Improved Linearity with Polarization Coulomb Field Scattering in AlGaN/GaN Heterostructure Field-Effect Transistors

The single-tone power of the AlGaN/GaN heterostructure field-effect transistors (HFETs) with different gate widths was measured. A distinct improvement in device linearity was observed in the sample with a larger gate width. The analysis of the variation of the parasitic source access resistance showed that, as the gate bias is increased, the polarization Coulomb field scattering can offset the increased polar optical phonon scattering and improve the device linearity. This approach is shown to be effective in improving the device linearity of AlGaN/GaN HFETs.

the two samples, the input power at the 1-dB compression point P IN-1dB was extracted from Fig. 1 Under every fixed gate bias, the P IN-1dB for Sample 2 is significantly larger than that for Sample 1; Δ is at least 38.71% and can reach up to 148.37% (at V GS = −1 V).
The linearity in power amplification is well known to be a complex phenomenon. The charge trapping in the surface state, gate-drain capacitance, self-heating effect, device transconductance, and parasitic source access resistance can affect the device linearity 7,10,[12][13][14][15][16] . Because both samples were fabricated on the same material and with the same device technology, the charge trapping in the surface state and the gate-drain capacitance should be the same. The DC current-voltage (I-V) characteristics and the transfer characteristics were measured for the two samples, as shown in Fig. 2. The currents are almost the same for the two samples; therefore, the influence of the self-heating effect on the linearity of the two samples should be consistent. Because of the polarization Coulomb field scattering, the gate width can affect the parasitic source access resistance (R S ) and transconductance (g m ) under the unit gate width 17 . Because the ohmic contact resistance R C (in the normalized unit "Ω·mm") is constant, R S here is exclusive of R C and refers only to the gate-source channel resistance. Considering that both samples have the same device size, except for their different gate widths, the intrinsic transconductance (g m0 ) under the unit gate width for the two samples should be the same. An analysis of the expression g m = 1/(1/g m0 + R S + R C ) indicates that the R S variation can affect g m , and then influence the gain and the device linearity 7,10 . Therefore, the improved linearity can be explained by considering the variation of R S . R S is determined by the scattering mechanisms in the gate-source channel. The main scattering mechanisms in the gate-source channel include polar optical phonon (POP), deformation potential (DP), piezoelectric (PE), interface roughness (IFR), dislocation (DIS), and polarization Coulomb field (PCF) scatterings. Among these, the two major mechanisms are POP and PCF scatterings, which can be changed with the increase of the gate voltage.
When the electron drift velocity is sufficiently increased, the POP and electron temperatures start to increase; the POP scattering is enhanced with the increase of the electron temperature, inducing an increase in R S

10
. For a clearer presentation, the POP scattering and the electron temperature as a function of V GS at V DS = 20 V can be calculated. Initially, the electron drift velocity v e in the gate-source channel can be obtained from the I-V characteristic by applying I DS = n 2D •q•v e . With the obtained v e , the electric field E GS in the gate-source channel can be determined by the dependence of the electron drift velocity on the electric field 18 . Then, the dissipated power per electron UI DS /N e in the gate-source channel can be calculated, as shown in Fig. 3(a). Here, U = E GS •L GS is the voltage applied along the gate-source channel, L GS is the gate-source distance, and N e = n 2D •L GS •W G is the number of electrons in the gate-source channel. Finally, based on the relationship between the electron temperature and the dissipated power per electron 18 , the electron temperature T e can be obtained, as shown in Fig. 3(b). As the gate bias is increased, the electron temperature is increased, and it remains at almost the same value for the two samples. This means that the influence of self-effect on R S is the same for the two samples 17 . The R S determined by the POP scattering R S POP can be calculated as follows 9 3 ) and P POP (y) = 1 + (1 + e −y )/y. As shown in Fig. 4(a), when the gate voltage is more than −2.5 V, the increased POP scattering causes R S to increase as the gate voltage is increased.
PCF scattering originates from the non-uniform distribution of the polarization charges at the AlGaN/GaN interface [8][9][10] . Before the device processing or without the gate bias, the polarization charges at the AlGaN/GaN interface are uniform. On one hand, to form the ohmic contacts, Ti/Al/Ni/Au was deposited and then rapidly thermally annealed at 850 °C. During the annealing process, the ohmic contact metal atoms can diffuse into the AlGaN barrier layer and change the barrier layer strain 9,19 . On the other hand, because of the converse piezoelectric effect, the gate bias can also change the strain of the AlGaN barrier layer under the gate region 9,20 . The strain variation of the AlGaN barrier layer causes the variation of the polarization charges. Then, the distribution of the polarization charges becomes non-uniform. Compared with the uniformly distributed polarization charges, the  non-uniformly distributed ones can generate an additional scattering potential, which can scatter the channel electrons. The additional polarization charges are defined as the difference between the non-uniformly distributed polarization charges and the uniformly distributed ones. After the device processing, the additional polarization charges near the ohmic contact area do not change, and their influence on the PCF scattering is constant. The additional polarization charge ∆σ under the gate region can be calculated as 10,20 :

GS ch
AlGaN where e 33 is the piezoelectric coefficient, C 33 is the elastic stiffness tensor of AlGaN, V ch is the potential in the channel, and d AlGaN is the thickness of the AlGaN barrier layer. As shown in (3), ∆σ is relevant to V GS . The larger ∆σ is, the stronger the PCF scattering. As V GS is increased, ∆σ decreases and the PCF scattering weakens. The PCF scattering is stronger in the sample with a larger width 17 . Therefore, under the same gate voltage, Sample 2 has a larger PCF scattering than Sample 1. The R S determined by the PCF scattering R S PCF can be obtained 11 , as shown in Fig. 4(b). R S PCF clearly shows a monotonic decline as the gate bias is increased. Because Sample 2, which has a larger width, has a stronger PCF scattering, its R S PCF is larger compared with Sample 1. As the gate bias is increased, the POP scattering is increased and the PCF scattering is decreased; together, these determine the variation of R S . The decreased PCF scattering can effectively offset the increased POP scattering, decrease the variation of R S , and then improve the linearity. This causes Sample 2, which has a larger PCF scattering, to have better linearity. The R S values for different scattering mechanisms were calculated 11,21 , as shown in Fig. 5(a) and (b). The POP, DP, and PE scatterings are enhanced with the increased gate bias, leading to the increase in R S . Among these three mechanisms, POP scattering is the major one. Conversely, PCF scattering is the only mechanism that is decreased with the increased gate bias. The decreased PCF scattering can offset the increased scatterings, causing the R S value to have a small variation. For a clear comparison, Fig. 5(c) shows the total R S for the two samples. As shown in Fig. 2(b), the threshold voltage for the two samples is −2.5 V, therefore the V GS in the range of −2.5 V to 2 V is effective. During the effective gate bias range, the R S for Sample 2 is flatter than that for Sample 1, which means that Sample 2 has a smaller R S variation. Based on g m = 1/(1/g m0 + R S + R C ), a smaller R S variation implies a smaller g m variation and better device linearity. Hence, Sample 2 shows better linearity.
In addition, when the gate bias is more negative, the PCF scattering is stronger than the POP scattering, and R S is decreased with the increased gate bias. As the gate bias is increased, the POP scattering is rapidly increased with the increase of the electron temperature. When V GS = −1 V was chosen as the DCQP, the offset effect between the PCF and the POP scattering was the most suitable for the power output. Therefore, when V GS = −1 V, the offset range for POP and PCF scattering is the largest, and the improvement in linearity is most apparent (corresponding to Δ = 148.37%). This further confirmed that PCF scattering exerts a vital influence on the device linearity by affecting R S .

Conclusion
The single-tone power of the AlGaN/GaN HFETs with different gate widths was measured, and the improvement in linearity was determined. The results indicate that PCF scattering can offset the increased POP scattering as the gate bias is increased, as well as enhance the linearity of the devices. Thus, the approach is effective in improving the device linearity of AlGaN/GaN HFETs.  use of a BCl 3 /Cl 2 gas mixture. Ti/Al/Ni/Au (300/1500/500/600 Å) was evaporated and annealed at 850 °C for 30 s in nitrogen atmosphere to form the drain and source ohmic contacts. The space between the drain and source ohmic contacts was 6 μm. Transmission-line matrix measurements showed that the specific contact resistivity of the ohmic contacts was 2 × 10 −5 Ω·cm 2 . Ni/Au (600/2000 Å) two-finger gate with 1-μm gate length (L G ) was fabricated and located in the middle of the drain and source ohmic contacts. Finally, the devices were passivated by using a 100-nm-thick SiN layer deposited by PECVD. Devices with gate width (W G ) of 546 μm (2 × 273 μm) and 780 μm (2 × 390 μm) were marked as Samples 1 and 2, respectively.

Methods
Measurements. The on-wafer RF power performance of uncooled devices were tested by using a Maury load-pull system. The I-V characteristics were measured with the use of an Agilent B1500A semiconductor parameter analyzer.