7.2.2 The Gate Source Capacitance ${\it C}_{\mathrm{gs}}$

Fig. 7.10 shows the gate source capacitance ${\it C}_{\mathrm{gs}}$ as a function of bias. The focus of the investigation is put on the understanding of the bias dependence of ${\it C}_{\mathrm{gs}}$. For a given gate length  ${\it l}_{\mathrm{g}}$ short channel effects influence the bias dependence. The following quantities are considered:

• Concentration of $\delta$-doping and backside doping, thus the sheet carrier density ${\it n}_{\mathrm{sheet}}$.

• Strong recombination in trapped semiconductors.

• The recess geometry and surface potential.

• The relation ${\it C}_{\mathrm{gs}}$/ ${\it C}_{\mathrm{gd}}$.

• Aspect ratio, i.e., for the given gate length   ${\it l}_{\mathrm{g}}$ the gate-to-channel separation  ${\it d}_\mathrm{gc}$.

• Cap doping, see e.g. [18].

• Activation from deep traps in the buffer or at the interfaces.

The consideration of these factors is based on the different bias dependence found in Fig. 4.4. ${\it n}_{\mathrm{sheet}}$, the carrier density, forms the second non-ideal capacitor plate. Thus, increased sheet carrier density ${\it n}_{\mathrm{sheet}}$ increases ${\it C}_{\mathrm{gs}}$ for a given bias. Once ${\it V}_{\mathrm{DS}}$ is increased, also the change of ${\it C}_{\mathrm{gs}}$ with bias depends on ${\it n}_{\mathrm{sheet}}$.

With increasing ${\it V}_{\mathrm{DS}}$ the overall generation/recombination changes due to the geometric enlargement of the space charge region. This results in a change of the channel carrier concentration that form ${\it C}_{\mathrm{gs}}$. Thus, generation/recombination serves as a buffer for carriers and adds up to or reduces the carrier concentration available.

Fig. 7.11 shows the simulated dependence and measurements of ${\it C}_{\mathrm{gs}}$. A change of ${\it C}_{\mathrm{gs}}$ in the simulation is observed, once the recombination/generation mechanisms are considered. A concentration ${\it N}_{\mathrm{T}}$= $10^{16}$cm$^{-3}$ in (3.59) for the Shockley-Read-Hall recombination model is considered. Since InGaAs is a direct semiconductor with a high carrier concentration available in the channel, also direct generation/recombination is considered and influences the increase of ${\it C}_{\mathrm{gs}}$. As ${\it C}_{\mathrm{gs}}$ is a rising function of ${\it V}_{\mathrm{GS}}$, the potential at the gate gets more positive, which leads to an increase of ${\it C}_{\mathrm{gs}}$ relatively to a unipolar simulation.

For the ${\it V}_{\mathrm{DS}}$ bias dependence the parameter to be controlled is the field dependence. Single recess devices have a small high field region due to the inner recess without being controlled by a surface depleted second recess. This leads to hot electrons which surmount the energetic barrier by RST. Under RF operation they are modulated parasitically by the ${\it V}_{\mathrm{GS}}$ bias in the barrier for increasing ${\it V}_{\mathrm{DS}}$ voltage. This charge modulation is responsible for the increase of the capacity ${\it C}_{\mathrm{gs}}$.

Optimized pseudomorphic devices with ${\it l}_{\mathrm{g}}$= 150 nm can reach ratios of ${\it C}_{\mathrm{gs}}$/ ${\it C}_{\mathrm{gd}}$= 8 [196], if ${\it C}_{\mathrm{gd}}$ is significantly reduced. As is shown in the next section ${\it C}_{\mathrm{gd}}$ is basically independent of the gate length ${\it l}_{\mathrm{g}}$. Thus, for decreasing gate length ${\it l}_{\mathrm{g}}$$\leq$ 100 nm the ratio decreases. Since ${\it C}_{\mathrm{gd}}$ decreases as a function of ${\it V}_{\mathrm{DS}}$, while ${\it C}_{\mathrm{gs}}$ increases, the ratio influences the ${\it V}_{\mathrm{DS}}$ bias dependence of ${\it f}_\mathrm{T}$.

The cap doping has a double fold influence on the gate charge. First, according to [18], a high cap doping concentration adds up to the carrier concentration of the $\delta$-doping. Furthermore, depleted caps with low doping concentrations $\leq 10^{15}$ cm$^{-3}$ change the field and thus carrier distribution in the channel, as discussed for the Ka-band power HEMTs.

In a dynamic sense any occupation of deep traps in GaAs based materials is too slow to follow the GHz frequencies of operation. Deep traps are normally not considered in device simulation, but they form, similar to the generation/recombination mechanism, a buffer of carriers.

Figure 7.11: $C_{gs}$ as a function of $V_{DS}$ without holes and with holes including generation/ recombination for a $l_g$= 140 nm pseudomorphic HEMT.

Figure 7.12: Simulated $C_{gd}$ as a function of $V_{DS}$ bias for $l_g$= 440 nm with the cap doping concentration as parameter.