3.9 Model Comparison

This chapter outlined a number of tunneling models useful for the simulation of tunneling in semiconductor devices. For practical device simulation, however, it is often not clear which model to select for the application at hand. Therefore, Table 3.3 summarizes the main model features and also gives the approximate computational effort. The following points can be concluded:

• Especially the FOWLER-NORDHEIM, SCHUEGRAF, and FRENKEL-POOLE models have a very low computational effort since they are compact models. However, they do not correctly reproduce the device physics and can only be used after careful calibration.

• The TSU-ESAKI formula with the analytical WKB or GUNDLACH method for the transmission coefficient combines moderate computational effort with reasonable accuracy. This approach can be used for the simulation of tunneling in devices with single-layer dielectrics.

• The inelastic TAT model allows simulation of all effects related with traps in the dielectric and, due to the analytical calculation of the overlap integral, poses only moderate computational effort. This model can be used for the simulation of leakage in EEPROMs or trap-rich dielectric devices (see Section 5.2.2.1).

• The TSU-ESAKI model with the numerical WKB, transfer-matrix, or QTB method to calculate the transmission coefficient represents the most accurate method usable for the simulation of tunneling through dielectric stacks, however, with high computational effort. The transfer-matrix method should not be used due to its poor numerical stability.

Table 3.3: A hierarchy of tunneling models and their properties. FOWLER-NORDHEIM model (1), SCHUEGRAF model (2), TSU-ESAKI analytic WKB (3), TSU-ESAKI GUNDLACH (4), TSU-ESAKI numeric WKB (5), TSU-ESAKI transfer-matrix (6), TSU-ESAKI QTBM (7), Inelastic TAT (8), FRENKEL-POOLE (9).

	1	2	3	4	5	6	7	8	9
FN tunneling	+	+	+	+	+	+	+
Direct tunneling		+	+	+	+	+	+
EVB tunneling process			+	+	+	+	+
QM current oscillations				+		+	+
Dielectric stacks					+	+	+
Numerical stability						-
Trap-assisted tunneling								+	+
Trap occupancy modeling								+
Transient TAT								+
Computational effort	low	low			high	high	high		low

A. Gehring: Simulation of Tunneling in Semiconductor Devices