arXiv:1112.1829v2 [physics.optics] 9 Dec 2011
Terahertz emission by diffusion of carriers and metal-mask dipole inhibition of
M. E. Barnes,1D. McBryde,1G. J. Daniell,1G. Whitworth,1A. L. Chung,1A. H.
Quarterman,1K. G. Wilcox,1H. E. Beere,2D. A. Ritchie,2and V. Apostolopoulos1, ∗
1School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, United Kingdom
2Semiconductor Physics Group, Cavendish Laboratory,
University of Cambridge, Cambridge CB3 0HE, United Kingdom
(Dated: December 12, 2011)
Terahertz (THz) radiation can be generated by ultrafast photo-excitation of carriers in a semicon-
ductor partly masked by a gold surface. A simulation of the effect taking into account the diffusion
of carriers and the electric field shows that the total net current is approximately zero and cannot
account for the THz radiation. Finite element modelling and analytic calculations indicate that the
THz emission arises because the metal inhibits the radiation from part of the dipole population,
thus creating an asymmetry and therefore a net current. Experimental investigations confirm the
simulations and show that metal-mask dipole inhibition can be used to create THz emitters.
PACS numbers: 79.60.Bm,73.20.Mf,87.15.ht,78.47.D-
THz time domain spectroscopy (THz-TDS) employs a
synchronous detection scheme with inherent high signal
to noise ratio which allows very accurate measurements.
In THz-TDS a gallium arsenide photo-conductive (PC)
emitter antenna is the most frequently used way of pro-
ducing radiation . A titanium sapphire (Ti:S) ultra-
fast laser is commonly used to excite carriers across the
band-gap of gallium arsenide. The pulsed illumination
from the laser combined with an applied electric bias cre-
ates a fast current change, which emits THz waves with
intensity proportional to the rate of change of current.
The photo-Dember (PD) effect is another THz emission
mechanism also based on ultrafast carrier transport. THz
radiation is produced by illumination of a semiconductor
surface by an ultrafast near infrared (NIR) laser with en-
ergy above the bandgap (usually Ti:S), but without the
application of electrical bias [2–4]. The strong absorption
of light near the surface creates a large carrier gradient
of electrons and holes, which initiates a diffusion current.
Because of the different mobilities, electrons and holes
spatially separate on a picosecond time scale. The result-
ing dipole radiates at THz frequencies but in a direction
perpendicular to the optical illumination. The PD effect
was not considered to be competitive with other genera-
tion techniques because of low output power, mainly due
to poor out-coupling [2–5]. However, Klatt et al. [6–8]
have demonstrated a lateral PD emitter, shown in Fig.
1(a), which takes advantage of the dipole created by lat-
eral diffusion currents created by metal masking. This
geometry exhibited bandwidth comparable to PC anten-
nae and a series of emitters was fabricated demonstrating
comparable power output to a PC antenna .
We envisaged an array of emitters in  based on the
principle given in  in order to improve ease of fabrica-
tion and performance. The simulation results, however,
indicated that the predicted THz radiation was much
weaker than expected. The emitters were fabricated and
measurements confirmed that they generate no measur-
able THz signal . This result conflicted with the cur-
rent understanding of the lateral PD effect, as outlined
in  and the fact that the emitters of  do produce
To understand this discrepancy between previous exper-
iments and theory, we used results from a 1 dimensional
simulation of the diffusion equation with a drift current.
The results of the simulation show that the net diffusion
current in the case of  or  is zero and cannot pro-
duce THz emission. Theoretical analysis of the emission
of a dipole under a metal sheet indicated that the dipole
radiation is inhibited, with a similar mechanism to the
one in . Therefore, the suppression of dipoles under a
semi-infinite metallic sheet creates the anisotropy needed
for net current and explains why a net dipole radiates in
the geometry of the lateral PD effect. This claim was in-
vestigated experimentally using semi-insulating (SI) and
low temperature (LT) grown GaAs substrates and the
results are found to be consistent with our hypothesis.
This mechanism indicates a novel method of generating
THz radiation that is based on the diffusion current cre-
ated by ultrafast radiation but also uses the inhibition of
radiation due to a metal surface. Emitters based on this
geometry could have similar or even higher bandwidth
to PC antennae without the requirement for an electric
The geometry of the lateral PD effect is a semicon-
ductor, such as gallium arsenide, partially masked by a
deposited metallic layer, as shown in Fig. 1(a). The ul-
trafast laser is focused on the edge of the metal so that
the metal obscures half of the beam profile. In order
to simulate the carrier diffusion, a 1D model was used
similar to the one in [3, 11]. Assuming carriers in the
semiconductor are generated proportional to the light in-
0 20 40
Current Density (104A m-1)
0 20 40
60 80 100
FIG. 1. (a) Illustration of the PD effect showing the coordi-
nate system used. (b), (c), (d) representation of the electron
density, hole density and current density. Each curve is at 20
ps intervals within a 100 ps time frame; progression of time
corresponds to a fall of the peak concentration or peak current
tensity below the metallic mask, the initial concentration
of carriers was taken to be a half-Gaussian distribution.
As the ultrafast pulse is approximately 100 times shorter
than the length of the THz pulse, it is assumed that
the carriers are generated instantaneously. The holes are
assumed to diffuse with a mobility 20 times lower than
that of the electrons . The resulting charge separa-
tion produces an electric field, which affects the motion
of the carriers. The equation describing the evolution
of the electron density, including both electric field and
∂x(neE) + D∂2ne
where the electron density is ne, the hole densiy is nh
and the electric field is E. The mobility, µ , and the dif-
fusion coefficient, D, follow the Einstein relation and the
temperature is assumed to be 3000 K for electrons and
300 K for holes [3, 11]. We assume that the tempera-
ture is constant during the simulation. The electron-hole
recombination time constant, τ1, is set at 20 ps for LT
and SI-GaAs and the electron-defect recombination time
constant, τ2, is set at 200 fs and used only in the case
of LT-GaAs [13–15]. The equation is solved numerically
for a half-Gaussian with waist of 100 µm. A mobility
of 8500 cm2V−1s−1was used both for SI and LT-GaAs.
Here the results for SI-GaAs are shown, in Fig. 1(b) the
temporal evolution of the electron concentration over 100
ps is shown in steps of 20 ps. In this graph the metal
sheet shadows the left region from 0 to 20 µm. The time
evolution shows that electrons are annihilated at every
step due to recombination and a large flux of electrons
towards the left due to diffusion is caused by the initial
large gradient. There is also diffusion towards the right
but it is not obvious due to the smoother gradient of the
concentration curves. A kink in the electron distribution
forms at the metal edge due to the fact that electrons
that diffuse to the left recombine at a much lower rate
due to the decreased hole density. The hole concentra-
tion profiles are shown in Fig. 1(c), diffusion of the holes
in this timescale is negligible on account of the lower
mobility and lower temperature. A peak forms in the
hole concentration at the metal edge because the maxi-
mum concentration of electrons moves to the right as a
result of diffusion. The current density that is created by
this time evolution can be seen in Fig. 1(d), which shows
a large positive current spike at the edge of the metal;
however there is also a negative current in the area of
the unmasked semiconductor. The total current is the
integration of these curves in space and the result is very
small but not zero. This small current is due to the effect
of the electric field, because the electrons travelling to-
wards the left are attracted by the entire hole population.
If the simulation runs only with the effects of diffusion
then the total current at any time is exactly zero. The
current density due to the electric field is approximately
4 orders of magnitude smaller in comparison to what our
simulation predicts for the diffusion current density of
the classical PD case [2–4]. In general, the ratio between
E-field and diffusion generated currents can be estimated
to be ∼ r2/λ2, where r is a typical length scale for the
diffusion and λ is the Debye length. The importance of
the E-field current is dependent on how the Debye length
compares with the diffusion distance, in the lateral PD
case λ ≫ r, and diffusion predominates. We conclude
that the current generated from the E-field is negligible
and would not be enough to create measurable THz ra-
diation, this is also confirmed experimentally in .
The conclusion from the simulation is that diffusion can-
not create a net total current even when starting with an
asymmetric carrier concentration. Although the simula-
tion is quite simple in assuming instantaneous generation
of carriers and stable carrier temperatures, these sim-
plifications do not alter the result that diffusion cannot
create a net current. This statement can also be sup-
ported with a theoretical argument that the microscopic
diffusion current is proportional to ∂ne/∂x, therefore the
total current due to diffusion will be the definite integral
?(∂ne/∂x)dx from a large negative to positive value. As
long as the initial concentration starts from zero and ends
to zero this integral will be equal to zero. Furthermore,
in diffusion an electron has an equal probability of diffus-
ing in any direction, so the net current due to diffusion
must be equal to zero for a large number of electrons.
Therefore diffusion cannot be solely responsible for THz
radiation for the lateral PD geometry; another effect
must be the cause of the THz emission. Fig. 2(a) shows
the emission of two dipoles, as simulated by finite el-
ement modelling from two equal oscillating currents in
anti-phase, 100 nm under the surface of the semicon-
ductor.In Fig. 2(a) there is no metal, which results
in quadrupole radiation that has no component in the
direction of y where the THz emission is measured ex-
perimentally. In Fig. 2(b) there is a metallic layer (gold)
with a refractive index estimated from . It can be
seen that the radiation from the dipole under the metal
is completely suppressed; only the dipole in the free area
is radiating and of course this gives THz emission in the
y-direction of the receiver. The suppression of radiation
happens due to the long wavelength of the THz radia-
tion in relation to the distance between the dipole and
metal. The radiation that is reflected by the surface of
the metal acquires a π-phase shift in relation to the non-
reflected radiation [17, 18]. Interference between the non-
reflected and reflected radiation is destructive and causes
the dipole under the metal to be suppressed, and no emis-
sion to be generated in the y direction .
We analytically studied the radiation of a dipole under
a semi-infinite metallic surface using . The problem
is considered in 2 dimensions, over a cross-section of the
emitter. The surface of the semiconductor and the metal
is in the x-direction and the THz wave is generated in
the y-direction, as shown in Fig. 1(a). An expression for
the radiated electric field from an oscillating dipole under
the surface is:
k (r0− y0)
Where r0is the distance of the dipole from the edge of the
metal sheet and y0is the distance in the vertical direc-
tion and k is the wavenumber. Φ is the Fresnel integral
defined by Φ(z) =?z
ical applies when x is positive and the positive sign when
x is negative. The derivation is done in free space which
underestimates the amount of suppression and a perfect
metal has been assumed.
Equation 2 is plotted in Fig. 2(c) using , where it
shows the dependence of the radiation in the y direction
as a function of the position of the dipole. As expected,
when under the metal there is suppression, whereas when
the dipole is out of the metallic region it emits. The
amount of suppression depends on how close the dipole
is to the metal and the oscillation frequency. Here the
dipole separation from the metal is set at 1 µm as an
approximation of the absorption length of GaAs at a
wavelength of 800 nm  and a frequency of 2 THz has
been chosen as a typical emission frequency. The emit-
ted radiation drops close to zero, even when the dipole
is just below the edge of the metal. The oscillations in
the strength of radiation reveal interference phenomena,
however in the case of experiment, where a wide spread
−∞eit2dt. The minus sign in the rad-
0 10 20x(µm)
Power Flow (norm. W/m)
FIG. 2. Finite element modelling of a simplified lateral PD
emitter represented by two oscillating currents in anti-phase
(a) without gold masking and (b) with gold masking.
shows a plot of equation 2 corresponding to the electric field
of a dipole radiating at 2 THz at a distance of 1 µm below
of dipoles is present, the oscillations are not expected to
A theory of how the lateral PD emitter works is proposed
here and it is straightforward to experimentally validate.
The hypothesis in  states that the discontinuity in the
carrier distribution will create a dipole directed towards
the metallic region while our theoretical model predicts
the formation of a net dipole in the opposite direction
due to the suppression of dipoles beneath the metal. In
THz-time domain spectroscopy the direction (sign) of the
E-field can be directly measured and compared between
experiments. Experimentally the THz radiation gener-
ated is collimated and focused with two parabolic mir-
rors onto an LT-GaAs receiver. A 5 µm-gap bowtie PC
antenna was used, as shown in Fig. 3(a) with the laser
focused on top of position A. The polarity of the THz
emission was mapped with the direction of current by
biasing the PC antenna in opposite polarities and one of
the measurements is shown in Fig. 3(c). The same PC
antenna (LT-GaAs) was then disconnected from the bias,
and translated across to the area B, shown in Fig. 3(a),
where a metallic edge was used as a lateral PD emitter.
The polarity of the THz waveform indicated that the
current was flowing as expected in our argument where
the radiating dipole is in the non-masked region of the
antenna. The LT-GaAs PC emitter was then replaced
with a dedicated LT-GaAs-PD emitter and we measured
the PD effect on two opposite edges of metal strips, ar-
eas C and D in Fig. 3(b); the beam waist at the focus
was approximately 60 µm. The results are shown in Fig.
3(d), where we note the expected polarity change be-
tween opposite edges. In Fig. 3(e) the spectra of PC and
PD antennae are illustrated, showing similar bandwidths
produced from the PD and PC emitter. The spectra were
obtained in ambient atmosphere and show water absorp-
SI-GaAs samples have also been used with similar re-
sults, however, the LT-GaAs samples had much larger
bandwidth and signal in comparison to the SI-GaAs. The
4 Download full-text
FIG. 3. Diagram showing the plasement of the laser beam
on (a) the bowtie PC emitter and (b) the lateral PD emit-
ter. (c) Shows the current recorded in the time domain for a
PC antenna. (d) shows THz emission at two opposite bound-
aries to observe the predicted sign change.
Fourier transform of (a) and (b) demonstrating comparable
bandwidth between the PC and PD emitter. The experiment
was performed in ambient atmosphere.
(e) shows the
LT-GaAs emitter was easier to saturate and thus a larger
area was illuminated, in relation to SI:GaAs but further
theoretical and experimental investigations are needed to
investigate these differences in performance between LT
In conclusion, in a partially metal-masked semiconduc-
tor, illuminated with ultrafast NIR radiation, carrier dif-
fusion and carrier recombination alone cannot account for
the observed THz radiation. We propose a new theory
for the THz emission due to dipole radiation suppression
from the metal mask and experiments confirm our model
for THz emission. This type of emitter does not suffer
from the lifetime issues of biased PC antennae as there
is no electrical bias requirement. Furthermore, emitters
based on lateral diffusion currents and dipole radiation
suppression are simple to fabricate, opening up possibili-
ties for easier THz integration and interfacing with other
elements. This concept gives rise to design proposals for
a series of emitters which would give similar performance
to a PC antenna, which is currently the standard THz
 P.U. Jepsen,
Laser & Photon. Rev. 5, 124 (2011).
Physical Review B 65, 165301 (2002).
 K. Liu, J. Z. Xu, T. Yuan, and X. C. Zhang, Physical
Review B 73, 155330 (2006).
 P. Gu, M. Tani, S. Kono, K. Sakai, and X. C. Zhang,
Journal of Applied Physics 91, 5533 (2002).
 M. B. Johnston, D. M. Whittaker, A. Dowd, A. G.
Davies, E. H. Linfield, X. Li,
tics Letters 27, 1935 (2002).
 G. Klatt, B. Surrer, D. Stephan, O. Schubert, M. Fischer,
J. Faist, A. Leitenstorfer, R. Huber,
Applied Physics Letters 98, 021114 (2011).
 G. Klatt, F. Hilser, W. Qiao, M. Beck, R. Gebs,
A. Bartels, K. Huska, U. Lemmer, G. Bastian, M. B.
Johnston, M. Fischer, J. Faist,
Optics express 18, 4939 (2010).
 G. Klatt, F. Hilser, W. Chao, R. Gebs, A. Bartels,
K. Huska, U. Lemmer, G. Bastian, M. B. Johnston,
M. Fischer, J. Faist, and T. Dekorsy, OSA / CLEO /
QELS 2010 (2010).
 D. McBryde, M. E. Barnes, A. L. Chung, Z. Mihoubi,
G. J. Daniell, A. H. Quarterman, K. G. Wilcox, H. E.
Beere, D. A. Ritchie, A. C. Tropper,
tolopoulos, “Simulation of metallic nanostructures for
emission of THz radiation using the lateral photo-
Dember effect,” (2011).
 K. Drexhage, Journal of Luminescence 1-2, 693 (1970).
 T. Dekorsy, T. Pfeifer, W. K¨ utt,
Physical Review B 47, 3842 (1993).
 J. S. Blakemore, Journal of Applied Physics 53, R123
 I. S. Gregory, W. R. Tribe, C. Baker, B. E. Cole, M. J.
Evans, L. Spencer, M. Pepper, and M. Missous, Applied
Physics Letters 86, 204104 (2005).
 I. S. Gregory, The development of a continuous-wave ter-
ahertz imaging system, Ph.D. thesis, University of Cam-
 C. Baker, Development of Semiconductor Materials for
Terahertz Photoconductive Antennas, Ph.D. thesis, Uni-
versity of Cambridge (2004).
 E. D. Palik, Handbook of optical constants of solids, Aca-
demic Press handbook series (Academic Press, 1985) pp.
xviii, 804 p.
 T.Doi,K. Toyoda,
Applied optics 36, 7157 (1997).
 H. Yasuda
Japanese Journal of Applied Physics 47, 1632 (2008).
 P. M. Morse and H. Feshbach, Methods of theoretical
physics (McGraw-Hill Book Company, Inc., New York,
 M. Abramowitz and I. A. Stegun, Handbook of Mathe-
matical Functions, with Formulas, Graphs, and Mathe-
matical Tables (Dover Publications, New York, 1972) p.
and D. A. Ritchie, Op-
and T. Dekorsy,
and T. Dekorsy,
and V. Apos-
and H. Kurz,