to about 10 ps. This effect is important for the development of fast PC antennas with sub-picosecond response times, which can be used for THz pulse emission [20]. With a bandwidth extending up to 5 THz and a good signal-to-noise ratio, such THz pulses are a promising tool for far-infrared spectroscopy of solids, liquids, and gases.
However due to the introduced defects and impurities the statistical probability of scattering is increased and the mobility of the carriers is therefore reduced, what causes an increase in resistivity. This leads on the opposite side to a decrease in the sensitivity of the device to external electrical fields.
Compared to the SI-GaAs antenna, the LT-GaAs-based antenna has a larger bandwidth of THz radiation owing to its shorter carrier lifetime (< 1 ps), but its
disadvantage lies in the lack of reproducible property.
2.2.3 Arsenic-ion-implanted GaAs
Implanting ions into semi-insulating materials will significantly change their original resistivity and temperature stability, as well as optical properties, such as τ c
or absorption coefficient α0 . The value of τ for As-implanted [21-22] or c
LT-GaAs antenna [23] is as short as 1 ps or less; hence, it influences THz radiation characteristics, including: pulse shape, pulse duration, and bandwidth. Concerning the quantity α0, its value is affected in the presence of impurity, bias field, or ion implantation. Nolte et al. pointed out that LT-GaAs exhibits an excess absorption relative to GaAs, depending on the growth conditions [24]. On the other hand, Lin et al. [25] found that the band edge of absorption coefficient α0of GaAs:As increases +
from to for different dosages. Therefore, one can deduce that the absorption coefficient of semi-insulating materials tends to be altered after ion implantation.
6.2 10× 3 2.2 10 cm× 4 -1
In practical experiments, one can choose ions with different energy and dose for implanting the antenna’s surface. The ion-implanted depth is determined by the ion energy, and can be calculated using the Stopping Range of Ions in Matter (SRIM)
software [26]. For As ion energy of 200 keV and 2 MeV, the implanted depths are about 0.1 mμ and 1 mμ , respectively.
In addition to As , many groups have investigated THz devices based on GaAs +
implanted with H+, N+, and O+. Salem et al. studied strip-line emitters based on GaAs:H, GaAs:N, GaAs:O, and also GaAs:As [27-28]. Recently, Winnerl et al. [29]
studied THz emitters implanted with dual energy implants of N+ and As ions of + various doses, and compared the results with that of SI-GaAs and LT-GaAs.
References
[1] D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984).
[2] D. H. Auston, Appl. Phys. Lett. 26, 101 (1975).
[3] G. Mourou, C. V. Stancampiano, A. Antonetti, and A. Orszag, Appl. Phys. Lett.
39, 295 (1981).
[4] X.-C. Zhang, B. B. Hu, J. T. Darrow, and D. H. Auston, Appl. Phys. Lett. 56, 1011 (1990).
[5] J. T. Darrow, X.-C. Zhang, D. H. Auston, and J. D. Morse, IEEE J. Quantum Electron. 28, 1607 (1992).
[6] M. Tani, S. Matsuura, K. Sakai, and S. Nakashima, Appl. Opts. 36, 7853 (1997).
[7] M. S. Markram-Ebied, “Nature of EL2: The Main Native Midgap Electron Trap in VPE and Bulk GaAs,” in semi-insulating III-V Materials, D. Look, Editor, Shiva Publishing Ltd., England (1984).
[8] N. G. Ainslie, S. E. Blum, and J. F. Woods, J. Appl. Phys. 33, 2391 (1961).
[9] G. R. Cronin and R. W. Haisty, J. Electrochem. Soc., 111, 874 (1964).
[10] J. B. Mullin, R. J. Heritage, C. H. Holliday, and B. W. Straughan, J. Cryst.
Growth, 3-4, 281 (1968).
[11] C. M. Hurd and W. R. McKinnon, J. Appl. Phys. 75, 596 (1994).
[12] S. E. Ralph and D. Grischkowsky, Appl. Phys. Lett. 59, 1972 (1991).
[13] M. Luysberg, H. Sohn, A. Prasad, P. Specht, Z. Lilienthal-Weber, E. R. Weber, J.
Gebauer, R. Krause-Rehberg, J. Appl. Phys. 83, 561 (1998)
[14] U. Siegner, R. Fluck, G. Zhang, U. Keller, Appl. Phys. Lett. 69, 2566 (1996) [15] G. D. Witt, Mater. Sci. Eng. B 22, 9 (1993)
[16] G. Segschneider, F. Jacob, T. Löffer, H. G. Roskos, S. Tautz, P. Kiesel, G. Döhler, Phys. Rev. B 65, (2002)
[17] M. Tani, K. Sakai, H. Abe, S. Nakashima, H. Harima, M. Hangyo, Y. Tokuda, K.
Kanemoto, Y. Abe, N. Tsukada, Jpn. J. Appl. Phys. 1 33, 4807 (1994).
[18] A. Othonos, J. Appl. Phys. 83, 1789 (1998)
[19] D. C. Look, D. C. Walters, G. D. Robinson, J. R. Sizelove, M. G. Mier, C. E.
Stutz, J. Appl. Phys. 74, 306 (1993)
[20] P. R. Smith, D. H. Auston, M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988)
[21] M. Tani, K. Sakai, H. Abe, S. Nakashima, H. Harima, M. Hangyo, Y. Tokuda, K.
Kanamoto, Y. Abe, and N. Tsukada, Jpn. J. Appl. Phys. 33, 4807 (1994).
[22] S. Gupta, J. F. Whitaker, and G. A. Mourou, IEEE J. Quantum Electron. 28, 2 (1992).
464
tal-Weber, Z.
[23] Wang, H.-H. Grenier, P. Whitaker, J. F. Fujioka, H. Jasinski, J. Lilien IEEE J. Selected Topics in Quantum Electron. 2, 630 (1996).
[24] D. D. Nolte, W. Walukiewicz, and E. E. Haller, Phys. Rev. Lett. 59, 501 (1987).
[26] J er and J. P. Biersack, available online at http://www.srim.org [25] G.-R, Lin, C,-C, Hsu, J. Appl. Phys. 89, 1063 (2001).
. F. Ziegl .
is, M. Chicoine, and F.
hler, J. Selected Topics in Quantum Electron.
[27] B. Salem, D. Morris, Y. Salissous, V. Aimez, S. Charlebo Schiettekatte, J. Vac. Sci. Technol. A 24, 774 (2006).
[28] B. Salem, D. Morris, V. Aimez, J. Beerens, J. Beauvais, and D. Houde, J. Phys.
Condens. Matter 17, 7327 (2005).
[29] S. Winnerl, F. Peter, S. Nitsche, A. Dreyhaupt, B. Zimmermann, M. Wagner, H, Schneider, M. Helm, and Klaus Ko
14, 449 (2008).
, (b) the bow-tie Fig. 2.1: Schematic view of (a) the photoconductive dipole antenna
antenna, and (c) the photoconductive strip line.*
*M. Tani, S. Matsuura, K. Sakai, and S. Nakashima, Appl. Opts. 36, 7853 (1997).
tic of an Auston antenna, used to generate subpicosecond optical pulse excites the sem
Fig. 2.2: Schema cycle bursts of THz
radiation. A iconducting substrate
*T. D. Do
in a region between two biased electrodes. This radiation is coupled into free space using a hemispherical substrate lens.*
rney, M. J. Rossowz, W. W. Symes, and D. M. Mittlemanz, Geophysics, 68, 308 (2003).
Chapter 3
Modeling of terahertz radiation from photoconductive antennas
ission efficiency of THz antennas ill allow greater control and wider applicability of THz radiation. Previously, Taylor et al.
Understanding the physics critical to the em w
[1-2] used the current-surge model to explain several characteristics of large-aperture PC antennas, including: THz pulse width, saturation, and pump wavelength dependence. In their model, the formation of THz pulses is associated with the carrier dynamics in PC material, and the time-dependent THz radiation is proportional to the time derivative of the surface photocurrent. In 1996, Taylor et al.
[3] used the drift-Poisson model to reproduce the bipolar THz radiation waveforms generated from different gap size of PC antennas. In their numerical simulation, they found that the negative peak of THz waveform becomes obvious if the pump fluence increases gradually. They attribute the formation of bipolar waveforms to the space-charge bias field screening effect, depending on the pump fluence and photoexcited carrier concentration.
In the following, we describe four theoretical models, including current-surge, Drude-Lorentz, drift-Poisson, and fullwave model. These models are usually adopted to interpret the characteristics of THz radiation.
3.1 Current surge model
This model assumes that the transient surface conductivity σs( )t grows rapidly
when an antenna is excited by a sub-picosecond optical pulse [4]:
(1 R) '
where R is the optical reflectivity of the illuminated area, μ is the carrier mobility, ( )t hν
opt( )
I t is the optical pump pulse intensity, is the photon energy, and τc is the
lifetime of the excited carriers. Or, for the peak surface conductivity:
1
is the value of the time-dependent mobility at the moment of maximum where μ1
is the incident optical fluence.
sand σ Fopt
In reality, the response of the photoconductor is slower than the rise time of the intensity of the excitation laser pulse because it takes up to several picoseconds for the transient mobility μ to reach its quasi equilibrium value. ( )t
Solving the Maxwell equations and taking into account the finite size of the emitter, one obtains for the radiated field E tr( ):
0
of free space, and N is the refractive index of the semiconductor. Eq. (3.1.3) contains the near-THz field screening effect, and its derivation will be detailed in Chapter 4.
By the Eq. (3.1.3), two important points should be noted:
(1) the radiated THz field should raise linearly with the increase of the
applied bias voltage at least in the area of the Ohm’s law validity. At very high bias fields, the field dependence of the surface conductivity
Er
σs have to be taken into account,
(2) Er increases and then saturates as the incident optical fluence grows.
3.2 Drude-Lorentz model
One usually use a simple one-dimensional Drude-Lorentz model to describe the behavior of the photo-excited carriers [5]. In Drude-Lorentz model, the current density is given by
fv
j= −qn (3.2.1)
where nf is the carrier density and v the velocity averaged over the carrier
distribution. The contribution by the holes is ignored for simplicity since their
contribution is very minor due their much larger effective mass. The change in carrier density over time can be described by:
+ ( )
f f
c
dn n
dt = −τ G t (3.2.2)
Here τc is the carrier lifetime, and the photo-generation rate decided by the
optical pump pulse. The motion of these generated carriers is slowed down by scattering, and their velocities can be described as:
( )
Where is the effective mass of the carriers, is the local field at the position of the carriers and When an electron (charge –q) separates from a hole (charge +q), a dipole is formed
Where is the effective mass of the carriers, is the local field at the position of the carriers and When an electron (charge –q) separates from a hole (charge +q), a dipole is formed