Microelectronic Engineering 86 (2009) 1866–1869
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Microelectronic Engineering
journal homepage: www.elsevier.com/locate/mee
Electronic structure of memory traps in silicon nitride
V.A. Gritsenko *, S.S. Nekrashevich, V.V. Vasilev, A.V. Shaposhnikov
Institute of Semiconductor Physics, Lavrentyeva av., 13, 630090 Novosibirsk, Russia
a r t i c l e
i n f o
Article history:
Received 2 March 2009
Received in revised form 11 March 2009
Accepted 11 March 2009
Available online 19 March 2009
a b s t r a c t
From experiments on photoluminescence in Si3N4 the polaron energy of 1.4 eV was determined. This
value is in agreement with the energy of thermal ionization determined from electron and hole transport.
Quantum-chemical simulation showed that Si–Si bond is able to capture holes and electrons in Si3N4.
Ó 2009 Elsevier B.V. All rights reserved.
Keywords:
Silicon nitride
Traps
Defects
Amorphous silicon nitride Si3N4 or SiNx<4/3 has property to
localize electrons and holes by deep traps with gigantic lifetime
(10 years at 450 K) in localized state [1]. This property (memory
effect) is widely used in silicon flash nonvolatile memory devices
[2]. In spite of 40 years history and wide practical application in silicon integrated circuits, the electron and hole trap nature (atomic
and electronic structure) in SiNx is still unclear. Now there is no
doubt, that hole and electron localization in SiNx is related to excess of silicon [3].
There are three models of electron and hole traps in silicon nitride. The first one is model of dangling Si bond as a capturing center. In [4–6] it was shown that in ESR experiments on silicon
nitride concentration of paramagnetic centers was found about
1016 cm3, meanwhile concentration of traps was about
1020 cm3, which raises serious doubts in correlation between dangling bonds and traps. Another model assumes presence of threefold coordinated negatively (K center) and positively (K+ center)
charged silicon atoms as traps for holes and electrons, respectively
[6]. In this model K-center captures two charge carriers (holes or
electrons) simultaneously, which explains absence or little paramagnetic signal in silicon nitride samples with injected carriers.
The third model suggests Si–Si bond as a memory trap in silicon
nitride.
Nitride Si3N4 and silicon oxide SiO2 has a similar electronic
structure. In SiO2 traps are mainly presented by vacancies of oxygen as Si–Si bond. A similar hypothesis about Si–Si bond or nitrogen vacancy in silicon nitride possibly responsible for electron and
hole localization had been discussed [1,3,7,8].
* Corresponding author. Tel.: +7 383 3333864.
E-mail address: [email protected] (V.A. Gritsenko).
0167-9317/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.mee.2009.03.093
In [7] authors introduced the hypothesis about polaron nature
of electron and hole localization in SiNx. The consequence of this
hypothesis is presence of the big Stokes shift in SiNx photoluminescence spectra, like one in SiO2. Present work has three aims: experimental determination of the polaron energy in SiNx from
photoluminescence spectra, comparison of the polaron energy
with experimental data on charge transport and with the results
of quantum-chemical simulation of the nitrogen vacancy and
Si–Si bond in silicon nitride.
Fig. 1 shows the experimental photoluminescence spectra excited with energy 5.2 eV, and photoluminescence excitation spectra, monitored at energy 2.4 eV, measured at room temperature.
Experimental PL and PLE spectra are fitted by Gaussian curves.
The PL spectra has maximum EL = 2.4 eV and full width at half
maximum (FWHM) 0.92 eV. The PLE maximum energy is
EE = 5.2 eV and the same FWHM 0.92 eV, as for PL spectra.
Fig. 2. shows the configuration diagram, deduced from PL and
PLE of SiNx. According to Fig. 2 the polaron energy Wp (or Frank–
Kondon shift) is equal Wp = (EE EL)/2 = 1.4 eV. The obtained polaron energy value can be compared to the thermal trap energy
Wt = 1.4 eV, obtained by charge transport fitting in SiNx within
multiphonon model of trap ionization [9]. Charge transport in SiNx
is controlled by trap ionization. In terms of multiphonon model
there are two key trap parameters: thermal energy Wt, and phonon
energy Wph. According to multiphonon model the thermal trap energy Wt (Frank–Kondon shift) can be obtained from the Stokes shift
of photoluminescence. SiNx.
For verifying the hypothesis about nature of memory traps in
Si3N4 the quantum-chemical simulation of the electronic and
atomic structure had been carried out for two point defects – nitrogen vacancy and nitrogen vacancy saturated with hydrogen atom
(Si–Si bond). Calculations were made within the framework of
V.A. Gritsenko et al. / Microelectronic Engineering 86 (2009) 1866–1869
1867
Fig. 1. Photoluminescence and photoluminescence excitation spectra of silicon
nitride at room temperature. PL was measured at 5.2 eV excitation energy,
photoluminescence excitation monitoring at 2.4 eV.
Fig. 2. Configuration diagram of optical transitions in SiNx.
Density Functional Theory with plane-waves basis set and pseudopotentials in the Quantum–Espresso simulation package. Selfconsisted total-energy calculation were made within plane-waves
cut-off energy 50 Ry, energy convergence threshold was set to
107 Ry. For simulation of trap in silicon nitride the 168-atomic
supercell had been constructed by translating the elementary
14-atomic unit cell of b-Si3N4 along main crystallographic axes.
Afterwards there are two kinds of defects were obtained from
the supercell: nitrogen vacancy and nitrogen vacancy saturated
by hydrogen atom.
Consideration of the nitrogen vacancy with hydrogen atom
makes sense since silicon nitride is usually synthesised from
hydrogenous substances. Hence there is always some amount of
hydrogen atoms is presented in the structure. Beside that, molecular dynamics simulation confirmed that hydrogen atom, if presented, is being steadily localized near the nitrogen vacancy.
The relaxed geometry of the nearest neighborhood of investigated defects in different charged states (neutral defect, defect
charged with electron and hole) is presented on Fig. 3. Big white
balls are silicon atoms, small grey balls are nitrogen atoms, small
white ball is hydrogen. It can be seen that defect geometry sufficiently depends on charge put into the defect supercell.
Fig. 4 shows distribution of the total charge density on the
nitrogen vacancy. The bonding orbital between silicon atoms No.
1 and No. 2 appears after geometry relaxation. There is also charge
of single unpaired electron near the silicon atom No. 3 is notable.
One of the most important trap parameters affecting retention
time is trap depth. To find out possibility of capturing of charge
carriers on the investigated defects, the localization energies of
electrons and holes had been calculated. These energies had been
calculated as difference of the electron affinities (or ionization
energies in case of hole capturing) in perfect cell and in the cell
containing defect:
DEe ¼ vebulk vedefect ; DEh ¼ /hbulk /hdefect ;
where
ve ¼ Eq¼1 Eq¼o ; /h ¼ Eq¼þ1 Eq¼o
Fig. 3. The relaxed geometry of the nearest neighborhood of investigated defects in different charged states (neutral defect, defect charged with electron and hole).
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V.A. Gritsenko et al. / Microelectronic Engineering 86 (2009) 1866–1869
Fig. 4. Bonding orbital between two silicon atoms (1,2), unpaired electron on the
atom No. 3.
Table 1
Calculated localization energies for charge carriers.
Nitrogen vacancy
Nitrogen vacancy + hydrogen
DEelectron (eV)
DEhole (eV)
2.6
1.8
1.9
0.9
Fig. 6. Partial density of states of Si-3p orbitals in Si3N4.
Fig. 5. Different experimental results for electron and hole trap energies in silicon
nitride.
Results of the localization energies calculation are given in the
Table 1.
Results of these calculations show, that nitrogen vacancy (and
so is nitrogen vacancy with hydrogen atom) is able to capture both
holes and electrons. The error in determination of the localization
energies for charge carriers (experimental result is 1.4 eV for electron and hole traps, Fig. 5) [1, 8–13] is mainly related to the inaccuracy of the exchange-correlation functional which had been used
in our calculations.
Analysis of partial density of states (PDOS) showed that defect
energy levels responsible for capturing charge carriers are formed
by 3s and 3p states of silicon (Fig. 6).
Of special interest is spatial distribution of charge of the captured carriers. Figs. 7 and 8 shows the surfaces of the equal charge
density (isosurfaces) of negative and positive charge put into the
supercell for both defects. These images were obtained by subtraction of total charge densities of charged and neutral defect at the
geometry of charged defect. The obtained results confirmed localization of charge carriers on the Si–Si defect.
According to quantum-chemical calculation excess silicon as Si–
Si bond or/and nitrogen vacancy are responsible for electron and
hole localization in silicon nitride.
Fig. 7. Distribution of charge density of captured (a) electron (b) hole on nitrogen vacancy.
V.A. Gritsenko et al. / Microelectronic Engineering 86 (2009) 1866–1869
1869
Fig. 8. Distribution of charge density of captured (a) electron (b) hole on nitrogen vacancy with hydrogen atom.
Acknowledgement
This work was supported by the Korea Ministry of Science and
Technology under the National Program for Tera-Level Nanodevices and project No. 70 SB RAS.
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