4.2.2.1 The Line Resistors

In Fig. 4.1 a deembedding concept is indicated by the dashed line. The line resistances ${\it R}_{\mathrm{S}}$, ${\it R}_{\mathrm{G}}$, and ${\it R}_{\mathrm{D}}$ are completely included in the simulation shell, since the source and drain resistors are partly defined by the semiconductor parts of the device, and the semiconductor-metal alloy at the ohmic contacts. Both inductances and capacitances are considered extrinsic. The resistances ${\it R}_{\mathrm{S}}$ and ${\it R}_{\mathrm{D}}$ are split into two contributions which have to be evaluated for each process and layout.

$${\it R}_{\mathrm{S}} = R_\mathrm {Ssemi/alloy} + R_\mathrm {SM}$$ (4.7)

and:

$${\it R}_{\mathrm{D}} = R_\mathrm {Dsemi/alloy} + R_\mathrm {DM}$$ (4.8)

For the metal part above the semiconductor-alloy-metal transition, an additional line resistor is added in the simulation, which is defined by the conductivity of the metal used and the geometry of the contact to the reference plane. The metal parts of ${\it R}_{\mathrm{S}}$ and ${\it R}_{\mathrm{D}}$, ${\it R}_{\mathrm{SM}}$ and ${\it R}_{\mathrm{DM}}$, are extracted by measurements of a short structure, or alternatively by pinch-off and cold transistor measurements [36,230,247]. DC- measurements of the ohmic resistances were performed for reasons of control. In agreement with measurements the extracted drain resistor can be bigger than the source resistor since at the drain side also for symmetrical devices the electrons have to pass the heterojunction, which leads to an additional contribution. The different ohmic contact situations were addressed in Chapter 3. The gate resistances ${\it R}_{\mathrm{G}}$ have to be known very well due to their influence on noise performance. They are dominated by the metal part of the gate, thus are determined by the width of the single gate-finger. A line resistor ${\it R}_{\mathrm{G}}$ typical for the gate processing technology is specified in the Schottky contact to obtain realistic intrinsic voltages. ${\it R}_{\mathrm{G}}$ is also an important parameter for the analysis of the output conductance since for simulations including self-heating ${\it R}_{\mathrm{G}}$ is a strong function of the gate temperature. The gate metal is one of the hottest parts of the device, which leads to changes of the resistance. This is one reason for effects such as the negative output conductance. To allow for the comparison with the resulting bias shift on transistor performance ${\it R}_{\mathrm{G}}$ is modeled:

$${\it R}_{\mathrm{G}} = R_\mathrm {G}({\it T}_\mathrm{L}) = R_\mathrm {G 300 K} \cdot (1 + \alpha \cdot ({\it T}_\mathrm{L}-T_0))$$ (4.9)

where $\alpha$ is the temperature coefficient of the metal conductivity. ${\it R}_{\mathrm{SM}}$ and ${\it R}_{\mathrm{DM}}$ are modeled equivalently. Typical values for the resistivity and $\alpha$ are compiled in Table 4.1. For the gate composite metal a typical value of $\alpha$ = 4 $\cdot 10^{-3}$ is assumed.

Table 4.1: Values for the different resistivities of IC metalization.

Metal	$\rho_{300 K}$	$\alpha$	References
	[$\Omega$$\cdot$cm]	[1/K]
Copper	1.71e-6	3.9e-3	[82,310]
Au	2.2e-6	3.4e-3	[82,173]
Silver	1.55e-6	3.8e-3	[173,310]
Aluminum	2.81e-6	3.9e-3	[173,310]
Ti	5.54e-6	4e-3	[173]
W	5.6e-6	4.5e-3	[310]