1. APPLIED PHYSICS LETTERS 97, 073104 2010
Surface carrier recombination of a silicon tip under high electric field
B. Mazumder, A. Vella,a F. Vurpillot, G. Martel, and B. Deconihout
Groupe de Physique des Materiaux, UMR CNRS 6634, CORIA UMR CNRS 6614, UFR Sciences Site du
Madrillet, Avenue de l’Université, B.P. 12 76801, Saint Etienne du Rouvray Cedex, France
Received 21 May 2010; accepted 12 July 2010; published online 17 August 2010
Using laser assisted atom probe tomography, we investigate the surface recombination processes of
a subwavelength Si tip illuminated by an ultrashort laser pulse under high electric field. In practice,
by changing the laser wavelength, we demonstrate the presence of a very long electron-phonon
relaxation time at the surface. It is experimentally shown that this behavior is common to indirect
band gap semiconductors. Furthermore, a simple model is developed in this paper to explain laser
wavelength dependence of our experimental results and estimate the surface recombination time.
© 2010 American Institute of Physics. doi:10.1063/1.3473816
During the past decade a few techniques suitable for recombination processes, extracted from the experimental re-
studying the surface carrier recombination time have been sults, are then discussed.
developed.1 Following four techniques have been particu- The instrument used in this study is a linear atom probe
larly useful: transient reflectivity and/or transmission, with a flight length of 10 cm LaWaTAP from CAMECA .10
transient-grating diffraction including two-beam self- The experiments are performed in ultrahigh vacuum
diffraction, photothermal deflection, and time resolved 10−7 Pa and the tip is cooled at 80 K. The laser system is
photoemission.2 However, only a few works exist on the sur- an amplified laser operating at 100 kHz, generating pulses of
face recombination processes under high electric field.3 500 fs with a tunable energy of up to 0.1 mJ/pulse a tunable
When an electric field is applied at the surface of the Si wavelength IR at = 1030 nm, green at = 515 nm, and
sample, a strong band bending was predicted by Tsong.4 This ultraviolet UV light at = 343 nm .
effect increases the band bending of the space-charge layer. Considering the field evaporation theory of a field
Since the band bending represents a potential barrier to one emitter,11 surface atoms are emitted with an evaporation rate
sign of carriers and a potential well to the other, its magni- K t given by
tude strongly influences the carrier densities near the surface
and their recombination time. Very long recombination time − Qn
K t =N exp , 1
in the presence of surface electrical field has already been k BT t
reported in the study of Si photoluminescence.5 with N the number of kink site surface atoms, the surface
A high electric field is always applied to the sample ana- atom vibration frequency, kB the Boltzmann’s constant
lyzed in atom probe tomography APT which seems to be 8.6 eV K−1 , and Qn the activation energy 0.1– 1 eV .
one of the most promising tools for the investigation of ma- As a result, the temperature variation in the tip apex can be
terials used in nanoelectronics, such as semiconductors or scanned as a function of time by measuring K t .
oxides.6,7 To optimize the performance of the APT analysis K t as measured for a p-doped 51018 cm−3 of boron Si
on semiconductors, the surface charge recombination pro-
tip using IR light is shown in Fig. 1 a . The Si tip has an
cesses after the laser excitation should be well understood.
end radius R = 55 5 nm and a cone angle below 10°,
Indeed, in laser assisted APT, surface atoms are removed one
as measured by transmission electron microscopy. The laser
by one by field emission from sharp tips with an end radius
intensity was tuned between 0.2 and 5.7 GW/ cm2 and the
of around 50 nm submitted to a high field of several tens of
polarization was set axial. The evaporation rate measurement
volts per nanometers; the interaction of the laser beam with
is derived from ion flight time spectra. Each spectrum
the tip increases its temperature and hence allows the evapo-
is sampled over more than 50 000 atoms. For I
ration of surface atoms.8,9 This temperature increase is re-
= 0.2 GW/ cm2 the main peak of the 28Si+2 ions is followed
lated to the charge recombination process and, since only
by two lower peaks of 29Si+2 and 30Si+2 isotopes. Increasing
surface atoms are evaporated, APT can be used as a new the laser intensity, it becomes more and more difficult to
technique to study the surface recombination process under distinguish the two isotopes due to the presence of a wide
high electric field. In addition to be of great importance for peak after the main Si peak. For I = 5.7 GW/ cm2, the wide
the APT, this study can also be of great interest for near-field peak totally overlaps the isotopes and its amplitude is almost
scanning optical microscopy and silicon photovoltaic devices equal to that of the main peak. However, using the green
community. light the ion flight time spectrum shows very well resolved
In this letter, we study the ion emission from subwave- silicon peaks for high laser intensity I = 4 GW/ cm2, as re-
length silicon tips as a function of laser wavelength and en- ported in Fig. 1 b .
ergy. To interpret these results, we develop a simple model The photon energy of IR laser pulses 1.2 eV is almost
for the thermal assisted evaporation based on the existence of equal to the indirect band gap energy of silicon 1.1 eV .
two surface relaxation processes. The typical times of these Since the photon energy of green light 2.45 eV is higher
than the band gap energy, it seems reasonable to think that
a
Electronic mail: angela.vella@univ-rouen.fr. the wide peak appears only when the laser excitation is reso-
0003-6951/2010/97 7 /073104/3/$30.00 97, 073104-1 © 2010 American Institute of Physics
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2. 073104-2 Mazumder et al. Appl. Phys. Lett. 97, 073104 2010
FIG. 2. Color online a Representation of tip geometries; b excitation
and two steps recombination processes; c simulated normalized evapora-
tion rate as function of time obtained for a Si tip with IR laser light and d
with green laser light. Different curves correspond to different carrier den-
sities N2 = 2 1020 cm−3, N2 = 8 1020 cm−3, N2 = 1021 cm−3, N2 = 3
1021 cm−3, and N2 = 7 1021 cm−3 bottom to top , respectively.
direction and it follows a Gaussian shape along the tip axis
direction with a typical width w. After the interaction with
FIG. 1. Color online Normalized evaporation rate as function of time the laser beam, electrons excited in the conduction band car-
obtained from an Si tip a for IR laser, using the laser intensities bottom to rier density N2 can relax their energy by a rapid recombina-
top I = 0.2 GW/ cm2, I = 1.2 GW/ cm2, I = 2.2 GW/ cm2, and I = 5.7 GW/ tion process due to electron-electron thermalization in the
cm2, respectively; b green laser light, smooth thick line corresponds to the conduction band intraband relaxation with typical time
best fit using Eq. 4 .
2 : dN2 / dt = −N2 / 2 and a long recombination process due
to interband electron-hole recombination with a typical time
nant with the band gap energy. To test this hypothesis and 1 : dN1 / dt = −N1 / 1 + N2 / 2, where N1 is the carrier density
also to check if this wavelength dependence is typical of in the bottom of the conduction band as schematically shown
silicon or can be extended to any indirect band gap semicon- in Fig. 2 b .13 We suppose that their energy is locally trans-
ductors, same experiments was conducted on silicon carbide ferred to the lattice by phonons excitation, leading to a tem-
SiC . The band gap energy of SiC is 2.36 eV, i.e., close to perature increase, so that the spatial and temporal heat evo-
the green photon energy 2.45 eV . The same behavior ob- lution takes place following the Fourier equation:
served for Si tip with IR green light was observed on SiC d
using green UV light. The same behavior was observed on G z,t dV = CV T t T t dV + − D T S+ z Tz
dt
a n-doped 51018 cm−3 of phosphorus and intrinsic Si tip,
showing that at T = 80 K the role of doping is negligible, as − S− z Tz , 2
expected.
where G z , t is the generation rate related to the recombina-
Considering the evaporation rate as a measure of the tip
tion process by
temperature variation, the presence of two peaks one narrow
and one wide , at high intensity for IR illumination, corre- N2 z,t N1 z,t
sponds to two heating processes delayed by several nanosec- G z,t = E2 + E1 , 3
2 1
ond. The temperature increase is related to the excitation of
charges and their recombination. Due to the long optical pen- where CV and D T are the volume specific heat and the
etration depth of Si at = 1030 nm 1 m Ref. 12 thermal conductivity of the Si tip, respectively. The values
and the small transverse dimensions of the tip D = 2R of CV and D T are reported in the literature for Si
= 100 nm , the laser excitation is uniform in the transverse nanowires,14,15 whose geometry is close to our tip geometry.
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3. 073104-3 Mazumder et al. Appl. Phys. Lett. 97, 073104 2010
Taking into account the tip shape, S+ z and S− z correspond Another important parameter of our model is the long
to surfaces perpendicular to the tip axis delimiting the el- recombination time 1 = 20 ns which is very long as com-
emental volume dV, as represented in Fig. 2 a . The tempera- pared to the Auger recombination time for a charge density
ture evolution at the tip apex T z = 0 , t , predicted by this of 1021 cm−3 Auger a few picosecond .18 However, a sub-
simple model, can be introduced in Eq. 1 to check the stantial part of the photogenerated holes is swept toward the
evaporation rate dependence as a function of energy and la- surface by the strong near surface electric field and rapidly
ser wavelength. The activation energy Qn in Eq. 1 was captured by the surface states. On the other hand, the photo-
fixed at 0.1 eV as reported by Thompson et al.16 generated electrons are rapidly swept toward the bulk. Due
The carrier density N2 and the size of the excited zone to this spatial charge separation, the value of the charge
w were deduced from experimental data as follow. Consid- density for Auger calculation should be as follows:
ering the tip as a semi-infinite cylinder hot wire model ,8 N2Vholes / Velectrons = N210−3, taking into account the effective
with Tmax, the maximal temperature reached after the laser volume occupied by holes Vholes R2h with h = 0.4 nm the
4
illumination, the cooling rate is governed by band bending depth and by electrons Velectrons R 2w .
Tmax As a conclusion, we studied the evaporation of a Si tip as
Tt . 4 a function of the laser wavelength and intensity using laser
2D assisted APT. We showed that it is possible to find a resonant
1+ 2 t
w laser wavelength for which a long evaporation process is
observed. We propose a model to explain this behavior tak-
Injecting Eq. 4 into Eq. 1 , this formula can be used to fit
ing into account the long recombination process of excited
the experimental behavior of the evaporation rate, as re-
charges at the surface of the tip under a high electric field.
ported in Fig. 1 b , with the fit parameters; Tmax = 180 K and
These results may be of significant importance for all people
w = 300 nm. Due to the energy conservation CV Tmax − T0
studying Si component for photovoltaic applications.
= N2 E2 + E1 , a temperature increase of 100 K corresponds
At last, our simple model allows an estimate of this sur-
to a charge density of N2 = 1021 cm−3, each charge transfer-
face recombination time and it explains well the role of the
ring an energy of E2 + E1 = 1.2 eV to the bulk.
laser wavelength on the evaporation process.
We fix the fast recombination time 2 = 2 ps as reported
in Ref. 13 and adjust the value of 1 at 20 ns to obtain a 1
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11
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18
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