7.2.1 The Transconductance ${\mit g}_{\mathrm{m}}$

Fig. 7.9 shows the dependence of the transconductance ${\mit g}_{\mathrm{m}}$ on ${\it V}_{\mathrm{GS}}$. For ${\it V}_{\mathrm{DS}}$, the ${\mit g}_{\mathrm{m}}$ decrease in compact models is attributed to the change of the effective mean carrier velocity ${\it v}_{\mathrm{eff}}$. As shown in Chapter 3 the term saturated effective mean carrier velocity is certainly not completely appropriate. Resolving this change in more physical terms the following factors of influence are found.

• Change of the parasitic modulation, i.e., increased number of electrons undergoing real space transfer into the barrier due to increased ${\it V}_{\mathrm{DS}}$ imposed fields, which effectively changes the velocity.
• Flattening of the velocity channel profile, which is a more macroscopic view of the occurring changes of occupation in k-space due to high fields.
• A thermal effect is found which has triple implications:
  • Increase of the resistance of the parasitic parts of ${\it R}_{\mathrm{S}}$, ${\it R}_{\mathrm{G}}$, and ${\it R}_{\mathrm{D}}$, while the external ${\mit g}_{\mathrm{m}}$ is scaled by ${\it R}_{\mathrm{S}}$.
  • Reduction of the barrier mobility, i.e. due to the temperature dependence of the low field mobility, which leads to an increase of the semiconductor contributions to ${\it R}_{\mathrm{S}}$ and ${\it R}_{\mathrm{D}}$.
  • For higher temperatures ${\it T}_\mathrm{L}$$>$ 400 K, which locally can occur, self-conduction of the semiconductor.

Figure 7.9: Simulated and measured $f_T$ and RF-$g_m$ as a function of $V_{GS}$ bias.

Figure 7.10: $C_{gs}$ and $C_{gd}$ as a function of $V_{DS}$ bias for constant $V_{GS}$.