Mechanism of GeO2 resistive switching based on the multi-phonon assisted tunneling
between traps
A. V. Shaposhnikov, T. V. Perevalov, V. A. Gritsenko, C. H. Cheng, and A. Chin
Citation: Applied Physics Letters 100, 243506 (2012); doi: 10.1063/1.4729589
View online: http://dx.doi.org/10.1063/1.4729589
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/100/24?ver=pdfcov Published by the AIP Publishing
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Mechanism of GeO
2resistive switching based on the multi-phonon assisted
tunneling between traps
A. V. Shaposhnikov,1T. V. Perevalov,1V. A. Gritsenko,1,a)C. H. Cheng,2and A. Chin2
1
A.V. Rzhanov Institute of Semiconductor Physics, Siberian Branch of Russian Academy of Science, 13/Lavrentieva Ave., 630090 Novosibirsk, Russia
2
Department of Electronics Engineering, National Chiao-Tung University, Hsinchu, Taiwan
(Received 16 May 2012; accepted 31 May 2012; published online 14 June 2012)
Model of evenly distributed traps in bulk dielectric is proposed for the resistive memory switching mechanism. Switching from high resistance to the low resistance state is explained by several-fold increase in trap concentration after the application of switching voltage. Both high and low resistance conductivities are governed by multi-phonon ionization and tunneling between neighboring traps. Thermal trap energy for oxygen vacancy and electron effective mass for crystal a-GeO2were calculated
using density functional theory and used for the fitting of our charge transport model of resistive memory. The model was verified on the TaN-GeO2-Ni structure with good semi-quantitative agreement
with experiment.VC 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4729589]
Resistive random access memory (RRAM) has attracted considerable attention as the most promising candidate for the next generation of nonvolatile memory (NVM) due to superior characteristics, which include its simple metal– insulator–metal (MIM) structure, high density, fast write/ erase switching times, low power consumption, and high en-durance. Resistive memory is by six orders of magnitude faster than conventional flash memory with floating gate and has a switching time in the range of 1–10 ns, switching volt-age in the range of 1–5 V, and the number of switching cycles 106–1012. Switching from the high-resistance to the low-resistance states is obtained by applying of a short volt-age pulse. Reverse transition occurs when an impulse of the longer duration is applied. Switching effect is observed in many dielectrics, such as SiO2, GeO2, HfO2, TiO2, Ta2O5,
Nb2O5, organic films, and graphene oxide.
Considerable efforts were applied to the investigation of the switching mechanisms in RRAM, but its exact nature remains unclear.1In metal oxides, metallic filament conduction model is widely accepted.2,3According to this model, heating in high electric fields results in the fast diffusion of oxygen atoms, leading to the creation of conductive metallic filament. Creation of conductive filament results in the transition of the dielectric from high resistive state to the low resistive state. However, the high current passing through the metallic filament is opposite to the required low power in large memory arrays. Besides, the random formation of metallic filament is difficult to control with a wide range of resistance distribution, which is tough challenge to realize in high density memory arrays.
GeO2has attracted attention as a promising material for
RRAM due to its high defect density4and small Ge-O bond formation energy.5Oxygen vacancies can be easily formed by interaction of GeO2with Ge at a very low temperature.
The first non-metal-oxide Ni/GeOx/TaN RRAM was
reported at 2010.6In sharp contrast to conventional conduc-tive filament RRAM, this device neither required a pre-forming process nor current compliance which simplifies the
memory circuit design considerably. Besides, very low sub-lW power to high-resistance state (HRS) and even lower reset power of only sub-nW to low-resistance state (LRS) were achieved. Such GeOxRRAM cannot be explained by
metallic filament model because the GeOxis a covalent-bond
oxide rather than the metallic oxide. Moreover, the extremely low reset power cannot be explained by the model of disruption of conductive filament. The switching effect of this type of RRAM is thought to be related to the formation and annihilation of oxygen vacancies.
The purpose of this paper is to develop alternative non-filament physical model which will be able to adequately describe resistance switching effect in dielectrics. We pro-pose a model for the resistive switching in RRAM based on the creation and annihilation of evenly distributed oxygen vacancies in the dielectric bulk.
For complementary metal-oxide-semiconductor transis-tor (CMOS) backend integration, a typical 0.5 lm isolation SiO2was deposited on 6-in. IC-standard Si substrate. Then
TaN was deposited by physical vapor deposition (PVD) and patterned to form the bottom electrode. The GeOxdielectric
was deposited by PVD with a thickness of 12 nm. The top electrode was formed by nickel (Ni) deposition and pattern-ing. The fabricated Ni/GeOx/TaN devices were measured by
DC current-voltage (I-V) set/reset, cycling, and retention at 85C under the similar charge-trapping flash memory tests.7
Fig. 1 shows the experimental hysteresis of current-voltage characteristics measured in HRS (curve 1) and LRS (curve 2). The current in the range 0–2.5 V of HRS curve 2 is related to the charge accumulation on traps in GeO2. Current
in the voltage range 2.5–4 V of LRS curve 1 exponentially increases with the voltage. At the high voltage of curve 1, GeO2 sample is switched to the low-resistance state, with
LgI-V characteristic described by curve 2 at the decreasing voltage. Very low self-compliance set current of 0.4 lA at 4 V (0.6 lW) to HRS, even lower reset current of only 16 pA at 1 V (16 pW) to LRS, and large HRS/LRS resist-ance window of 170 were achieved at 0.5 V read voltage. The HRS/LRS resistance window becomes larger and >500 at a read voltage of 1 V.
a)Author to whom correspondence should be addressed. Electronic mail:
According to the proposed model, GeO2sample in the
high resistance state has low concentration of traps (oxygen vacancies). In this state, charge transport is governed by the multi-phonon ionization and tunneling between traps (cur-rent in the voltage range 2.5–4 V on the curve 1).8–11This is illustrated by the inset in the lower part of Fig.1.
Application of the high voltage results in many fold increase of traps concentration. Drastic increase in trap con-centration results in exponential increase in tunneling proba-bility of electrons between traps and therefore greatly increased current. This is illustrated by inset in the top of Fig.1.
Quantitative theory of charge transport in dielectrics based on multi-phonon-assisted traps ionization and tunnel-ing between traps was developed in Ref. 11. We have applied this model to describe charge transport both in high and low resistance states to explain resistive switching in GeO2. In this model, phonon-assisted trap ionization and
tun-neling probabilityP is given by
P¼ ffiffiffi p p hWt mN2 3pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2kTðWopt WtÞ exp Wopt Wt 2kT exp 2N 1 3 ffiffiffiffiffiffiffiffiffiffiffiffiffi2mWt p h ! sinh eFN 1 3 2kT ! : (1)
Here,N is bulk trap concentration, WtandWoptare the
ther-mal and optical energies of trap ionization, m* is the tunnel-ing electron effective mass,F¼ V/d is electric field, d is the thickness of dielectric, andT is the temperature. Compared to work in Ref.11, we substituted hyper sinus with exponent
in Eq.(1)to take into account probability for electron tunnel-ing in the direction opposite to electric field.
In the first approximation, we neglect electric field non-uniformity in dielectric created by the space charge of car-riers captured on traps. In the simplest one-dimensional model, the current density is given by the equation:
J¼ eN23P: (2) We used Eqs.(1)and(2)to fit experimentalI-V curves, there high and low resistance states described by different trap concentrationN1andN2. According to formula (1), the slope
of the LgI-V line allow us to determine the trap density in high resistive state (N1¼ 6 1018cm3) and low resistive
state (N2¼ 6 1020cm3).
Fitting of experimental current-voltage characteristics requires us to know three more parameters: thermal Wt and
optical Wopt trap energies and electron tunneling effective
massm*. To further reduce the number of unknown free fit-ting parameters, we assumed relation Wopt¼ 2Wt. This
rela-tion was established for multi-phonon trap ionizarela-tion model in the charge transport experiments for electrons and holes in Si3N4(Refs.12and13) and Al2O3.14
Unfortunately there is no available experimental data on the electron effective massm* and thermal ionization energy Wt. To obtain a good starting guess and verify that oxygen
vacancy defect in GeO2indeed could be a trap for electrons,
we conducted a first principle quantum-chemical simulation of a-quartz GeO2.
Electronic structure of hexagonal GeO2, with a structure
similar to a-quartz, was investigated using plane-wave norm-conserving pseudopotential technique based on the first-principles density functional theory (DFT) in the quantum Espresso code.15 Ground-state properties were obtained by minimizing the total energy. It is widely known that DFT approach, both in local density approximation (LDA) and gradient corrected approximation (GGA) consistently under-estimate band gap of dialectics. Various techniques are used to address this shortcoming, including time-dependent DFT, many-particle GW approximation, and various hybrid DFT functionals, combining exact Hartry-Fock exchange with appropriate LDA/GGA formulation for electron correlation. The downside of all these methods is much higher demand on computational resources.
In this work, we used HSE hybrid functional to calculate electronic band structure of primitive GeO2cell with
com-parison of GGA PZ functional. Electronic structure of GeO2
was calculated previously in the work.16
Band structure of GeO2was calculated for primitive
tri-gonal cell, consisting of 3 Ge atoms and 6 O atoms, on the uniform Monkhorst-Pack grid of k-points with density of 10 10 10. Fig. 2 presents the calculated band structure along high symmetry lines in the first Brilluene zone with HSE hybrid functional. While GGA potential expectedly underestimate band gap, HSE correctly predicts experimen-tal value of 5.72 eV.17a-quartz GeO2is an indirect band gap
dielectric with conduction band minimum in Gamma point and valence band maximum in M-point. Electron and hole effective masses were estimated from band structure calcula-tions. Electron effective mass tensor is rather isotropic with
FIG. 1. Hysteresis of current-voltage characteristic in Ni-GeO2-TaN
struc-ture (shown on the top) at room temperastruc-ture. Curve 1 corresponds to HRS and measured at the rising ramp voltage. Curve 2 corresponds to LRS and measured at the decreasing ramp voltage. Solid lines represent experimental data, and dotted lines represent theoretically fitted curves. GeO2film
thick-ness is 12 nm, Ni contact area is 1.13 104cm2. Insets in the lower and upper parts illustrate the picture of low and high trap concentration in high and low resistive states, respectively.
lowest massmk¼ 0.38 meand highestm?¼ 0.48 me. Similar
values were obtained for silicon nitride Si3N4.12,13 Top of
the valence band is rather flat (see Fig.2) suggesting heavy holes withmh 10 me.
Effective masses calculated within plain GGA DFT and with the use of more advanced hybrid functional do not dif-fer much, to a degree of 10% which is beyond the precision attainable by our approach. This can be explained by the fact that energy correction due to inclusion of exact Hartry exchange for unoccupied levels is roughly the same for all k-vectors in the Brilluene zone. To obtain results suitable for direct comparison with experimental XPS and UPS spectra (Ref.18), calculated partial density of states (PDOS) for 4s, 4p valence states of Ge atom and 2s, 2p states for O atom were weighed with experimental photoionization cross-section from Ref.19(Fig.3). Again, PDOS calculated with HSE shows quite good agreement with experimental data.
For the calculation of electronic properties of oxygen vacancies, we constructed a 72 atom supercell, consisted of 8 primitive trigonal cells. Oxygen polyvacancies are created by removing one or more O atoms from within the same GeO4tetrahedron. To calculate the energy levels of vacancy
defects, we calculated total energy of supercells with added or subtracted electron to the lowest unoccupied and highest occupied states, respectively. Long-range coulomb diver-gence is taken into account by the addition of compensating charge to obtain total cell charge neutrality.
Energy levels of defects in different charge states calcu-lated using the following formula:
Ee¼ ðE1d E 0 dÞ ðE 1 b E 0 bÞ (3)
ThereEdrepresents the total energy of supercell with defect
in various charged states,Ebis total energy of bulk supercell.
Here, term ðE1 d E
0
dÞ represent the energy difference
between negatively charged and neutral defect supercell. This value is corrected with the electron affinity term
Eaf f ¼ ðE1b E0bÞcalculated for bulk supercell. Thus, all
errors due to supercell approximation are effectively cancelled.
This technique allows us to estimate the energy level of electron traps in GeO2, which corresponds to thermal trap
energy Wtin multi-phonon trap ionization model described
previously, Wt¼ Ee. Direct estimation of optical excitation
energies requires us to calculate empty localized energy lev-els associated with the defect, taking into account electron subsystem relaxation due the electron excitation. This work is in progress. In this work, we estimated optical trap energy using experimental ratioWopt/Wt¼ 2.20,21
Our results, obtained with GGA HSE functional for sin-gle oxygen vacancy, show the appearance of two localized electronic states in the band gap (Fig.4). The low state has a bonding nature (r), and the upper empty state is non-bonding (r*). According to our model, electrons injected from contact (TaN) are captured by empty non-bonding localized states in the band gap of GeO2. Subsequent
FIG. 2. Band structure of GeO2calculated with hybrid HSE potential along
high symmetry lines in the first Brillouin zone of primitive 9-atom trigonal cell. FIG. 3. Comparison of experimental UPS and XPS valence band spectra (solid line) of amorphous GeO2from Ref.18with calculated PDOS for
a-GeO2(dotted line). Calculated PDOS for 4s, 4p valence states of Ge atom
and 2s, 2p states for O atom weighed with experimental photoionization cross-section Ref.19.
FIG. 4. Total density of states for bulk GeO2supercell and supercell with
electron multi-phonon assisted ionization and tunneling between neighboring traps provides low and high resistive conductivity of GeO2.
Single oxygen vacancy in various dielectrics (SiO2,
Al2O3, ZrO2, HfO2, Ta2O3, TiO2) is a widely acknowledged
trap responsible for charge accumulation and excess leakage current. In this work, we assume single oxygen vacancy to be the primary defect responsible for RRAM switching mechanism. For the single oxygen vacancy, using hybrid HSE DFT potential, we calculated the value of trap thermal ionization energy Wt as 1.5 eV. Optical trap ionization
energy can be estimated asWopt¼ 2Wt¼ 3.0 eV.
Using the theoretically calculated values forWt¼ 1.5 eV,
Wopt¼ 3 eV, m* ¼ 0.38 me as the starting guess parameters,
and values for concentrationN in high (N1¼ 6 10 18
cm3) and low resistive state (N2¼ 6 10
20
cm3), using Eqs. (1)
and(2), we obtained best fitting values for electron effective mass m*¼ 0.2 me and trap thermal ionization energy
Wt¼ 1.42 eV (Fig.1).
The thermal energyWt¼ 1.42 eV obtained from the
fit-ting of experimental data to Eqs.(1) and(2)is in very good agreement with theoretically calculated energy for the oxy-gen vacancy defectEe¼ Wt¼ 1.5 eV.
The obtained value form*¼ 0.2 meis close to the
exper-imental values of tunnel effective masses in high-k dielec-trics Al2O3 0.28me, 22 HfO2 0.1me, 23 0.17me, 24 and Ta2O5 0.3me. 25
Theoretically calculated conduction band mass m*¼ 0.38 meis twice as high as obtained fitting value.
Ex-perimental tunnel effective mass describe electron transport in the gap of dielectric, while theoretically calculated elec-tron effective mass pertain to elecelec-tron transport at the bottom of conduction band. This may explain the observed differ-ence between tunnel and free electron effective mass in GeO2. More detailed investigation is required.
Our theoretical model cannot adequately describe the experimentalLgI-V low-resistance curve (2) in the low volt-age range 0-1.5 V (see Fig.1). This divergence can have two possible explanations. First, our simple model neglects the spatial charge distribution in dielectric created by carriers captured on traps. Second, we assume the existence of only one type of defect, namely single oxygen vacancy, described by single level in the gap. In real dielectrics, polyvacancies may play an important role. Polyvacancies can create multi-ple defect levels in the band gap, each characterized by its own value of energy level. Investigation of the possible role of polyvacancies in the dielectrics conduction mechanism is the topic for future work.
In conclusion, we proposed a simple model for describ-ing resistive switchdescrib-ing of RRAM dielectrics assumdescrib-ing the same multi-phonon assisted electron tunneling mechanism for both high resistance state and low resistance state. Switching from high resistive state to low resistive state is explained by the drastic increase in the concentration of traps and corresponding increase in electron tunneling probability between neighboring traps. We suggest that primarily trap in GeO2 is an oxygen vacancy, which is the most widely
acknowledged defect in dielectrics such as SiO2, Al2O3,
ZrO2, HfO2, Ta2O3, TiO2. Using the proposed model, we
obtained the value of trap thermal ionization energy Wt¼ 1.42 eV, which is in very good agreement with
theoreti-cally calculated energy level for oxygen vacancy 1.5 eV. Obtained value for electron tunnel effective mass m*¼ 0.2 me is twice lower compared to theoretically
calcu-lated effective mass for the free conduction band electron but is close to experimentally determined tunnel effective masses for other high-k dielectrics.
This work was supported by the grant No. 24.18 of Rus-sian Academy of Sciences, grant No. 5.12 of Siberian Branch of Russian Academy of Sciences and the National Science Council, Taiwan, under Grant No. NSC-100-2923-E-009-001-MY3. The computations were conducted at the Novosi-birsk State University Supercomputer Center.
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