Threshold voltage mapping at the nanoscale of GaN-based high electron mobility transistor structures using hyperspectral scanning capacitance microscopy

Hyperspectral scanning capacitance microscopy (SCM) measures dC / dV − V spectra at every XY location of a semi-conductor sample surface area. We report its application to GaN-based HEMT structures to map threshold voltage ( V th ) at the nanoscale. The consistency between the conventional SCM data and the hyperspectral SCM data set of the same area on the HEMT surface provides evidence for the reliability of hyperspectral SCM. We developed a method to extract a map of V th distribution across the surface of the HEMT structure at the nanoscale from the hyperspectral SCM data set. The map reveals that most of the fissures (i.e., enlarged pits formed at threading dislocation surface endings) on the nitride sample surface reduce local V th . Other variations in V th in regions free of the fissures could be a result of thickness and/or composition inhomogeneities in the Al x Ga 1 − x N barrier layer. Conventional SCM and other techniques cannot provide these detailed insights obtained through hyperspectral SCM.

GaN-based high electron mobility transistors (HEMTs) have a wide range of important applications, including highpower switching 1,2 and radio frequency (RF) 3 applications.Currently the lateral dimensions of GaN-based HEMTs are being decreased down to the sub 100 nm scale to enable ultrafast performance 4,5 .The threshold voltage (V th ) of a GaNbased HEMT is a measurement of the gate voltage required to turn it off.Uniformity and reproducibility of V th at the nanoscale are critical in small-scale devices.For example, even with the application of reproducible processing steps, regions with different V th will lead to variations in the properties of HEMTs fabricated from the same wafer.As a result, mapping V th distribution of the HEMT structure at the nanoscale becomes increasingly important.However, there is no standard method for such V th mapping to date.Although Schaadt et al 6 mapped lateral variations in V th in a HEMT structure using scanning capacitance spectroscopy (SCS), the technique is unable to correlate V th changes to specific nanoscale features.Herein, we report the mapping of V th at the nanoscale by applying hyperspectral scanning capacitance microscopy (SCM) to GaN-based HEMT structures and establish a direct correlation between nanoscale features and local V th by employing a multi-microscopy 7 approach.
SCM is an atomic force microscopy (AFM)-based technique for characterisation of the local carrier density and type near the surface of semiconductors 8 .Individual local dC/dV − V spectra can be collected using SCS mode in SCM 9 .In conventional SCM, surface topography, a dC/dV amplitude map (measured using the output, in mV, of an ultrahigh-frequency resonant capacitance sensor 10 ), and a dC/dV phase map are acquired simultaneously so that the surface features and local electrical properties can be directly correlated.However, conventional SCM has a limitation in that the entire image is scanned at a single dc bias, which may not be the appropriate bias to deplete a HEMT sample in all locations.To investigate the impact of the features on a sample surface, the dc bias needs to be optimised 11 .The optimisation that we have previously documented 11 is based on manually performing SCS measurements at certain positions on the sample surface.It is impractical to do this at each position at the nanoscale.
Hyperspectral SCM addresses this issue, giving additional insights into structure or device properties 12 .It measures local dC/dV − V spectra at every XY location, producing an integrated 3D data set.Instead of employing contact mode, spectrum acquisition is embedded in the hold segment of a force curve that is part of a map captured in fast force volume (FFV) mode 13 .As shown in Fig. 1, a conductive tip approaches the surface at each pixel in the image, then contacts the surface for a short period (the 'hold segment') while an ac bias sweeps the whole range of increasing dc biases to collect the dC/dV amplitude response, after which the tip is retracted and moves to the neighboring pixel to repeat the same process.This is in contrast to conventional SCS, which is operated with the microscope in contact mode, so that large shear forces may arise during attempts to map dC/dV − V spectra across the sample.This can damage the tip and lead to inconsistent performance between dC/dV − V spectra making data difficult or impossible to interpret.To reach nanoscale resolution, it is also important that the pixel size is small enough that the depletion region achieved at the tip extends beyond the edges of the pixel.(We note here that for a blunt tip the radius of the depletion region below the tip is approximately equal to the radius of the tip-sample contact area 14 ).Otherwise, nanoscale features may be so small that they can be easily missed in the gap between two neighboring pixels 6,15 .
Hyperspectral SCM has three main advantages over conventional SCM.First, both topography and a set of dC/dV −V spectra are acquired simultaneously, so any of the spectra can be selected, displayed, and exported through single or multiple point(s) selection at any region of interest for further comparison and analysis.Second, the data set can generate all slices of dC/dV amplitude contrast at all the dc biases, which can highlight the evolution of the dC/dV amplitude contrast with the changing dc bias.Third, the dC/dV − V spectrum at each pixel can be further analysed to calculate the value of a specific physical parameter at that pixel, and hence a new map of the physical parameter is generated, providing more insights.
Our HEMT structure was grown on a Si (111) substrate by metal organic vapor-phase epitaxy (MOVPE).The epitaxial structure is similar to that described elsewhere 11 in terms of the buffer structure and the GaN channel.The barrier structure of the HEMT in this case does not include a GaN cap but consists of a 13 nm-thick AlGaN barrier including a nominally 1nm-thick AlN exclusion layer, as measured by high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) (see supplementary material).The AlN fraction of the barrier is estimated as 31% based on calibration data from AlGaN structures grown on sapphire.Furthermore, there are three differences regarding sample fab-rication and experimental setup compared to those described in reference 11 .First, conventional metal-stack Ohmic contacts on GaN-based HEMTs require annealing at temperatures up to 850 °C, which can adversely affect material properties 16 .So, here, according to an alternative method described in 16 , scratches were first scribed on the sample surface and then filled with indium metal from a soldering iron to fabricate Ohmic contacts.The depth of the scratches was carefully controlled so that the indium metal directly contacted the twodimensional electron gas (2DEG) layer near the surface but did not reach the conductive Si substrate (see supplementary material).This avoids complications in data interpretation that may arise from applying a bias across multiple heterointerfaces in the epitaxial structure.Also, as the Ohmic contact is directly connected to the 2DEG, charging effects during the electrical characterisations 17 are avoided.Second, the employed Adama AD-450-AS TM tip was milled before being used to perform conventional and hyperspectral SCM measurements so that the tip radius is bigger than the initial 10 nm and strong electrical signals can be achieved 14 .The tip was milled in-situ by scanning it across a 10 µm × 10 µm area of the sample surface in contact mode multiple times, with an increased deflection setpoint and a faster scan rate compared to those used during V th imaging.SCS measurement was performed after each complete scan of the area.This tip-milling procedure was stopped once the peak height of the collected dC/dV −V spectra reached 200 mV.Third, when performing hyperspectral SCM measurements, the tip scanned the sample in FFV mode instead of in contact mode.
However, there is a trade-off between topographical resolution and electrical signals.A blunt conductive tip can provide strong electrical signals 14 but the topographical resolution is sacrificed.Therefore, a multi-microscopy 7 approach was employed to solve this dilemma.The sample was first scanned in PeakForce Tapping TM mode using a sharp Bruker ScanAsyst-Air TM tip with a nominal radius of 2 nm to achieve a high-resolution topographical image.Then, we changed to a milled Adama AD-450-AS TM tip and scanned the same area to perform conventional SCM and hyperspectral SCM measurements with strong electrical signals (We note that the tip should not be milled to such an extent that it is larger than the electrical features of interest).Eventually, both highresolution topographical images and strong conventional & hyperspectral SCM signals are achieved for the same area, allowing a direct correlation between surface features and local electrical properties.The detailed method of identifying the same area in each technique is described in the supplementary material.In practice, hyperspectral SCM measurement was done first, followed by conventional SCM measurement.However, here, for easier presentation of the data, the conventional SCM data will be presented before the hyperspectral SCM data.
The hyperspectral SCM measurement was performed in DCUBE-SCM mode using a Bruker Dimension Icon Pro AFM coupled with a Bruker SCM module.It was taken at room temperature using a 90 kHz ac bias and a 990 MHz capacitance sensor.128 pixels × 128 pixels were collected in an 1 µm × 1 µm area on the sample surface.The detailed method of choosing pixel size is described in the supplementary material.At each pixel, a 1 V ac bias swept a dc bias range from 0 V to 8.2 V. Collecting one dC/dV − V spectrum at each pixel takes about one second.Thus, to record the hyperspec-tral SCM data set presented here took about 5 hours.
A high-resolution topographical image of the sample surface was captured in PeakForce Tapping TM mode (Fig. 2 (a)), showing nanoscale fissures (of length 60 -100 nm, and width 25 -40 nm) that have been previously reported in similar Al-GaN/GaN heterostructures 18 .However, the impact of fissures on local V th has previously not been fully understood, and this topic is investigated using conventional and hyperspectral SCM in this letter.The same area was subsequently scanned in conventional SCM mode and hyperspectral SCM mode and their topographical images are shown in Fig. 2 (b) and (c) respectively.Matching of the broad features in the three topographic images in Fig. 2 confirms that the same area was scanned in the three different modes.
Two positions of interest are marked in the three images in Fig. 2: a measurement point on a fissure ('f') and another on a non-fissure region ('n') are indicated by a yellow dot and a blue dot respectively.The test conditions for the local dC/dV − V spectra measurements using SCS mode are the same for both positions, with a 1.6 V ac bias sweeping the same range of the dc biases from 0 V to 8.2 V.The two resulting dC/dV − V spectra are shown in Fig. 3 (a).It can be seen that there is a peak shift towards negative voltage in the fissure position ('f') relative to the non-fissure position ('n').A shift in the peak position in the corresponding dC/dV − V spectrum indicates a difference in V th 11 .Here, it indicates that the fissure position ('f') has a smaller V th than the non-fissure position ('n').
Based on the dC/dV − V spectra in Fig. 3 (a), the optimisation of dc bias for mapping conventional SCM dC/dV amplitude contrast of the HEMT sample was performed subsequently.The optimum dc bias values were determined as 2.6 V and 3.8 V and the corresponding dC/dV amplitude images are shown in Fig. 4 (a) and (b).The regions with fissures appear bright in the dC/dV amplitude image at the lower dc bias (Fig. 4 (a)) while dark at the higher dc bias (Fig. 4

(b)).
There is contrast inversion between the two corresponding dC/dV amplitude images which is typical for HEMT structures, as we reported previously 11 .The same area was scanned in hyperspectral SCM mode.The local dC/dV − V spectra of the same two positions of interest (labelled as 'f' and 'n' in Fig. 2) are extracted and plotted in Fig. 3 (b).We observed that peaks in hyperspectral SCM are consistently stronger than those in SCS which we very tentatively attribute to differences in the tip-sample contact force in the two modes.However, the relation between the dC/dV − V spectra captured on and off the fissure is consistent in both SCS and hyperspectral SCM measurements (Fig. 3).Besides, two dC/dV − V amplitude slices at the fixed dc biases 2.5 V and 4.6 V from the hyperspectral SCM data set are extracted and shown in Fig. 4 (c) and (d) respectively.Changes in the appropriate dc bias ranges between the two experiments are attributed to increasing tip wear particularly during the conventional SCM optimisation.However, the contrast of the dC/dV amplitude slices from the hyperspectral SCM data set is consistent with the contrast of the conventional SCM images at both lower and higher dc biases (Fig. 4).The contrast inversion observed in these images between low and high dc bias is explained in reference 11 .These observations suggest that the hyperspectral SCM data are reliable.
The hyperspectral SCM data set was further processed to map the V th distribution in the HEMT at the nanoscale.Hyperspy 19 was used for the relevant data analysis.First, we manually estimate the approximate peak position range, peak intensity range, and full width at half maximum (FWHM) range of the dC/dV −V spectra in the data set, and then input them into the program.Then, as shown in Fig. 5 (a), the local dC/dV − V spectrum captured in hyperspectral SCM mode is fitted to determine the peak position which is defined as the local V th value.After fitting each dC/dV −V spectrum at each pixel, a map of local V th distribution at the nanoscale is achieved (Fig. 5 (b)).Change in peak width and peak height from pixel to pixel is also noticed in our data, as reported previously by Schaadt et al 15 .The origin of the change is still under investigation.Here, we focus on the peak position to generate the V th map.
The position of fissures determined from Fig. 2 are highlighted in the dC/dV amplitude images (Fig. 4) and the local V th map (Fig. 5) of the same area.As all the images are in nanoscale resolution, the nanoscale fissures can be directly correlated to their local dC/dV amplitude contrast and local V th so that the impact of the fissures on the local electrical properties can be conveniently examined.In the nanoscale V th map (Fig. 5 (b)), most of the regions with fissures have a local V th value lower than the averaged V th value of 3.74 ± 0.16 V of the whole area.It also shows V th variation in non-fissure regions (e.g., the area surrounded by red dotted lines).
The data in Fig. 2 (b) show that the tip size of the milled tip is sufficiently small to allow imaging of most of the fissures.The electrical features observed in SCM (Fig. 4 and Fig. 5 (b)) are larger in lateral extent than the topographic features.Hence, the tip-sample contact area is smaller than the lateral extent of the electrical feature.This is true even when the topographic fissure size is smaller than the probe.Thus, although there will be some impact of the finite tip size on the reliability of the measurement, the errors should be fairly small.The 2DEG layer is located at a depth of about 14 nm below the sample surface while the AFM-measured depth of the fissures is about 2 nm (Fig. 2 (a)), so the fissures do not penetrate through the entire barrier layer.Transmission electron microscopy (TEM) measurement of the fissures also confirmed that they end within the barrier layer (data is shown in supplementary material).Hence, it can be concluded that most of the surface fissures locally reduce the V th .Fissure formation has been linked to threading dislocations (TDs) 18 .Typical examples are the arrays of fissures shown in Fig. 2 (a).The segregation of unintentional impurities such as oxygen to the cores of dislocations in GaN may make the dislocations negatively charged 20 .In the case of GaN-based HEMTs, negatively charged dislocations can result in local depletion of 2DEG.Schaadt et al 6 suggested this could cause a shift in V th near the dislocations.Hence, more generally, GaN-based HEMTs with TD-related defects may suffer from lower local V th at the defects, which requires further investigation.Another potential reason for the lower V th at the fissures could be the reduced local strain and hence reduced local 2DEG sheet carrier density resulting from strain relaxation by the fissures.
The V th variation in non-fissure regions may indicate thickness or Al content inhomogeneity in the Al x Ga 1−x N barrier layer 6,21,22 .Using a theoretical expression for the relation between a change in threshold voltage ∆V th and a change in barrier thickness ∆d for an Al x Ga 1−x N barrier layer 6 , we found that a thickness change of about 1 nm can result in a threshold voltage shift of about 0.31 V for our sample with a 13 nm thick Al 0.31 Ga 0.69 N barrier layer.We also calculated that an Al content variation ∆x ≈ 0.06 in the Al 0.31 Ga 0.69 N barrier layer would yield ∆V th comparable to that of a 1 nm thickness variation in our case.Therefore, based on the nanoscale V th map, local thickness or Al content variation in the non-fissure regions of the Al 0.31 Ga 0.69 N barrier layer can be estimated.The average V th value for a 39 nm × 39 nm area (5 pixels × 5 pixels) at the fissure 'f' in Fig. 5 (b) is 3.44 ± 0.11 V. Similarly, the average V th values for the two non-fissure regions 'n 1 ' and 'n 2 ' in Fig. 5 (b) are 3.92 ± 0.02 V and 3.68 ± 0.10 V, respectively.The V th shift between the two non-fissure regions 'n 1 ' and 'n 2 ' is about 0.24 V which corresponds to barrier thickness variation of about 0.8 nm or Al content variation of about 0.05 (or a combination of both).The V th difference between the fissure ('f') and the non-fissure region ('n 1 ') is about 0.48 V. Hence, both fissures and barrier inhomogeneities could be obstacles to a uniform and reproducible V th distribution for all nanoscale HEMTs in large-scale wafers.Nanoscale HEMTs with gate contacts on or off fissured regions may therefore show different V th values.
In conclusion, we applied hyperspectral SCM to GaNbased HEMT structures to map V th at the nanoscale.The reliability of the hyperspectral SCM data set is illustrated by the consistency of dC/dV −V spectra and dC/dV amplitude contrast between the conventional SCM data and the hyperspectral SCM data set of the same area on the HEMT surface.We have devised an approach for visualising the V th distribution in the HEMT at the nanoscale through the in-depth analysis of the hyperspectral SCM data set.The V th map indicates that the majority of fissures result in a decrease in the local V th .Additionally, variations in V th within non-fissure regions may stem from inhomogeneities in the thickness and/or Al content within the Al x Ga 1−x N barrier layer.The inhomogeneities can be further quantified based on the local V th difference in the non-fissure regions.Such detailed insights obtained by hyperspectral SCM can not be provided by conventional SCM or other techniques.Hence, this approach can allow researchers developing growth protocols for nanoscale HEMTs to identify which defects lead to the most substantial changes in V th .This will facilitate intelligent decision-making in the optimisation of epitaxial growth.

FIG. 1 .
FIG. 1.The working principle of hyperspectral SCM: (a) schematic of scan pattern during the acquisition of hyperspectral SCM data 12 .Reproduced with permission from Microscopy Today 26 (6), 18-27 (2018).Copyright 2018, Microscopy Society of America.(b) patterns of the input dc bias (red) and the corresponding output dC/dV amplitude (blue) in the hold segment.

FIG. 2 .
FIG. 2. Topographic images of the same area on the HEMT surface captured (a) using a sharp Bruker ScanAsyst-Air TM tip in PeakForce Tapping TM mode, (b) using a milled Adama AD-450-AS TM tip in conventional SCM mode, and (c) in hyperspectral SCM mode.The broad features marked with red arrows match each other in the three images, indicating that the same area was scanned.All the fissures are highlighted in yellow in image (a).Corresponding locations of a fissure ('f') and a non-fissure region ('n') in the images are indicated by a yellow dot and a blue dot respectively.

FIG. 4 .
FIG. 4. dC/dV amplitude images of the same area in Fig. 2. (a) and (b) were captured in conventional SCM mode at ac bias value of 1.6 V with dc bias value of 2.6 V (on the left flank of the peaks in Fig. 3 (a)) and 3.8 V (on the right flank of the peaks in Fig. 3 (a)) respectively.(c) and (d) were sliced from the hyperspectral SCM data set at the dc bias value of 2.5 V (on the left flank of the peaks in Fig. 3 (b)) and 4.6 V (on the right flank of the peaks in Fig. 3 (b)) respectively.The position of all the fissures is highlighted in yellow.

FIG. 5 .
FIG. 5. (a) Determination of local V th value by fitting the raw data of a local dC/dV − V spectrum captured in hyperspectral SCM mode.Local V th value is defined as the peak position.(b) V th distribution of the same area in Fig. 2 after fitting each dC/dV − V spectrum at each pixel.Fissures are highlighted in yellow.The V th variation in non-fissure regions is highlighted in red.A fissure ('f') and two non-fissure regions ('n 1 ' and 'n 2 ') are labelled.