Interplay Between γ –Ray Irradiation and 3DEG for Dosimeter Applications

This work investigates the cumulative dose 60 Co gamma ( γ ) – ray irradiation effects on enhancement mode HEMT devices inheriting 3D – Electron and Hole Gases for dosimeter applications. The devices are irradiated through a 60 Co source and demonstrate the enhancement in the drain current metrics. To elucidate, the said devices were irradiated through different mechanisms and the Compton effect was investigated through contour plots via TCAD simulations. The degradation of Schottky Gate contact and insulator charging affects the 2D – Hole Gas at the GaN cap and thereby affects the bottleneck at the 3DEG sheet. This signiﬁcantly affects the OFF – state leakage components of the said device and can therefore be exploited for potential use in sensing and dosimeter applications. The leakage components can be exploited further to improve the linearity of the dosimeter by considering different grading proﬁles of the AlGaN layer. In this regard, a workﬂow for optimizing the sensitivity and linearity of the dosimeter through different graded proﬁles is also presented. Amongst all, gaussian graded proﬁles have been identiﬁed as the best – case scenario considering the sensitivity and exhibiting a linear operation.


I. INTRODUCTION
Gallium Nitride (GaN) based devices have established themselves as the viable solution for fulfilling the needs of various space and research agencies. It has replaced Silicon, which has reached its theoretical limits, for being the dominating material for various space applications [1]- [5]. The exciting intrinsic properties of GaN, such as the wider direct band -gap, higher breakdown fields, and higher saturation velocity, enable compatibility of such devices for high power and RF applications [6]. Due to the inherent polar nature of the GaN crystal, AlGaN/GaN heterostructures support a 2 -Dimensional Electron Gas (2DEG) channel The associate editor coordinating the review of this manuscript and approving it for publication was Giambattista Gruosso . supported by the spontaneous and piezoelectric polarizations. Ibbetson et al. [7] reported that there is a contribution from the surface like donor states as well that maintains charge neutrality with respect to the 2DEG. The electron carriers in the 2DEG channel are free to move virtually in a 2D space between Source and Drain electrodes and are tightly confined along the third direction, i.e., along the device depth. It is for this reason, GaN based devices can exhibit higher carrier mobilities in the 2DEG channel and announce their compatibility for high frequency applications [6].
The 3 -Dimensional Electron Gas (3DEG) concept was conceptualized and demonstrated experimentally by Jena et al. [8] in 2002. The group demonstrates that by grading the AlGaN layers, the net positive polarization charge localized at the AlGaN/GaN can be spread across the entire VOLUME 10, 2022 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ AlGaN layer. This will subsequently smear the electron charge across the entire AlGaN layer in a 3D space, giving rise to higher conductivity without external doping. The concept was eventually exploited to realize polarization doped field effect transistors (PolFET), which exhibit higher carrier mobilities due to the absence of ionized impurity scattering [9]. Park et al. [10] have proposed and demonstrated experimentally a 2D/3D hybrid channel AlGaN/GaN HEMT architecture which exhibits a quasi 3DEG profile. The architecture as proposed exhibits a flatter transconductance (g m ) profile which improves the linearity performance in comparison to the conventional HEMT architectures. Further, the proposed architecture combines the advantages of High Electron Mobility Transistor (HEMTs) and Metal Semiconductor Field Effect Transistor (MESFETs), in realizing a custom transconductance profile that can be tailored for achieving a higher peak transconductance g m(Max) and hence higher device gain, or for achieving a broader transconductance profile. Further, due to the graded nature of the AlGaN layer, the effective barrier height increases that limit the gate leakage current, thereby improving the breakdown characteristics of the device. It is widely known that the electron saturation velocity (ν sat ) of the GaN channel decreases with the electron density [11]. The ν sat of the GaN channel therefore, is directly responsible for controlling the transconductance and current gain profiles of a conventional HEMT [11]. Accordingly, the linearity performance of such architectures gets degraded. This eventually translates into a higher intermodulation distortion through an increased contribution from the higher order harmonics. Bajaj et al. [11], [12] have demonstrated graded AlGaN channel PolFETs in which spreading the polarization charge across the graded AlGaN layers in a 3D space results in a distributed electron density and renders a constant ν sat as a function of gate bias. This significantly suppresses the higher order harmonics and improves the linearity of the device [13]. A novel enhancement -mode HEMT architecture incorporating back-to-back graded AlGaN layers to exploit the 3D polarization engineering for realizing 3DEG and 3DHG (hole gas) was demonstrated by Luo et al. [14]. This is in contrast to the standard enhancement -mode HEMTs realized through doped GaN cap layers [15]- [18] that suffer from threshold voltage instabilities. The group reports a significant enhancement in the drain current metrics in comparison to the conventional counterpart. Further studies on the architecture [19] reveal an enhancement in the OFF -state breakdown characteristics of the proposed architecture by 23 times compared to the conventional architecture, considering similar gate -drain spacings and physical gate lengths. Deng et al. [20] further proposed an enhancement to the original stack by incorporating a GaN buffer between the positive and negative graded AlGaN layers. The 3DEG realized by the positive graded AlGaN layer was used as a conduction channel, while the 3DHG realized by the negative graded AlGaN layer was used as a back barrier to further suppress the buffer leakage current. Apart from this, several experimental and theoretical reports suggest the role of the strong bonding nature of III -V binary and ternary nitrides [21]- [24] for the radiation hardness of GaN devices.
Radiation induced defects, including radiation induced traps and stress, may alter the material and electrical properties of AlGaN/GaN heterostructures [21]- [25] and lead to the departure from the expected results. In this regard, several attempts have been made to assess the reliability of GaN HEMTs in the presence of ionizing radiations for specific applications in nuclear reactors and space. Several studies have also reported the sensitivity of GaN HEMT devices towards the ionizing X -Rays [26]- [28] and γ -Rays [28]- [32]. The impact of γ -Rays irradiation on reported HEMT architectures is compiled in Table 1 [28]- [32].
The impact of ionizing radiation as observed from Table 1 (γ -Rays) on conventional HEMT architecture, having a Schottky Metal -Semiconductor (MS) Gate contact, is negligible as far as the change in peak transconductance g m(Max) and pinch -off voltage (V TH ) is considered. The ON -State Current (I ON ) however, show significant enhancement with γ -Rays dose compared to X -Ray irradiation [26]- [28]. The MOSHEMT architectures, on the other hand, demonstrate a significant shift in the V TH which is enhanced primarily due to the charging of the insulator at MOS/MIS Gate contact. The OFF -state current (I OFF ) for both X -Ray [26]- [28] and γ -Ray [28]- [32] irradiation as reported show significant degradation, which causes a major concern regarding the reliability issues of such devices for prolonged use.
A close observation into the cases compiled in Table 1 calls for a principal requirement for detecting ionizing radiations at a low and high dose to avoid the system failure due to a drift in the operating conditions [33]- [35]. There have been attempts made to utilize GaN HEMTs as a comparator to detect ionizing radiations [36], thin film GaN HEMTs for the detection of X -Rays [37], ultrahigh gain AlGaN/GaN HEMTs for the detection of X -Rays and Protons [38], [39], or an attempt to utilize intrinsic properties of GaN to realize Schottky diodes for the detection of α -Particles [40]. However, to the best of the author's knowledge, discrete GaN HEMT devices have not been exploited yet for γ -Ray based dosimeter applications.
This work is an attempt to provide solutions for the early detection of γ -Rays by exploiting the concept of 3DEG inherent in graded AlGaN layers. A detailed study regarding the impact of γ -Rays on the device characteristics and its subsequent optimization for improved sensitivity as a γ -Ray dosimeter is presented in this paper. The contributions of this work are follows: • The influence of the cumulative dose 60 Co gamma (γ ) -ray irradiation on the enhancement mode HEMT device incorporating positive and negative graded AlGaN layers has been presented.
• The impact of γ -rays in generating the Compton electrons, and thus the electron hole pairs in the target device is investigated in depth through contour plots via TCAD simulations.
• The interaction of γ -rays with 3DEG and its pronounced effect on depleting the 2DHG has been exploited for the dosimeter applications and hence the impact of sensitivity towards γ -ray dose has also been carried out under different dose rate environments.
• The sensitivity of the dosimeter has been optimized by considering different graded profiles and it is observed that the gaussian graded AlGaN profile demonstrates the best-case scenario for dosimetry considering linearity and sensitivity metrics.
The device architecture investigated for dosimetry and the models adopted for Victory TCAD Simulations [41] is discussed in Section 2. Sensitivity analysis and optimization of the device architecture as a function of γ -Ray dose is presented in Section 3. Finally, the paper is concluded in Section 4.

II. DEVICE ARCHITECTURE AND CALIBRATION
This section of the paper presents a detailed insight into the TCAD workflow for calibrating the device architecture. The calibration has been validated by developing and realizing the devices through process recipe and virtual fabrication process.

A. DEVICE ARCHITECTURE UNDER TEST
A schematic view of the enhancement mode HEMT device incorporating positive and negative graded AlGaN layers is depicted in Fig. 1(a), and the calibrated simulation deck depicting transfer characteristics is shown in Fig. 1(b). The positive and negative graded AlGaN layers are with regards to an increase/decrease in the Aluminum mole fraction (χ Al ) with the growth direction of the graded AlGaN layers [20]. The device dimensions are briefly summarized in Table 2.
The device dimensions and the reference data for calibrating the simulation deck in TCAD are as per Deng et al. [20]. The device architecture has a trench gate arrangement supported by a 10 nm HfO 2 dielectric layer, exhibiting a physical gate length (L G ) of 0.5 µm. Starting with the Sapphire Substrate, the epi layer stack of the DUT consists of a 500 nm negative graded AlGaN layer which is supported by a 100 nm AlN nucleation layer. The negative gradient of χ Al spreads the net negative polarization charge in a 3D space, which is screened by the development of a 3DHG acting as a back barrier. The back barrier helps to limit the gate leakage current and consequently improves the OFF -state breakdown characteristics. A 100 nm positive graded AlGaN layer supported by a 700 nm GaN buffer on top of the negative graded AlGaN layer is subsequently grown. The positive gradient of χ Al spreads the net positive polarization charge localized at the AlGaN/GaN (Buffer) interface across the entire AlGaN layer in a 3D space, to smear the electron gas and realize a 3DEG sheet for conduction. Finally, the epi stack consists of a 20 nm partially doped GaN top layer which exhibits a 2DHG (hole gas) localized at the GaN (top)/AlGaN layer interface to realize an enhancement mode operation. The device architecture exhibits vertical conduction through the formation of an electron accumulation layer (EAL) [20] at the sidewalls of the trench gate when the gate bias is ramped VOLUME 10, 2022  above the threshold voltage. This, in essence, depletes the 2DHG at GaN (top)/AlGaN layer interface and exhibits an electrical gate length of 120 nm.

B. SIMULATION AND CALIBRATION METHODOLOGY
Silvaco's Victory device simulator tool [41] has been used to carry out the initial calibration of the simulation deck to capture the device's physics and mimic the actual device behavior. Since the device architecture incorporates a partially doped GaN top layer, a Concentration dependent Shockley -Read -Hall (consrh) recombination model was invoked to capture the trap -assisted recombination as a result of trapping states evolved in the partially doped GaN top layer. The carrier statistics are modeled by invoking fermi -dirac statistics (fermi). The degradation in the Gate contact (leading to an increase in OFF -state current) with cumulative γ -Ray dose is captured by invoking the Schottky Tunneling model (ust). The error in the device threshold voltage and the maximum drain current is reduced by tuning the work function of gate contact and the individual spontaneous and piezoelectric polarization components of the AlGaN and GaN layers. Further, since the surface states on AlGaN play a major role in maintaining the charge neutrality with respect to the channel, donor like surface states at the SiN x /AlGaN and SiN x /GaN (top) interface were defined with an energy level E T = 0.5 eV, and interface trap density of 3×10 13 cm −2 . The capture cross sections for electrons (σ n ) and holes σ p were set to 1×10 −13 cm 2 . Further, since the bulk traps in GaN buffer are responsible for the degradation in the output admittance parameters [42]- [44], acceptor type traps with E T = 0.45 eV and bulk trap density of 1.5×10 16 cm −3 were defined in GaN buffer with capture cross sections, σ n and σ p set to 1×10 −13 cm 2 respectively. The trapping definitions are in accordance with the experimental studies on similar AlGaN/GaN heterostructures [42]- [44]. Yang et al. [45] have also demonstrated through DLTS measurements the evolution of electron and hole traps in doped GaN cap layers, which realize enhancement mode operation. Accordingly, acceptor type traps with E T = 0.85 eV and bulk trap density of 4×10 16 cm −3 with σ n and σ p as 1×10 −15 cm 2 and donor type traps with E T = 0.49 eV, bulk trap density of 3.2×10 16 cm −3 with σ n and σ p as 1×10 −19 cm 2 was defined at the doped GaN top layer in accordance with the DLTS studies [45]. Finally, Albrecht low field mobility model [41] to tune ON -state resistance, and GaNsat high field mobility model [41] to capture the velocity saturation at high fields, were also invoked. In addition to this, to irradiate the DUT with γ -Rays, considering 60 Co source, Radiation Effects Module (REM) [41] was invoked in accordance with the methodology presented by Sehra et al. [24].

C. PROCESS RECIPE FOR THE VIRTUAL FABRICATION OF DUT
The process recipe for the Virtual Fabrication of DUT through TCAD presented in this section, is an extension of the work reported by Peng et al. [19]. Starting with the standard wafer cleansing procedure, the epi layer stack is grown in accordance with the structure depicted in Fig. 1(a) using Metal -Organic Chemical Vapor Deposition (MOCVD) technique on a Sapphire substrate. The active area of the device consists of the positive graded AlGaN layer, which houses the 3DEG channel. The precursors helping in the growth of respective GaN, AlGaN, and AlN layers are the trimethylgallium and ammonia (NH 3 ) with H 2 carrier gas. The χ Al in negative graded AlGaN layer can be controlled by linearly decreasing the TMAl flow to zero, while grading the TMG flow to account for the χ Ga with the growth direction. Similarly, for positive graded AlGaN, the TMAl flow is linearly increased from zero, with the growth direction, while the TMG flow is adjusted to account for the χ Ga . The GaN -top layer is selectively etched towards end point using BCl 3 /Cl 2 based ICP -RIE for dry etching. After this appropriate masking is done and selective ion implantation is carried out for doping of GaN -top layer with Silicon to regulate threshold voltage [14], [19], [20]. Standard ohmic contacts are defined using photolithography and e -beam evaporated Ti/Al/Ni/Au stack and standard lift off procedures. The samples are then subjected to rapid thermal processing (RTP) to complete Source and Drain ohmic contact formation. Post ohmic contact formation, device mesa isolation is carried out through dry etching using BCl 3 /Cl 2 based ICP -RIE. This is followed by the deposition of SiN x passivation layer using Atomic Layer Deposition (ALD) technique. ICP -RIE is then carried out to define the gate trench window. The trench gate formation is then followed up, first by the deposition of HfO 2 through ALD followed by e -beam evaporation of Ni/Au stack for the Gate electrode using standard lift off procedures. Finally, contact windows are opened to get the metal contacts. The process recipe is illustrated in Fig. 2 (i)-(j).
The process steps described above are validated through Silvaco's Victory Process Simulation tools [41] as shown in Fig 3(a) and the transfer characteristics of the virtually fabricated device is shown in Fig. 3(b). The virtually fabricated device is simulated using the trapping parameters given in Section II(B). The proximity of the transfer characteristics with the TCAD analysis validates the process recipe for the fabrication of the DUT.

III. RESULTS AND DISCUSSIONS
The device architecture under study is evaluated for dosimeter applications considering the interaction of γ -Rays from 60 Co source with the 3DEG channel housed by the positive graded AlGaN layers. A detailed analysis is presented with regards to the impact on OFF -state and ON -state characteristics of the device with cumulative dose effects of γ -irradiation. Silvaco's Radiation Effects Module (REM) [24], [41] is used to set up a radiation environment from 60 Co source with a dose rate of 3 kGy/hr in accordance with the experimental studies [24], [30]- [32].

A. VALIDATION OF RADIATION ENVIRONMENT
To validate the Silvaco's Radiation Effects Module (REM) [24], [41] in capturing the reported experimental effects, the module was initially calibrated against the experimental set reported by Sharma et al. [31] at a dose rate of 3 kGy/hr. This calibration is done to capture the experimental γ -ray effects on the AlGaN/GaN material system using the REM module. The calibrated radiation module will be used in the later sections with the calibrated simulation deck of 3DEG HEMTs to assess their sensitivity towards γ -rays. A comparison of the resulting transfer characteristics is shown in Fig. 4(a)-(c) for low and high dose γ -rays. The close proximity of the TCAD data with the experimentally irradiated devices validates the formulations of the Radiation Environment thus set up to test the 3DEG HEMTs for dosimeter applications.

B. IMPACT ON DC CHARACTERISTICS
A comparison of the resulting transfer characteristics under pristine and subsequent γ -Ray irradiation stage is depicted in Fig. 5(a) and enlarged view of the drain current is shown in Fig. 5 Fig. 6(c) and (d) under OFF state for pristine condition and radiated state. The charge buildup disrupts the charge balance of the 3DEG channel with 2DHG at GaN top layer, which is responsible for creating a bottleneck towards the flow of carriers and helps in realizing an enhancement mode operation. This disruptive effect on 2DHG is exploited in this work to realize a fairly linear response for dosimeter applications.
The principal effect of the interaction of γ -Rays with the GaN HEMTs reported in the literature is the enhancement in sheet carrier density which is coupled to the negative shift in the device threshold voltage (− V th ) [23], [28]- [32], [46]. The enhancement in drain current has also been linked with the improvement of carrier mobilities [32], [47]. This improvement, in turn, can be an effect from the relaxation of  V TH as a function of TID level. All the terminals of the DUT were grounded during the exposure to mimic the experimental setup as per [26]- [28]. VOLUME 10, 2022 piezoelectric coefficients and structural reordering [32], [47] or through the improvement in the surface roughness [31]. Annealing of active traps post irradiation [48] and subsequent generation of interstitial/point defects in the form of nitrogen vacancies acting as donors [30] can also improve the carrier densities. Apart from these, reduction in the channel resistance [30]- [32] or decrease in activation energy coupled with an increase in the minority carrier diffusion lengths [49], [50] has also been observed to improve the drain current of the device.
The graded AlGaN layers housing the 3DEG channel can exhibit higher carrier mobilities due to the absence of impurity scattering [9]. The enhancement in drain current observed from Fig. 5 (a-b) points towards the possibility of enhancement in carrier mobilities to be the dominant reason for the observed effects, which gets translated towards the increase in peak transconductance as depicted in Fig. 5 (c-d). Further, since a major area of the DUT in the form of access regions is being exposed to direct interaction with the γ -Rays, the charge buildup consequently disrupts the 2DHG at the GaN top layer. This eventually aids the 3DEG carrier concentration in the positively graded AlGaN layer. The control for the depletion of 2DHG, however, remains with the Gate electrode. As the gate bias is raised above the threshold voltage, the conduction band is pulled below the fermi level, which pulls the electrons, consequently developing an electron accumulation layer (EAL) at the sidewalls of the trench gate [14], [19], [20]. This essentially depletes the 2DHG at the interface of GaN(top)/AlGaN near the gate electrode and opens up a conducting path for the carriers from Source to Drain electrode. It is for this reason, the threshold voltage shift associated with γ -irradiation is negligible for the DUT even at a higher dose, as depicted in Fig. 5(e).
Since a major portion of the access region of the device is exposed, there is also a high possibility of active traps being annealed due to the interaction with energetic photons. The heat generation, in essence, can be estimated by the formulation given by William et al. [51], as per Equation 1.
where, c is the conversion factor equal to 1.6×10 −13 WsMeV −1 , E γ is the energy of the γ -Rays in MeV, µ γ is the linear absorption coefficient corresponding to γ -Rays with energy E γ given in cm −1 , and φ γ is the photon flux density corresponding to the γ -Rays with energy E γ given in cm −2 s −1 . Further, the thermal conductivity κ (in Wcm −1• C −1 ) relates the heat transfer Q T and temperature gradient T x as per Equation 2.
Using Equations 1 and 2, with µ γ and φ γ as 0.33 cm −1 and 10 15 cm −2 s −1 respectively [30], the average temperature change ( T ) is estimated to be ≈ 184 • C at the positively graded AlGaN layer, which is in line with the earlier reports [30], [52]. This annealing effect has been captured in TCAD simulations using a thermal model associated with the insulator charging for the charge buildup, as demonstrated by Sehra et al. [24]. The annealing effects due to the energy transfer from the energetic γ -Ray photons leads to crystal reordering. This is responsible for the sudden jumps observed in ON -State and OFF -State currents for the initial dose ( Fig. 5(a)), which starts saturating as the γ -Ray dose is increased. The electron -hole pairs generated post irradiation rearranges under the applied electric field. It aids the conducting path through the positive graded AlGaN towards the Source electrode via EAL at the sidewalls and GaN top layer. This is depicted in Fig. 7(a) for brevity. The leakage paths in OFF -state post irradiation is depicted in Fig. 7(b). It has also been reported that the degradation of the Schottky gate contact results in an increase of gate leakage current [23], [28]- [32], [49], [53]. As opposed to the common trend, some experimental studies have reported conflicting results demonstrating degradation of the drain current [49] or marginal improvement in the gate leakage current post irradiation [47]. Consequently, the interaction of γ -Rays on the device characteristics and the radiation induced traps so evolved are dependent upon a number of factors, including the quality of grown epi -layers. Further, the increase in OFF -state current recorded with γ -irradiation (as shown in Fig. 5(a)) is again linked with the insulator charging that disrupts the 2DHG at GaN top layer as observed in Fig. 6(d). This has a direct consequence in establishing a charge transfer in accordance with the trap assisted tunnelling (TAT). The TAT is dictated by the evolution of radiation induced traps that favor hole trapping due to a reduction in the barrier height [28]- [32], [49], [53], [54]. It effectively reduces the channel depletion as observed under the Source electrode at GaN top and graded AlGaN layers. In essence, it provides a leakage path from the GaN top layer to the positive graded AlGaN layers. Apart from these, the charge buildup in the insulator provides a leakage path, assisted by surface states on the GaN top and positive graded AlGaN layers, which is directly responsible for the increase in OFF -state leakage current (as shown in Fig. 5(a)).

C. SENSITIVITY ASSESSMENT
To analyze the sensitivity of the DUT towards the ionizing radiation, DC characteristics of the device has been extracted as a function of γ -Ray dose at each stage. The ON -state and OFF -state currents recorded at V GS = 3 V and V GS = −1 V, respectively, are shown in Fig. 8(a), while the peak transconductance is shown in Fig. 8(b). The choice for V GS = −1 V for OFF -state is taken in accordance with the saturation observed in OFF -state current (as observed from log scale in Fig. 5(a)). Further, V DS has been set at 0.5 V in lines with the TCAD calibrations (Fig. 4). In conjunction with the explanation provided in the previous section, the enhancement in ON -state current initially exhibits a fairly linear operation at a low dose, and eventually proceeds towards saturation with a higher dose. This is due to the saturation in the enhancement of the carrier mobilities and traps being annealed out due to the interaction with the energetic photons. The saturation in ON -state currents with increasing γ -Ray dose can also be linked with the fact that there is an incessant increase in the defect density with the γ -Ray dose. The increase in carrier mobilities is dominated primarily by the relaxation in film strain, increase in diffusion lengths, or active trap annealing for the lower doses. For the higher dose, however, the impurity scattering becomes dominant due to higher defect densities. This leads to the degradation of the carrier mobilities and hence the diffusion lengths. At this point, the contribution from the other factors discussed in the previous section, negate the effect of mobility degradation, as a result of which a saturation in the ON -state current is observed. A similar effect has been experimentally observed by Lee et al. [50], where a linear increase in diffusion lengths has been recorded for the low doses up to 200 Gy. This correlates well with the observed trend in I ON for the doses up to 1 kGy as shown in Fig. 8(a), which is eventually translated into g M(max) as shown in Fig. 8(b). A close observation into Fig. 8(a) demonstrates a linear increase in OFF -state current with γ -Ray doses above 1 kGy. Contour plots of electron concentration depicted in Fig. 6(d) at 10 kGy demonstrate the insulator's charge buildup that aids the reverse leakage To illustrate this, the evolution of leakage paths with different γ -dose through the device is shown in Fig. 9 (a)-(d) using conduction current density contours under pristine state and for different dose. It is evident from the contour plots of Fig. 9 (a)-(d), that, as the irradiation dose is increased from 2kGy to 8kGy, there is a prominent leakage path from the 3DEG housed by positive graded AlGaN layer towards the Source electrode as compared to the pristine state ( Fig. 9(a)). The leakage path is a consequence of the TAT and hopping mechanisms due to the available surface states along the sidewalls of the GaN top layer. As the dose increases, the carrier injection and carrier hopping become more significant, increasing the leakage area near the sidewalls of the GaN top layer, as shown in Fig. 9(d). This is in conjunction with the EHP driven by the electric fields, shown in Fig. 7(b). The leakage area is expected to get broader with the γ -Ray dose until the region reaches the Drain electrode. At this point, there will be a direct injection of the carriers between Source and Drain electrodes via the passivation layer, consequently resulting in a premature breakdown of the device. To sum up, the increase in I ON and I OFF recorded as a function of γ -Ray dose, for the said DUT can be exploited for dosimeter applications. The device exhibits linear characteristics with regards to the increase in I ON for γ -Ray doses up to 1 kGy. This points towards a higher sensitivity of the device towards the early detection of low dose γ -Rays. In addition to this, the device as observed also demonstrates a linear trend in I OFF with cumulative dose γ -Ray effects, pointing towards the compatibility of the DUT for the detection of high dose γ -Rays as well. Finally, a high stability of the resulting dosimeter can be established primarily due to the negligible shifts in the device threshold voltage even at a higher dose. As a consequence, the operating conditions of the dosimeter remains intact. In addition, experimental reports [54], [55] suggest the recovery of such irradiated samples post high temperature annealing process, which adds up to the stability of the DUT for dosimetry applications.

D. SENSITIVITY OPTIMIZATION USING GRADED PROFILES
The graded channel HEMTs have been observed to offer improved linearity and lower intermodulation distortion by tailoring their transconductance characteristics to achieve a broader profile [10]- [12]. This is in contrast to the fact that the grading may in fact be tailored by controlling the flow of trimethylgallium (TMG -Ga (CH 3 ) 3 ) and trimethylaluminum (TMAl -Al 2 (CH 3 ) 6 ) precursors during growth in an MOCVD Chamber. To this extent, there have been several reports that explore other grading profiles for various applications which include the square root [56] and parabolic grading [57] for improved linearity for LNA applications. Parabolic and S -graded (ERFC profile) buffer layers have also been used for reducing threading dislocations [58], [59] in various optoelectronic applications [60]. In this regard, the performance of such graded profiles is further explored for dosimetry based on the original structure. Venkatesan et al. [56] have demonstrated an improvement in the linearity performance of the device comes with a trade off in the drain current metrics. This trade off can be linked with the fact that the resulting electron profile in the channel (σ Channel ) is dependent upon the divergence of polarization field (P Pol ) along the growth direction, as dictated by Equation 3 [8], [9].
In this regard, a linear graded profile will render a uniform profile, and a parabolic grading will yield a linear variation of electron concentration across the entire AlGaN layer. Additionally, gaussian grading would result in electron concentration that follows 2x.e −x 2 , assuming the peak is centered at zero with a standard deviation of 1 √ 2 and S -shaped (i.e., erfc) would follow a 2.e −x 2 √ π variation.
Since the polarization field depends on the contributions from both the spontaneous and piezoelectric coefficients, the resulting profiles will be approximate [8], [9]. A depiction of the different grading profiles and the resulting electron concentrations is shown in Fig. 10(a) and Fig. 10(b), respectively, and agrees with Equation 3. These profiles are investigated for dosimetry under cumulative dose γ -Ray irradiation effects.
The effect of cumulative dose γ -Ray irradiation on the evolution of ON -and OFF -state drain current along with the impact on device transconductance for all the graded profiles (i.e. Parabolic, Gaussian, ERFC and Linear) is depicted in Fig. 11(a-c), respectively. A significant impact on the trends of ON -and OFF -state currents is observed with different graded profiles as shown in Fig. 11 (a-b). The trends of peak transconductance follow closely to that of ON -state current and gets saturated early from low dose γ -rays (Fig. 11(c)). As expected, all the profiles exhibit a similar trend in the I ON and I OFF with γ -Ray dose, and suggests the possibility of detecting low and high dose γ -Rays. The conduction paths for the parabolic profile for both ON -State and OFF -State conditions under linear variation is depicted in Fig. 12(a-b) and Fig. 12(c-d), respectively at a different dose.
As observed from Fig. 12(a-b) for low dose γ -Rays up to 1 kGy, the dominant path for the conduction current is through the formation of EAL at the sidewalls of the trench gate in the parabolic graded AlGaN and GaN top layers. As the dose increases, two conduction paths are observed (shown in Fig. 12(b)). One is due to a spillover and carrier injection from parabolic graded AlGaN into GaN top layer, which depletes the 2DHG. The other path is carved out in the passivation layer through the charge buildup, courtesy of the Compton electrons. However, the increase in defect densities limits the carrier diffusion lengths and the carrier mobilities, as discussed in the previous section. The increase in I ON thus gets saturated as the investigation proceeds towards a higher dose. However, in the OFF -state condition, a new dominant leakage path emerges out through the GaN top layer compared with the linear counterpart. This can be understood from the electron concentration plots compiled in Fig. 10(a). The peak in carrier concentration for parabolic graded profile occurs in the vicinity of the GaN top layer, which houses the 2DHG to realize enhancement mode operation. The carrier injection, in this case, aided by the TAT through the trapping states evolved in GaN top layer is dominant due to a spillover of the charge carriers into the GaN top layer. This eventually depletes the 2DHG at the region not covered by the Source electrode. As a consequence of this, a new conduction path in the OFF -state condition emerges (shown in Fig. 12 (c-d)) that aids the drain current (I OFF ) in the absence of EAL and presence of 2DHG at the trench gate and GaN top layers, respectively. A linear variation in I OFF is thus observed for the higher dose γ -Rays (shown in 11 (b)).
Current density contour plots recorded under ON -State and OFF -State conditions for low and high dose γ -Rays to investigate the conduction paths for gaussian graded AlGaN layer is shown in Fig 13 (a-d). Fig. 13(a-b) depicts the conduction paths under ON -State and low dose γ -Rays, and in Fig. 13(c-d) under OFF -State and high dose γ -Rays. The conduction paths under ON -State, as observed from  Fig. 13(a-b) are similar to the ones recorded for parabolic graded in Fig. 12(a-b), except that the spillover effect is not observed (as seen in Fig. 13(b)). However, under OFF -state conditions (in Fig. 13(c-d)), the EHP generation aided by the Compton electrons produced from high dose γ -Rays result in an excitation of electrons. Under the applied bias, this aids the charge spillover into the GaN top layer from the graded AlGaN layers. This charge sharing is again facilitated by the vicinity of peak electron concentrations near the GaN(top)/AlGaN interface (as depicted in Fig. 10(b)).
The contour plots of conduction current density depicting the current paths for the resulting DUT for ERFC graded AlGaN is depicted in Fig. 14 (a-d). The current paths for the ON -State biased device at a low dose as shown in Fig. 14(a-b) correspond to that of a linear graded AlGaN layer, except that the spread of 3DEG charge is limited compared to its linear counterpart. This correlates well with the electron concentration plots as a function of AlGaN depth depicted in Fig. 10(b). The dominant conduction path for ERFC graded AlGaN under low dose γ -Rays remains similar to the other profiles investigated. However, the conduction current through the passivation layer is negligible, identical to that of its linear counterpart. This is primarily due to the shift in peak electron concentration away from the GaN(top)/AlGaN interface (as depicted in Fig. 10(b)). Under OFF -State conditions, since, the peak in electron concentration is centered away from the interface, the spillover of excited electrons to the GaN top layer is not observed. As a result, the current leakage paths are similar to the linear profile shown in Fig. 9. As observed from Fig. 14(c-d), the dominant leakage paths in OFF -State (for ERFC graded AlGaN) have a dominant path due to the hopping from the available surface traps and the TAT through the trapping states that evolved under high dose γ -Rays.

E. COMPARISON OF SENSITIVITY TOWARDS γ -RAY DOSE
This section gives a numerical insight into the dosimeter sensitivity based on the different grading profiles investigated in the previous section. The analysis is divided into two parts, i.e. considering the best-case scenarios for detecting low dose and high dose γ -Rays. The sensitivity of the device to the γ -Ray dose can be modeled directly by recording the change in drain current with the cumulative γ -Ray dose at each stage. Mathematically, this can be represented by Equation 4.
where, S γ −Ray is the sensitivity of the device (in mA/mm/kGy) to the incident γ -Rays, I IrradiatedS2 and I IrradiatedS1 are the resulting currents (in mA/mm) post irradiation at doses (in kGy) D Stage2 and D Stage1 respectively. To evaluate sensitivity with respect to the pristine conditions, D Stage1 is set to 0 kGy to indicate pristine condition. On the basis of these, curve fitting techniques are used to evaluate the overall sensitivity of the device for the low and high dose γ -Rays. A comparison of all the profiles investigated for the early detection of low dose γ -Rays using I ON is depicted in Fig. 15(a), and for the detection of high dose γ -Rays using I OFF is shown in Fig. 15(b). The sensitivity metric dictated by Equation 4 and extracted from Fig. 15 (a) and (b) is compared for all the different profiles and summarized in Table 3.
A superficial look into Table 3 shows that the linear profile is best suited for detecting low dose γ -Rays. However, on investigating the Coefficient of Determination (R 2 Value) and Pearson's Correlation Coefficient (Pearson's R), it is revealed that the gaussian graded profile follows a more linear  approach towards the dosimetry. This is observed for the case of higher dose γ -Rays as well. For standalone dosimeters, the linear graded and gaussian graded profiles are best suited for detecting low and high dose γ -Rays, respectively. However, for generic dosimetry, for the detection of both low and high dose γ -Rays, gaussian graded profiles gives the best performance in terms of both the sensitivity to ionizing radiation and following a linear approach.  responsible for the enhanced sensitivity observed when irradiated at lower electric fields [61]- [65]. This phenomenon is commonly referred to as Enhanced Low Dose Rate Sensitivity (ELDRS) [61]- [65]. Accordingly, it is imperative to investigate the device under such environments and comment about its sensitivity capabilities. In this regard, the 3DEG HEMT as a dosimeter is further evaluated under different dose rate conditions as the radiation environment where the dosimeter is employed will be different. Accordingly, the best -case scenario identified in Section 3.5 is investigated under a 60 Co source with a dose rate of 0.07 rad/sec [28] and 50 rad/sec [29]. The sensitivity profiles of a gaussian graded 3DEG HEMT for the detection of low dose γ -Rays using I ON is depicted in Fig. 16(a), and for the detection of high dose γ -Rays using I OFF is shown in Fig. 16(b). The sensitivity metrics for the linear region are compiled in Table 4. A parallel shift in the trend of ON and OFF state currents with low and high dose γ -Rays are observed in Fig. 16(a) and Fig. 16(b), respectively, considering dose rates of 50 rad/sec and 0.07 rad/sec. This suggests that the dosimeter sensitivity is not significantly affected even with low and mid -range dose rates as compiled in Table 4. The slight change in sensitivity recorded for 50 rad/sec and 0.07 rad/sec is due to the spread of the annealing effect from the energetic photons which is significantly reduced due to the photon flux density at low dose rates [51], [66]. This will also lead to the early saturation observed in the OFF -state current at a low dose rate of 0.07 rad/sec and considering high dose γ -Rays as shown in Fig. 16 (b).
At a lower dose rate (0.07 rad/sec), a significant amount of time is required for irradiating the devices at a high dose of γ -Rays (for 6 kGy ∼ 100 Days at 0.07 rad/sec), during which the trapped carriers get emitted at various instances depending upon their time constants. As a consequence of this, early saturation is observed in OFF -state current from 6 kGy onwards, as depicted in Fig. 16(b). In this regard, the sensitivity metric for the detection of high dose γ -Rays at a lower dose rate (i.e., 0.07 rad/sec) corresponds to a range up to 6 kGy. Further, the R 2 Value and Pearson's R coefficient compiled in Table 4 remains close to unity, thereby validating the linearity of the 3DEG HEMT for dosimeter applications. Moreover, since the sensitivity metrics are not significantly affected at lower dose rates, it can be suggested that the ELDRS effect is not observed in the device under test. This is also in agreement with the experimental results reported by Jiang et al. [28] which evinces that such an effect is due to the high electric field exhibited by GaN devices compared to the bipolar base oxides [64], [65]. Since the interaction between the radiation induced traps with the electron/hole/proton transport (which dictates ELDRS effect) is fundamentally different in crystalline wide -bandgap GaN compared to amorphous SiO 2 [28], [63], and due to the strong bonding nature of III -V binary and ternary nitrides [21]- [24], the ELDRS effect is not prominent in such devices.

IV. CONCLUSION
A HEMT device architecture exhibiting positive and negative graded AlGaN layers supporting 3DEG for conduction and 3DHG for back barrier is investigated for dosimeter applications. The key takeaway points from the detailed analysis are as follows. The linear variation recorded in I ON with γ -Ray irradiation validates the device architecture for the early detection of low dose γ -Rays. The device architecture, as investigated, exhibits a linear variation in I OFF for the detection of high dose γ -Rays as well. The negligible shift observed in the device threshold voltage even for higher dose γ -Rays validates the stability of the operating conditions for the proposed dosimetry. A detailed physical insight towards the irradiation effects on the device has been presented with the validation from the experimental sources to establish the device for stable dosimeter applications. Finally, the sensitivity of the device has been optimized by investigating different grading profiles for the best-case scenarios. On that account, the gaussian graded profile has been identified as the bestcase scenario regarding the sensitivity and exhibiting a linear operation.