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Chapter 3 Fabrication and Characterization Methods

3.2 Measurement and Parameters Extraction

An automatic measurement system consisted of a person computer (PC), Agilent-4156C, Agilent-4284A, Agilent switch, and a probe station is used for DC and low-frequency measurement of the fabricated devices. The properties of the La2O3 MIM capacitor are measured by the temperature-controlled chuck of the probe station, such as leakage current, capacitance density, breakdown biased voltage, and reliability characteristics. For all of electrical measurements, the voltage and the altering signal are applied to the top electrode while the bottom electrode was grounded.

The leakage current-voltage (J-V) measurements are preformed on the Agilent-4156C semiconductor parameter analyzer in the temperature range from 25 °C to 125 °C to evaluate the conduction mechanisms of the La2O3 MIM capacitors. After taking about 30 minutes to stabilize the temperature of wafer and chuck, the measurement starts at 0 V and sweeps towards the high electric field region with a 0.1 V voltage step. Afterwards, the numerical fitting of the measured J-V data is carried out according to the theories and the equations stated in chapter 2.

The capacitance-voltage (C-V) curves are measured by the Agilent 4284A precision impedance meter, and the dielectric loss-voltage (D-V) curves could also be observed at the same time. The biased voltage on the top electrode of the La2O3 MIM capacitor sweeps from

−2 V to 2 V at frequencies varying from 10 kHz to 500 kHz by applying an ac signal with

25-mV amplitude. The thermal stress on this MIM capacitor is also carried on with measurement temperatures varying from 25 °C to 125 °C. Together with the La2O3 physical thickness obtained from transmission electron microscope (TEM), the dielectric constant of the deposited La2O3 film (kLa2O3) could be determined as

, where ε0 is the permittivity of free space, S is the capacitor area, d is the physical thickness of the La2O3 film, and C is the capacitance at zero bias, at 100 kHz, and at 25 °C.

Consequently, the equivalent oxide thickness (EOT) of the deposited La2O3 film could be calculated by

, where kSiO2 is the dielectric constant of the silicon dioxide.

As for the accuracy of analog functions performed by the MIM capacitors, the dependence of capacitance on the biased voltage (V), the temperature (T), and the frequency (F) are investigated. For one thing, C-V curves in the voltage range from −1.5 V to 1.5 V are fitted by the following second order polynomial equation as

( )

=

(

= ×0

) (

× 2+ × +1

)

C V C V α V β V (3-3)

, where C(V=0) is the capacitance at zero bias, α (ppm/V2) is the quadratic voltage coefficient of capacitance, and β (ppm/V) is the linear voltage coefficient of capacitance. The parameter β could be cancelled by circuit design [121], but the parameter α could not. Therefore, only the parameter of α under various measurement frequencies and various temperatures are discussed in this thesis. What is more, for the discussion of the thermal stability of the MIM capacitors, the temperature coefficient of capacitance (TCC) is extracted as the slope of a capacitance-temperature (C-T) plot in the temperature range of 25 °C to 125 °C, as shown in Eq. 3-4.

(

125

)

( )

= ×

= oTCC C T

C T C T (3-4)

As a result, the TCC (ppm/°C) for a certain bias and a certain frequency condition could be obtained. In this work, the temperature coefficients of capacitance (TCC) at zero bias are fitted to exhibit the temperature dependency of capacitance.

Concerning the frequency dispersion in MIM capacitors, the frequency coefficient of capacitance (FCC) could be defined as the slope of a C-log10F plot in the frequency range from 10 kHz to 500 kHz by

, where C(F = 10 kHz) is the capacitance at 10 kHz, the minimum frequency we measure. In this study, the frequency coefficients of capacitance at zero bias are derived as the indicators of the frequency dependency of capacitance.

Moreover, from the viewpoint of practical use, it is very important to clarify the stability of MIM capacitor properties during long-term voltage stress. Therefore, the constant voltage stress (CVS) in the range of −4 V to −5 V at the temperature of 25°C is conducted by utilizing the Agilent-4156C semiconductor parameter analyzer. The C-V and J-V characteristics of La2O3 MIM capacitors are also measured at various time intervals during CVS testing. To inspect the stress induced instability of La2O3 MIM capacitor, the relative leakage current variation and the relative capacitance variation during stressing compared to fresh conditions are observed as

, where J(t=0) and C(t=0) are the initial leakage current density and the initial capacitance

density, respectively. The leakage current and the capacitance measured at various time intervals during CVS testing are extracted at the applied voltage at −1 V and 0 V, respectively.

In the same way, the relative variation in dielectric loss, in quadratic voltage coefficient of capacitance, and in temperature coefficient of capacitance caused by CVS with respect to its initial values are acquired as following

( ) ( ) ( )

Here, D(t=0) and D(t) are the dielectric loss at V=0 before and during stressing monitored by the Agilent 4284A precision impedance meter. α(t=0) and α(t) are the extracted quadratic voltage coefficients of capacitance before and during stressing. TCC(t=0) and TCC(t) are the deduced temperature coefficients of capacitance before and during stressing.

Additionally, the charge injecting into the dielectric film of the MIM capacitor during stressing could be determined by Qinj (C/cm2) from the integration formula

( )

0

=

t

inj stress

Q J t dt (3-10)

, where Jstress(t) is the current density as a function of time flowing through the La2O3 film and the term “t” also refers to the stress time. More specifically, the Qinj is the area under the curve of the Jstress versus stressing time, as schematically described in Fig. 3-3.

On the other hand, the reliability issues include time-zero dielectric breakdown (TZDB) and time-dependent dielectric breakdown (TDDB) are discussed to demonstrate the lifetime and integrity of the dielectrics of fabricated MIM capacitors. In the first place, the TZDB measurement method was a J-V measurement with increasing applied voltage until the

dielectric breakdown, and then the cumulative results of the breakdown field (EBD, MV/cm) are obtained because of the wide range of EBD data. In the second place, the TDDB measurements are carried out by means of the CVS at 75°C with appreciable current flow (Jstress) through the dielectric, and the evolution of the Jstress with time during the CVS could be monitored. When a sudden jump in Jstress occurrs, the time of this event is called as the time to breakdown (tBD) point. The charge to breakdown (QBD) of MIM capacitor defined by the necessary charge density injection until the dielectric breakdown could be computed from the following equation

Hence, the tBD and QBD could be estimated in this work. The statistics of TDDB are described by the Weibull distribution [30]

( )

= −1 exp ⎟ shape factor or Weibull slope, as depicted in Fig. 3-4. By extrapolating all the αC data with respect to applied voltages, the lifetime projection of La2O3 MIM capacitors to operational voltages could be realized, as schematized in Fig. 3-5. Furthermore, βC is also useful in predicting lifetime distribution for various capacitor areas. For example, the relationship between the scale factor ratio (αCC0) and the area ratio (S/S0) could be described as the following equation [30]

1

, where the S0 and the αC0 are the initial area and the scale factor of capacitor, respectively.

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