Piezoelectric charge densities in AlGaN/GaN HFETs. Asbeck, P M, Yu, E T, Lau, S S, Sullivan, G J, Hove, J V., & Redwing, J Electronics Letters, 33(14):1230–1231, July, 1997.
doi  abstract   bibtex   
Indexing terms: Microwave power transistors, Gallium nitride, Field effect transistors New estimates of the piezoelectric charge density at (0001) AlGaN/ GaN interfaces are provided. Undoped HFET structures grown by both MBE and MOCVD, on sapphire and SiC substrates, exhibit electron densities of ~5 × 10 13 cm-2 · x A L (where x A L is the aluminium mol fraction in the AlGaN), which can be attributed to piezoelectric effects. These have a significant influence on the design and behaviour of III-V nitride HFETs. Introduction: Heterostructure field-effect transistors (HFETs) based on the AlGaN/GaN system have recently been shown to be very attractive candidates for high voltage, high power amplification at frequencies well into the microwave region [1-4]. The behaviour of these devices is under intense investigation. It has previously been shown that the nitrides have appreciable piezoelectric coefficients, and that on (0001) faces of the wurtzite structures typically used to form HFETs, electric polarisation should occur, resulting in potentially large charge densities and associated electric fields [5, 6]. In this Letter, we report new estimates of the magnitude of these charge densities and detail a number of their expected effects on HFET characteristics. Analysis: A representative FET layer structure consists of a 50nm layer of AlGaN, on top of a 3 µ m layer of GaN, deposited on a sub-strate of sapphire or SiC. Appreciable 2D electron gas (2-DEG) densities are found at the AlGaN/GaN interface, even if all the layers are grown without intentional doping [7]. The layers are usually under stress due to either a lattice mismatch between epitaxial layers of different alloy compositions, or a thermal expansion mismatch between the epitaxial layers and the substrate (which may be partially or entirely relaxed). There is, in particular, a large amount of strain at the AlGaN/GaN interface, due to the difference in lattice constants between these two materials (2.4% difference between AlN and GaN at room temperature). The biaxial stress and strain associated with the lattice mismatches generates a piezolectric polarisation P Z (where the z axis lies along the [0001] direction, normal to the HFET surface), given by [5] Here, d 31 is the piezoelectric strain ceofficient for AlGaN, c IJ are the elastic stiffness coefficients, and ε XX is the strain in the x direction (taken to be equal to ε YY. The electrical effects of the polarisation can be determined by considering that there is a piezoelectrically-induced charge density Q PZ = qN PZ = div P. At the interface between pseudomorphically-grown AlGaN and GaN, there is a change in strain (and stress) because of the difference in lattice-constants. Correspondingly , there is a piezoelectric positive (donor-like) charge density due to the difference between the polarisations within the AIGaN and the GaN. The magnitude of the interfacial charge density is essentially independent of the level of strain common to both AlGaN and GaN (assuming equal piezoelectric coefficients for the two materials), and thus is independent of the details of the sub-strate, buffer and sample bending. At the top of the AlGaN layer (and, possibly, at the bottom of the GaN layer) there will be negative (acceptor-like) PZ charge densities. The PZ charge density at the AlGaN/GaN interface will be largely compensated for by electrons that form a 2D electron gas at the interface; charge at the top of the AlGaN will be compensated for by either charged surface states for a free surface, or carriers in the metal layer for a metal contact. A schematic, approximate, band diagram of the resulting undoped AlGaN/GaN interface is shown in Fig. 1, along with a schematic representation of the charge densities. The sign of the piezoelectric charges is dependent on the crystal orientation. GaN and AlGaN layers grown by MBE and MOCVD typically grow in (0001) directions, that is, with the A (or Ga) face at the surface [8]. According to eqn. 1, and the value of d 31 =-2 × 10-10 cm/V for AlN given in [9], donor-like PZ charges result at the AlGaN/GaN interfaces (although this assignment differs from [5, 6]). Polarisation is directed from the A face to the B face (as is the case in CdS, which also forms in the wurtzite structure and has d 31 \textless 0 [9]). For crystals grown on (000_1) or B faces, an opposite sign of charge is expected. The density of electrons in the 2-DEG at the interface departs somewhat from the piezoelectrically-induced (PZ) donor density N PZ , because a net charge density is required to terminate the electric field in the AlGaN layer. This electric field is fixed by the potential drop in the AlGaN determined by the fermi level positions at the surface and at the interface. We find that the 2-DEG density is given by Here, N PZ , the PZ donor density at the interface, is given by N PZ = (P 1 Z-P 2 Z)/ q. C B is the geometric capacitance associated with the AlGaN layer of thickness h B (C B = ε / h B); φ S is the depth of the fermi level at the AlGaN surface with respect to its conduction band edge, ∆ E C is the conduction band offset between AlGaN and GaN (in the given strained condition), and ε FN is the height of the fermi level above the conduction band in the GaN (which is a function of N S). P 1 Z and P 2 Z are the polarisations in the AlGaN and the GaN, associated with the strains ε XX 1 and ε XX 2 in the two materials, respectively. Assuming a coherent interface between the layers, by Vegards law, we expect ε XX 1-ε XX 2 is proportional to the aluminium mol fraction of the AlGaN layer. Thus, N PZ is approximately proportional to x A L. In general, however, d 31 may vary with x A L (and probably increases in magnitude as the aluminium content rises). Experimental results: In Fig. 2 the measured sheet carrier concentrations N S are shown against x A L in AlGaN/GaN HFET structures grown without intentional doping. These data were obtained from Hall measurements on structures with free surfaces. The data include reported values for MOCVD [7], as well as for MBE growth (shown here for the first time). The results of the two growth methods agree well, and indicate a value of N S that rises approximately linearly with x A L , following dN S / dx A L = 5 × 10 13 cm-2. This slope may rise slightly for increasing x A L. The results for both sapphire sub-strates and SiC coincide closely. Fig. 1 Band diagram and schematic doping density resulting from piezoe-lectric charge density Fig. 2 Experimental values of N S against x AL for various undoped MBE-and MOCVD-grown AlGaN/GaN HFET structures q MOCVD grown MBE grown Discussion: The origin of the charges in these undoped FETs has not yet been identified [7]. The assignment of the observed charge densities to the 'piezoelectric doping' described here is more plausible than assuming that there are residual impurities in the GaN or AlGaN. It has been reported that samples of GaN or AlGaN grown individually have resulted in low doping levels. Also, Fig. 2 shows the essential equivalence of MBE and MOCVD-grown materials, which may be expected to have different residual doping levels. In accordance with eqn. 2, the electron density at the interface for a given value of x A L is expected to vary somewhat as a function of thickness of the AlGaN layer, and the overall value of N S is expected to be lower than N PZ The data suggest that the difference N PZ-N S is relatively small. This may correspond to the fact that the electric field in the AlGaN layer is small. The experimental value of dN S / dx A L obtained by fitting the data of Fig. 2 is larger, by a factor of 1.8, than the corresponding value estimated by Martin et al. based on published values of piezoelectric coefficients [6]. To make the earlier estimates, an interpolation had been necessary in order to arrive at an estimate for d 31 of GaN. The bowing of the curve of N S against x A L suggests that d 31 increases with x A L. The dominance of PZ charge densities has numerous consequences for the HFET design. Although the PZ charge exists at the plane of the heterojunction, it is not expected to degrade the mobility of the 2-DEG, because the PZ charge is very uniformly distributed (with every atom at the heterojunction having a small amount of strain-induced charge) unless substantial interface roughness is present. Recessing the Schottky gate region produces only a minor effect on the threshold voltage (since N S varies only slowly with h B). Reducing the AlGaN thickness in the source and drain ohmic contact regions can assist in producing ohmic contacts, but etching it away completely can eliminate the conductivity in the underlying GaN. Also, buffer layers of AlGaN beneath a thin conducting channel produce distortions of carrier densities in the channel, due to the PZ charges at their interfaces. The extremely strong influence of PZ effects on device behaviour suggests numerous additional possibilities for design and optimisation of III-V nitride devices. Conclusion: We have shown that, through the PZ effect, donor-like charge densities of the order of 5 × 10 13 cm-2 · x A L are produced at pseudomorphic AlGaN/GaN interfaces. The existence of the piezoe-lectric charges provides an insight into the relative performances of various HFET structures.
@article{asbeck_piezoelectric_1997,
	title = {Piezoelectric charge densities in {AlGaN}/{GaN} {HFETs}},
	volume = {33},
	doi = {10.1049/el:19970843},
	abstract = {Indexing terms: Microwave power transistors, Gallium nitride, Field effect transistors New estimates of the piezoelectric charge density at (0001) AlGaN/ GaN interfaces are provided. Undoped HFET structures grown by both MBE and MOCVD, on sapphire and SiC substrates, exhibit electron densities of {\textasciitilde}5 × 10 13 cm-2 · x A L (where x A L is the aluminium mol fraction in the AlGaN), which can be attributed to piezoelectric effects. These have a significant influence on the design and behaviour of III-V nitride HFETs. Introduction: Heterostructure field-effect transistors (HFETs) based on the AlGaN/GaN system have recently been shown to be very attractive candidates for high voltage, high power amplification at frequencies well into the microwave region [1-4]. The behaviour of these devices is under intense investigation. It has previously been shown that the nitrides have appreciable piezoelectric coefficients, and that on (0001) faces of the wurtzite structures typically used to form HFETs, electric polarisation should occur, resulting in potentially large charge densities and associated electric fields [5, 6]. In this Letter, we report new estimates of the magnitude of these charge densities and detail a number of their expected effects on HFET characteristics. Analysis: A representative FET layer structure consists of a 50nm layer of AlGaN, on top of a 3 µ m layer of GaN, deposited on a sub-strate of sapphire or SiC. Appreciable 2D electron gas (2-DEG) densities are found at the AlGaN/GaN interface, even if all the layers are grown without intentional doping [7]. The layers are usually under stress due to either a lattice mismatch between epitaxial layers of different alloy compositions, or a thermal expansion mismatch between the epitaxial layers and the substrate (which may be partially or entirely relaxed). There is, in particular, a large amount of strain at the AlGaN/GaN interface, due to the difference in lattice constants between these two materials (2.4\% difference between AlN and GaN at room temperature). The biaxial stress and strain associated with the lattice mismatches generates a piezolectric polarisation P Z (where the z axis lies along the [0001] direction, normal to the HFET surface), given by [5] Here, d 31 is the piezoelectric strain ceofficient for AlGaN, c IJ are the elastic stiffness coefficients, and ε XX is the strain in the x direction (taken to be equal to ε YY. The electrical effects of the polarisation can be determined by considering that there is a piezoelectrically-induced charge density Q PZ = qN PZ = div P. At the interface between pseudomorphically-grown AlGaN and GaN, there is a change in strain (and stress) because of the difference in lattice-constants. Correspondingly , there is a piezoelectric positive (donor-like) charge density due to the difference between the polarisations within the AIGaN and the GaN. The magnitude of the interfacial charge density is essentially independent of the level of strain common to both AlGaN and GaN (assuming equal piezoelectric coefficients for the two materials), and thus is independent of the details of the sub-strate, buffer and sample bending. At the top of the AlGaN layer (and, possibly, at the bottom of the GaN layer) there will be negative (acceptor-like) PZ charge densities. The PZ charge density at the AlGaN/GaN interface will be largely compensated for by electrons that form a 2D electron gas at the interface; charge at the top of the AlGaN will be compensated for by either charged surface states for a free surface, or carriers in the metal layer for a metal contact. A schematic, approximate, band diagram of the resulting undoped AlGaN/GaN interface is shown in Fig. 1, along with a schematic representation of the charge densities. The sign of the piezoelectric charges is dependent on the crystal orientation. GaN and AlGaN layers grown by MBE and MOCVD typically grow in (0001) directions, that is, with the A (or Ga) face at the surface [8]. According to eqn. 1, and the value of d 31 =-2 × 10-10 cm/V for AlN given in [9], donor-like PZ charges result at the AlGaN/GaN interfaces (although this assignment differs from [5, 6]). Polarisation is directed from the A face to the B face (as is the case in CdS, which also forms in the wurtzite structure and has d 31 {\textless} 0 [9]). For crystals grown on (000\_1) or B faces, an opposite sign of charge is expected. The density of electrons in the 2-DEG at the interface departs somewhat from the piezoelectrically-induced (PZ) donor density N PZ , because a net charge density is required to terminate the electric field in the AlGaN layer. This electric field is fixed by the potential drop in the AlGaN determined by the fermi level positions at the surface and at the interface. We find that the 2-DEG density is given by Here, N PZ , the PZ donor density at the interface, is given by N PZ = (P 1 Z-P 2 Z)/ q. C B is the geometric capacitance associated with the AlGaN layer of thickness h B (C B = ε / h B); φ S is the depth of the fermi level at the AlGaN surface with respect to its conduction band edge, ∆ E C is the conduction band offset between AlGaN and GaN (in the given strained condition), and ε FN is the height of the fermi level above the conduction band in the GaN (which is a function of N S). P 1 Z and P 2 Z are the polarisations in the AlGaN and the GaN, associated with the strains ε XX 1 and ε XX 2 in the two materials, respectively. Assuming a coherent interface between the layers, by Vegards law, we expect ε XX 1-ε XX 2 is proportional to the aluminium mol fraction of the AlGaN layer. Thus, N PZ is approximately proportional to x A L. In general, however, d 31 may vary with x A L (and probably increases in magnitude as the aluminium content rises). Experimental results: In Fig. 2 the measured sheet carrier concentrations N S are shown against x A L in AlGaN/GaN HFET structures grown without intentional doping. These data were obtained from Hall measurements on structures with free surfaces. The data include reported values for MOCVD [7], as well as for MBE growth (shown here for the first time). The results of the two growth methods agree well, and indicate a value of N S that rises approximately linearly with x A L , following dN S / dx A L = 5 × 10 13 cm-2. This slope may rise slightly for increasing x A L. The results for both sapphire sub-strates and SiC coincide closely. Fig. 1 Band diagram and schematic doping density resulting from piezoe-lectric charge density Fig. 2 Experimental values of N S against x AL for various undoped MBE-and MOCVD-grown AlGaN/GaN HFET structures q MOCVD grown MBE grown Discussion: The origin of the charges in these undoped FETs has not yet been identified [7]. The assignment of the observed charge densities to the 'piezoelectric doping' described here is more plausible than assuming that there are residual impurities in the GaN or AlGaN. It has been reported that samples of GaN or AlGaN grown individually have resulted in low doping levels. Also, Fig. 2 shows the essential equivalence of MBE and MOCVD-grown materials, which may be expected to have different residual doping levels. In accordance with eqn. 2, the electron density at the interface for a given value of x A L is expected to vary somewhat as a function of thickness of the AlGaN layer, and the overall value of N S is expected to be lower than N PZ The data suggest that the difference N PZ-N S is relatively small. This may correspond to the fact that the electric field in the AlGaN layer is small. The experimental value of dN S / dx A L obtained by fitting the data of Fig. 2 is larger, by a factor of 1.8, than the corresponding value estimated by Martin et al. based on published values of piezoelectric coefficients [6]. To make the earlier estimates, an interpolation had been necessary in order to arrive at an estimate for d 31 of GaN. The bowing of the curve of N S against x A L suggests that d 31 increases with x A L. The dominance of PZ charge densities has numerous consequences for the HFET design. Although the PZ charge exists at the plane of the heterojunction, it is not expected to degrade the mobility of the 2-DEG, because the PZ charge is very uniformly distributed (with every atom at the heterojunction having a small amount of strain-induced charge) unless substantial interface roughness is present. Recessing the Schottky gate region produces only a minor effect on the threshold voltage (since N S varies only slowly with h B). Reducing the AlGaN thickness in the source and drain ohmic contact regions can assist in producing ohmic contacts, but etching it away completely can eliminate the conductivity in the underlying GaN. Also, buffer layers of AlGaN beneath a thin conducting channel produce distortions of carrier densities in the channel, due to the PZ charges at their interfaces. The extremely strong influence of PZ effects on device behaviour suggests numerous additional possibilities for design and optimisation of III-V nitride devices. Conclusion: We have shown that, through the PZ effect, donor-like charge densities of the order of 5 × 10 13 cm-2 · x A L are produced at pseudomorphic AlGaN/GaN interfaces. The existence of the piezoe-lectric charges provides an insight into the relative performances of various HFET structures.},
	number = {14},
	journal = {Electronics Letters},
	author = {Asbeck, P M and Yu, E T and Lau, S S and Sullivan, G J and Hove, J Van and Redwing, J},
	month = jul,
	year = {1997},
	keywords = {HEMTs, HFET, MBE, MOCVD},
	pages = {1230--1231},
}

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