6. Electrical behavior of dielectric material

The quality of dielectric material can be electrically characterized by current-voltage (I-V) and capacitance-voltage (C-V) technique. In order to employ the above techniques, the grown/deposited layers on SiC should be sandwiched between two metal electrodes. A different type of current conduction mechanisms were observed and presented in this section, based on dielectric thickness and applied electric field across electrode. In this section SiO2 z3/z+\*/% !.! z /z z#0!z %!(!0.%z+\*z %z /1."!^z1,0\_z ^^z \* z\$%/z .!¥ search group are continuously working to investigate the current conduction mechanism and charge management of gate dielectric material and SiC system (Gupta, S.K. 2010a ; Gupta, S.K. 2010b ; Gupta, S.K. 2011b ; Gupta, S.K. 2012).

#### 6.1. Direct tunneling

layer, justify its nomenclature. ALD is usually carried out on a native oxide (SiO2) surface followed by ozone cleaning of SiC surface. This limits the crucial lowest EOT that ALD can ,.!/!\*0(5z 00%\*^z w0!.)%\*0! z /1."!\_z 3\$%\$z .%/!/z 5z 0\$!z w(!\*%\*#z 0.!0)!\*0z ,.+!¥ dure, is not favorable surface. It was observed that ALD of HfO2 and ZrO2 from chloride or

other organic precursors do not easily nucleate on HF treated SiC surface.

218 Physics and Technology of Silicon Carbide Devices

Figure 7. Schematic of the cyclic process of Atomic layer deposition process

Schrödinger equation describes that there is a finite probability that a particle can tunnel through a non-infinite potential barrier. As the width of potential barrier decreases, the ,.+%(%05 z +" z ,.0%(!/ z c!(!0.+\*/ z \* z \$+(!/d z ,!\*!0.0%\*# z 0\$.+1#\$ z 0\$! z ..%!. z 5 z -1\*¥ tum-mechanical tunneling, rises exponentially. In sufficiently thin oxides (below 5 nm), %.!0z-1\*01)z)!\$\*%(z01\*\*!(%\*#z0\$.+1#\$z0\$!z,+0!\*0%(z..%!.z\*z+1.^z\$%/z-1\*¥ tum-mechanical phenomenon can easily be understood by recognizing that the electron or hole wave function cannot immediately stop at the barrier (SiO2/4H-SiC interface), but rather it decreases exponentially into the barrier with a slope determined by the barrier height. If the potential barrier is very thin, there is non-zero amplitude of the wave "1\*0%+\*z .!)%\*%\*#z 0z 0\$!z!\* z +"z 0\$!z..%!.z)!\*/z z\*+\*w6!.+z,.+%(%05z "+.z 0\$!z!(!¥ tron or hole to penetrate the barrier. It is well known that the barrier heights of hole tunneling in the SiO2 layer from the metal gate and from the Si substrate are higher than the corresponding values for electrons, moreover, the hole mobility in SiO2 is lower than the electron mobility, therefore the main contribution to conduction in SiO2 is due to electrons. Since in n-type 4H-SiC mobility of electrons is much higher than that of hole, therefore, the described conduction mechanism in case of Si can be fully applied to 4H-SiC. The metal/SiO2 and SiO2/4H-SiC interfaces are at the position X = 0 and X = toxt respectively, in our notation. Voxt= V (0)-V (toxt) is the voltage drop in the oxide layer, where V(x) is the potential in the oxide at position X.

At low gate voltages (figure 8 (a)), electrons can move from the gate metal through SiO2 0+z 0\$!zGw%z/1/0.0!z+\*(5z5z 01\*\*!(%\*#z %.!0(5z 0\$!z!\*0%.!z+4% !z 0\$%'\*!//z%^!^z5z 01\*¥ \*!(%\*# z 0\$! z 0.,!6+% ( z ,+0!\*0%( z ..%!. z !03!!\* z #0! z \* z Gw% z /1/0.0!^ z \$! z -1\*¥ tum-mechanical phenomenon of a trapezoidal barrier tunneling is termed as direct tunneling effect. It contributes significantly to the conduction through the SiO2 only in ultra thin oxide layers (toxtTzHz\*)d^z0z\$%#\$!.z#0!z2+(0#!z c"%#1.!zKz cdd\_z 0\$!z\* z!\* ¥ ing causes the potential barrier shape to become triangular. Electron tunnel from the gate to the SiO2 conduction band, through the triangular potential barrier and finally, moves in the SiO2 conduction band to the 4H-SiC substrate. The conduction mechanism through a triangular potential is called Fowler-Nordheim (F-N) tunneling, which is described in next section.

Figure 8. a) The band diagram of negative gate bias the closed circle represents one electron injected from gate to the SiC conduction band through trapezoidal energy barrier (b) tunneling across triangular energy barrier

#### 6.2. Fowler-Nordheim tunneling

Fowler-Nordheim tunneling in metal oxide semiconductor (MOS) can be observed when the oxide thickness will be less than 50 nm, the oxide potential barrier is usually assumed to be a triangular one, free of charge gate insulator. As a consequence, when we apply a uniform electric field across the MOS structure and thickness of the potential barrier at the semiconductor Fermi level and the potential φ(x), at the distance x from semiconductor/oxide interface vary linearly with the applied voltage.

Figure 9. Energy band diagram for F-N tunneling

The insulating region is separated by an energy barrier with barrier height qqg, measured from the Fermi energy of metal to the conduction band edge of the insulating layer. The distribution functions at both sides of the barrier are indicated as in the figure 9. In the derivation of current density (J) as a function of applied voltage we have to consider some assumptions like effective-mass approximation, parabolic bands and conservation of parallel momentum (Chung, G. Y., 2001). The net tunneling current density from metal to semiconductor can be written as the net difference between current flowing from the metal region to the semiconductor region and vice versa. This expression for current density is usually written as an integral over the product of two independent parts, which only depend on the energy perpendicular to the interface: the transmission coefficient T (E) and the supply function N (E).

$$J = \frac{4\pi m\_{eff}q}{h^3} \int\_{E\_{\text{min}}}^{E\_{\text{max}}} T(E)N(E)dE \tag{2}$$

This expression is known as Tsu-Esaki formula. This model has been proposed by Duke and was used by Tsu and Esaki for the modeling of tunneling current in resonant tunneling devices. The calculation of current density requires not only the knowledge of the energy dependent transfer coefficient, but also the energy dependent electron probability (supply function). Using theTsu-Esaki formula for current density the Fowler-Nordheim formula can be derived as:

$$J \alpha A E^2\_{\text{dif}} \exp\left(-\frac{B}{E\_{\text{dif}}}\right) \tag{3}$$

Where, Line denotes the electric field in dielectric, A and B are constants dependent on barrier configuration for oxide layer separated by metal and semiconductor, the constants A and B are given by:

$$A = \frac{q^3 m\_{\rm eff}}{8\pi \pi m\_{\rm dle} hq \, \mathcal{O}\_{\rm B}} \; B = \frac{4\sqrt{2m\_{\rm dle} (q \, \mathcal{O}\_{\rm B})^3}}{\Im \hbar q} \tag{4}$$

Where, op is the height of the potential barrier measured from the Fermi level of metal to the conduction band in the dielectric, m;;; is the effective electron mass in electrode material and matel is the effective electron mass in the dielectric material. This physical model has been directly applied to in order to establish the validation of Fowler-Nordheim tunneling with the oxide thickness limit.

#### 6.3. Schottky emission

The Schottky emission is an electrode limited process occurring across the interface between a semiconductor (or metal) and an insulating film as a result of barrier lowering due to the applied electric field and the image force as shown in figure 10. Normally, the S-E current conduction process is an electrode-limited conductivity that depends strongly on the barrier between the metal and insulator and has the proclivity to occur for insulators with fewer defects.

Figure 10. Energy band diagram for Schottky emission in metal oxide silicon carbide (MOSiC) structure

Schottky emission from the metal cathode or from the oxide states is assumed to be the limiting mechanism for filling or emptying the oxide traps. For the emission from a semiconductor the Schottky emission current conduction is given by (Chang S.T., 1984)

$$\log A^\* T^2 \mathbb{E} \exp\left[\frac{-q\left(\rho\_\oplus - \sqrt{qE/4\pi\varepsilon\_i}\right)}{kT}\right] \tag{5}$$

Where, J is the current density; A\* iseffective Richardson constant; T, the absolute temperature; q, the electronic charge; @w, the potential barrier at the metal and insulator interface; E, electric field in insulator; ¿, dielectric constant; and k, the Boltzmann constant.

The potential barrier lowering in the MOSiC structures caused by image forces as shown in figure 10 is often neglected in the calculation of the tunneling current, based on an argument that for large barriers in the case of semiconductor and insulator the image-force lowering of the barrier is very small, and this was supported by experimental evidence at the time. In case of very thin oxides, however, this might not be the case, and the barrier lowering can have an impact on the calculation of the tunneling current.

The potential barrier lowered with respect to ideal structure has been termed to an effective trapezoidal barrier in order to account for image force effect. The image-barrier height lowering can be described by:

$$
\Delta \phi\_B = \sqrt{\frac{qE\_{uu}}{4\pi\varepsilon\_0\varepsilon\_r}}\tag{6}
$$

Where, ΔΦΒis the image-barrier height lowering, and E "is the applied electric field at the metal-semiconductor interface, & is permittivity of vacuum and & relative dielectric constant of insulating layer.

#### 6.4. Poole-Frenkel conduction

#### 6.4.1. Classical theory of Poole-Frenkel conduction

In ideal metal oxide semiconductor diode, it is assumed that current conduction through the insulator is zero. Real insulator, however, show the current conduction mechanism which may the function of thickness of the insulator or applied electric field or both. In the classical Poole-Frenkel conduction model effective mechanism can be analyzed by the analogue of Schottky emission (Wright P. J., 1989) where as transport of charge carriers is governed by trapping and de-trapping in the forbidden band gap of an insulator, which reduces the barrier on one side of the trap. At zero electric field amount of free charge carriers can be determined by the trapped ionization energy (qф), which is the amount of energy required for the trapped electron to escape the intluence of the positive nucleus of the trapping center when no field is applied. When electric field is applied, the ionization energy of trapping center decreases in the direction of applied electric field by the amount of △Φρ=βΕΥ as shown in figure 11. As the electric field increases, the potential barrier decreases on the right side of the trap, making it easier for the electron to vacate the trap by thermal emission and enter the quasi-conduction band of the crowd material. Quasi-conduction band edge is the energy at which the electron is just free from the influence of the positive nucleus. The term quasi-conduction is generally used in amorphous solid, which have no real structure. In MOSiC structure, of course, electron would escape from gate metal to the conduction band of semiconductor through the insulator. Since we will deal here with the P-F mechanism in amorphous dielectrics, we will refer to its quasi-conduction band. For the Poole-Frenkel conduction mechanism to occur the trap must be neutral when filled with an electron, and positively charged when the electron is emitted, the interaction between positively charged trap and electron giving rise to the Coulombic barrier. On the other hand, a neutral trap that is, a trap which is neutral when empty and charged when filled will not show the Poole-Frenkel effect.

According to the Poole-Frenkel model, the magnitude of the reduction of trap barrier height due to the applied electric field as shown in figure 11 is given by

$$
\Delta q \rho = \beta \sqrt{E} \tag{7}
$$

Where ß is Poole-Frenkel constant, is given by

$$
\beta = \sqrt{\frac{q^3}{\pi \varepsilon\_0 \varepsilon\_r}} \tag{8}
$$

Finally, quasi conduction band edge is lowered or in other words, the trap barrier height is reduced due to the applied electric field. From Equation 8, it is clear that { is a material parameter, depending on the dielectric constant. Therefore, materials with larger dielectric constants will be less sensitive to the field-induced trap barrier lowering effect in the P-F conduction.

Figure 11. Figure 11.Coulombic potential distribution in the presence of applied electric field showing the Poole-Frenkel effect

#### 6.4.2. Poole-Frenkelconduction in MOSiC structure

P-F conduction mechanism is most often observed in amorphous materials, particularly dielectrics, because of the relatively large number of detect centers present in the energy gap. In fact, the particular host material, where the defects reside, can basically be viewed as acting only as a medium for localized detect states. Transformation of charge is therefore, mainly between localized electronic states (Lenzlinger, M., 1969). Thus it is reasonable to expect the P-F effect to occur, at least to some extent, in any dielectric. The main physical properties effecting the current conduction in different dielectrics are the relative dielectric constant, ε,, and the ionization potential. The l'-F conduction effect has been observed in many dielectric materials, which are used in microelectronic device fabrication. For example, in SisN, films, the dominating current transport mechanism is the P-F conduction. The thin films with high dielectric constants, such as Tagos and BaSrTiO, which hold great potential for use as the gate oxide in DRAMs, have shown that current conduction in these materials is bulk-limited which is governed by the P-F conduction. Currently, one of the most important dielectric materials used in microelectronics is SiO2, which can be easily thermally grown on SiC substrate.

Figure 12. Energy band diagram for Poole-Frenkel conduction in MOSiC structure having multiple Coulombic traps

Figure 12 shows the P-F conduction in MOSiC structure that is basically a parallel plate capacitor. The trapezoidal band diagram of MOSiC structure drawn for the silicon dioxide layer is replaced in figure 11 by a random distribution of Coulombic traps in the vicinity of the quasi-conduction band edge as shown in figure 12. The dashed line indicates the quasi-conduction band of the oxide in the absence of any traps. When an electric field is applied as shown, the trapped electrons can enter the oxide's quasi-conduction band by the Poole-Frenkel mechanism and flow from the oxide across the SiC/SiO2 interface into the silicon carbide conduction band edge. The Poole-Frenkel effect can be observed at the high electric field. The standard quantitative equation for P-F conduction is

$$J\alpha E \exp\left[\frac{-q\left(\rho\_B - \sqrt{qE / \pi \kappa\_i}\right)}{kT}\right] \tag{9}$$

7.2. Fixed oxide charges (Qfix)

after oxidation.

determined by:

possible H+

These are positive or negative charges located near the SiO2/4H-SiC (less than 25 Å from the interface) interface due to primarily structural defects in the oxide layer. The origin of fixed \$.#!z !\*/%05z%/z.!(0! z0+z0\$!z+4% 0%+\*z,.+!//\_z+4% 0%+\*z)%!\*0z\* z0!),!.01.!\_z++(¥ ing condition of the furnace and also on polytypes of Silicon carbide. Qfix highly depends on the final oxidation temperature. For higher oxidation temperature, a lower Qfix3%((z !z +¥ served. However, if it is not permissible to oxidize the wafer at high temperatures, it is also possible to reduce the Qfixby annealing the oxidized wafer in a nitrogen or argon ambient

The fixed charge can be determined by comparing the flatband voltage shift of an experimental xz1.2!z3%0\$zz0\$!+.!0%(z1.2!\_z,.+2% ! z5z0\$!z+4% !z0\$%'\*!//z\* z3+.'z"1\*0%+\*z %""!.!\*¥

Where, £MS is the difference of work function between metal and semiconductor, which

This oxide charge may be positive or negative due to the hole and electron trapped in the bulk of the oxide. These trapping may results from ionizing radiation, avalanche injection, Fowler-Nordheim tunneling or other similar processes. Unlike the fixed charge, this chare \*z(/+z!z.! 1! z5z\*\*!(%\*#z0.!0)!\*0^z4% !z\$.#!/z\*z!z0.,,! z%\*z0\$!z+4% !z 1.¥ ing device operation, even if not introduced during device fabrication. During the device operation electrons and/or holes can be injected from the substrate or from the gate material. \*!.#!0%z . %0%+\*z (/+z ,.+ 1!/z !(!0.+\*w\$+(!z ,%./z%\*z 0\$!z +4% !z \* z /+)!z +"z 0\$!/!z !(!¥ 0.+\*/z\* u+.z\$+(!/z.!z/1/!-1!\*0(5z0.,,! z%\*z0\$!z+4% !^z\$!z+4% !z0.,,! z\$.#!z%/z1/1(¥ ly not located at the oxide/4H-SiC, but is distributed through the oxide. The distribution of Qoxtmust be known for proper interpretation of C–V curves. Oxide trapped charge can be

The origin of this oxide charge is due to the presence of ionic impurities such as Na+

in the oxide films. These ionic impurities may be resulted from the ambient, which,

was used for thermal oxidation. Negative ions and heavy metals ions may also contribute to this

(10)

Materials and Processing for Gate Dielectrics on Silicon Carbide (SiC) Surface

http://dx.doi.org/10.5772/52553

227

. *Q VC oxt FB oxt* (11)

, Li+ , K+ and

ces of metal and 4H-SiC. Fixed charge related to the flatband voltage is given by:

must be known in order to determine the value of Qfix.

Where, the symbols have their usual meaning.

7.4. Mobile oxide charge (Qmob)

7.3. Oxide trapped charge (Qoxt)

( ) *Q VC fix ms FB oxt* 

Where, J is the current density; T, the absolute temperature; q, the electronic charge; £B, the ,+0!\*0%(z..%!.z0z)!0(z\* z0\$!z%\*/1(0+.z%\*0!."!az\_z!(!0.%z"%!( z%\*z%\*/1(0+.az<sup>i</sup> , dielectric constant; and k, the Boltzmann constant.
