Analytical Study of ZnO-based HEMT for Power Switching

We investigate the power switching mechanism to evaluate the power loss ( P D ) and eﬃciency ( η ) in MgZnO/ZnO (MZO)-based power high electron mobility transistor (HEMT), and physical parameters respon-sible for P D in molecular beam epitaxy (MBE) and dual ion beam sputtering (DIBS) grown MZO HEMT and compare the performance with the group III-nitride HEMTs. This work extensively probes all physical parameters such as two-dimensional electron gas (2DEG) density, mobility, switching frequency, and device dimension to study their impact on power switching in MZO HEMT. Results suggest that the MBE and DIBS grown MZO HEMT with the gate width ( W G ) of ∼ 205 and ∼ 280 mm at drain current coeﬃcient (k) of 11 and 15, respectively, will achieve 99.96 and 99.95% of η and 9.03 and 12.53 W of P D , respec-tively. Moreover, W G value for DIBS-grown MZO HEMT is observed to further reduce in the range of 112-168 mm by using a Y 2 O 3 spacer layer leading to the maximum η in the range of 99.98-99.97% and the minimum P D in the range of 5-7 W. This work is signiﬁcant for the


Introduction
To counter the issue of rising CO 2 emissions, renewable and cost-effective energy sources are [1,2]in substantial demand. It is well-know that enhancing the system efficiencies of energy conversion and power generation with improved power switching devices and control techniques can significantly contribute towards reduction in energy demand [3]. Solid-state power transistors equipped with high-efficiency power conversion in power electronic converters are one of the prominent solutions for effective energy utilization [4].
Various material systems have been explored to devise efficient power transistors, such as, Si, GaAs etc. As Si and GaAs-based power devices have reached their theoretical limits of power density [3,5], wide bandgap materials, such as GaN-based high electron mobility transistors (HEMT) are being extensively explored to further push the efficiency and power density limits of power devices [4]. ZnO is another promising wide bandgap material system that displays large energy bandgap (3.37 eV) [6], high breakdown field (∼ 3M V /cm) [7], and large saturation drift velocity (≈ 10 7 cm/s) [6] and this material system has not been explored extensively for power HEMT applications. ZnO-based heterostructures have shown higher two-dimensional electron gas (2DEG) density (∼ 10 13 − 10 14 cm −2 ) [6,8,9] than that exhibited in the GaN-based heterostructures, which is one of the crucial parameters to realize high current densities in power HEMTs. In addition, ZnO, as a material, provides unique advantages of high-quality material production at lower temperatures (100 to 300 ℃) using even a cost-effective polycrystalline growth system along with the accessibility to large-area ZnO substrates at relatively low cost [6,10,11]. Sasa et al [12], Koike et al [13], and Ye et al [14] have realized high-quality epitaxially-grown MgZnO/ZnO (MZO) based HEMT. Moreover, reports of realizing high 2DEG yielding sputtered [6,9,15,16] MZO heterostructures are available in the literature, suggesting the possibility of achieving large-area and therefore, low-cost ZnO-based power HEMTs.
In this work, we have assumed the operating point (900 V, 30 A) for the evaluation of power device performance parameters essential for the electric vehicle converters, which require a voltage range of 600-900 V and a power rating > 20 kW [17,18].This work extensively evaluates the power device performance parameters, such as, power dissipation (P D ), power dissipation density (P DD ), and power efficiency (η) of MZO HEMT with respect to operating point coefficient of drain current (k), 2DEG density (n s ), and switching frequency (f s ), analytically. The performance of power HEMT is investigated for MZO system realized both by molecular beam epitaxy (MBE) as well as cost-effective sputtering systems. Further, as the electron mobility is one of the important parameters for power transistor application due to its direct proportionality to the conduction losses of the transistor, this work also qualitatively explores the impact of a thin Y 2 O 3 layer as a spacer layer in sputtered MZO heterostructure, as it is observed to enhance the electron mobility in dual ion beam sputtering (DIBS)-grown MgZnO/CdZnO heterostructure [19]. The obtained results suggest that to achieve the minimum value of P D , a device W G value of ∼205 and ∼280 mm is necessary for MZO HEMTs grown by MBE and DIBS, respectively. Moreover, the insertion of Y 2 O 3 spacer layer in the MZO HEMT further reduces W G value in the range of 112-168 mm. This work also provides an insight for a device designer to select the optimum k values for the selected f s while designing a power HEMT. The findings of this work suggest that the DIBS-grown MZO heterostructure can be explored as a cost-effective high-power HEMTs with potential application in power switching devices.

ANALYTICAL MODEL FORMULATION
It is known that in switching operation the transistors alternate between ONstate and OFF-state, as shown in fig. 1, where in the ON-state the gate opens the channel and allows the electrons flow through the device while in the OFFstate the gate closes the channel and blocks the current flow. For efficient switching, the OFF-state operation point conditions should be at large positive drain voltage (V OF F ) and negligible drain current (I D ), which requires a strong gate blocking capability [20]. However, at a high positive drain voltage (V D ), the gate-blocking capability of the HEMT degrades and gives rise to subthreshold leakage current. It is well-known that the value of V D at which  To understand more on power switching efficiency, one needs to investigate the losses that take place in power HEMT. It is well-known that the nonideal behavior of a power switch is described in terms of conduction and switching losses that are analyzed in the next section.

Conduction Loss
This accounts for the voltage drop across the series resistance from source to drain terminals (contact and sheet resistance) of the transistor, as shown in fig.  2. The sources of the conduction losses are: (a) ON-state nonzero voltage due to the device ON-state resistance (R ON ), and (b) OFF-state nonzero current due to the leakage effect. However, the leakage effect (current) is marginal and does not vary significantly with V D and therefore, it is neglected in this work like others in the published literature [21].
Based on the ON-state resistance, the direct-current (DC) power dissipation becomes [21,22]: where, D is the duty cycle. R ON is the sum of sheet resistance (R sh ) and the drain and source contact resistance (R c ). Here, the effect of R c is neglected as the value R c of is much less as compared to that of R sh . Therefore, R ON is expressed as [21,22]: where, q and µ are the charge and mobility of electron, respectively. For an estimation of the device dimension, we assume a constant electric field distributed across the drain to gate depletion region and hence, gate to drain length (L GD ) can be given by equation (4) [21]. Further, the total gate width (W G ) is calculated in terms of maximum current density (J max ) and the operational current bias (I ON ). Therefore, W G can be expressed as in equation (5) [21]: where, E BR is the breakdown electrical field. J max = qn s v s [23], where v s is saturation velocity of electron.

Switching Loss
This occurs during device switching from OFF-to ON-state and vice versa.
To calculate the switching losses, gate to drain capacitor (C gd )-based model, a schematic of which is shown in fig. 3, is considered. When gate to drain region is in the reverse bias condition, the modulation of the depletion region width (x d ) during the switching operation corresponds to charging and discharging of C gd . The energy dissipated in each charging and discharging cycle needs to be multiplied by the switching frequency (f s ) to obtain the switching losses [21]. Based on the switching frequency and charge accumulated in between the gate to drain contact, the switching losses can be written as [21,22]: where, E br is the gate to drain depletion region extension in the gate to drain access region. The power dissipation (P D ), being the combination of the conduction and switching losses, can be expressed as: In addition, the power efficiency of the HEMT is defined as the ratio of output power (P out ) to the summation of P out and P, and can be written as: where P out = V OF F I ON Further, the power dissipation density (P DD ) is considered as the total power loss divided by the active area of power HEMT, as expressed by equation (9) [21,22]:

RESULTS and DISCUSSION
To fig. 4(a) exhibits the comparative analysis of the variation of P D and P DD for AlGaN/GaN and MgZnO/ZnO HEMTs with respect to operating point coefficient (k) of I D . Here, we have assumed V OF F = 900 V, I ON = 30 A, f s = 500 kHz, duty cycle = 10% for power dissipation calculation, and S = 1.4 for the operation of the device in the safe mode. It is observed that P D is higher at the lower value of k (k ¡ 5) owing to higher value of R ON which is associated with the higher conduction loss, as per equations (2) and (5). P D decreases up to certain critical values of k (k = 5) for AlGaN/GaN HEMT, while k = 11 for MBE-grown and 15 for DIBS-grown MZO HEMTs. On the other hand, P D increases beyond the critical value of k owing to switching losses, as described in equations (5) and (6). The smallest value of P D of 3.7 W is observed at k = 5 (W G = 93 mm) for AlGaN/GaN HEMT and 9.03 and 12.53 W at k = 11 (W G = 205 mm) and 15 (W G = 280 mm) for MZO HEMTs grown by MBE and DIBS, respectively. Higher values of P D in MZO HEMT are mainly due to the lower 2DEG mobility, which leads to the high values of R sh and R ON . In addition to this, large dislocation and alloy disorder scattering also influence the rise in R sh in DIBS grown MZO-based HEMT [25,26]. The values of P DD at minimum D are 942 W/cm 2 for AlGaN/GaN HEMT and 1044 and 1062 W/cm 2 for MZO HEMTs by MBE and DIBS, respectively. For increasing k, P DD saturates to 528 W/cm 2 (W G = 524 mm) for AlGaN/GaN HEMT and 551 and 570 W/cm 2 (W G = 786 and 880 mm) for MZO HEMT by MBE and DIBS, respectively.
The increase in P D beyond the critical level of k is mainly because P S increases with k ( ∝ W G ). Fig. 4 The variation of (a) P D and P DD , and (b) η with respect to k for AlGaN/GaN and MgZnO/ZnO HEMTs.  fig. 5(a) that the value of η is decreased with rise in 2DEG density from 1 × 10 13 to 1 × 10 14 cm −2 at lower value of k (< 20) as R ON rises with the value of 2DEG density. For k < 20, the conduction losses are increased, however, for higher value of k (≥ 20), the power efficiency is approximately equal for all values of n s , as evident from equations (1-3). On the other hand, switching losses are not affected by the change in n s , as observed from equation (5). When n s increases W G reduces and overall the value of P SL remains constant. Fig. 5(b) shows the variation of η with respect to f s in which three values of f s is considered such as 500 kHz, 1 MHz, and 5 MHz. The drop in efficiency with increasing k is more prominent for higher values of f s , as observed from equation (6). At f s = 1 and 5 MHz, the values of η declines for k > 51 and k > 6, respectively. Inset of fig. 5(b) shows the range of k with respect to different values of f s for the η max obtained for MZO power HEMT. To design a power HEMT at a specific value of f s , one can easily evaluate the range of permissible W G values with respect to the power efficiency.
Khan et al [19] have reported the insertion of Y 2 O 3 spacer layer between the substrate and CdZnO buffer layer in the DIBS-grown MgZnO/CdZnO (MCO) HEMT, the 2DEG mobility is enhanced by 6× as compared to that for MCO HEMT without any spacer layer. Even though the lattice matching of Si/ZnO is much better as compared to that for Si/CdZnO, we assume a maximum of 6× enhancement of µ for the DIBS-grown MZO HEMT using Y 2 O 3 spacer layer. For this study, 3× or 6× values of µ are assumed for DIBSgrown MZO HEMTs and are presented as MZY1 and MZY2, respectively. The less improvement in µ is assumed considering a maximum of 6× enhancement of µ is not achievable due to the change in experimental parameters.
As observed in fig. 6(a), for MZY2, the minimum value of P D is ≈ 5 W at k = 6 (W G = 112 mm) which is very close to the minimum P D value of AlGaN/GaN HEMT (≈ 3.7 W at k = 5, W G = 93 mm). For MZY1, the minimum value of P D is 7 W at k = 9 (W G = 168 mm). For lower k, the relatively higher values of P D for MZY2 as compared to that for AlGaN/GaN is due to the higher R ON for MZY2. The values of P DD corresponding to the minimum P D values are 1022, 1085 W/cm 2 and the P DD curve saturates at 536, 525 W/cm 2 for MZY1 and MZY2, respectively.  6 The variation of (a) P D and P DD , and (b) η with respect to k for AlGaN/GaN and MZY HEMTs. Fig. 6(b) shows the comparative analysis of η as a function of k for AlGaN/-GaN and MZY based HEMTs. The maximum value of η (η max ) remains at 99.98% for 5≤ k ≤ 8 for MZY2 HEMT and this value is similar to that for AlGaN/GaN HEMT. η max remains at 99.97 % for 6≤ k ≤ 14 for MZY1 HEMT that is 0.01% less than that for MZY2 and AlGaN/GaN HEMTs.
For the 900 V and 30 A power application, W G for AlGaN/GaN HEMT is evaluated to range from 93 mm (for P D minimum) to 524 mm (for P DD saturation). Similar experimentally reported values of W G (200-340 mm) is reported elsewhere for the current range of 20-60 A [27,28]. At f s = 500 kHz and duty cycle = 10%, the model predicts 81 W of maximum P D , as in fig. 4(a), in AlGaN/GaN HEMT and this value is close to the experimental report of 119 W [29]. Similar values of maximum P D for MBE-grown MZO, and DIBS-grown MZO and MZY HEMTs, as in fig. 4(a), are 82, 97, and 81 W, respectively. Thus, to achieve the comparable power efficiency with minimal power dissipation in MZO HEMT with respect to those for AlGaN/GaN HEMT, one can easily play with DIBS growth parameters and choose a little larger W G . This, coupled with reduced manufacturing cost of DIBS-grown ZnO-based HEMTs are promising for large-area power switching applications.

CONCLUSION
In this work, an analytical model is utilized to investigate the power switching and evaluate the power efficiency and loss parameters of MZO HEMT and compare those with the group III-nitride counterparts. A W G value of ∼ 205 and ∼280 mm for MBE-and DIBS-grown MZO HEMT are found to be essential to attain η max of 99.96 and 99.95% and the minimum P D of 9.03 and 12.53 W, respectively. Moreover, W G value for DIBS-grown MZO HEMT is observed to further reduce in the range of 112-168 mm by using a Y 2 O 3 spacer layer leading to max in the range of 99.98-99.9% and the minimum P D in the range of 5-7 W. This work also provides an insight on the allowed W G values while designing a DIBS-grown power HEMT at a fixed f s with respect to the desired power efficiency. This work is significant while designing a cost-effective DIBS-grown MZO HEMTs for power switching applications.

ACKNOWLEDGMENT
Sanjay Kumar would like to thank DST for providing DST-INSPIRE PhD fellowship.