7.3.1 Understanding the Output Characteristics

In Fig. 7.20 several regions are indicated in the output characteristics of a high-power HEMT.

• Region I is determined by a deteriorating pinch-off for ${\it V}_{\mathrm{DS}}$$\geq$ 4 V.

• Region II shows a bias region, where generation/recombination processes affects the output conductance before high field generation due to impact ionization is significant.

• Region III is determined by inverse currents through the gate-diode in combination with impact ionization in the channel.

• In Region IV self-heating starts to be clearly visible.

• Region V is the linear region, strongly influenced by the ohmic contact situation.

• Region VI is the region of non reversible device damage due to a combination of a power dissipation of ${\it P}_{\mathrm{diss}}\geq$ 2 W/mm (a power compliance is used to protect the device) and high fields leading to impact ionization.

Figure 7.21: Measured and simulated $f_T$ as a function of $V_{DS}$ bias.

Fig. 7.21 shows the simulated and measured of ${\it f}_\mathrm{T}$ versus ${\it V}_{\mathrm{DS}}$ bias with ${\it V}_{\mathrm{GS}}$ as a parameter. Generally a decrease is seen, however, the data at different ${\it V}_{\mathrm{GS}}$ biases suggest different paths for this decrease.

Figure 7.22: Measured transconductance $g_m$ versus $V_{GS}$  at $V_{DS}$=1.5 V and different $T_L$ for a 4$\times 40$ $\mu$m high-power AlGaAs/InGaAs HEMT.

To evaluate the substrate temperature as a source of degradation of ${\it f}_\mathrm{T}$ with bias Fig. 7.22 shows the measured dependence of ${\mit g}_{\mathrm{m}}$ at the lattice temperature ${\it T}_\mathrm{L}$ between 348 K and 473 K for ${\it V}_{\mathrm{DS}}$= 1.5 V. A reduction of 60 mS/mm / 100 K is found, which amounts to about 13% per 100 K. A pronounced reduction of the second peak of ${\mit g}_{\mathrm{m}}$ similar to Fig. 7.4 is visible.

To optimize a given pseudomorphic HEMT structure with respect to output power, gain, and the breakdown voltage at a given frequency, a combination of simulations, small-signal measurements, and load-pull measurements is used. For the given double recess structures, Fig. 7.23 defines the terminology for the geometric quantities.

Figure 7.23: Geometry for a double recess.

For the pseudomorphic HEMT the limiting mechanism prevailing is the diode due to thermionic field emission. The critical field thus prevails at the drain side of the gate contact in the barrier and channel layer. In a systematic approach two concepts can be applied for optimization to achieve breakdown hardness. The first concept is based on a depleted outer recess. As shown in Fig. 7.24, the field prevails between the carrier concentration at the lateral edge of the outer recess and the gate metal. In this case ${\it d}_\mathrm{R}$ is limited and the depth ${\it d}_\mathrm{DR}$ needs to be large enough to enable the surface potential to deplete the cap. The doping concentrations in the cap and of the $\delta$-doping have to be chosen accordingly. The length of the second recess ${\it l}_{\mathrm{DR}}$ relaxes the maximum fields in the spacer and thus in the channel at high operational ${\it V}_{\mathrm{DS}}$ bias, typically $\geq$ 5 V. The exact geometry determines, for which bias situations how much of the underlying barrier and channel is depleted. Using such a concept, extremely high on- and off-state breakdown voltages, as shown in Chapter 6, can be achieved for the pseudomorphic AlGaAs/InGaAs/GaAs power HEMT.

Figure 7.24: Electric field for $V_{DS}$= 5 V, $V_{DS}$= 8 V and $I_D$$\approx$ 250 mA/mm for a $l_g$= 190 nm HEMT with a depleted recess.

Figure 7.25: Electric field for $V_{DS}$= 5 V, $V_{DS}$= 8 V and $I_D$$\approx$ 250 mA/mm for a $l_g$= 190 nm HEMT with a non-depleted outer recess.

If the second recess is chosen to be not depleted, as shown Fig. 7.25, then the inner recess length ${\it l}_{\mathrm{R}}$ is of primary importance to determine the fields in barrier and channel. A sharp drop occurs between the drain site of the gate and the lateral edge of the first recess. The sum of the length ${\it l}_{\mathrm{DR}}$ and ${\it l}_{\mathrm{Co}}$ recess leads to a marginal additional relaxation. The depth of the inner recess is of no importance, once it exceeds a certain value. For the second concept, the first recess protects the diode especially for the off-state. As a rule of thumb it was found that using such a concept for a ${\it l}_{\mathrm{g}}$= 200 nm device, a maximum breakdown voltage of ${\it BV}_{\mathrm{GD}}$= 11 V evolves. Comparing Fig. 7.24 and Fig. 7.25 the advantage of the depleted cap can be seen resulting in a reduction of the channel fields.

Once the HEMT opens for rising ${\it V}_{\mathrm{GS}}$ the second recess relaxes the fields for the on-state. For ${\it V}_{\mathrm{GS}}$$\geq$  ${\it V}_{\mathrm{GS}}$ for ${\it g}_{\mathrm{m,max}}$ a significant amount of carrier populates the spacer and the maximum field is relaxed by the length ${\it l}_{\mathrm{R}}$ only, as seen in Fig. 7.26. The high concentration of carriers causes impact ionization effects as demonstrated in Chapter 3.

Figure 7.26: Two-dimensional view of the carrier concentration in [cm$^{-3}$] for a HEMT for $V_{DS}$= 5 V and $I_D$= 150 mA/mm.

Fig.7.27 shows the maximum electric field in the channel for the case of a non-depleted cap versus inner recess length ${\it l}_{\mathrm{R}}$.

Figure 7.27: Maximum electric field for an open device ($I_D$= 250 mA/mm) as a function of inner recess length $l_R$ for a non-depleted recess concept.

Figure 7.28: Electric field for two different surface potentials for $V_{DS}$= 17 V for a $l_g$= 300 nm pseudomorphic HEMT.

A linear dependence of the maximum field on the recess length is observed. Fig. 7.28 shows the electric field in the channel as a function of position along the channel for a device with ${\it l}_{\mathrm{g}}$= 300 nm and ${\it V}_{\mathrm{DS}}$= 17 V. The strong dependence of the maximum fields on the surface potential is visible. The field calculated for Potential 1 in Fig. 7.28 exceeds the breakdown field of GaAs of about E$^{crit}_n$= 6.8e5 V/cm, taken e.g. from Table 3.26. Potential 2 is determined to match the surface potential of about 0.8 eV measured for AlGaAs. Potential 1 corresponds to a surface charge concentration of -1$\times$ 10$^{12}$ cm$^{.2}$. Only the depleted cap in Fig. 7.28 for surface Potential 2 allows hot electron reliable operation. The bias situation is chosen to yield ${\it I}_{\mathrm{D}}$= 100 mA/mm and the maximum ${\it V}_{\mathrm{DS}}$ voltage for this device with a non-symmetric recess. Only the strong pinning of the surface potential allows for the power HEMT optimization. Thus, the main task of optimization by device simulation is to make sure, that, given the uncertainty of the etch depth ${\it l}_{\mathrm{DR}}$ in Fig. 7.23, the cap is depleted.

Figure 7.29: $f_T$ versus recess length $l_R$ for $V_{DS}$= 1.5 V and 5 V.

Figure 7.30: Measured drop $\Delta$ $f_T$/$\Delta$$V_{DS}$  versus  $T_{sub}$.

This argumentation in a modified form is also useful for InAlAs/InGaAs devices. As stated in [281] the occurrence of additional space charge regions in the device is undesirable, since it provokes additional generation/recombination and the holes lead to undesirable potential shifts at the source side of the gate, as discussed in the next section. However, a relaxed inner recess relaxes the fields for the on-state breakdown at the drain side of the gate, and can, in combination with a carefully chosen moderate channel In content, allow to build metamorphic power HEMTs.

As short channel effects were discussed earlier, Fig. 7.29 shows the simulated drop of ${\it f}_\mathrm{T}$ with ${\it V}_{\mathrm{DS}}$ for a pseudomorphic AlGaAs/InGaAs HEMT with a non-depleted recess. As can be seen, the innermost spacer length ${\it l}_{\mathrm{R}}$ influences the current gain. Again, this can be understood by the occurrence of real space transfer. Higher fields, which prevail under the first recess without the relaxation of the second, enhance with shorter recess length and provoke a relatively higher drop of ${\it f}_\mathrm{T}$, once ${\it V}_{\mathrm{DS}}$ rises. In Fig. 7.30 a measured comparison of the decrease $\Delta {\it f}_\mathrm{T}$/ $\Delta {\it V}_{\mathrm{DS}}$ as a function of temperature ${\it T}_\mathrm{L}$ is shown for a 4$\times$40 $\mu$m pseudomorphic HEMT with ${\it l}_{\mathrm{g}}$= 210 nm. The drop was determined between ${\it V}_{\mathrm{DS}}$= 1.5 V and ${\it V}_{\mathrm{DS}}$= 5 V for ${\it V}_{\mathrm{GS}}$ for ${\it g}_{\mathrm{m,max}}$. It can be observed in Fig. 7.30 that the decrease $\Delta {\it f}_\mathrm{T}$/ $\Delta {\it V}_{\mathrm{DS}}$ calculated is less pronounced once the temperature ${\it T}_{\mathrm{sub}}$ increases.