Effect of Electric Field On Electron Mobility in Sub-100 nm InAlN/GaN High Electron Mobility Transistors

Electron mobility is important for electron velocity, transport current, output power, and frequency characteristics. In conventional mobility extraction methods, electron mobility is usually extracted directly from the measured gate capacitance ( C G ) and current-voltage characteristics. When device gate length ( L G ) scales to sub-100 nm, the determination of C G becomes more difficult not only for the measure equipment but also the enhanced effect from parasitic capacitance. Here in this paper, the C G extracted from high-frequency small-signal equipment circuit is used for the InAlN/GaN high electron mobility transistors (HEMTs). Electron mobility of the device with L G of 60-nm under V DS of 0.1 V and 10 V is extracted using two-dimensional scattering theory, respectively. The obtained results show that under a high electric field, the electron temperature ( T e ) and addition polarization charges ( ∆σ ) increase, resulting in the enhanced polar optical phonon (POP) as well as polarization Coulomb field (PCF) scatterings and degradation of the electron mobility. This study makes it possible to improve the electron mobility by reducing T e and ∆σ for the InAlN/GaN HEMTs application.AlGaN/GaN heterostructure field-effect transistors with different gate lengths were fabricated. Based on the chosen of the Hamiltonian of the system and the additional polarization charges, two methods to calculate PCF scattering by the scattering theory were presented. By comparing the measured and calculated source-2 ( I − V ) the InAlN/GaN HEMTs using B1500A parameter capacitance-voltage − using The S-parameters with

Polar optical phonon (POP) and polarization Coulomb field (PCF) scattering have been demonstrated as the main scattering mechanisms in GaN HEMTs 10,14,15 . Electron density (n2D) and electron temperature (Te) dominate POP scattering 10,14 . Addition polarization charges (∆σ) and device dimension (gate length LG, source-drain spacing LSD, et al.) present significant influence on PCF scattering 12,15,16 . In conventional mobility study, the devices with micrometer gate length are usually used 8,17,18 . As devices scale down, the electric field in the channel will increase. The channel electrons can accurate under a high electric field and then Te increases. Scaling down also changed the device dimension and the effect of ∆σ on small device dimension becomes more significant. Hence, POP and PCF scatterings will be changed with the electric field and device scaling down. But to the best of our knowledge, there are few reports about it. Therefore, extract and study the electron mobility in GaN HEMTs with nanometer LG is meaningful.
In general, the electron mobility extraction is based on the directly measured gate capacitance (CG) and current-voltage characteristic 8,17,18 . As devices scale down, the accurate capacitance of small LG, especially nanometer LG, is difficult to obtained by directly measurement. In this paper, high-frequency small-signal equipment circuit are used for the CG extraction. The electron mobility of the InAlN/GaN HEMTs with LG of 60 nm under drain-source (VDS) of 0.1 V and 10 V is extracted with two-dimensional scattering theory. The obtained results show that under high electric field, the increased Te and ∆σ enhance POP and PCF scatterings, resulting in degradation of electron mobility. This makes it possible to further improve device performance for the InAlN/GaN HEMTs application.

Results and discussion
A. Low-Field Electron Mobility  Devices with source-drain distance (LSD) of 2 µm, gate length (LG) of 60 ~ 150 nm, and gate width (Wg) of 20 × 2 µm were fabricated. To extract electron mobility, the determination of the electron density (n2D) is very important. In conventional mobility extraction methods, n2D is usually extracted directly from the measured gate capacitance (CG) of the device with a micrometer gate 8,17,18 . For the devices with sub-100 nm LG, not only the small gate length requires higher accuracy on the capacitance measurement equipment, the effect from the gate parasitic capacitance (CGext) on the nanometer gate cannot be ignored [19][20][21] . The T-shape gate with a larger gate head also increases CGext, as shown in Figure 2 [19][20][21] . Therefore, the extraction of n2D from the directly measured gate capacitance is not applicable for the sub-100 nm devices.  Another possible method to obtained CG is from high-frequency S-parameters.     is modulated with the gate voltage, but that of the non-gate region (access region) is unchanged. Therefor RSD can be written as 15,24 Here RG and Raccess are the resistances under the gate region and under the access region, respectively.
LGS and LGD are the gate-source and gate-drain distances, respectively. q is the electron charge. n2D is the electron density under the gate region, as shown in Figure 5. n2D0 is the electron density under the access region, which is the same with the electron density under the gate region at VGS = 0 V. µG and µaccess are the electron mobility under the gate region and under the access region, respectively.
Here µPOP, µPCF, µAP, µIFR, and µDIS are the electron mobility limited by POP, PCF, AP, IFR, and DIS scatterings, respectively, which can be obtained by using twodimensional scattering theory 10,15 . Hence µG and µaccess can be determined and is shown in Figure 7. It is significant that POP and PCF scatterings demonstrate the electron mobility. POP scattering is relevant with n2D and electron temperature (Te). Both increase can enlarge the collision probability between the carriers and lattice atoms, resulting in enhanced POP scatting 10,14 . Here VDS = 0.1 V, channel electric field is very low. Te is at the temperature and is unchanged. n2D is the only factor that affects POP scatting. Under the gate region, n2D increases with VGS and enhances the POP scatting.
PCF scattering comes from the non-uniform of the polarization charges in the InAlN barrier 12,25 . Due to the converse piezoelectric effect, the applied gate voltage can change the polarization charges of the InAlN barrier under the gate region and causes the addition polarization charges (∆σ) 16,26 . ∆σ can cause the PCF scattering potential and result in PCF scattering. Here a more negative VGS causes more ∆σ under the gate region, and leads to larger PCF scatting. Therefore, PCF scattering is enhanced when VGS is shifted to more negative. It can be seen that at VGS < -2 V, PCF scattering demonstrates the total electron mobility. With VGS increases to more than -2 V, the increased n2D causes that POP scattering plays a lead role on electron mobility. Then the total µG presents a tread that it increases to a peak and then decreases with the increase of VGS.
Under the access region, the electron density is unchanged with VGS. Therefore, POP, AP, IFR, DIS scatterings are not affected with VGS. As the gate voltage increases, ∆σ decreases and PCF scattering is weakened. Because LG is 60 nm and LSD = 2 µm, the effect of ∆σ under the small gate region on the large access region is weak, causing PCF scatting of µaccess is weaker than that of µG. Based on the extracted µG and µaccess in Figure7, RG, Raccess and RSD can be calculated by using (1), as plotted in Figure 8. The measured RSD is extracted from transfer characteristic in Figure 6. It is shown that the calculated and measured RSD present a good consistence, confirming the accurate of the two-dimensional electron system scattering theory.  The S-parameter with frequency of 1 to 50 GHz at VDS = 10 V are also measured. Then by subtracting CGext, CGint as a function of VGS is plotted in Figure 10. n2D is calculated with integration of Cgint with VGS. This is also shown in Figure 10 (see right Y-axis).    InAlN/GaN HEMT with LG = 60 nm, the output current saturation is due to the electron velocity (ve) saturation. In this condition, because the drain-source is very high (VDS = 10 V) and LSD is 2 µm, the electric field in the drain-source channel, especially in the gate channel region is very high. The high electric field can accurate the electrons to high ve. The electrons with high ve own a high electron temperature (Te), which presents significant influence on electron transport 27,28 . Figure 11(b) plots the measured transfer characteristic at VDS = 10 V of the same device. With the obtained n2D in Figure 10 and the drain current ID in Figure 11(b), ve is obtained from ID = n2Dqve. Based on the dependence of ve on electric field (E) in GaN HEMTs, E can be determined 27 . Figure   12 depicts ve and E in the gate channel region as a function of VGS. When VGS increases from -3.5 V to 1 V, ve decreases from 1.24 × 10 7 cm/s to 7.38 × 10 6 cm/s, and E decreases from 23.99 kV/cm to 9.12 kV/cm. The supplied power per electron Pe = EID/n2D is calculated with the obtained E. Based on the relationship between Te and Pe, Te can be determined 27,28 . Figure 13 presents Pe and Te as a function of VGS. As VGS increases, Pe decreases from 4.79 × 10 -8 W to 1.08 × 10 -8 W, and Te decreases from 521.7 K to 518.7

B. High-Field Electron Mobility
K. At VDS = 0.1 V, because the low electric field, electron temperature is at the room temperature (Te = 300 K). Compared with Vds = 0.1 V, Te increases from 300 K to ~ 520 K, resulting in an 73% increase of Te.
With the obtained n2D and Te, the electron mobility at VDS = 10 V can be calculated by using 2D scattering theory. Figure 13 shows the calculated µG and µaccess at VDS = 10 V. POP and PCF scatterings are still the main scattering mechanisms at VDS = 10 V, which is the same with that at VDS = 0.1 V. Compared with the electron mobility at VDS = 0.1 V, µaccess presents a slight decrease, but µG shows a large decrease. The influence of electric field on the electron mobility is discussed in the following part.     The increase of ∆σ and Te enhances PCF and POP scatterings at VDS = 10 V, as shown in Figure 16. Therefore, a significant decrease of µG at VDS = 10 V is demonstrated.

Conclusions
In summary, CG extracted from high-frequency small-signal equipment circuit is