Conclusions

We have performed a comparative study between THz radiation waveforms -GaAs d G :As⁺ antennas under various pump fluence

for large-aperture biased SI an aAs

s and bias field. The THz pulses emitted from our GaAs:As⁺ antenna have narrower peak width, wider bandwidth, and higher peak THz amplitude than those obtained from the SI-GaAs antenna. The peak frequency and bandwidth difference between these two types of antennas have increasing trends with increasing pump fluence. From the pump fluence dependence of peak THz amplitude, we have found that SI-GaAs and GaAs:As⁺ antennas both exhibit anomalous saturation behaviors which can be reproduced numerically by incorporating nonlinear effects into a rigorous electromagnetic wave propagation model. Above pump fluence of 20μJ/cm², the GaAs:As⁺ antenna obtained better emission efficiency relative to the SI-GaAs antenna. On the basis of numerical simulation, we have deduced that this better

emission efficiency stems from the fact that both types of antennas have different quantities, including: linear absorption coefficient, refractive index, and carrier mobility. For the GaAs:As⁺ antenna, the first two quantities are larger, whereas the last is smaller in comparison with the SI-GaAs antenna. We have also inferred from our simulation that the band filling and two-photon absorption effects are responsible for the anomalous saturation behavior. In the bias field dependence of measured peak THz amplitude, we have found that the emission efficiency of the GaAs:As⁺ antenna is higher than that of the SI-GaAs antenna, and that the relative emission efficiency reaches maximum at specific bias field. This particular behavior convinces us that a more rigorous model is required for interpreting the bias field dependence of peak THz amplitude instead of the scaling rule, and we believe that it will be an important topic worthy of being investigated further.

Refer nces

[1] T. Hattori, K. Tukamoto, and H. Nakatsuka, Jap. J. App. Phys. 40, 4907 (2001).

s, A. Armitage, P. G. Huggard,and A. Hussain, Phys. Med. Biol. 47,

aas Wynne, Rev. Sci. Instrum. 77, 083111 (2006).

nger Berlin

[7] B

[8] T ng-Cheng Chang, and Ci-Ling Pan, Opt. Exp. 13,

echnical Digest, 265 (1999).

[10] R. R. Jones, D. You, and P. H. Bucksbaum, Phys. Rev. Lett. 70, 1236 (1993).

e

[2] S. R.Andrew 3705 (2002).

[3] G. Zhao, R. N. Schouten, N. van der Valk, W. T. Wenckebach, and P. C. M.

Planken, Rev. Sci. Instrum.73, 1715 (2002).

[4] A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, App. Phys. Lett. 86, 121114 (2005).

[5] David A Turton, Gregor H Welsh, John J Carey, Gavin D Reid, Godfrey S Beddard, and Kl

[6] S. Winnerl, A. Dreyhaupt, F. Peter, D. Stehr, M. Helm, and T. Dekorsy, Nonequilibrium Carrier Dynamics in Semiconductors (Spri

Heidelberg), 110, 73 (2006).

. B. Hu and M. C. Nuss, Opt. Lett. 20, 1716 (1995).

ze-An Liu, Gong-Ru Lin, Yu 10416 (2005).

[9] S. Ramsey, E. Funk, and C. H. Lee, in The Int. Topical Meeting on Microwave Photonics '99, T

[11] X. Zhang and R. R. Jones, Phys. Rev. A 73, 035401 (2006).

.J. Cook, J.X. Chen, E.A. Morlino, R.M. Ho

[12] D chstrasser, Chem. Phys. Lett. 221

[15] J. T. Darrow, Xi,-C. Zhang, D. H. Auston, and J. D. Morse, IEEE J. Quantum

19.

004).

Tokuda, K.

[21] S itaker, and G. A. Mourou, IEEE J. Quantum Electron. 28,

[22] W er,

Z., IEEE J. Selected Topics in Quantum Electron. 2, 630 (1996).

(1999).

[13] P. K. Benicewicz and A. J. Taylor, Opt. Lett. 18, 1332 (1993).

[14] T.-An. Liu, M. Tani, C.-L. Pan, J. Appl. Phys. 93, 2996 (2003).

Electron. 28, 1607 (1992).

[16] Q. Chen and X.-C. Zhang, Appl. Phys. Lett. 74, 3435 (1999).

[17] Bahaa E. A. Saleh and Malvin Carl Teich, Fundamentals of Photonics (John Wiley & Son, 1991), Chap.

[18] F. Kadlec and H. Nemec, P. Kuzel, Phys. Rev. B 70, 125205 (2

[19] J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Publishing Company, 1996).

[20] M. Tani, K. Sakai, H. Abe, S. Nakashima, H. Harima, M. Hangyo, Y.

Kanamoto, Y. Abe, and N. Tsukada, Jpn. J. Appl. Phys. 33, 4807 (1994).

. Gupta, J. F. Wh 2464 (1992).

ang, H.-H. Grenier, P. Whitaker, J. F. Fujioka, H. Jasinski, J. Liliental-Web

[23] D. D. Nolte, W. Walukiewicz, and E. E. Haller, Phys. Rev. Lett. 59, 501 (1987).

.-R, Lin, C,-C

[24] G , Hsu, J. Appl. Phys. 89, 1063 (2001).

[26] G (1994).

ntals of Photonics (John

-Hill Publishing

[31] T er, H. G. Roskos, and H. Kurz, Phys. Rev. B 53,

db.de/cgi-bin/dokserv?idn=975373056.

[25] A. J. Taylor, P. K. Benicewicz, and S. M. Young, Opt. Lett. 18, 1340 (1993).

. Rodriguez, S. R. Caceres, and A. J. Taylor, Opt. Lett. 19, 1994 [27] Q. Chen and X.-C. Zhang, Appl. Phys. Lett. 74, 3435 (1999).

[28] Bahaa E. A. Saleh and Malvin Carl Teich, Fundame Wiley & Son, 1991), Chap.19.

[29] F. Kadlec and H. Nemec, P. Kuzel, Phys. Rev. B 70, 125205 (2004).

[30] J. W. Goodman, Introduction to Fourier Optics (McGraw Company, 1996).

. Dekorsy, H. Auer, H. J. Bakk 4005 (1996).

[32] T. Löffler, T. Hahn, M. Thomson, F. Jacob, and H. G. Roskos, Opt. Exp. 13, 5353 (2005).

[33] N. Hasegawa, Dissertation, University of Frankfurt (2004), http://deposit.d

able 4.1: Parameters used in THz radiation simulations for SI-GaAs and GaAs:As⁺

ntennas

0

T

a

γ

α (cm^-1)

Nmax

(cm^-3)

α′′

(cm/GW) n^L μ^e , μ_h β′′

(ps²km^-1) (cm/GW) (cm²V^-1s^-1)

SI-GaAs 6.5 10× ³ 2.0 10× ¹⁸ 286 3.4 1000, 50 120 3.2 GaAs:As⁺ 6.7 10× ³ 2.0 10× ¹⁸ 286 3.6 800, 20 120 3.2

tic of a large-aperture photoconductive ante

Zhang, D. H. Auston, and J. D. Morse, IEEE J. Qu

Fig. 4.1: Schema nna with a voltage V .* _b

* J. T. Darrow, Xi,-C. antum Electron. 28, 1607

(1992).

Fig. 4.2: antenna with a

*T. Hattori, K.

Experimental setup for a large-aperture photoconductive voltage V .* _b

Tukamoto, and H. Nakatsuka, Jap. J. App. Phys. 40, 4907 (2001).

Fig. 4.3: Transient normalized photoreflectance changes for SI-GaAs (solid blue

0 1 2 3 4 5 6 as a function of time delay t at various pump fluences F. The bias field applied to the antennas was kept at 0.6 kV/cm. (c) Fourier-transformed

amplitude spectrum E of the waveforms in (a), and (d) r E of the r

waveforms in (b).

1 2 3 4 5 6

Fig. 4.5: (a) Measured THz waveforms Er , (b) corresponding Fourier-transformed

amplitude spectrum E , (c) simulated Er r and (d) E for SI-GaAs (blue r

full line) and GaAs:As⁺ (red full line) antennas at pump fluence 58 J / cm2

F = μ . Both Er and E are normalized to their peak amplitude. r

0 10 20 30 40 50 60

Fig. 4.6 (dashed line) obtained

from (dashed line), and

(c) m f (dashed line)

fluence F for both SI-G

: (a) Measured peak width dt (full line) and peak shift tp

Fig. 2(a) and 2(b), (b) simulated dt (full line) and tp

easured peak frequency fp (full line) and bandwidth d obtained from Fig. 2 (c) and 2(d) as a function of pump

aAs (blue) and GaAs:As⁺ (red) antennas.

0 25 50 75 100 125 150

Fig. 4.7:

F for both SI-GaAs

(blue) and GaAs:As⁺ (red) antennas. The green dash-cross and full lines are the ratio

(a) Measured (dashed-marks), (b) fitting (dashed line), and simulated (full line) THz peak amplitude Ermax

versus pump fluence

ρ ( ^≡ (Ermax

easured and simulated case. The bias field Eb was kept at 0.6 kV/cm

0.55 0.6 0.65 0.7 0.75 0.8

Fig. 4.8: Measured peak THz amplitude Ermax

from SI-GaAs (blue dashed-circle) and GaAs:As⁺ (red dashed-triangle) antennas, and the relative emission efficiency ρ (green dashed-cross) as a function of bias field Eb at pump fluence F =58 J / cmμ ².

Chap

Mid-s

For the sake of generating giant THz radiation fields of up to a hundred ilovolts per centimeter, the gap size (G) of a biased PC antenna ought to be larger

an 1 cm at least [1]. In a practical experimental configuration for such a mtosecond

optical regenerative am z power, while also

employing a param to tune excitation wavelength

and rem experimental

setup for a sm power

from small-gap biased PC antennas are considerably lower than that from large-aperture ones [2-4]. Therefore, a compromise between large-aperture and sm hoose mid-size-gap PC antennas (0.05 mm < G <

2 mm) as THz emission sources inasmuch as one can avoid employing a bulky system for a large-aperture antenna, while benefiting from its higher THz radiation compared to a small-gap antenna. Besides, a mid-size-gap PC antenna offers the significant advantages of being easily fabricated, optically aligned, as well as easily tunable for

ter 5

ize-gap antennas

k th

large-aperture antenna, one requires a high bias voltage supply and fe plifier in order to obtain high TH

etric generator and cooling system

ove excessive heat from antennas, respectively. Contrarily, the all-gap antenna (G < 0.05 mm) is compact, but the THz radiation

all-gap biased PC antennas is to c

THz ra

eld screening effect by calculating the continuity quation for electrons and holes together with Poisson equation. On the other hand, diation power in contrast to nonlinear crystal based THz emitters, and thus it has sparked considerable interest.

5.1 Space-charge bias field screening effect

When a laser light with photon energy larger than the material bandgap is incident upon a biased PC antenna, electrons are excited into the conduction band and become electron-hole pairs. Then electrons and holes move toward the metallic electrodes due to electric attraction force. electrons move to the anode due to its negative charge, and holes move to the cathode due to its positive charge. The separation of electrons and holes results in an electric field that is opposite to the bias field. This space-charge field cancels the bias field partially or completely depending on the photoexcited carrier concentrations. We call this phenomenon as space-charge

bias field screening effect, or space-charge screening effect for brevity.

The space-charge bias field screening effect is often demonstrated in electrical device simulation. In 1996, G. Rodriguez and A. J. Taylor [5] use it to interpret the bipolar THz radiation waveform from bias PC antennas. In their analysis, they consider the space-charge bias fi

e

they include the near-THz field screening effect by incorporating a saturation term ,

( ) ( )

μ_n , η₀ / 1 + _dc

q n x t n , into the following transport equation:

( ) ( )

For different gap size of PC antenna, they found that the negative peak becomes more obvious if the pump fluence increases.

5.2 Theoretical methodology

Figure 5.1 schematically draws our THz antennas with different bias voltage Vb

and G. We start from considering how the bias field Eb of multi-GaAs:As ⁺

s along both the gap direction x and the depth direction z (or the propagation direction of pump pulse) before laser pulse excitation. Provided that a bias voltage Vb

is applied to a multi-GaAs:As⁺ based antenna in the absence of optical pump pulse, the distribution of Eb along x will be nonuniform instead of being simply an average value /V G . The formation of a nonuniform E_b b is due to defects existing within the

antenna, thus altering its electrostatic properties including Eb and space-charge E

concentration. The bias V and b have traditionally been determined

²_{V Eb} ^q _{p x z( , ) n x z( , ) N x zt( , ) N x za( , ) ,}

ε ^{⎡⎣ − ⎤⎦}

−∇ = ∇⋅ = − + − (5.2.1)

ε

in which q and stand for electron charge and electric permittivity, p and n are the trap and acceptor concentrations are den

1

hole and electron concentrations, while the

oted by Nt and Na⁻. All the concentrations on the right side of Eq. (5.2.1) obey Fermi statistics as follows:

( , ) _v{1 exp[( _{f v} ( , )) / ]}

U values are reported to be about U －0.670eV for SI-GaAs [6] and U －0.3eV for

multi-GaAs:As , respectively. For our multi-GaAs:As⁺ antenna, the PC material consists of u As:As⁺ and SI-GaAs parts. The latter has a thickness of

300 m

− + (5.2.5)

where Nc and Nv are the conduction and valance-band effective densities of states, Nt0

and Na are the trap and acceptor concentration, the level of the Fermi energy Uf is determined by letting Eq. (5.2.1) = 0, Uc and Uv are the energy levels of conduction and valence band, a

, depending on the doped concentration or ion-implantation conditions, the

d c c

+ [7]

the m lti-Ga

which value is very much larger than the former layer (~100 nm). To match be located at Uc－0.690eV and μ

the experimental result, Ud and Ua are assumed to Uv + r SI-GaAs case since the SI-GaAs 0.0261eV. These two values are closed to that fo

V part provides the major contribution for THz radiation. For a given bias b, the

ield E at the metal-semiconductor potential at the anode depends on the maximum f max

junction due to image-force lowering, and is given as:

_{V x(} = =_{0) Vb}+ _{qEmax/ 4πε} . (5.2.6)

The solutions of V and Eb b are obtained by calculating Eq. (5.2.1) through Eq. (5.2.6) iteratively.

When laser pump pulses propagate through the antenna with time t, a certain amount of n and p are excited and subjected to electric fields. Both n and p obey the

current-continuity equations:

α

and I_opt stand for the absorption coefficient and the averaged

photogeneration rate, and J and Jn p are the current densities for electron and hole. The averaged photogeneration rate I is defined by: _opt

π

ν π ^{− − −} α ⁻

ν, xm, v, and R refer to pump fluence, photon energy, position of maximum

photogeneration rate, phase velocity of pump pulse, and reflection coefficient, respectively.

In addition to Jn and Jp, the separation between n and p also causes a net-charge concentration Δ ≡ −( p n) , which is the main factor that produces

space-charge field E . The relationship between Es s and

Δ

is described using the Poisson equation: In the near-field regime, the creation of J induces a THz field E satisf

wave equation [8]: where μ is the magnetic permittivity. In the far-field regime, the THz radiation field Er(t) can be obtained by evaluating the broadband Huygen-Fresnel diffraction integral [5.9] of near-field E as follows:

0 0

In Fig. 5.1 we schematically illustra late Er(t). These quantities include the point '

te the quantities used to calcu

x

on the antenna’s surface, the observation point

x

,

the relative vector

r '

of '

x

with respect to x, the distance

r '

from to , x' x

the normal ˆz to the surface, the differential area ds on the surface, and the radiation propagation speed c0 in vacuum. The cos( , ')z rˆ term in Eq. (5.2.14) is known as the obliquity factor. We assume that the observation point locates at the z axis (x= ), 0 and the distance from the antenna’s surface to the observation point is assumed to be 60 cm.

W ile solving Eq. condition was applied to the

pump pulse incident surface, and an absorption boundary condition was assumed on the outer surface. In addition, experimental values including F, pulse duration wt, carrier lifetime c

h (5.2.13), a reflection boundary

τ , and spot size wx are substitute

. According to our previous experimental result [10], the ef

d into Eqs. (5.2.1) - (5.2.14) for

The positive peak E_r^maxcan be obtained by evaluating the maximum . (5.2.14). The relationship between E_r^maxand F can be approximately described by the scaling ru

where the saturation fluence F represents as: s

= +

In calculating Eq. (5.2.1)-(5.2.14), we consider two-dimensional (x d z) cture without the component in the y direction (the lateral gap direction). This

an stru

omission is because of the lack of the component of bias field in the y direction. Thus, if the carrier concentration n (or p) and photogeneration rate I_opt both are the functions of y-variable in Eq. (5.2.7), the integration of I_opt( , , , )x y z t with respect to y will be equal to an averaged rate I_opt(x z t, , ). In the first term of the left-hand

side and the second term of the ri

erage carrier concentration n(x,z,t). In addition, the integration of the thir

ght-hand side of Eq. (5.2.7), the integration of n(x,y,z,t) with respect to y will obtain an av

d term of the right-hand side of Eq. (5.2.7) with respect to y, that is, ∇ ⋅

∫

^{n x( , , , ) ( , , )E x z t dyb} will become

The appendix B demonstrates that how we solve Eqs. (5.2.7)-(5.2.13) using some programming routines of Mathematica v 6.0. More complex routines will be developed in the future works.

+

5.3 Experimental methods

We performed the experiments by em ain spectroscopy as shown in Fig. 5.2. Each THz radiation emitter consists of ip lines with

Au metallic coating layers of 300 nm ulti-energy

arsenic-ion-implanted GaAs (m ) or semi-insulating GaAs (SI-GaAs) rated in Fig. 5.3. When a pump pulse with 800-nm wavelength propagates through the Au coating layer of 300 nm, it will attenuate completely due to the very much small skin depth (~5 nm) of Au, and are not able to excite any carrier beneath the metallic part. In other word, the PC material below the transmission lines will have no contribution to the generation of THz radiation in our case. The transmission line length L and width W are 10 mm and 0.1 mm. For each material, we

1, 0.2, and 0.5 mm. Each sample is imp

ploying THz time-dom

two coplanar str , and was fabricated on m ulti-GaAs:As

antenna as illust

chose four samples with different G of 0.02, 0.

16 ions/cm² lanted with energy of 50, 100 and 200 keV at dosage arsenic ions of 10

and furnace annealed at 600^oC with 60min processing. By a transient photo-reflectance measurement the carrier lifetime τ of our multi-GaAs:As⁺ and

SI-GaAs samples were estimated to be as short as 0.7 and 2.5 ps, respectively. The ion implantation depth was estimated to be about 100 nm by SIMS (Secondary Ion Mass Spectroscopy) measurement.

To control an average bias field strength Eb (~ 3.5 kV/cm) for preventing the risk of antenna damage, the V (=Eb b

×

G) applied to the anode were: 7, 35, 70, and 175 V for G = 0.02, 0.1, 0.2, and 0.5 mm, respectively. The experimental setup for the generation and measurement of THz radiation was similar to the common free space electro-optical (EO) detection [12] from the emitter of biased PC antennas [13]. In detail, the pump or probe pulses with 800-nm wavelength and 130-fs pulse width was also provided by the mode-locked Ti: sapphire laser operating at the repetition rate of 85 MHz and pump power of 500 mW. The pump pulse has spot size wx of 0.1-mm diameter, and was normally incident upon the antenna’s surface. The laser excitation positions are depicted in Fig. 5.2. In the case of G = 0.02 and 0.1 mm, xm = G/2, that is, the spot positions were central with respect to gap so that both illuminations were nearly uniform. In the case of G = 0.2 and 0.5 mm, xm = G/4, the spot positions were off gap center and near the anode, so that both cases belong to edge-illuminations.

From the values of pump power, spot size, and repetition rate, the pump fluence F was estimated to be70 J / cm ,μ ² corresponding to generated carrier concentration of

18 -3

2.0 10 cm× . Thus the pump fluence (F =70 J / cmμ ²) used in the experiment is

considerably larger that the saturation fluence (F_s =25 J/cmμ ²) estimated from Eq.

(5.2.16). The generated THz radiation beam was thus collimated and focused onto the EO sensor of ZnTe with thickness of 1.5 mm by a pair of off-axis paraboloidal mirrors with 12-cm focal length. The distance between the emitter and EO sensor is about 50 cm. Since the THz radiation was collected by parabolic mirrors in this experiment, the temporal resolution would be limited by group velocity mismatch between the optical probe beam and THz radiation. The other coherent polarized probe beam was collimated onto the EO crystal and the polarization was modified because of the modified refractive index from THz field. The probe beam was then transmitted through r and sampled the THz field from the time delay

ump and probe beam.

+

the analyze between the p

5.4. Results and discussions

5.4.1 Trap-enhanced bias field

Before presenting the experimental data, w lti-GaAs:As antennas with numerical results which will be compared with the corresponding measured results. The measured THz waveforms for SI-GaAs will also be shown without any explanation of numerical simulation.

e analyze our mu

For multi-GaAs:As antennas, Figure 5.4 shows on a logarithmic scale the simulated bias field E (x) as a function of position x for four different G in the absence of pump pulses excitation. E

+

b

ach Eb(x) in Fig. 5.4 is near the edge of the anode (0≤ ≤x 10 mμ ) and at depth z=0.1 mμ . As seen in this figure, the Eb(x) established G, one can find much

stronger E (x) with the larger G. Besides, one common feature in all the cases is that the Eb(x) will grow very rapidly if x approaches the anode ( ~ 0x ). For instance, Eb(x) reaches field strength of as high as 10³ kV/cm at x 0.5 m

near the anode are highly nonuniform. For different values of

b

μ

< in the case of

0.5 mm

.

G= This gap-dependent strong bias field is a consequence of the PC antennas with larger G being applied by larger bias voltage.

Because the absorption coefficient of the PC material is about 10⁶ m^-1, the main absorption range of pump pulses is from z= to 0 z=2 m,μ and is relatively much smaller than the antenna’s gap size. Thus, for a given x, Eb is uniform along the ithin this absorption r is somewhat similar to the distribution of the magnetic field genera agnetic bar. Provided that the length of a magnetic bar is 20 cm, then the m ield will be uniform near the bar.

5.4.2 Evolutions of p in antenn

z-direction w ange. This

ted from a m agnetic f

arameters as

Next we study the variations of some physical parameters with time at specific pump depth z and pump fluence F. As an example, Fig. 5.5 shows the calculated

(

n x, )t , Δ( , )x t , E x t , and _s( , ) E x t( , ) for the case of G=0.5 mm. As can be seen from Fig. 5.5(a), at x=0.12 mmthe photo-excited electron concentration n exhibits a maximum peak which is the signature of an edge illumination. After excitation, both the photo-excited electron and hole are subjected to Es and thus move in opposite directions since both possess opposite charges. Of importance, the carrier separation leads to two positive peaks in Δ as depicted in Fig. 5.5(b) where one peak locates at around the gap center and the other peak is near the anode. Obviously, the magnitude ral peak. The large peak has

of the peak near the anode is much larger than that of the cent

a magnitude of 10² of the small peak. This extremely large peak arises from the combination of three mechanisms: the first is that electron mobility is much larger

le it cond i e enhanced bias f anode speeds up

the movement of electron near the anode, and the third is that large amounts of electrons are absorbed by the anode.

The space-charge bias-field screening

than ho mobil y, the se s that th ield near the

phenomenon associated with the two Δ peaks is demonstrated in Fig. 5.5(c). We can see from this figure that the nonuniform bias field E diminishes from its initial value E to a lower value with t. This behavior originates from the mechanism that the small

s b

Δ peak at gap center produces an

opposite field canceling out the original field between the gap center and anode, while the large Δ peak near the anode creates a strong opposite field that screens the original enhanced bias field near the anode. The near-field THz radiation E was obtained from the solution of Eq. (5.2.12), with the result presented in Fig. 5.5(d). It is

opposite field canceling out the original field between the gap center and anode, while the large Δ peak near the anode creates a strong opposite field that screens the original enhanced bias field near the anode. The near-field THz radiation E was obtained from the solution of Eq. (5.2.12), with the result presented in Fig. 5.5(d). It is

在文檔中 半絕緣砷化镓與砷離子佈植砷化镓天線兆赫茲輻射實驗與模擬分析 (頁 93-0)