Dielectric relaxation in hafnium oxide: A study of

JOURNAL OF APPLIED PHYSICS 110, 104108 (2011)

Dielectric relaxation in hafnium oxide: A study of transient currents and admittance spectroscopy in HfO2 metal-insulator-metal devices C. Mannequin,1 P. Gonon,1,a) C. Valleé,1 A. Bsiesy,1 H. Grampeix,2 and V. Jousseaume2 1

Microelectronics Technology Laboratory (LTM), Joseph Fourier University–French National Research Centre (CNRS), 17 Avenue des Martyrs, 38054 Grenoble Cedex 9, France 2 CEA-LETI MINATEC, 17 Avenue des Martyrs, 38054 Grenoble Cedex 9, France

(Received 2 August 2011; accepted 17 October 2011; published online 29 November 2011) Dielectric relaxation is studied in 10 nm HfO2 thin films which are deposited by atomic layer deposition on TiN and Pt electrodes. Transient currents are recorded from 103 s to 10 s, as a function of bias (0.1 V to 1 V) and temperature (20 C to 180 C). A Curie-von Schweidler law is observed, I ¼ Q0/ta. The power law exponent a is constant with bias and strongly depends on the temperature (varying in the 0.65–1.05 range, with a peak at 75 C). The amplitude Q0 is described by a relation of the form Q0 ¼ C0Vb, where the factor C0 is weakly activated and the exponent b varies with temperature (in the 0.9–1.5 range as T varies). Transient currents are discussed along with tunneling based models from the literature. To complement transient current experiments, admittance spectroscopy (conductance G and capacitance C) is performed at low frequencies, from 0.01 Hz to 10 kHz. The dispersion law of the conductance is of the form G xs. The capacitance is the sum of two terms, a non-dispersive term (C1) and a low-frequency dispersive term, CLF xn. The critical exponents s and n verify s a and n 1a. At room temperature, the dielectric constant is expressed as e0 ¼ De0 fn þ e0 1, where e0 1 ¼ 11.1, n 0.2/0.3 (Pt/TiN), and De0 1.5/0.7 (Pt/TiN). C 2011 American Institute of Physics. [doi:10.1063/1.3662913] V

I. INTRODUCTION

HfO2 has recently gained importance in microelectronics as a high-k dielectric material for several applications, including field-effect transistor (FET) gate stacks,1 integrated metal-insulator-metal (MIM) capacitors,2 and non-volatile resistive random access memories (RRAMs).3 These applications require a tight control of HfO2 electrical properties and a good understanding of dielectric phenomena that govern HfO2 based devices. Dielectric relaxation, i.e., the time response of polarization when the dielectric material is subjected to a voltage stress, impacts several device performances, such as the leakage current level (through displacement currents) or the frequency dispersion of the capacitance (through dispersive polarization mechanisms). Time dependent polarization can arise from several mechanisms (charge trapping, charge hopping, and so on) that can be studied by recording transient currents, i.e., dc currenttime (I-t) curves, where V is fixed and the current is recorded at given times. Another usual way to characterize dielectric relaxation is admittance spectroscopy (Y-f), where a fixed ac voltage is applied to the material and the ac current (thus the admittance) is recorded at given frequencies. These two techniques complement each other because, in theory, the frequency response (Y-f) is related to the Fourier transform of the time response (I-t). Despite the technological importance of HfO2, the number of studies reporting on transient currents (I-t) in this material are quite limited,4–8 as are those related to admittance spectroscopy (Y-f).9 Following the application of a step volta)

Author to whom correspondence should be addressed. Electronic mail: [email protected].

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age, long-lasting current decays (up to 104 s) were reported,4,5 pointing to the presence of very slow polarization processes in HfO2 thin films. The negative impact of dielectric relaxation for dynamic random access memory (DRAM) applications was highlighted by Reisinger et al.4 Another serious problem is the threshold voltage (Vt) drift observed in FETs making use of HfO2 gate stacks.1,6 When the gate is biased, Vt is observed to shift with time, indicative of material charging. Upon bias removal, Vt relaxes toward its initial value very slowly, with relaxation times that can exceed 104 s.1 These examples show the technological importance of studying dielectric relaxation in HfO2 because it can adversely affect device performance in terms of speed and stability. In this work we report on dielectric relaxation in 10 nm HfO2 films, which are deposited by atomic layer deposition (ALD), a leading technique for the deposition of high-k dielectrics in microelectronics. The I-t and Y-f responses are studied as functions of several parameters, including the nature of the bottom electrode (TiN or Pt), the bias voltage, and the temperature. A detailed analysis of the time and frequency response is carried out and the experimental results are discussed along with physical models from the literature. II. EXPERIMENT

10 nm HfO2 films are grown by atomic layer deposition TM (ALD) using a Pulsar reactor from ASM Company. Deposition is carried out at 350 C and 1 Torr using alternate cycles of H2O and HfCl4. Two kinds of wafers (200 mm) were used, namely Pt(25 nm)/TiN(10 nm)/Si (referred to hereafter as “Pt electrode”) and TiN(25 nm)/Si (referred to as “TiN electrode”). Top gold electrodes (2 mm in diameter)

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are deposited on the HfO2 films by Joule evaporation through a shadow mask. In that way MIM capacitors consisting of Au/10 nm HfO2/(Pt or TiN) stacks are fabricated. Electrical measurements are performed in air (clean room environment) using a Signatone probe station equipped with a temperature-controlled hot chuck. The source is applied to the top electrode (Au) using a compliant gold wire that is attached to a micropositioner. The ground is applied to the bottom electrode (Pt or TiN) using a tungsten needle probe, which is put in direct contact with the bottom electrode by punching through the HfO2 film. Transient currents (I-t) are recorded using a Keithley 2635 Source Measure Unit (SMU), as a function of bias voltage (0.1 V to 1 V, with 0.1 V steps) and temperature (20, 50, 75, 105, 140, and 180 C). The following measuring procedure is used. At a given temperature (starting from 20 C), the MIM device is biased (starting from þ 0.1 V at the top electrode) and I is recorded as a function of time (charge current). Once the I-t has been recorded, the sample is shortcircuited and is left to relax for the same amount of time as during the biasing period. During the short-circuit period, a current of the opposite sign is observed (discharge current). However, for conciseness, only the charge current will be presented in this paper. Then, the bias voltage is increased (DV ¼ þ 0.1 V) and a new charge-discharge cycle is performed. Following the last cycle (at 1 V), the temperature is increased and the whole bias procedure is repeated for the new temperature. Impedance spectroscopy (Y-f) is carried out using a Novocontrol analyzer working in the 0.01 Hz–10 kHz range. Y-f characteristics are recorded from 20 C to 180 C (starting from 20 C), using a fixed ac voltage of 0.5 Vrms. Structural properties of HfO2 films were studied using x-ray photoelectron spectroscopy (XPS), attenuated total reflectance (ATR) infra-red spectroscopy, ellipsometry spectroscopy (ES), and x-ray diffraction (XRD). Results of structural analysis can be found elsewhere.10 Briefly, it is found that the HfO2 films deposited on the Pt electrode are crystallized in the monoclinic phase, while those deposited on the TiN electrode consist of a mixture of monoclinic (major) and orthorhombic (minor) phases. The energy bandgap of the films is around 5.5 eV. XPS performed on thinner films (2 nm) deposited on Pt reveals a sharp HfO2/Pt interface (absence of PtO oxides). On the contrary, films deposited on TiN show the presence of TiOxNy at the HfO2/ TiN interface. III. TRANSIENT CURRENTS (I-t) A. The I-t response as a function of bias and temperature

Figure 1 and Fig. 2 illustrate typical I-t responses. Figure 1 shows I-t at a given bias (0.5 V), for different temperatures. The current first increases from 20 C to 50 C, then keeps almost the same value in the 50–140 C range (for clarity, only the characteristics at 50 C and 140 C are shown in Fig. 1). Finally, from 140 C to 180 C the current increases again. This behavior is observed at all voltages. Figure 2 shows I-t at a given temperature (75 C), for different biases. Current level

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FIG. 1. Some typical I(t) characteristics recorded at a given dc bias (0.5 V), as a function of temperature.

increases with bias. This observation is made at all temperatures. Transient currents recorded for films deposited on TiN and Pt are very similar (I-t shape and current levels). At short times (t < 102 s), I-t characteristics seem to level off toward a plateau. At present, it is not clear whether this plateau is physical, or if it is related to the SMU bandwidth. For this reason, current at t < 102 s will not be discussed. At long times (t > 1 s, I < 109 A), spectra are noisy because the SMU current range is fixed at 100 nA. Current range is deliberately fixed (at the expense of sensitivity) to avoid problems with automatic range switching and to maintain the same sampling conditions (same SMU feedback impedance) during the whole measurement period. As a consequence, analysis of the I-t characteristics are carried out in the 0.1–1 s range, a time interval for which data are most reliable. In the 0.1–1 s range (the range of confidence), the current is observed to decay as a ta law, I ¼ Q0 =ta

(1)

where a is the power-law exponent (usually close to 1) and Q0 is the amplitude (when a ¼ 1, Q0 has the dimension of a charge). Equation (1) is known as the Curie-von Schweidler law.11


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FIG. 3. Exponent a appearing in the Curie-von Schweidler law (I ta), as a function of bias and at different temperatures.

FIG. 2. Some typical I(t) characteristics recorded at a given temperature (75 C), as a function of the dc bias.

Exponent a is plotted as a function of bias in Fig. 3, for several temperatures. At a given temperature, a is observed to be almost constant with bias (for each temperature, average values are listed in Table I). On the other hand, a marked temperature dependence is observed (see Fig. 4). Figure 4 shows that a varies from 0.65 to 1.05, with a peak around 75 C. Previous works have quoted a ¼ 0.95 for poly-Si/ 10 nm ALD HfO2/Si stacks (at 1 V),4 a ¼ 1.02 for Al/5 nm ALD HfO2/0.9 nm SiO2/Si (at 1.75 V),7 and a 1 for polySi/6 nm HfO2/1 nm SiO2 structures (at around 1 V).6 Here, it is shown that a can significantly depart from 1, and that a strongly depends on temperature. The amplitude Q0 (Eq. (1)) is shown as a function of bias in Fig. 5. Q0 varies almost linearly with bias, except at 180 C where a supralinear behavior is noticed. The magnitude of Q0 is almost constant with temperature up to 105 C, and increases above. To take into account the bias and the temperature dependences, Q0 is written as, Q0 ¼ C 0 Vb

(2)

where C0 and b are two empirical parameters (when b ¼ 1, C0 has the dimension of a capacitance). The temperature

dependence of b and C0 is shown in Fig. 6. Again, it is noted that results are similar for the Pt and TiN electrodes. In HfO2, the relaxation current was found to increase linearly with bias,5 or exponentially.6 Present results (Fig. 2 and Fig. 5) rather agree with a linear increase, though the exact variation of I(t) with V appears to be more intricate (I Vb, Eq. (2)), especially with temperature (T dependence of b, Fig. 6). For HfO2, there is a general agreement that transient currents are weakly activated.4,7 The amplitude of transient currents has been reported to be constant from 77 K to 398 K,4 or multiplied by a small factor ( 4) from 75 K to 300 K.7 The same general trend is observed here, at least up to 140 C (Fig. 1). It is pointed out that because both the slope (a) and the amplitude (Q0) vary with T, the TABLE I. Parameter a is extracted from fitting a ta law to experimental I(t) in the 0.1–1 s range (a is an average value calculated from the different bias measurements). Parameters s, m, and n are extracted from fitting fs, fm, and fn1 laws to experimental G(f), C(f), and dC(f)/df, in the 0.1–1 Hz range. TiN electrode

Pt electrode

T( C)

a

s

m

n

a

s

m

n

20 50 75 105 140 180

0.69 1.00 1.07 0.99 0.90 0.66

0.67 0.86 1.00 0.96 0.90 0.91

0.025 0.058 0.056 0.071 0.058 0.017

0.30 0.27 (0.02) (0.01) 0.30 0.16

0.82 1.02 1.04 0.90 0.78 0.68

0.79 0.97 1.00 0.93 0.80 0.66

0.029 0.034 0.032 0.033 0.046 0.088

0.19 (0.01) (0.01) (0.02) 0.12 0.26


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FIG. 4. Exponent a as a function of temperature. For a given temperature, points are the values measured at different biases (from Fig. 3). The line joins average values.

temperature variation of I depends on the time at which I is measured. For instance, in Fig. 1 (Pt electrode), I-t curves at 50 C and 20 C cross at t 0.5 s. Therefore, it could have been concluded that the current increases with T (t < 0.5 s), or is constant with T (t ¼ 0.5 s), or even decreases with T (t > 0.5 s). Therefore, in the transient regime, care must be exercised when discussing I(T). It is worth noting that within the time of experiment (10 s), steady state currents are not reached, even at the highest temperature of investigation (180 C). This is consistent with previous works in 10 nm HfO2 films that have shown that, at 100 C, transient currents dominate up to 100 s.4 On the contrary, at 125 C, Zafar and co-workers8 observed steady state currents as soon as t > 0.1 s (in 4 nm HfO2/1.5 nm SiO2 stacks), that could be related to higher electric fields (V > 1 V) and to more conducting films (tunneling conduction). Zafar et al.8 also reported space charge limited (SCL) transient currents, appearing in the I-t characteristics as a broad current peak. Although this behavior is not reported here (bias lower than 1 V), we do observe similar broad current peaks (usually followed by breakdown), but only at higher biases (3 V) and at much longer times (e.g., at 50 C a SCL peak appears around 103 s). These phenomena will be discussed in a separate paper. In previous studies,12,13 we reported resistance switching (RS) in similar films, but RS occurs at even higher biases (4 V). Under present experimental conditions the voltage stress is limited to 1 V (field in the 0.1–1 MV/cm range). Thus, the above phenomena (SCL transients, RS), and more generally wear-out and prebreakdown phenomena, are absent.

FIG. 5. Amplitude Q0 appearing in the Curie-von Schweidler law (I ¼ Q0/ta), as a function of bias, at different temperatures.

B. Comparison with existing models

Although the Curie-von Schweidler law has been known for a long time, underlying polarization mechanisms are still uncertain. Several polarization processes have been invoked, including dipolar polarization (alignment of pre-existing dipoles along the electric field; however, this process requires large free volume and is unlikely to occur in inorganic solids), charge trapping14–21 (creation of a space charge by the trapping of injected electrons), short-range charge hopping22–25 (movement of trapped charges between two adjacent sites), and electrode polarization26,27 (fieldinduced drift of bulk charges toward electrodes where they accumulate). Let us first consider the trapping mechanisms. According to Walden,17 injected electrons are trapped at defects, building a negative space charge close to the cathode. The negative space charge leads to a decrease of the electric field at the cathode/dielectric interface, so that the injected current decreases, up to a point where the field vanishes and so does the current. Walden17 assumed that part of the injected charge (Q) is trapped (QT), the ratio (dQT/dQ) being proportional to the injected current, i.e., (dQT/dQ) ¼ (I/I0)n1, where I is the current at t, I0 is the current at t ¼ 0, and n is a critical parameter (n 1). Considering a general injection


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independently obtained by Cherki et al.19 and by Wintle.20 These authors19,20 both showed that, IðtÞ ¼ AV

FIG. 6. Exponent b and factor C0 describing the amplitude (Q0 ¼ C0Vb), as a function of temperature.

law of the form I(Es) ¼ I0(Es) exp[f(Es)], where Es is the field at the interface and f is a function describing the injection law, Walden17 showed that, IðtÞ ¼ I0

t 1=n 0

t

(3)

where t0 is a parameter that depends on the considered injection law (f function). Therefore, within Walden’s model, a ¼ 1/n ( 75 C) can be explained by an increase of the tunneling distance. Temperature favors detrapping. Therefore, the band bending at the interface decreases and the distance (x) of traps, whose level faces the metal Fermi level, increases. The model predicts a simple linear dependence of Q0 with V, which almost agrees with the present experiments. The temperature dependence of Q0 is contained in t0. The trapping time constant t0 ¼ 1/cn depends on the electronic density (n) at the cathode Fermi level and on the capture coefficient (c) at oxide traps. This latter coefficient has a weak temperature dependence (c T3/2 in SiO2),29 so the model qualitatively agrees with the weak temperature dependence of C0 (Fig. 6). We now turn to tunnel hopping models. Two groups22,24 analyzed transient currents due to charges that tunnel between adjacent potential wells (bulk process). According to the analysis of Holten and Kliem,22 the transient current can be written as, IðtÞ ¼ AV fðTÞ

1 t

(5)

where A is a constant and f(T) ¼ (kT)1[exp(U/kT) þ 1]1 is a function that takes into account the well asymmetry (U is the energy difference between two adjacent potential wells). Jameson et al.24,25 proposed, 1 t 3 þ Ln IðtÞ ¼ AVgðTÞ (6) t t0 where g(T) ¼ (kT)Ln[(1 þ exp(lE/kT))/2] (l ¼ qd is the dipole associated with a charge q tunneling between wells separated by a distance d) and t0 is a time constant. These


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models capture the linear dependence of the current with V and its weak temperature dependence (I T1 in Eq. (5) when U 0, or I Tþ1 in Eq. (6)). As they imply bulk mechanisms (tunnel hopping), they can explain the similitude between TiN and Pt electrodes. However, the models fail in predicting a < 1 (the logarithmic term in Eq. (6) leads to an effective a slightly less than 1,25 but it cannot account for a much lower than 1 as quoted in Fig. 4). The above short review of existing models shows that none fully agrees with experiments. Therefore, it is difficult to draw conclusions about physical mechanisms. It is quite clear that a tunneling mechanism is at work (at least in the 50–140 C range). The decrease of a with T is consistent with detrapping (because detrapping slows down the rate of current decay), which is in favor of trap-assisted tunneling models.19,20 At 180 C the current (or C0 in Fig. 6) markedly increases. This is probably due to a change of regime, from tunneling to thermionic emission (over the Schottky barrier height for trap-assisted tunneling models). Experiments also show a transition from 20 C to 50 C (Fig. 1, Fig. 4), the origin of which is unclear and needs further investigation. IV. IMPEDANCE SPECTROSCOPY (Y-f)

The frequency dependence of the capacitance (C) and conductance (G) are shown in Fig. 7 and Fig. 8. The frequency of analysis was limited to 10 kHz because of the series resistance. The series resistance (Rs) is at the origin of a

FIG. 8. Conductance as a function of frequency, at several temperatures.

FIG. 7. Capacitance as a function of frequency, at several temperatures.

cut-off frequency (1/2pRSC) above which C drops by several decades and G saturates (which could be erroneously attributed to a dielectric relaxation). In our case we estimate Rs to be around 50–100 X. The value of Rs is observed to be strongly dependent on the top electrode deposition technique, suggesting that Rs is related to the top contact. Below 10 kHz (< 1/2pRSC), the series resistance plays no role, and the data (C,G) can be analyzed as depending on the dielectric only. The quantities C and G define the complex admittance Y ¼ G þ jCx and the complex permittivity e ¼ e0 je00 ¼ Y/jxC0, where C0 is the air (or geometric) capacitance (2.78 nF). From the value of C at 10 kHz, we get e0 11 (TiN electrode) and e0 11.5 (Pt electrode). These values correspond to capacitance densities around 10 fF/lm2 (a little bit less than previous reported values of 13 fF/lm2 for 10 nm ALD HfO2).2 The frequency dispersion of the capacitance is significant. As can be seen in Fig. 7, at 20 C the capacitance increases by about 40% when the frequency decreases from 10 kHz to 0.01 Hz, while at 180 C it increases by about 150% in the same frequency range. The dc conductance (Gdc) cannot be observed (it would appear as a plateau in G-f characteristics), even at the lowest frequency (0.01 Hz) and at the highest temperature (180 C). At 20 C, Gdc < 109 S (Fig. 8), in agreement with dc transient currents (Fig. 1) which show that the steady state conductance is lower than 1010 S.


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Fourier analysis of the I-t response transforms the results from the time domain into the frequency domain, so in principle Y-f characteristics should contain the same information as I-t characteristics.11,30 It has been shown that e00 (x) can readily be obtained from I(t) using the Hamon approximation,30 e00 ðxÞ ¼ IðtÞ=xC0 V

(7)

where I(t) is the current measured at the time t under a dc bias V, C0 is the air capacitance (2.78 nF), and the frequency f ¼ x/2p is related to t according to,30 f ¼ 0:1=t

(8)

Because G ¼ xe00 C0, Eq. (7) leads to a very simple expression for G(f), Gðf Þ¼ IðtÞ=V:

(9)

An example of a G(f) characteristic that is calculated using the Hamon approximation (Eq. (9)) is shown in Fig. 9. The agreement with experimental G is very good in the 0.01–1 Hz range. The calculated G(f) characteristic (Hamon approximation, Eq. (9)) significantly deviates from the experimental one when f > 10 Hz. Within the Hamon calculation, f > 10 Hz corresponds to t < 0.01 s (Eq. (8)). This time domain is the one for which a plateau is observed in I-t characteristics (see Fig. 1). It seems to confirm that this plateau is not physical (because it leads to a Hamon G characteristic that deviates from the experimental one). The Fourier transform of the Curie-von Schweidler law (Eq. (1)) leads to,11,30 C xm ; s

Gx;

Fig. 10 and listed in Table I. There is a reasonable agreement between a and s values (especially for the Pt electrode), verifying the relation s ¼ a. However, the relation m ¼ 1 a is not verified. For instance, when a is lower than 1 (20 C, 140 C, 180 C), we measure m values in the 0.01 range, well below 1 a (see Table I). Discrepancy between m and 1 a comes from the nondispersive part of the capacitance. To correctly extract m from C(f), we must consider that the capacitance is the sum of a low-frequency dispersive term (CLF xn, where n now replaces m), and a second term (C1) that is constant in the frequency range of interest (because its relaxation frequency is well above 10 kHz), C ¼ CLF ð xn Þ þ C1

(12)

where in theory n ¼ 1 a. Because C1 and CLF cross in the frequency range of interest, the effective power exponent (m, measured from C) is lower than the theoretical power exponent (n, measured from C C1). The constant term C1 can be eliminated by working with the derivative of C, dC=dx ¼ dCLF =dx xn1

(13)

An example of dC/df plot is provided in Fig. 11. The power law predicted by Eq. (13) is well verified. The n values that are extracted from dC/df plots are listed in Table I and compared to 1 a in Fig. 12. The agreement is now good for the Pt electrode (Fig. 12). Some discrepancy is still observed for the TiN electrode, but the general behaviors of n(T) and

(10) (11)

where in theory m ¼ 1 a and s ¼ a. As stated in Sec. III, extraction of a from I-t data is performed in the 0.1–1 s range. Thus, to compare a with exponents m and n, these latter parameters are extracted from C(f) and G(f) characteristics in the 0.1–1 Hz range (equivalence between frequency and time domains within the Hamon approximation, Eq. (8)). Results are depicted in

FIG. 9. Comparison between the experimental conductance and the conductance that is calculated according to the Hamon approximation.

FIG. 10. Critical exponents s and m describing the frequency dispersion of the conductance (G fs) and capacitance (G fm). These parameters are extracted from fits to experimental data in the 0.1–1 Hz range. Comparison with a and 1 a is provided.


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FIG. 11. Example of the derivative of capacitance with respect to the frequency.

1 a(T) are similar. Discrepancy for the TiN electrode comes from a relaxation which superimposes on CLF (such a relaxation is seen around 10 Hz at 140 C, Fig. 7 and Fig. 8) and impedes to get a correct value for n. This relaxation could be due to the TiON interfacial layer at the TiN/HfO2 interface. Knowing n, the CLF(x) curve can be reconstructed from the dC/df curve (CLF ¼ jdC/dfj f/n), and C1 can be calculated (C1 ¼ C CLF), see Fig. 13. As expected, C1 is constant with frequency and is identical for the Pt and TiN electrodes. CLF indeed decreases with frequency as a power law, up to 10 Hz. Above 10–100 Hz, it becomes constant (Pt) or increases (TiN) with frequency. This latter behavior

FIG. 12. Critical exponent n describing the frequency dispersion of the derivative of capacitance (dC/df fn1). Parameter n is extracted from fits to experimental data in the 0.1–1 Hz range, and compared to 1 a.

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FIG. 13. Low-frequency dispersive part (CLF) and non-dispersive part (C1) of the capacitance.

is not physical and should be disregarded (showing the limits of the present analysis). Finally, within the range of confidence (f < 10 Hz), the dielectric constant can be expressed as n

e0 ¼ De0 f þe0 1

(14)

where e0 1 ¼ 11.1 (for both Pt and TiN), n 0.2 (Pt) or 0.3 (TiN), and De0 1.5 (Pt) or 0.7 (TiN). These values are given at 20 C (for which n þ a ¼ 1 is verified for both the TiN and Pt electrodes). IV. CONCLUSION

Dielectric relaxation is studied in 10 nm HfO2 thin films, which are deposited by the ALD technique on TiN and Pt electrodes. The time response, I(t), is recorded from 103 to 10 s, as a function of bias (0.1 V to 1 V) and temperature (20 C to 180 C). A Curie-von Schweidler law is observed, I ¼ Q0/ta. The power law exponent a is constant with bias. It depends on the temperature (varying in the 0.65–1.05 interval with a peak at 75 C). The amplitude Q0 can be described by a relation of the form Q0 ¼ C0Vb, where the factor C0 is weakly activated and the exponent b varies with temperature (in the 0.9–1.5 range as T varies). Transient currents weakly vary with temperature (50–140 C range), implying a tunneling mechanism. Tunneling-based models are reviewed (Fowler-Nordheim injection followed by trapping, trapassisted tunneling, bulk tunnel hopping). No model is able to fully describe the data, pointing out the need for further theoretical modeling. The frequency response, Y-f, is recorded at low frequencies, in the 0.01 Hz–10 kHz range. The G(f) characteristic which is extracted from I(t) by using the Hamon approximation is verified to be consistent with experimental G(f). The dispersion law of the conductance (G xs) is consistent with current transients (s a). It is necessary to take into account a non-dispersive term in the capacitance, so that C ¼ C1 þ CLF, where C1 is constant with frequency and CLF xn is a low-frequency dispersive term (n 1 a).


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ACKNOWLEDGMENTS

Financial support from Re´gion Rhoˆne-Alpes is gratefully acknowledged. 1

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