Understanding the AlGaN-GaN heterostructure
In this article, I discuss the value of the AlGaN-GaN heterostructure for use in high electron mobility transistor (HEMT) devices. I begin with the motivation for HEMTs and why the AlGaN-GaN heterostructure makes a good candidate for such devices. I then go into detail on the heterostructure’s valuable properties (high density of 2DEG that accumulates at the heterointerface, confinement of the 2DEG due to the potential well at the heterointerface, intrinsic polarization that helps drive electrons to the potential well). Finally, I provide a high-level overview of how to turn the heterostructure into a controllable device. The article ends with a FAQ section, which mainly consists of questions I had in researching this topic and the answers I subsequently found. I hope you enjoy!
Table of contents
· Motivation: Can we increase conductivity of the MESFET?
· Idea: Separate carriers from ionized donors (impurities)
· Crystal structure and origins of intrinsic polarization
· Formation of 2DEG
∘ Case 1: n-doped AlGaN
∘ Case 2: undoped AlGaN
· Applications: HEMT
∘ Step 1: Add gate control
∘ Step 2: D-mode to E-mode
· Summary
· FAQ
∘ Why does 2DEG density depend on barrier thickness?
∘ Can strain be manually applied to increase 2DEG density?
∘ What is the origin of surface donor states in AlGaN?
∘ How can you understand the described electron redistribution in terms of the chemical potential?
· About the author
· Sources and further reading
Motivation: Can we increase conductivity of the MESFET?
First, let’s discuss the motivation for why we would want an AlGaN/GaN heterostructure in the first place. Note that most of this section is structured around the explanation given by Streetman & Banerjee (2000, pp. 288–289).
Let’s say you need a transistor for a high-frequency application. Your first choice might be a MESFET, which is basically a JFET in which the width of the depletion region that pinches the channel is due to the presence of a Schottky diode instead of a PN junction. MESFETs are faster and have higher frequency response than MOSFETs, as there is no oxide capacitance limiting how fast you can transition from an on to an off state.
Also, MESFETs can be made from materials like GaAs or GaN, which have a higher electron mobility than Si. These are difficult to use in MOSFETs, because in the case of GaN, there is no native oxide (like SiO₂ for silicon) that forms a high-quality, defect-free interface with GaN.
If you want to make the MESFET operate even faster, you have to increase the transconductance, which is related to the channel’s conductivity. High conductivity allows for rapid changes in current, allowing the MESFET to respond quickly to high-frequency signals, i.e., quickly switch on/off. This is especially useful for power applications, as operation at higher frequencies often allows more efficient conversion of power (reduced energy losses) and smaller-sized passive components like capacitors and inductors.
One straightforward way of increasing the conductivity is increasing the doping in the channel, which, in turn, raises the carrier concentration. For example, if we have a channel formed in this n-type GaAs layer below, we could increase the concentration of the Si atoms serving as the donors. (Si has one extra valence electron than Ga.) However, we have to remember that the mobility of the carriers is also important.
The problem is that at a certain point, the increase in carrier concentration that increased doping provides is accompanied by a significant decrease in carrier mobility due to impurity scattering. As you can see in the picture below, increased doping leads to increased ionized donors, and thus a mobile electron moving through the channel is more likely to be deflected off of its original path by virtue of Coulombic attraction to one of the positively charged ions.
Idea: Separate carriers from ionized donors (impurities)
What we need is some way of creating a high electron concentration in the channel of a MESFET other than doping, or at least a way to separate the conductive carriers from ionized impurities.
This is a perfect job for heterojunctions. Because of the valence and conduction band discontinuities at the interface of two materials, which is due to a difference in their bandgaps and electron affinities, many heterostructures can be used for quantum confinement of carriers via a potential well, and thus the creation of a highly localized and conductive channel at the interface. And importantly, the potential well the carriers are confined to will physically separate them from any ionized donors or acceptors if they’re present in the material.
In particular, AlGaN/GaN heterostructures have shown great promise in high-power and high-frequency devices. This is because no intentional doping is required to generate two-dimensional electron gas (2DEG) at the AlGaN/GaN interface.
Even if you do use an n-doped AlGaN layer to provide carriers (as shown in the figure below), the carriers will eventually make it to the potential well, where they will be physically separated from the ionized donors.
As we’ll soon see, the high concentration of 2DEG that accumulates at the interface is related to the spontaneous and piezoelectric polarization that occurs throughout the heterostructure and the resulting high electric field in the AlGaN layer. We will explore this more by first discussing the origin of the intrinsic polarization and then the way 2DEG forms at the interface.
Crystal structure and origins of intrinsic polarization
GaN can take several forms, but the easiest to grow and the most stable is the wurtzite crystal. It is characterized by lattice parameters:
- a: edge length of the basal hexagon
- c: height of the hexagonal prism
The atoms are arranged in alternating layers, each layer consisting of two closely spaced hexagonal layers, one of Ga atoms and the other of N atoms. The faces of these bilayers are grown perpendicular to the c-axis (i.e., the growth direction is along the c-axis).
Within the wurtzite crystal, each Ga atom is surrounded by four N atoms, forming an asymmetric tetrahedron. In particular, the crystal structure is non-centrosymmetric (lacking a center of symmetry) because the core atom does not exactly lie in the tetrahedral center.
Recall that the electric dipole moment is a vector pointing from a negative charge to an equal-magnitude positive charge. It’s proportional to the distance of separation between the charges, and in the case of analyzing a material like GaN (with mixed covalent-ionic or “polar-covalent” bonds), it indicates the separation of charge due to uneven electron distribution.
If we examine one of the tetrahedrons of the GaN crystal, the Ga-N bond along the c-axis is longer than the other bonds. Thus, the negative dipole moment (relative to the c-axis) of the “northernmost” cation-anion bond (P_1 in the figure below) is longer than the positive “southern” cation-anion dipole moments (P_2, P_3, P_4) and the c-axis components of the latter won’t completely counteract the former. As a result, there is a net negative polarization (acting down along the c-axis) which is equal to that of bulk. We call this net polarization the spontaneous polarization (P_sp) of the material because it occurs even without the application of an external electric field.
In terms of the lattice parameters, we can say that the c/a ratio in the wurtzite structure is less than the ideal tetrahedral value, for which all dipole moments cancel out. This induces a displacement between the cation and anion centers (the central Ga anion is not exactly located at the tetrahedral center), generating a net dipole moment along the c-axis. For a more mathematical derivation, see Troy et al. (2021).
Now let’s examine the heterostructure of AlGaN interfaced with GaN. AlGaN has the same structure as GaN, but Al atoms are smaller than Ga atoms. When Al is substituted for Ga in the GaN crystal lattice to form AlGaN, the overall lattice shrinks because the Al-N bond lengths are shorter than the Ga-N bond lengths. This reduction in bond length leads to a smaller lattice constant in AlGaN compared to GaN. Therefore, at the interface, AlGaN is “stretched” so that the lattice constant roughly matches that of GaN.
We can see this in the “post-contact” picture. Once again, tensile strain is created due to a lattice mismatch between the two materials. Just to make this really clear, let’s examine a tetrahedron at the AlGaN-GaN interface.
The picture below isn’t drawn to scale, but on the right you can see that the bond lengths and angles are changed due to the strain. In particular, the c-axis component of polarization from the bonds forming the “base” of the tetrahedron (from P_2, P_3, and P_4) is less pronounced since the corresponding cation-anion bond angles have widened. Therefore, it doesn’t counteract P1 as much, and there is a larger net negative polarization. We can attribute this new component of the polarization to piezoelectric effects (P_pe), i.e., it is strain-induced.
To summarize,
- Asymmetry found in the AlGaN and GaN wurtzite structures leads to spontaneous polarization and is referred to as spontaneous since it occurs without any external electric field applied.
- Tensile strain induced because of the lattice mismatch between AlGaN and GaN creates piezoelectric polarization and is primarily found in the AlGaN. (It’s not found in the GaN layer since it’s thicker and should be fully relaxed due to its relative thickness.)
Now we’ll see how the electric field caused by the polarization helps drive the electrons towards the triangle-shaped potential well at the interface and form the 2DEG.
Formation of 2DEG
Note that most of the information in this section comes from He et al. (2015).
Case 1: n-doped AlGaN
Let’s first examine the case of n-doped AlGaN coming into contact with GaN, as the formation of the 2DEG is easy to understand in this case.
In the figure below, we have the “pre-contact” energy band of an n-doped layer of AlGaN, and we’re assuming the AlGaN layer is under the same tensile strain as when growing on GaN. Initially, conductive electrons drift under the polarization-induced electric field from one side to the other, so in the middle panel, we have a current (as indicated by the slanted Fermi level) until equilibrium is reached on the right. In accumulating at the positive end of the AlGaN, the electrons leave behind fixed positive charges, symbolized by the pink plus signs.
Now let’s look at the full heterostructure, i.e., the “post-contact” picture. Because the Fermi level of GaN is initially lower than that of AlGaN, once contacting GaN, electrons on the AlGaN side will flow into the GaN and form 2DEG. This process will continue until the Fermi levels of AlGaN and GaN become equal to each other, as shown on the right.
Case 2: undoped AlGaN
Interestingly, the formation of 2DEG at the heterointerface has also been observed when undoped AlGaN contacts GaN. But how do we explain the formation of the 2DEG when there are no donors to contribute conductive electrons?
The formation of the 2DEG at the interface can actually be well explained by assuming the existence of donor states on the AlGaN surface. Below, we have the energy band diagram of undoped AlGaN with surface donor states at energy E_s. If the AlGaN layer is thick enough, the donor state level E_s will reach the Fermi level (see FAQ). The electrons will then be stimulated into the conduction band and drifted toward the other side by the polarization-induced electric field.
Just as in the previous case, once AlGaN makes contact with the GaN layer, electrons will flow into the GaN side. The electrons will accumulate at the interface and form 2DEG.
Applications: HEMT
Step 1: Add gate control
In order to turn this heterostructure into a useful device such as a high electron mobility transistor (HEMT), which can be considered a special high mobility case of MESFET, we have to be able to control the interfacial density of the 2DEG, i.e., how conductive the channel is. One simple strategy is to add a Schottky contact — a metal gate interfacing with the AlGaN.
The density of electrons in the 2DEG layer in the potential well can be controlled by the gate voltage. At zero bias, the conduction-band edge at the interface is already below the Fermi level, implying a large density of the 2DEG. A negative voltage is required to move the Fermi level below the conduction band at the interface and deplete the 2DEG. Of course, by applying a positive voltage, you can increase the 2DEG density even more.
Thus, with a typical Schottky contact at zero gate bias, the 2DEG is already formed and current is flowing. These devices are known as depletion mode (D-mode) or normally on because the gate needs to be negatively biased to deplete the transistor channel.
Step 2: D-mode to E-mode
For RF applications, D-mode transistors are commonly used. However, they aren’t ideal for power electronic applications. Engineers don’t want unnecessary power flowing when voltage is not applied, so D-mode transistors require additional space and circuitry to switch them off. Also, they aren’t fail safe like E-mode transistors. Therefore, for power electronics, E-mode transistors are preferred to suppress unwanted power flow. A lot of research is going into commercially viable ways of making these transistors normally off.
In order to obtain E-mode operation, the 2DEG density in the gated region must be reduced to 0 at 0-V gate bias. Some methods to achieve this are as follows:
Approaches for creating E-mode HEMT (Greco et al., 2018)
- Recessed gate structure via local plasma etch process. Make the AlGaN barrier so thin that it can’t produce 2DEG.
Problems: Damage induced by the etching process can increase gate leakage current and V_Th non-uniformity; thinness limited by tunneling thickness - Fluorine-based plasma. Plasma bombards AlGaN under the gate, creating acceptors that deplete the 2DEG.
Problems: Charge trapping effects can increase gate leakage current and V_Th non-uniformity; V_Th instability after high-temperature annealing - P-doped semi gate + buffer engineering. P-type semiconductor gate depletes the 2DEG. AlGaN buffer beneath the GaN channel helps maintain high V_Th.
Problems: High Mg (acceptor) ionization energy
While methods (1) and (2) have been the subject of much experimentation, they have some limitations related to gate leakage current, threshold voltage spatial non-uniformity, and temperature instability. There is even trouble with the reproducibility of the plasma etch process used in (1) and the ion implantation process used in (2).
Probably the most promising approach is (3), which commonly uses a p-GaN “cap” layer on the AlGaN/GaN heterostructure under the gate contact region. In this case, the p-GaN layer lifts up the band diagram, resulting in the depletion of the 2DEG channel even in the absence of an externally applied bias.
Even though there are still a few problems that are being worked out with this method, e.g., the high ionization energy of magnesium atoms that usually serve as the acceptors and create the p-doping, this process is receiving great attention within the scientific community and is the only “real” normally-off GaN HEMT commercially available to date are based on a p-GaN gate (Greco et al., 2018).
The operation principle of the normally-off HEMT using a p-GaN gate is shown below. On the left, we see the “base case” from before, where the use of a standard Schottky contact as a gate electrode onto an AlGaN/GaN heterostructure leads to the normally-on operation of the device. In other words, the conduction band edge at the interface lies below the Fermi level.
On the right, we see the band diagram after the introduction of a p-GaN cap layer onto the AlGaN. The conduction band of the AlGaN is lifted up, thus leading to the depletion of the 2DEG. In this way, in principle, the normally-off operation of the device can be achieved.
Summary
- Both spontaneous and piezoelectric (lattice-mismatch induced) polarization contribute to the accumulation of 2DEG at the AlGaN-GaN interface
- These electrons have high mobility because they don’t experience impurity scattering (from ionized dopants)
- Thus, the AlGaN-GaN heterostructure is useful for high electron mobility transistors (HEMTs)
- By itself, the AlGaN-GaN heterostructure accumulates 2DEG at 0V bias (is normally on)
- Power electronics prefer normally-off devices; this can be achieved by the addition of a p-GaN cap that depletes the 2DEG at 0V bias
FAQ
Why does 2DEG density depend on barrier thickness?
First, the interfacial density (concentration) of the 2DEG n_S can be derived from the equations in the figure below (He et al., 2015):
There are three dipoles. First, ±σ_AlGaN, the AlGaN polarization-induced charge; second, ±σ_GaN, the GaN polarization-induced charge; third, the 2DEG and the ionized surface charge σ_S. These three dipoles are equivalent to three planar plate capacitors C1, C2, and C3 respectively. Each of these capacitors only has a nonzero electric field between its two parallel planes and has no effect on electrons outside its inner body. The internal electric field intensity of a planar plate capacitor is given by E = σ/ε, where σ is the quantity of electric charges on opposite planes, ε is the dielectric constant of the dielectric medium of the capacitor. In the area where two or more pairs of charged planes overlap, the net electric field is the algebraic sum. Thus, the electric field intensity in the AlGaN layer is determined by the charges of C1 and C2, i.e., the AlGaN polarization-induced charge and the 2DEG:
From equation (3), we can see the direct dependence of the 2DEG interfacial density on the barrier thickness d: as d decreases, n_S becomes smaller.
We can also understand this physically as follows. Consider an undoped AlGaN barrier with a surface state at an energy E_D below the conduction band edge, as shown in the figure below. Note that with n_S = 0 (no 2DEG accumulated), there is a constant electric field in the AlGaN layer due to the unscreened polarization dipole (the dipole formed by the 2DEG and the uncovered donors counteracts the intrinsic polarization of the material, see figure above). Therefore, as the layer thickness d increases, the potential drop V_AlGaN across the layer increases proportionally.
In terms of the relative energies of E_F and E_D, the difference of E_F — E_D decreases with increasing d. In other words, as the AlGaN layer thickness increases, the donor states are effectively lowered in potential or, equivalently, raised in energy on the band diagram.
At a critical thickness, the donor energy E_D reaches the Fermi level E_F (b in the figure above). Electrons are then stimulated from the occupied surface donor states to empty conduction band states at the interface, creating the 2DEG and leaving behind a positive surface charge. Until all the surface states are empty, the Fermi level remains virtually constant at the donor energy (becomes pinned), but more and more electrons transfer with increasing barrier thickness (Goyal et al., 2012). (This is why E_F in the third panel of the first figure in this section is constant.)
For a good explanation of the effects of the barrier thickness on the continuity of the depletion region and potential issues with control (the electric field from the gate being able to “reach” conductive carriers), see the section “HEMT/pHEMT” in this MiniCircuits article.
Can strain be manually applied to increase 2DEG density?
As we’ve seen, the intrinsic polarization of AlGaN/GaN heterostructure helps drive carriers toward the potential well at the interface, but it also helps “shape” the potential well. (Recall that in an energy band diagram, the presence of an electric field will change the slope of the energy bands.) Researchers like Jiang et al. (2017) have harnessed this fact to “manually” increase the intrinsic polarization of the material, thus creating a deeper potential well capable of confining even more carriers.
What is the origin of surface donor states in AlGaN?
In general, the surface donor states come from cation dangling bonds (DBs). There are two inequivalent DBs that can occur at the surface, one on the cation (Al, Ga) and one on the anion (N). Because the cation is less electronegative, when a bond is left dangling, the unpaired electron occupies an orbital that is higher in energy because the cation does not pull the electron as close/stabilize the electron as much as the anion would. Therefore, cation DB states are always higher in the band gap and tend to behave as donors, as electrons occupying these states can be more easily excited into the conduction band.
If you want a more precise answer, there are a few studies that have investigated what sort of surface reconstruction best explains experimental observations of surface donor state energy levels.
It’s well known that once exposed to air, nitride surfaces easily oxidize, and some experiments have suggested a possible relation between oxidation and the origin of the 2DEG. Miao et al. (2010) investigated structures and energies of many different reconstructions on oxidized (0001) surfaces of GaN and AlN and analyzed the results in terms of the electron counting rule and oxide-stoichiometry matching.
How can you understand the described electron redistribution in terms of the chemical potential?
This is a more general question, but one I’d like to walk through since I had to refresh my knowledge of thermodynamics this year, and the links between concepts like “Fermi level” and “chemical potential” weren’t immediately apparent to me.
My favorite explanation of chemical potential is by Cook & Dickerson (1995). As formulated in this paper, the chemical potential μ can be understood as the change in internal energy of the system when one more particle is added while holding volume and entropy constant. If you consider extra terms associated with the electric field (i.e., dU_tot = dU + dU_E, where dU_E = EdP, E is the electric field, and P is the uniform polarization), then the polarization is also held constant.
Now consider the electrons moving from the negative side to the positive side in the middle panel of the figure below. The “driving force” behind the electrons redistributing is due to a spatial gradient in the chemical potential dμ/dx. In many cases, dμ/dx is mostly attributable to the concentration gradient, which is why Fick’s laws of diffusion hold. However, in this case, dμ/dx largely arises due to the potential drop across the AlGaN layer.
Let’s assume that when we add an electron anywhere in the layer, the volume, entropy, and polarization will remain roughly the same, satisfying our constancy constraints. Cook & Dickerson (1995) provide a more nuanced picture of what happens, but this simplification suffices for our purposes.
So how does μ vary with location? Near the negative side, μ should be higher because in order to add an electron, it must be able to 1) occupy an available state (likely with an energy a little below E_F since some states below E_F should be unoccupied at T>0) and 2) overcome the potential energy barrier of the negative polarization charges. In this case, (2) is more significant, so the added electron will have to carry a higher energy if added near the negative end. An electron added near the negative end thus changes the internal energy by a greater amount (when volume, entropy, and polarization are held constant) and possesses a greater chemical potential.
Note that the Fermi level E_F is actually the chemical potential of electrons in the system, so it is “slanted” (there is a spatial gradient) when the system is out of equilibrium.
Once equilibrium is reached (right panel), dμ/dx = 0, and there is no way the system can reduce its free energy by moving electrons or other particles from places of higher μ to those of lower μ. At this point, the driving force toward equilibrium has redistributed the mobile electrons and uncovered some positive bound charges (the ionized donors), and the original intrinsic polarization-induced electric field is reduced.
However, as apparent from the figure, the electric field isn’t completely reduced to zero. This is because at some point, the difference in the potential energy barriers that the negative and positive ends pose to electrons (2) is balanced by the fact that as electrons accumulate at the positive end, the next available energy state becomes higher in energy (1). So even though the positive end might pose a smaller potential barrier, an electron added there would have to occupy a higher energy state not already occupied by other accumulated electrons.
