Transient Charging and Discharging Behaviors

Fig. 6-4 shows the trapped charge density Nt as a function of the rise time and fall time (here T_r=T_f) of input pulse waveform at various frequencies (f= 1k, 10k, 100k, and 1M Hz). The Nt remained constant even with a great variety of rise time and fall time ranging from 2 ns to 1 µs except the one measured at f= 1M Hz. Since the rise time and fall time are highly associated with the scanned energy range of interface states in the Si forbidden bandgap [6.1] and the Nt at low frequencies are almost independent of rise time and fall time, the injected channel electrons from the Si conduction band states may directly tunnel into and out of the border traps in the HfO2

high-k dielectric within the durations of transient charging (Vpeak, ON state) and discharging (V_base, OFF state) stages, respectively. This may also eliminate the possibility of two-step capture and emission process (in which an efficient thermal Shockley-Read-Hall capture into an interface trap followed by a trap-to-trap tunneling transition and vice versa [6.16]).

Fig. 6-5 shows the trapped charge density Nt as a function of the base level voltage V_base of input pulse waveform at various frequencies. When the negative V_base was increased, the Nt at low frequencies grew gradually and eventually became saturated. Also, note that the N_t at various frequencies are almost identical at V_base= 0

~ -0.2 V. This suggests that the negative bias voltage of Vbase plays a significant role to pull out the trapped electrons from the border traps during the transient discharging stage. Fig. 6-6 shows the trapped charge density Nt as a function of the duty cycle of input pulse waveform at various frequencies. Similar to the capture and emission of the interface states, the transient charging and discharging of border traps should both occur within one pulse cycle to constitute the recombination charge pumping current.

With very small (~0%) or very large (~100%) duty cycles, the charge carriers may not have enough time to tunnel into or out of the border traps in the HfO2 high-k dielectric, and only the interface states that can exchange charge carriers in a very short time could be observed such as the one measured at f= 1M Hz. In addition, symmetric transient charging and discharging behaviors could also be clearly observed at very small and very large duty cycles, therefore suggesting equal forward and reverse tunneling time constant in the elastic direct tunneling model⁶.

Fig. 6-7 shows the trapped charge density Nt as a function of transient charging time at various peak level voltages V_peak by changing the ON time within one pulse cycle at f= 10k Hz. The Nt began to increase rapidly at the transient charging time

~10^-7 sec in a power law relation and eventually became saturated except the one with V_peak= +0.5 V where only the interface states were observed, thus implying the transient charging effect may occur within 50-100 ns. Symbols are measurement data, dotted line is the fitting line for the interface state density, while solid lines are the model-fitting results using the charge trapping model with dispersive capture time constants [6.17], [6.18]:

6 This proves our previous assumption of elastic direct tunneling due to the symmetric transient charge trapping and de-trapping behaviors, and the temperature dependence observed before may result from the following-up lattice-relaxation multi-phonon emissions (thermal energy transitions) by changing

where t is the transient charging time, Nbt(t) is the detected border trap area density (cm^-2) as a function of transient charging time, N_it is the interface state density, N_bt,0 is the pre-existing border trap area density in the HfO2 high-k dielectric, τ is the capture time constant, and β is the distribution factor of capture time constant (β= 1 for SiO2).

Although the N_bt,0 and τ vary, the β is ~0.32 for various V_peak, and this also confirms that the border traps in the HfO2/SiO2 high-k gate stack should be spatially located at the bulk layer of HfO₂ high-k dielectric, not at the SiO₂ interfacial oxide.

Fig. 6-8 shows the trapped charge density Nt as a function of transient discharging time at various peak level voltages Vpeak by changing the OFF time within one pulse cycle at f= 10k Hz. Similar to the transient charging behavior, transient discharging behavior could also be well described by the charge de-trapping model with dispersive emission time constants which is similar to the charge trapping model. The Nbt,0 and τ of transient discharging behavior are near to those of transient charging behavior, and the β is also ~0.32. Because the distribution of tunneling time constant is highly associated with the tunneling distance from the Si substrate surface to the localized border traps and the previous studies about slow high-k traps using positive bias temperature instability (PBTI) stress and static I_d-V_g characteristics [6.18] also exhibited the same β (~0.32) value, it may be concluded that the fast and slow traps in the HfO2 high-k dielectric have similar space trap distribution and that the fast high-k traps might be identical to the slow high-k traps in properties but just located deeper inside the Hf-based high-k dielectric.

6.5 Space and Energy Distribution of Border Traps

Fig. 6-9 shows the detected border trap area density Nbt as a function of the frequency of input pulse waveform at various peak level voltages V_peak by

transforming the frequency and voltage dependences as shown in Fig. 6-3. These frequency and voltage dependences of N_bt could also be transformed into the relations corresponding to the tunneling distance from the Si substrate surface and the trap energy depth from the HfO2 conduction band edge, respectively.

Fig. 6-10 shows the schematic band diagram of the TaC/HfO₂/SiO₂/p-Si NMOS device biased in the strong inversion region with the illustrations of tunneling distance and carrier energy coordinates. If the transient charging and discharging of border traps mainly occur at the Si conduction band edge through direct tunneling and the border traps are widely distributed over a defect band in the HfO2 high-k dielectric [6.14], the N_bt could be regarded as the equivalent border trap area density D_bt at one specific energy level (cm^-2eV^-1), which is the integration of border trap volume density ρ_bt (cm^-3eV^-1) from the base oxide thickness x₁ to the maximum tunneling distance xmax in the HfO2 high-k dielectric since there should be negligible border traps in the thermally-grown interfacial oxide SiO2:

.

The trap energy depth Et from the HfO2 conduction band edge could be approximately obtained at various peak level voltages if the two-band structure (SiO₂ and HfO₂) with trapezoidal potential barriers is assumed:

), electric fields in the SiO₂ and HfO₂ dielectrics, respectively, and x₁ is the base oxide thickness (1.0 nm). If the tunneling transition is an elastic direct tunneling process with symmetric forward and reverse tunneling time constants, the tunneling time constants between the available Si conduction band states and localized border traps

),

reduced Planck constant, Φ_c1 (3.1 eV) is the conduction band offset of SiO₂, and m₁^* (0.42 m0) and m2*

(0.18 m0) are the effective mass of electrons in the SiO2 and HfO2

dielectrics, respectively [6.12], [6.26]. Then, the maximum tunneling distance xmax

that can be reached during the given pulse cycle could be extracted from (6.5) with the above physical model parameters. Finally, the space and energy distribution of border trap volume density ρ_bt could be obtained as follows:

) .

model-extracted data points, and 3D-mesh is the smoothed surface profiling of these points. As the tunneling distance reaches the HfO₂ high-k dielectric (x >1.0 nm), the ρbt began to increase gradually and eventually became saturated. Moreover, the ρbt

increases exponentially with the decreasing trap energy depth E_t, and the variation of the ρbt seems to be less sensitive to the tunneling distance. These results suggest that most of the pre-existing high-k border traps are located in the HfO2 bulk layer and that considerable parts of these border traps are positioned at the shallow energy levels.

Moreover, similar space and energy distribution of border traps could be observed by the low-frequency charge pumping in this chapter and the low-frequency C-V measurement in chapter 5. However, there is some discrepancy in the order of magnitude of detected border trap volume densities due to the different testing conditions, rapid recombination of majority and minority carriers for charge pumping

and small-signal frequency response for C-V measurement.

6.6 Summary

The pre-existing high-k traps located near the HfO2/SiO2 interface or the so called border traps could instantly exchange charge carriers with the underlying Si substrate through direct tunneling, and these border traps (detected fast high-k traps) could be measured and analyzed by the low-frequency charge pumping method with fixed base level voltage and varying amplitude. As compared to the interface state density measured at f= 1M Hz, the additional trapped charge density measured at lower frequencies could be attributed to the contribution from the border traps in the HfO₂ high-k dielectric. Moreover, various transient charging and discharging characteristics of these border traps could be observed by varying the rise time and fall time, peak and base level voltages, and duty cycle of input pulse waveform. In addition, the transient charging and discharging behaviors of the border traps could be observed in the time scale of 10^-8-10^-4 sec by changing the ON and OFF times within one pulse cycle at a specific frequency, and this method is much faster than the known pulse Id-Vg technique (~1-10 µs). Also, the transient charging/discharging behavior could be well described by the charge trapping/de-trapping model with dispersive capture/

emission time constants used in the static positive bias stress, thus suggesting similar space trap distribution of fast and slow traps in the HfO₂ high-k dielectric. Finally, the frequency and voltage dependences of the border trap area density could be transformed into the relations corresponding to the tunneling distance and trap energy depth by using an elastic direct tunneling model between the Si conduction band states and localized border traps through trapezoidal potential barriers. Based on this physical model, the space and energy distribution of the border traps in the HfO₂

high-k dielectric could be profiled as a smoothed 3D-mesh. Although the energy scan of border traps over a defect band is based on the assumption of elastic direct tunneling at a specific single energy level, this assumption could help us realize and profile the truly three dimensional border trap distribution in space and in energy levels to a certain extent.

Fig. 6-1 Measurement system setup of charge pumping method. The gate of a NMOS device is connected to a pulse generator, and a reverse bias voltage Vr is applied to the source and drain, while the charge pumping current Icp is measured at the grounded substrate.

Peak Level Voltage (V)

0.0 0.5 1.0 1.5 2.0

C ha rge P um p ing C ur re nt ( A )

10^-11 10^-10 10^-9 10^-8 10^-7 10^-6

High

Low

Poly-Si/TaC/HfO₂/SiO₂/p-Si nMOSFET, W/L= 6860/0.5 µµµµm EOT= 1.77 nm

f= 1k, 2k, 5k, 10k, 20k, 50k, 100k, 200k, 500k, and 1M Hz

Fig. 6-2 Charge pumping current I_cp of the poly-Si/TaC/HfO₂/SiO₂/p-Si high-k gate stack with EOT= 1.77 nm as a function of peak level voltage V_peak at various frequencies.

Peak Level Voltage (V)

0.0 0.5 1.0 1.5 2.0

T ra p p e d C h a rg e D e n s it y ( c m -2 )

10⁹ 10¹⁰ 10¹¹ 10¹²

Low

High

f= 1k, 2k, 5k, 10k, 20k, 50k, 100k, 200k, 500k, and 1M Hz

Fig. 6-3 Trapped charge density N_t of the dual-layer HfO₂/SiO₂ high-k gate stack as a function of peak level voltage Vpeak at various frequencies. The inset illustrates the definition of input pulse waveform parameters.

Rise/Fall Time (s)

10^-9 10^-8 10^-7 10^-6

T rap p ed C h ar g e D en si ty (cm -2 )

10¹⁰ 10¹¹ 10¹² 10¹³

f= 1k Hz f= 10k Hz f= 100k Hz f= 1M Hz

Fig. 6-4 Trapped charge density Nt as a function of the rise time and fall time (here T_r=T_f) of input pulse waveform at various frequencies (1k, 10k, 100k, and 1M Hz). Rise time and fall time are highly associated with the scanned energy range of interface states in the Si forbidden bandgap.

Base Level Voltage (V)

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0

T ra p p e d C h a rg e D e n s ity (c m

-2

)

f= 1k Hz f= 10k Hz f= 100k Hz f= 1M Hz

0 2x10¹¹ 4x10¹¹ 6x10¹¹ 8x10¹¹ 1x10¹²

Fig. 6-5 Trapped charge density Nt as a function of the base level voltage Vbase of input pulse waveform at various frequencies (1k, 10k, 100k, and 1M Hz).

The negative bias voltage of V_base plays a significant role to pull out the trapped charge carriers during the transient discharging stage.

Duty Cycle (%)

0 20 40 60 80 100

T rap p ed C h ar g e D en si ty (cm -2 )

10¹⁰ 10¹¹ 10¹² 10¹³

f= 1k Hz f= 10k Hz f= 100k Hz f= 1M Hz

Fig. 6-6 Trapped charge density Nt as a function of the duty cycle of input pulse waveform at various frequencies (1k, 10k, 100k, and 1M Hz). Symmetric transient charging and discharging behaviors could be observed at very small and very large duty cycles.

Transient Charging Time (s)

10^-8 10^-7 10^-6 10^-5 10^-4

T ra p p e d C h a rg e D e n s it y ( c m -2 )

10⁹ 10¹⁰ 10¹¹ 10¹²

+0.5V +1.0V +1.5V V_peak= +2.0V

Interface State Density N_it Symbols: measurement data

Solid lines: model fitting

Fig. 6-7 Trapped charge density Nt as a function of transient charging time at various peak level voltages V_peak by changing the ON time of input pulse waveform at f= 10k Hz. Symbols are measurement data, dotted line is the fitting line for the interface state density, and solid lines are the model fitting results.

Transient Discharging Time (s)

10^-8 10^-7 10^-6 10^-5 10^-4

T ra p p e d C h a rg e D e n s it y ( c m -2 )

10⁹ 10¹⁰ 10¹¹ 10¹²

Interface State Density N_it

V_peak= +2.0V

+1.5V

+1.0V

+0.5V Symbols: measurement data

Solid lines: model fitting

Fig. 6-8 Trapped charge density N_t as a function of transient discharging time at various peak level voltages Vpeak by changing the OFF time of input pulse waveform at f= 10k Hz. Symbols are measurement data, dotted line is the fitting line for the interface state density, and solid lines are the model fitting results.

Frequency (Hz)

10³ 10⁴ 10⁵ 10⁶

B o rd er T rap D en sit y ( cm

-2

)

0 2x10¹¹ 4x10¹¹ 6x10¹¹ 8x10¹¹

High

V_peak= 0.6~2.0 V Step= 0.1 V

N

_t

= I

_cp

/qfA

_G

= N

_bt

+ N

_it

Fig. 6-9 Border trap area density N_bt of the dual-layer HfO₂/SiO₂ high-k gate stack as a function of the frequency of input pulse waveform at various peak level voltages Vpeak. As can be seen, Nbt increased exponentially with the decreasing frequency and the increasing peak level voltage.

Fig. 6-10 Schematic band diagram of the dual-layer HfO2/SiO2 high-k gate stack biased in the strong inversion region with the illustrations of tunneling distance and carrier energy coordinates.

1.0 1.2 1.4 1.6 1.8 2.2 2.0

0.8 1.0 1.2 1.4 1.6

B o rd e r T ra p D e n s it y ( c m

-3

e V

-1

)

Tunn eling

Dista

nce ( nm) Tr ap E ne rg y De pt h (e V)

2x10¹⁷ 5x10¹⁷ 1x10¹⁸ 2x10¹⁸ 5x10¹⁸ 1x10¹⁹

Fig. 6-11 Space and energy distribution of border trap volume density ρ_bt in the dual-layer HfO2/SiO2 high-k gate stack. Symbols are model-extracted data points, and 3D-mesh is the smoothed surface profiling of these points.

在文檔中 以二氧化鉿為基底之高介電常數閘極介電層中的電荷捕捉與逃逸之電特性分析 (頁 108-126)