Caughey-Thomas Mobility

This model demonstrates how to use the Caughey-Thomas high field saturation model for the electron and hole mobility. Field dependent mobility dramatically increases the nonlinearity of the problem. It is necessary to use the continuation study extension to obtain convergence in the high field limit.

Introduction

With an increase in the parallel component of the applied field, carriers can gain energies above the ambient thermal energy and be able to transfer energy gained by the field to the lattice by optical phonon emission. The latter effect leads to a saturation of the carriers mobility.

The Caughey-Thomas mobility model adds high field velocity scattering to an existing mobility model (or to a constant input mobility). The Caughey-Thomas model is based on equations presented in Ref. 1.

The electron (μn,lo) and hole (μp,lo) mobilities are determined by the following equations:

Here T is the lattice temperature, μin,n and μin,p are the electron and hole input mobilities, and Fn and Fp are the driving forces for electrons and holes (currently Fn = E||,n and Fp = E||,p, where E||,n is the component of the electric field parallel to the electron current and E||,p is the component of the electric field parallel to the hole current). All other parameters in the model are material properties (note that v0,n and v0,p are the saturation velocities for electrons and holes and have units of m/s). The material properties for Silicon are also obtained from Ref. 1.

Model Definition

The model represents a simplified 2D MOSFET where the n-doped drain and source are respectively located on the left and right side of the geometry; see Figure 1. The gate is positioned on top of the p-doped silicon section, which is located at the center of the device.

The model consists in sweeping the drain to source voltage form 0 V to 1 V under a gate to source voltage of 0 V. Sweeping the drain voltage creates an important electric field at the left side of the gate at the junction between the n- and p-doped regions. In order to ensure convergence of the nonlinear model, a solver continuation parameter is used to ramp up the electron and hole driving forces (Fn and Fp) as the drain voltage is swept.

Figure 1: Schematic of the modeled device.

Results and Discussion

Figure 2 shows the effect of the Caughey-Thomas mobility model on the solution. The comparison of the constant mobility (the driving forces are multiplied by 1·10-6) and the Caughey-Thomas mobility (Fn and Fp multiplied by 1) models shows a more pronounced saturation effect for the Caughey-Thomas model.

Figure 3 shows that the electron mobility varies substantially along the device. The electron mobility is 3 order of magnitude lower in the vicinity of the drain-gate junction as a consequence of the high electric field generated by the applied potential on the drain contact.

Figure 4 and Figure 5 show the effect of the mobility model on the electron drift velocity. Figure 4 shows the electron drift velocity for the Caughey-Thomas mobility model (Fn and Fp multiplied by 1) and Figure 5 for the constant mobility model (Fn and Fp multiplied by 1·10-6). A comparison of the two figures clearly shows an important reduction of the electron drift velocity when the field effect is taken into account.

Figure 2: Comparison of the terminal current for the constant mobility and Caughey-Thomas mobility. The current is lower and levels off more rapidly due to the fact that the mobility decreases when the electric field is high.

Figure 3: Plot of the electron mobility at a drain-source voltage of 1 V. The mobility varies by 3 orders of magnitude over the modeling domain.

Figure 4: Plot of the electron drift velocity using Caughey-Thomas mobility. The drift velocity can barely exceed 1.15 x 105 m/s.

Figure 5: Plot of the electron drift velocity for the constant mobility case. Since the mobility does not decrease as the electric field increases, the drift velocity becomes very high.

Reference

1. C. Canali, G. Majni, R. Minder, and G. Ottaviani, “Electron and Hole Drift Velocity Measurements in Silicon and Their Empirical Relation to Electric Field and Temperature,” IEEE Transactions on Electron Devices, vol. 22, no. 11, pp. 1045–1047, 1975.

Note the correction in: G. Ottaviani, “Correction to ‘Electron and hole drift velocity measurements in silicon and their empirical relation to electric field and temperatures’,” IEEE Transactions on Electron Devices, vol. 23, no. 9, pp. 1113, 1976.

Semiconductor_Module/Transistors/caughey_thomas_mobility

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Global Definitions

Parameters 1

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Name	Expression	Value	Description
Wfin	10[nm]	1E-8 m	Height
Lg	100[nm]	1E-7 m	Width
tox	1[nm]	1E-9 m	Gate oxide thickness
Vds	0[V]	0 V	Drain source voltage
Vgs	0[V]	0 V	Gate source voltage
ds	0	0	Continuation parameter