Conduction Mechanism

There may be different conduction mechanisms in the insulator thin film, including Schottky-Richardson emission [50], Frenkel-Poole emission [50,51], Fowler-Nordheim tunneling [50,51], and trap assisted tunneling [52,53] illustrated in Fig 3-8. The Schottky-Richardson emission generated by the thermal ionic effect is caused by the electron transport across the potential energy barrier via field-assisted lowering at a metal-insulator interface. The leakage current governed by the Schottky-Richardson emission is as following:

(

¹

)

* 2 2

SR SR

J =A T exp β E −φ_SR k T_B

where βSR =

(

q³ 4πε ε0

)

¹² , q is the electronic charge, is the effective Richardson constant,

A*

φSR is the contact potential barrier, is the applied electric field,

E

ε0 is the permittivity in vacuum, ε is the high frequency relative dielectric constant, is the absolute temperature, and is the Boltzmann constant. We can find the slope of the leakage current equation.

T k_B

( )

12 * 2

lnJ_SR =β_SRE k T_B +⎡⎣ln A T −φ_SR k_BT⎤⎦

SR B

Solpe=β k T

The Frenkel-Poole emission is due to field-enhanced thermal excitation of trapped electrons in the insulator into the conduction band. The leakage current equation is:

(

¹²

)

FP 0 FP

J =J exp β E −φ_FP k T_B

where J₀ =σ₀E is the low-field current density, σ₀ is the low-field conductivity, ^βFP=

(

^{q3 πε ε0}

)

^12, q is the electronic charge, φ_FP is the contact potential barrier, is the applied electric field, E ε₀ is the permittivity in vacuum, ε is the high frequency relative dielectric constant, is the absolute temperature, and

is the Boltzmann constant. We can find the slope of the leakage current equation.

T kB

1

( )

2 0

lnJ_FP =β_FPE k T_B +⎡⎣ln J −φ_FP k T_B ⎤⎦

FP B

Solpe=β k T

The Fowler-Nordheim tunneling is the flow of electrons through a triangular potential barrier. Tunneling is a quantum mechanical process similar to throwing a ball against a wall often results that the ball goes through the wall without damaging the wall or the ball. It also loses no energy during the tunnel event. The probability of this event happening, however, is extremely low, but an electron incident on a barrier typically several nm thick has a high probability of transmission. The Fowler-Nordheim tunneling current I_FN is given by the expression [54]:

( )

2

FN G FN FN

I =A A ε_oxexp −B ε_ox

where the A_G is the gate area, ε_ox is the oxide electric field, and and are usually considered to be constant. and are given as the following:

AFN B _FN AFN B_FN

( ) ( )

3 6

AFN =q m m_ox 8πhΦ =_B 1.54 10× ⁻ m m_ox Φ _B

(

³

)

^{12 7}

^{( )}

¹²

BFN =8π 2m_oxΦ_B 3eh=6.83 10× ^⎡⎣ m m_ox Φ_B^3⎤⎦

where is the effective electron mass in the oxide, m is the free electron mass, is the electronic charge, and is the barrier height at the silicon-oxide interface given in units of eV in the expression for

mox q

ΦB

B .FN Φ_B is actually an effective barrier height that take into account barrier height lowering and quantization of electrons at the semiconductor surface. Rearranging I_FN formula gives by:

(

²

) (

²

) ( )

ln I_FN A_{G ox}ε =ln J_FN ε_ox =ln A_FN −B_FN ε_ox

A plot of ^ln

(

^{JFN εox2}

)

^versus

(

^1εox

)

should be a straight line if the conduction through the oxide is pure Fowler-Nordheim conduction [54].

In the trap assisted tunneling model, it is assumed that electrons first tunnel through the SiOX interfacial layer (direct-tunneling). Then, electrons tunnel through traps located below the conduction band of the high-k thin film and leak to substrate finally [52]. The equation of leakage current density is [53]:

( )

J=α E exp_ox −β E_ox

From the equations as shown above, leakage current behaviors of insulate films can be investigated further on the leakage current density J electric field characteristics such as vs.

E J E¹² plots.

The plot of the nature log of leakage current density versus the square root of the applied electric field was observed. It is found that the leakage current density is linearly related to square root of the applied electric field. The linear variations of the current correspond either to Schottky-Richardson emission or to Frenkel-Poole conduction mechanism. For trap states with coulomb potentials, the expression is virtually identical to that of the Schottky-Richardson emission. The barrier height, however, is the depth of the trap potential well, and the quantity β_FP is larger than in the case of Schottky-Richardson emission by a factor of 2.

Leakage conduction mechanism is also investigated to support the comments on the electrical improvement of Al2O3 film. Fig. 3-9(a) plots ln (J/E) versus reciprocal of electric field variation for the SCCO2-only treated Al2O3 film, and a schematic

energy band diagram accounting for leakage transport mechanism shown in the inset.

A good linear fitting explains Fowler-Nordheim (F-N) tunneling [55] occurs in the electric fields higher than 0.5 MV/cm. Also, it is consistent with the electrical behavior of SCCO2-only treated Al2O3 film in Fig. 3-9 that leakage current density sharply increases, while gate bias voltage larger than 0.5 MV/cm. This could be attributed to the trap-assisted tunneling due to numerous traps inside the SCCO2-only treated Al2O3 film [56]. For the SCCO2 with co-solvent treated Al2O3 film, a plot of leakage current density versus the square root of the applied field (E^1/2) gives a good representation of the leakage behavior at high electric fields, as shown in Fig. 3-9(c).

The leakage current density of the SCCO2 with co-solvent treated Al2O3 is linearly related to the square root of the applied electric field, demonstrating Schottky-Richardson emission transport mechanism [57]. The Schottky-type conduction can be verified by comparing the theoretical value of βSR =

(

q³ 4πε ε0

)

¹²

with the calculated one obtained from the slope of the experimental curve ln J versus E^1/2 [58], where q is the electronic charge, ε₀ the dielectric constant of free space, ε is the high frequency relative dielectric constant. The Schottky emission generated by the thermionic effect is caused by electron transport across the potential energy barrier via field-assisted lowering at a metal-insulator interface, shown in the insert of Fig.

3-9(c), and independent of traps. Additionally, the evolution of conduction mechanisms from trap-assisted tunneling to Schottky emission can confirm these defects inside low-temperature-deposited Al2O3 film is minimized effectively by implementing the proposed SCCO2 technology. The leakage current densities of Al2O3 films after different treatments are shown as a function of applied positive gate bias voltage in Fig. 3-10, and the lower leakage current still could be acquired after SCCO2 with co-solvent and H2O vapor treatment, especially treated with SCCO2

fluids. Generally, in positive gate bias, the sources of electron are (1) the interface states, (2) defects in depletion region, (3) back electrode of substrate, [59] and the later two source are negligible due to the p-type signal-crystal Si wafer is used in this work. For SCCO2-only treated Al2O3 film, the great quantity of interface states still

exist which generate electron-hole pair and lead to higher leakage current, as described in the inset of Fig. 3-10. After SCCO2 with co-solvent treatment, the interface states were deactivated, hence the leakage current is reduced. The reduction of interface states would be proved in capacitance-voltage measurement.

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