Dynamic behavior

We will now consider the dynamical properties of HEMTs, in particular their behavior as am- plifiers. The most common configuration for HEMT based amplifiers is the common source one, where the source is grounded, the signal to be amplified is applied to the appropriately biased gate electrode and the amplified signal is collected by a load impedance at the appro- priately biased drain electrode. For a sinusoidal signal applied to the gate, the drain current and voltage change over time in a sinusoidal way too, as shown in Fig. 1.10. In particular, the drain current and voltage follow the so called load line, which is determined by the load impedance and is generally elliptical, reducing to a line in the case of a purely resistive load, which is the case of Fig. 1.10(b). The transistor works as a current(power) amplifier if the current(power) of the outcoming signal is higher than the current(power) of the incoming signal. The ratio between current(power)of the output and incoming signals defines the gain. The frequency dependence of the current and power gain are among the most important parameters describing the transistor frequency performance.

The simplest way for understanding the evolution of the transistor properties with frequency is to start with its behavior under small signal conditions. In this case, the transistor behaves linearly and can be represented by an equivalent circuit, as shown in Fig. 1.11. The elements that constitute this relatively complicated circuit have in most cases a simple physical origin. So RSand LSare the resistance and inductance of the source electrode and access region.

Analogously, RD, RG, LD and LG are the resistances and inductances of the drain and gate

electrodes. CGS, CGDand CDSare, respectively, the gate-source, gate-drain and drain source

capacitances. RDSis the drain-source resistance and is related to short channel effects and

buffer conductivity. RGS has a less evident physical origin, it has been introduced mainly

for improving the agreement between the circuit model and experimental data. However, it induces minor corrections. Among all these components, the most important ones are by far gm and CGS. The other components are less important and can be considered as parasitic

I_DS V_DS V_DS,0 V_DS,max V_DS,min I_DS,min I_DS,max VGS,0 load line V_knee V_BR I_DS,sat V_GS,0 V_DD G D S load V_GSsin(ωt) a) b)

Figure 1.10: (a) Common source configuration for an HEMT based amplifier. (b) Corre- sponding loadline superposed on the HEMT’s output characteristic. This graph shows the drain-source voltage and current evolution during a sinusoidal gate voltage sweep.

components. If these parasitic components are negligible, the current gain GIcan be easily

worked out: GI=

gm

2πf CGS

(1.31) where f is the frequency. From this equation, we see that the current gain decreases with frequency. If expressed in dB, the gain is found to decrease at a rate of 20 dB/decade and becomes unity at the transition frequency ft:

ft=

gm

2πCGS

(1.32) Therefore, for f > ft, the transistor no more amplifies the current. In the ideal case, all the

gate-source capacitance is used to modulate the 2DEG electrons. If 〈ve〉 is the mean electron

velocity under the gate electrode, we have gm= CGS〈ve〉Lg. Writing now 〈ve〉 = Lg/τ, where τ

is the transit time for electrons under the gate, we obtain: ft=

1

2πτ (1.33)

Therefore, the faster the electrons transit under the gate, the higher ft will be. High ftcan

be thus obtained by reducing Lgand by increasing the electric field under the gate so that

electrons reach their saturation velocity. The highest possible value for ftis therefore

ft ,max=

vsat

2πLg

(1.34)

Considering that for GaN vsat= 2.5 × 107cm/s, and taking 10 nm as the lower bound for Lg,

transition frequencies in excess of 1 THz can be theoretically reached. In real devices, however, CGScontains also fringing parasitic components that lower the gm/CGSratio [51]. A second

1.4. High electron mobility transistors drain gate source LS RS RDS RGS RG RD LG CDG LD CDS CGS gm(VGS,τ) (a) (b)

Figure 1.11: (a) Small signal equivalent circuit of an HEMT. (b) Frequency dependence of the current (GI) and power (U ) gain. The cutoff frequencies ft and fmax are indicated.

gate at relatively low velocities and are accelerated to vsat only at the right side of the gate.

This further lowers the maximum value of ft. Furthermore, the effect of the other parasitic

elements is not completely negligible. An expression for fttaking into account the parasitic

components is the following one [52]: ft= gm 2π 1 (CGS+CGD) + ³_R S+RD RDS ´ (CGS+CGD) + gmCGD(RS+ RD) (1.35)

If not managed properly, parasitic components can have a significant impact on ft, especially

in deeply scaled transistors where the low Lg makes CGSsmall, enhancing the effect of the

parasitic source and drain resistances.

Regarding the power gain, the situation is more complicated as many definitions have been given for this parameter. The Mason’s unilateral power gain U is the most commonly used and is defined as the power gain when the drain to gate feedback is suppressed. Its frequency behavior is not different from the current gain. It also decreases with frequency at a rate of 20 dB/decade and becomes equal to one at a frequency indicated as fmax. Therefore, as for

the current gain, the higher fmax is, the higher the gain at a given frequency will be. However,

fmaxcan be quite different from ft[53]:

fmax= ft 2 q RS+RG+RGS RDS + 2π ftCGDRG (1.36)

For power amplifier applications, fmax is more critical than ftas amplifiers have to amplify

power rather than current. In order to obtain a high fmax, it is required to have a high ftand

low parasitic resistances. In particular, the gate resistance RGplays a major role and is usually

minimized by using T-shaped gates (Fig. 1.8), where a small gate foot, necessary for high ft,

can be combined with a large gate head, which minimizes RG.

In conclusion, good transistors for small signal regime applications are characterized by high cutoff frequencies, which is obtained with short electron transit times, low access and output

resistances and low gate resistances. The electron transit time is minimized by a high electron mobility and saturation velocity and at the same time a low Lg. Therefore, very thin barriers

are required, as short channel effects limit the lowest possible Lgto ∼ 5dB. Low RSand RDcan

be obtained with low resistivity ohmic contacts and short source-to-gate and gate-to-drain distances. Low RG are finally obtained with T-shaped gates. At present, the best reported

values for ftand fmaxare 453 GHz and 554 GHz, respectively, obtained in AlN/GaN ultrascaled

HEMTs (20 nm Lg) with self-aligned ohmic contacts [54].

Let’s consider now the large signal behavior, which is the most relevant one if the transistor has to be integrated in a power amplifier. The situation is well described by Fig. 1.10. Increasing the input power, which is equivalent to increasing the gate voltage swing, has the consequence of increasing the drain voltage and current swing. Therefore, the output power increases linearly with the input power. However, the output power is limited. The maximum power is reached when the voltage swing at the gate is large enough to bring the device, during the same sweep, from pinch-off to the maximum possible drain-source current. If VDS,maxand

VDS,mi nare the maximum and minimum drain-source voltages reached during the sweep

and IDS,maxand IDS,mi nthe maximum and minimum current attained during the sweep (Fig.

1.10), the output power is Pout=¡IDS,max− IDS,mi n¢ ¡VDS,max− VDS,mi n¢ /8. The maximum

possible power Pmaxis attained if the load impedance is such to make VDS,mi n= Vkneeand

VDS,max= VB R. Here, Vkneeis the knee voltage, which is the drain voltage where IDS starts

saturating at its maximum possible value, and VB Ris the breakdown voltage. Therefore:

Pmax=

IDS,max(VB R− Vknee)

8 (1.37)

Therefore, a high output power can be attained if the breakdown voltage is high and if the ON- resistance is minimized in order to have a small Vknee. A high 2DEG density is also desirable

because it translates in a high IDS,max. It is important to stress the fact that VB R depends

critically on the transistor geometry. In particular, short gate lengths and short gate-drain distances reduce VB Ras a consequence of the increase of the peak electric field at the drain

side of the gate. Thus, transistors designed for operation at high frequency can reach lower power densities if compared to the ones operating at lower frequencies. This is well illustrated in Fig. 1.4(b), where it can be clearly seen that the maximum power density achievable in AlGaN/GaN based HEMTs decreases as the frequency of operation gets higher.

The last parameter of interest for the characterization of high power transistors is the power added efficiency (PAE), which measures the efficiency of the transistor as an amplifier:

P AE =Pout− Pi n PDC

(1.38) where Pi nand Pout are the input and output power, respectively, and PDCis the DC power

necessary for biasing the transistor at its work point. A high power gain is important for getting a high PAE because it is proportional to the Pout− Pi n. The PAE increases also if VDS,maxis

1.5. AlGaN/GaN HEMTs: state of the art and technological limits