Equivalent oxide thickness

The English term equivalent oxide thickness (EOT, dt. "Equivalent oxide thickness") referred to in the semiconductor technology, a reference value of a thin film , mainly of layers of novel high-k dielectrics with silica , the Standardgatedielektrikum in metal-oxide-semiconductor field effect transistors ( MOSFETs).

background

The electrical properties of a MOSFET are determined, among other things, by the gate dielectric, which separates the gate electrode from the conductive channel in the semiconductor. The physical properties (thickness, band gap, dielectric constant) influence the threshold voltage of the transistor, for example. Since the beginnings of microelectronics in the 1960s, ( thermal ) silicon dioxide has mainly been used as a gate dielectric. Analogous to the constant shrinking of the structures, the thickness of the dielectric was also reduced, so that in the mid-2000s it was only in the range of 1 to 2 nanometers. With these layer thicknesses, the influence of leakage currents through the dielectric due to the so-called tunnel effect can no longer be neglected. For a further miniaturization of the integrated circuits , the reduction of these leakage currents is therefore essential. However, simply increasing the layer thickness is not acceptable, since this would increase the threshold voltage of the transistors (and thus the operating voltage) and reduce the maximum switching speed.

To solve the problem, the use of materials with a higher dielectric constant ( high-k dielectric ) than silicon dioxide ( ) applies . A layer of high-k dielectric with a dielectric constant of 39 can be ten times as thick as a silicon oxide layer. The term EOT was introduced to provide an easy way of comparing the new layers with silicon dioxide. This becomes all the more important if one takes into account that the dielectric constant of a very thin layer does not necessarily correspond to that of a bulk layer, depends on the manufacturing method and can change with the layer thickness. ${\displaystyle \varepsilon _{\mathrm {r} }=3{,}9}$

definition

Dielectric constant and EOT for a 10 nm thick layer of selected materials ${\displaystyle \varepsilon _{\mathrm {r} }}$

material	${\displaystyle \varepsilon _{\mathrm {r} }}$	Band gap in eV	Crystal structure	EOT 10 nm in nm
thermal SiO 2	3.9	8.9	amorphous	-
Si 3 N 4	7th	5.1	amorphous	5.6
Al 2 O 3	9	8.7	amorphous	4.3
Y 2 O 3	15th	5.6	cubic	2.6
ZrO 2	25th	5.8	mono., tetrag., cubic	1.6
HfO 2	25th	5.7	mono., tetrag., cubic	1.6
La 2 O 3	30th	4.3	hexagonal, cubic	1.3
Ta 2 O 5	26th	4.5	orthorhombic	1.5
TiO 2	80	3.5	tetrag. ( Rutile , anatase )	0.5

The EOT of a dielectric layer indicates how thick an electrically comparable silicon dioxide layer would be. In this context, electrically comparable means when it has the same capacitance-voltage characteristic or the same capacitance per unit area.

Capacity per unit area:

${\displaystyle C_{\square }={\frac {\varepsilon _{0}\varepsilon _{\mathrm {r} }}{d_{\mathrm {ox} }}}}$

Calculation of the EOT:

${\displaystyle {\begin{aligned}C_{\mathrm {\square ,SiO_{2}} }&={\frac {\varepsilon _{0}\varepsilon _{\mathrm {r,SiO_{2}} }}{d_{\mathrm {ox,SiO_{2}} }}}=C_{\mathrm {\square ,high-k} }={\frac {\varepsilon _{0}\varepsilon _{\mathrm {r,high-k} }}{d_{\mathrm {ox,high-k} }}}\\&\Leftrightarrow {\frac {\varepsilon _{\mathrm {r,SiO_{2}} }}{d_{\mathrm {ox,SiO_{2}} }}}={\frac {\varepsilon _{\mathrm {r,high-k} }}{d_{\mathrm {ox,high-k} }}}\\&\Leftrightarrow {\frac {\varepsilon _{\mathrm {r,SiO_{2}} }}{\varepsilon _{\mathrm {r,high-k} }}}\cdot d_{\mathrm {ox,high-k} }=d_{\mathrm {ox,SiO_{2}} }=\mathrm {EOT} \\\end{aligned}}}$

With

• ${\displaystyle \varepsilon _{\mathrm {r,SiO_{2}} }}$ ... the relative permittivity of thermal silicon dioxide
• ${\displaystyle \varepsilon _{\mathrm {r,high-k} }}$ ... the dielectric constant of the high-k layer
• ${\displaystyle d_{\mathrm {ox,high-k} }}$ ... the thickness of the high-k layer
• ${\displaystyle d_{\mathrm {ox,SiO_{2}} }}$ ... the equivalent thickness of a layer of thermal silicon dioxide

literature

• Mohan V. Dunga, Xuemei (Jane) Xi, Jin He, Weidong Liu, Kanyu M. Cao, Xiaodong Jin, Jeff J. Ou, Mansun Chan, Ali M. Niknejad, Chenming Hu: BSIM 4.6.0 MOSFET Model - User's Manual . University of California, Berkeley, Department of Electrical Engineering and Computer Sciences, 2009, p. 1-7 ( PDF ).

Individual evidence

1. ↑ H. Huff, D. Gilmer: High Dielectric Constant Materials. VLSI MOSFET Applications . Springer, Berlin 2004, ISBN 3-540-21081-4 , pp. 263 .
2. ^ Howard R. Huff, David C. Gilmer: High dielectric constant materials . Springer, 2005, ISBN 3-540-21081-4 , pp. 131 .