TiO₂-based MIM capacitors featuring suppressed leakage current by embedding Ge nanocrystals

Abstract

With Pd as the electrode, crystalline TiO₂-based MIM capacitors were found to demonstrate improved leakage current performance when nitrogen plasma treatment was adopted due to the passivation of grain boundary related defects. Through the introduction of Ge nanocrystals into crystalline TiO₂, the leakage current can be further suppressed by more than 3 orders of magnitude to 1.1 × 10⁻⁷ A cm⁻² at −1 V while maintaining a high capacitance density of 25.2 fF μm⁻². The major role of the nanocrystals is to trap electrons and then suppress leakage current by inducing the Coulomb blockade effect or building an internal field to compensate the applied external field. The MIM capacitor technology not only exhibits performance which is notably advantageous over other TiO₂-based capacitors, it also possesses the capability to be implemented in low-leakage/high-reliability analog and mixed signal MIM capacitors for next generation circuits.

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Metal–insulator–metal (MIM) based capacitors have been recently recognised as feasible passive components for radio frequency (RF) and analog and mixed signal (AMS) integrated circuits (ICs). Unlike in DRAM applications, in addition to meeting requirements for leakage current and capacitance, MIM capacitors for AMS applications also require good voltage linearity, low temperature coefficients, small loss tangents and small capacitance changes under stress. Conventionally, to achieve AMS MIM capacitors with high capacitances, a large portion of the chip area is occupied by employing Si₃N₄ or SiO₂ as the dielectric. Shrinking the thickness of these dielectrics may be beneficial to attain a higher capacitance density. However, this comes at the cost of deteriorated leakage current performance, which will prevent the use of the dielectrics in further applications. With the advent of high-permittivity (high-κ) dielectrics, the requirement of a large area to implement high-capacitance capacitors is relieved. The flourishing development of high-κ dielectrics has ushered in a new era for high-performance MIM capacitors. Among the many promising high-κ dielectrics, TiO₂ has long attracted intensive interest because its rutile phase exhibits a high κ value in the range of 90–170, depending on the crystallization orientation. Even with the potential to achieve a high κ value, one inherent material property that limits further application of TiO₂ in MIM capacitors is its high electron affinity, which consequently results in a high leakage current. Therefore a high work function (WF) electrode is always employed for TiO₂-based MIM capacitors to suppress the leakage current. In addition, doping TiO₂ with specific metal compounds such as TiO₂–LaAlO,¹ TiTaO,² TiNiO,³ TiHfO,⁴ TiZrO,⁵ TiPrO,⁶ and Sr_xTi_yO_z⁷ has been proposed as an alternative approach to improve its leakage performance. Although doped TiO₂ yields inspiring results, maintaining dopant uniformity requires rigorous process control. Furthermore, reduced leakage can also be obtained by stacking with another dielectric with a larger band gap such as a SiO₂/TiO₂ stack.⁸ However, the capacitance density will be inevitably compromised because a larger band gap dielectric is usually accompanied by a lower κ value.

In this work, significantly improved leakage current performance for TiO₂-based MIM capacitors was accomplished by introducing Ge nanocrystals into TiO₂. Embedding nanocrystals in dielectrics has been widely adopted in the technology of charge trap flash memory since nanocrystals offer a large amount of trapping sites which allow electron storage. Although a memory effect is not the required function for MIM capacitors in AMS applications, the main reason to introduce nanocrystals is to utilize the trapped electrons to induce the so-called Coulomb blockade effect or build an internal field to compensate the applied external one, and therefore reduce leakage current. Recently, the effect of nanocrystal size on dielectric behavior has been studied by investigating a sample of SiO₂ embedded with Ge nanocrystals.⁹ The research provides a clear understanding of the quantum size effect of the nanocrystals on capacitance. However, the leakage current reduction related to nanocrystal incorporation has never been explored in the literature. The results in this work prove the idea by demonstrating a relatively high capacitance density of 25.2 fF μm⁻² with a leakage current of 1.1 × 10⁻⁷ A cm⁻² at −1 V, which is lower than capacitors without incorporated Ge nanocrystals by a factor of more than 3000. Aside from the ameliorated leakage performance, the capacitors with Ge nanocrystals also exhibit a small loss tangent of 0.020, a low temperature coefficient of capacitance (TCC) of 88 °C per ppm, and enhanced reliability in terms of a small capacitance change of 1.04% under −1.5 V constant voltage stress after 10-year operation.

SiO₂ on Si was used as the starting material to form the MIM capacitors. 50 nm of Pd was first deposited as the bottom electrode. The reason to adopt Pd lies in its relatively high WF of 5.1 eV. Then 29 nm of TiO₂ film was deposited as the dielectric of the capacitors (denoted as TiO₂ samples). Next, rapid thermal annealing (RTA) at 500 °C was performed to crystallize the TiO₂. To explore the impact of Ge nanocrystal incorporation on the electrical characteristics, the aforementioned 29 nm of TiO₂ was replaced with a TiO₂/Ge/TiO₂ laminate structure of 11.5/1.5/11.5 nm for some samples (denoted as TiO₂–Ge samples). With the same RTA conditions,¹⁰ Ge nanocrystals embedded in the crystalline TiO₂ were formed for the TiO₂–Ge samples. Next, nitrogen plasma treatment (NPT) at 300 °C was performed for 1 min on some samples to investigate how nitrogen radicals affect device performance. Finally 50 nm of Pd patterned with a size of 100 μm × 100 μm was formed as the top electrode. Besides electrical characterization, transmission electron microscopy (TEM) and X-ray photoelectron spectroscopy (XPS) were also used to respectively confirm the formation of nanocrystals and the bonding structure of the annealed film.

Fig. 1(a) shows the cross-sectional TEM image of a TiO₂–Ge-NPT sample. Nanocrystals with a size of ∼1.5 nm can be clearly observed between the top and bottom TiO₂ after annealing. To further analyze the bonding structure of the nanocrystals, XPS was performed and the result is displayed in Fig. 1(b). As can be seen in the Ge 3d spectrum, there is a peak at a binding energy of 29.1 eV, which corresponds to Ge–Ge bonding, and a smaller peak at 32.0 eV, which can be assigned as GeO_x. Although GeO_x exists, the fraction is small since the area of the Ge–Ge peak is much higher than that of the GeO_x peak. This result implies that the nanocrystals shown in the TEM image are mainly composed of Ge. The formation of a small amount of GeO_x is reasonable because the electronegativity of Ge is larger than that of Ti and therefore it is relatively difficult for Ge atoms to obtain O atoms from the pre-existing TiO₂.

Fig. 1 Physical analysis of a TiO₂–Ge-NPT sample. (a) Cross-sectional TEM image. (b) XPS Ge 3d spectrum.

Fig. 2 shows the capacitance–voltage (C–V) characteristics for the samples with different processing conditions measured at 10 kHz and 1 MHz. At 0 V, the TiO₂ samples display the highest capacitance density of 33.8 fF μm⁻² (EOT of 1.02 nm), while the values for the TiO₂-NPT and TiO₂–Ge-NPT samples decrease to 30.2 fF μm⁻² (EOT of 1.14 nm) and 25.2 fF μm⁻² (EOT of 1.37 nm) respectively, where EOT denotes equivalent oxide thickness. The κ value of TiO₂ is 110.8, which implies the formation of crystalline dielectric after RTA. With NPT, the value slightly decreases to 99.0, which is due to the formation of TiON.⁷ With the additional incorporation of Ge nanocrystals, the κ value further drops to 75.5, because Ge has a much smaller κ value than TiO₂. Besides the κ value evolution for the different processing conditions, it is also found that the NPT process significantly mitigates the dependence of capacitance on applied voltage for the TiO₂ samples, which makes the capacitors more feasible for circuit applications. This can be ascribed to the passivation of grain boundary-induced defects in the crystalline TiO₂ by nitrogen radicals.⁸ The much improved frequency dispersion of capacitance for the NPT-processed samples is mainly ascribed to the reduction of vacancy-induced mobile charges due to the passivation effect.

Fig. 2 C–V characteristics for the TiO₂-based MIM capacitors with various processing conditions measured at 10 kHz (half-filled symbols) and 1 MHz (open symbols).

Based on the same mechanism, as shown in the current–voltage (I–V) curves in Fig. 3(a), the TiO₂-NPT samples demonstrate a leakage current that is reduced by a factor of 3652 as compared to the TiO₂ samples at a bias voltage of −1 V. Note that the current shown in the figure was measured by sweeping the voltage from zero to a positive or negative bias. With Ge nanocrystals embedded in the TiO₂, for the TiO₂–Ge-NPT samples, the leakage current was further reduced to 1.1 × 10⁻⁷ A cm⁻² at −1 V, lower than that of the TiO₂-NPT samples by over 3 orders of magnitude. Since the leakage current improvement may result from a thicker EOT due to the lower κ value with the introduction of NPT and Ge nanocrystals, the leakage current at −1 V as a function of EOT for different processing conditions, which was obtained from separate experiments, is shown in Fig. 3(b). Apparently, even with the same EOT, the TiO₂–Ge-NPT samples show the lowest leakage current, which confirms that Ge nanocrystals play an essential role in the leakage current improvement. The result of leakage current suppression is consistent with other nanocrystal based devices.^11–13

Fig. 3 (a) I–V curves for TiO₂-based MIM capacitors with various processing conditions. (b) Leakage current (measured at −1 V) as a function of EOT for TiO₂-based MIM capacitors with various processing conditions.

The major mechanism behind the phenomenon can be understood from the band diagram of Ge-embedded TiO₂ shown in the inset of Fig. 4. Due to the conduction band offset of 0.33 eV between Ge nanocrystals and rutile TiO₂,¹⁴ some of the injected electrons from the electrode would be trapped in the Ge nanocrystals, just like in the operation of nanocrystal-based memory devices. Once the nanocrystals are occupied with electrons, two possible effects may occur.¹² (1) These trapped electrons in the nanocrystals will prevent subsequent electrons from further injection, and therefore reduced leakage current is obtained. This is the so-called Coulomb blockade effect.^11–13 Observation of the Coulomb blockade effect in a practical device at room temperature (300 K) requires the charging energy (e²/C_S)^15,16 to be 3 times higher than the thermal energy (k_BT, 25.9 meV at 300 K). Note that C_S denotes self-capacitance of the sphere and can be expressed as 4πε₀ε_rR where R is the radius of the nanocrystal. Based on the electrical and physical parameters of Ge nanocrystals (ε_r ∼ 12.6 from capacitance measurement and R ∼ 0.75 nm from TEM image), C_S is 1.05 aF and the charging energy is 152.32 meV. Since the charging energy is larger than the thermal energy at 300 K, it proves that a Coulomb blockade could possibly occur in this work. (2) These trapped electrons in the nanocrystals build up an internal electric field which compensates the applied external field. It is the reduced effective electric field across the dielectric that causes the reduced leakage current. The internal electric field can be estimated as follows. For both the TiO₂–Ge-NPT and TiO₂-NPT samples, the current conduction mechanisms are found to be Poole–Frenkel emission (not shown). For a given electric field E₁, the leakage currents for the TiO₂–Ge-NPT samples and TiO₂-NPT samples are respectively J₁ and J₂, where J₁ is smaller than J₂. Since the leakage current through NPT-processed TiO₂ should be the same under an equal electric field E₁ for both types of samples, the difference between J₁ and J₂ is attributed to the internal electric field which compensates the applied external field. To obtain J₁ in the TiO₂-NPT samples, the applied electric field should be decreased to E₂, which is the effective electric field in the TiO₂–Ge-NPT samples under E₁. In other words, even though E₁ is applied in the TiO₂–Ge-NPT samples, it experiences an effective electric field of E₂ and therefore a lower leakage current is obtained. The difference between E₁ and E₂ is the estimated internal electric field that compensates the applied external field. From the data, the internal electric field is about 0.7 MV cm⁻¹. The effect of a built-in internal electric field can be proven by showing the bi-directional I–V characteristic for the TiO₂-NPT samples with and without Ge nanocrystals, as shown in Fig. 4. Cusps are observed for both types of capacitors where the current crosses zero, indicating the size of the hysteresis loop. The cusps can be found when the magnitude of the external field is equal to that of the internal field. The higher absolute voltage of the cusps for the TiO₂–Ge-NPT samples implies that a larger amount of electrons can be trapped in the nanocrystals and therefore the cusps can be formed near the starting voltage of the sweep (±2 V). This phenomenon also suggests that the nanocrystals indeed store electrons during voltage sweeping and have a pivotal role in suppressing the leakage current. Note that although NC-based traps may contribute to trap assisted tunneling (TAT) current, this is not the leakage conduction mechanism for the current between ±2 V, which is inferred from the following viewpoints. (1) TAT happens when electrons are captured in the traps and then emitted to the anode. However, from the hysteresis I–V curve, even though some electrons are tunneling from the cathode to NC-based traps, the electrons are captured (or stored in traps) without being emitted between ±2 V, and therefore the assistance role of these traps for electron tunneling vanishes. (2) The leakage current demonstrates a dependence on the measurement temperature (not shown), which conflicts with the temperature-independent nature of carrier tunneling. Therefore the leakage current between ±2 V is not from TAT, and the Coulomb blockade effect plays an important role in this voltage range. This inference is consistent with the simulation and experimental results in the literature^17,18 where TAT is prohibited by the Coulomb blockade effect at low electric field and can occur at high electric field. From the aforementioned discussion, nanocrystals with smaller size are beneficial to enhance the Coulomb blockade effect. On the other hand, since the internal electric field is generated by the trapped charges, it is expected that a higher density of Ge nanocrystals would lead to a larger internal electric field, which is beneficial to suppress leakage current. Therefore, to further optimize the performance, smaller nanocrystals with a higher density are desirable, which may be achieved by depositing a thinner Ge layer with optimum annealing conditions, such as different thermal annealing time, ramp rate and ambient temperature.

Fig. 4 Bidirectional I–V characteristics for TiO₂-NPT and TiO₂–Ge-NPT samples with voltage sweeping between ±2 V. The inset shows the band diagram (not to scale) for the TiO₂–Ge-NPT samples.

Fig. 5(a) displays the dependence of normalized capacitance on measurement temperature. As compared to the TiO₂-NPT samples, which have a temperature coefficient of capacitance (TCC) of 113 ppm per °C, the TCC for the TiO₂–Ge-NPT samples improves to 88 ppm per °C, which can be explained by the reduced electron injection and causes a longer relaxation time, consequently leading to a smaller capacitance variation. Besides the requirement of low leakage current and small TCC, low dielectric loss is also a prerequisite for passive element applications. Dielectric loss quantifies the inherent electrical energy dissipation of a dielectric. The loss tangent results are shown in Fig. 5(b). At 1 MHz, the loss tangent for the TiO₂-NPT samples is about 0.045. The value becomes 0.020 for the TiO₂–Ge-NPT samples, which is an improvement of a factor of 2.2. Since the loss tangent is dependent on the conductance of the dielectric, once the leakage current can be reduced, an improved loss tangent is expected, as is observed for the TiO₂–Ge-NPT samples.

Fig. 5 (a) Temperature-dependent normalized capacitance and (b) loss tangent for the TiO₂-NPT and TiO₂–Ge-NPT samples. ΔC denotes the difference between zero-biased capacitance (C₀) at 25 °C and elevated temperature.

Fig. 6(a) shows the impact of Ge nanocrystal incorporation on the reliability performance, which is quantified by capacitance variation as a function of constant voltage stress time for the NPT samples. For the TiO₂–Ge-NPT samples, an extrapolated capacitance variation of 1.04% after 10-year operation under a −1.5 V stress can be obtained. This performance is superior to that without incorporated nanocrystals, which is 1.58%, and the suppressed capacitance variation is mainly ascribed to fewer electron injections and trapped charges. Fig. 6(b) shows the stress induced leakage current (SILC) for TiO₂–Ge-NPT samples under different stress voltages measured at 25 °C. Leakage current degradation of less than 25% was observed, which implies that the bonding strength of the nitrogen passivated TiO₂ is robust enough to restrain defects from generating during electrical stress, and no percolation leakage paths are formed since no abrupt leakage current is observed after stress. Although the SILC is insignificant, it is perceived that TAT is the major mechanism. It is the increased number of oxide traps after stress that makes TAT become more pronounced.

Fig. 6 (a) Capacitance change (ΔC_stress/C₀) as a function of stress time for the TiO₂-NPT samples with and without Ge nanocrystals, measured at room temperature with the stress voltage at −1.5 and −2.5 V. ΔC_stress denotes the difference between the zero-biased capacitance (C₀) of the fresh and stressed devices. (b) SILC performance for the TiO₂–Ge-NPT samples where J₀ and J₁₀₀₀ respectively denote the current for the fresh condition and 1000 s of stress.

Table 1 summarizes the major device parameters for TiO₂-based^{1,3,4,6–8,19,20} and other recently published Gd₂O₃/Eu₂O₃,²¹ and Al₂O₃/ZrO₂/SiO₂/ZrO₂/Al₂O₃ (AZSZA)²² MIM capacitors with various electrodes for AMS applications. Nitrogen plasma treatment of Ge nanocrystal-embedded TiO₂ provides another promising avenue to obtain high capacitance density with much improved leakage current.

Table 1 Comparison of major device parameters of TiO₂-based and other recent MIM capacitors with various dielectrics

Dielectric material	Dielectric thickness (nm)	Top/bottom electrode	Electrode WF (eV)	Capacitance (fF μm^−2)	Leakage at −1 V (A cm^−2)	Reference
TiO2/Ge NCs/TiO2 NCs: nanocrystals	11.5/1.5/11.5	Pd/Pd	5.1/5.1	25.2	1.1 × 10^−7	This work
TiO2–LaAlO	15	Ir/TaN	5.3/4.6	24	1.4 × 10^−7	1
TiNiO	20	Ni/TaN	5.1/4.6	17.1	7.7 × 10^−6	3
TiHfO	12	TaN/TaN	4.6/4.6	28	4.8 × 10^−6	4
TiPrO	16	Ir/TaN	5.3/5.6	20	1.2 × 10^−7	6
SrxTiyOz (SrO/TiO2)	29.9/14.9	Pt/Pt	5.6/5.6	∼22.5	∼1.0 × 10^−5	7
TiO2/SiO2	14.5/2.5	Al/Tan	4.3/4.6	11.9	8.3 × 10^−7	8
TiO2	25	Ni2Si/Ni2Si	4.6/4.6	17	1.2 × 10^−5	19
SiO2/TiO2/SiO2	2/16/2	TaN/TaN	4.6/4.6	12.4	8.8 × 10^−7	20
Gd2O3/Eu2O3	8/8	Pt/Pt	5.6/5.6	12.5	1.0 × 10^−7	21
AZSZA	1/7/3/7/1	TaN/TaN	4.6/4.6	7.4	1.1 × 10^−8	22

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In conclusion, the leakage current of crystalline TiO₂-based MIM was greatly improved by using nitrogen plasma treatment and embedding Ge nanocrystals. The mechanism of nanocrystal induced leakage current reduction involves the Coulomb blockade effect or the internal electric field compensation effect. When integrating these processes, the resulting MIM capacitors exhibit a low leakage current of 1.1 × 10⁻⁷ A cm⁻² at −1 V while maintaining a high capacitance density of 25.2 fF μm⁻². In addition, the promising characteristics of the MIM capacitors are also evidenced by the small TCC of 88 ppm per °C, low loss tangent of 0.020, low SILC, and desirable capacitance change of 1.04% after 10-year operation under −1.5 V. The desirable performance proves the suitability of the nanocrystal-embedded MIM capacitors for advanced AMS applications.

Acknowledgements

This work was supported by the National Science Council of Taiwan under Contract NSC 101-2628-E-007-012-MY3 and NSC 101-2120-M-009-004.

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