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Solid State Phenomena
ISSN: 1662-9779, Vol. 242, pp 312-315
doi:10.4028/www.scientific.net/SSP.242.312
© 2016 Trans Tech Publications, Switzerland
Submitted: 2015-05-21
Accepted: 2015-05-22
Online: 2015-10-23
Characterization of Si convertors of beta-radiation in the scanning
electron microscope
M.A. Polikarpov1,a and E.B. Yakimov2,3,b *
1
National Research Center Kurchatov Institute, Moscow, 123182 Russia
2
Institute of Microelectronics Technology RAS, 142432, Chernogolovka, IPTM, Russia
3
National University of Science and Technology MISiS, Moscow, Russia
a
polikarpov.imp@gmail.com, byakimov@iptm.ru
Keywords: Beta-voltaics, SEM, simulation
Abstract. The approach for imitation of beta radiation using the e-beam of scanning electron
microscope (SEM) for semiconductor energy converter testing is proposed. It is based on the
Monte-Carlo simulation of depth-dose dependence for beta-particles and a determination of
collection probability from the EBIC measurements of collection efficiency dependence on beam
energy. Experiments with the 63Ni radiation source confirm that such approach allows to predict the
efficiency of semiconductor structures for radiation energy conversion to electric power.
Introduction
In beta voltaic batteries energy of nuclear radiation is directly converted to electric power using a
semiconductor convertor. The principle of such converters is similar to that of solar cells. The
electron-hole pairs are created by beta particles emitted from radioactive isotopes, then they diffuse
to a collector and are separated by the built-in electric field of a collector (depletion region of the
Schottky barrier or p-n junction) to generate electric current. If a Si based structure is used as the
convertor, the MEMS technology can be applied for fabricating a beta voltaic microbattery
compatible with IC technology. Thus, a battery can be integrated on the same chip with other
micro/nano devices or components, i.e., “battery-on-chip” can be realized. 63Ni isotope is probably
the most suitable for such applications because Ni can be used simultaneously as a circuit element,
e.g. for interconnections. Radioactive isotopes are rather expensive, therefore for a successful
design and optimization of effective converters methods for their testing before radioactive isotope
deposition should be developed. A good idea is to use for this purpose e-beam of SEM, which could
imitate the beta radiation. This idea was realized in some works (for example see [1]) and beam
energy of 17 keV corresponding to the mean energy of electrons emitted by the 63Ni isotope was
usually used for the beta radiation imitation. However, elastic and inelastic scattering and
absorption inside the 63Ni film modify significantly the spectrum of electrons emitted from the film.
Depth-dose functions describing the depth dependence of excess carrier generation rate in Si, SiC
and GaN for beta particles emitted from 63Ni films of different thickness were calculated in [2,3] by
the Monte-Carlo program taking into account an isotropic emission of radiation, the full beta energy
spectrum for the 63Ni isotope and inelastic and elastic scattering processes in a Ni film. It was
shown that a decay of these functions with a depth is close to exponential one while the depth-dose
functions for monoenergetic electron beam perpendicular to the surface are rather well described by
the Gaussian functions [4,5]. For this reason it is impossible to imitate the beta particle depth-dose
function using one or a few e-beam energies and other approaches for beta-radiation imitation using
SEM should be developed.
In the present paper one of such approaches based on the calculated depth-dose functions and on
then experimentally determined collected probability by the EBIC investigations of particular
semiconductor structures is discussed. The main features of such approach are illustrated by the
results of Si and SiC based structure investigations.
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans
Tech Publications, www.scientific.net. (#103369937, California Institute of Technology, Pasadena, USA-12/11/17,10:49:45)
Solid State Phenomena Vol. 242
313
Numerical simulation
h(z)
A spectrum of electrons living the 63Ni film differs essentially from that emitted by the 63Ni
isotope due to scattering and absorption in the film [6]. However, for the induced current simulation
it is more useful to calculate the depth-dose function for beta particles emitted from 63Ni film
because they are emitted in a wide angle range. Such calculations for Si, SiC and GaN were carried
out in [2,3] by the Monte-Carlo method. It was shown that the normalized depth-dose function
depends on the Ni film thickness and is saturated at thicknesses exceeding 4-5 µm. For the
illustration the normalized depth-dose functions in Si obtained by the Monte-Carlo simulation for
thin (10 nm) and thick (3000 nm) 63Ni films are shown in Fig. 1. The depth-dose functions
calculated for for e-beam perpendicular to a surface with energy of 17.1 eV, which is the average
energy of beta-particles for 63Ni, and 40 keV, which is the maximum energy for the most of SEMs,
are presented in the same Figure for a comparison. It is seen that a distribution of excess charge
carrier generation rate under the beta radiation is indeed qualitatively different from those for a
monoenergetic electron beam.
Therefore it is impossible to simulate the
beta radiation with a SEM e-beam by a
corresponding choice of one or a few beam
1
energies and other approaches should be
4
developed. As shown in [7,8], the induced
current in semiconductor structures can be
2
calculated as a convolution of depth-dose
function with the collection probability, i.e.
0.1
the probability that a minority carrier
generated at a depth z below the surface will
1
3
be collected by a collector. Thus, if the
depth-dose function for beta radiation is
0.01
simulated by the Monte-Carlo method to
0
2
4
6
8
10
12
14
calculate the induced current value the
z, µm
collection probability for the structure under
study should be determined. The collection Fig. 1. Normalized depth-dose functions in Si
probability for the particular structure calculated for beta-particles emitted from 63Ni
depends on the parameters of this structure film with a thickness of 10 nm (1) and 3000 nm
only. The approach proposed in the recent (2). The depth-dose functions for e-beam
paper is based on the determination of perpendicular to a surface with energy of 17.1 and
collection probability by fitting the collected 40 keV are shown by curves 3 and 4, respectively.
current dependence on beam energy
measured in the Electron Beam Induced
Current (EBIC) mode.
A few ways can be used to obtain the collection probability from the collected current
dependence on beam energy. For the simple structures such as the Schottky barriers or p-n junctions
the main parameters of the structure under study such as the depletion region width, the metal
thickness, the diffusion length, the junction depth, the surface recombination velocity and the
diffusion length values in n- and p-regions for p-n junctions can be obtained by fitting the
experimental dependence of collected current Ic in the EBIC mode on beam energy Eb. Then the
collection probability can be calculated using these parameters by the numerical solution of
homogeneous diffusion equation [9]. The similar procedure can be used for the structures with the
Schottky barriers. Such approach is illustrated in Fig. 2, where the normalized Ic(Eb) dependence
measured on Si p-i-n diode with a very thin passivation layer and the p-n junction depth of 70 nm is
fitted with calculated one. The corresponding collection probability calculated using the parameters
obtained by fitting the Ic(Eb) dependence is shown in Fig. 3. For more complex structures the
collection probability can be calculated from the measured collection efficiency dependence on
beam energy by the methods proposed in [10] or [11]. Then the induced current can be easily
314
Gettering and Defect Engineering in Semiconductor Technology XVI
calculated for any depth-dose function. To
obtain other parameters of semiconductor
energy convertor e-beam current of SEM
should be adjusted to obtain the collected in
the EBIC mode current equal to the
calculated value of induced current. Using
such value of e-beam current other
parameters of semiconductor convertor
necessary for the prediction of its efficiency,
such as the open-circuit voltage and the fill
factor can be obtained.
Ic/(IbEb)
250
200
150
100
50
0
0
5
10
15
20
Eb, keV
Experimental verification
To check the approach proposed the
current induced by the 63Ni radioactive
source with an activity of 1.3 mCi/cm2 in the
Si p-i-n diode with an area of 8 mm2
presented in Figs. 2 and 3 and in a SiC
Schottky diode with an area of 4 mm2 were
measured. Simultaneously the induced
current values are calculated using the
1.0
depth-dose dependence calculated by the
0.8
Monte-Carlo method for this radiation
source and the collection probabilities
0.6
obtained by fitting the corresponding Ic(Eb)
dependences. Experimental induced current
0.4
densities measured using the 63Ni
radioactive source are 21 nA/cm2 and
0.2
7 nA/cm2 for Si and SiC structures,
0.0
respectively. The corresponding calculated
0
2
4
6
8
10
values are 20 and 7.2 nA/cm2, respectively.
z, µm
Taking into account that the exact thickness
of radioactive film is unknown, the precision
Fig. 3. Calculated collection probability for a Si of calculation of converter parameters can
p-i-n diode.
be discussed as rather good. The
corresponding open-circuit voltage and
maximum power of converters were estimated as 390 mV and 1.5 nW/cm2, respectively, for the SiC
detector and 90 mV and 0.85 nW/cm2 for the Si detector.
Collection probability
Fig. 2. Experimental (symbols) and simulated
(line) normalized collected current dependences
on beam energy for Si p-i-n diode.
Summary
Thus, the approach for imitation of beta radiation using the e-beam of SEM for the prediction of
efficiency of semiconductor structure for the conversion of radiation energy to electric power is
proposed. The experimental verification of approach proposed was carried out and its reliability was
confirmed. The work was partially supported by the Russian Foundation for Basic Research (grant
14-29-04056).
Solid State Phenomena Vol. 242
315
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