Does GaN HEMT require modulation doping?

28/09/2026

10–15 minutes

electronics, gan, hemt, materials, semiconductors, technology

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GaAs HEMT cannot work without modulation doping. It is a fact that we have proven using Silvaco TCAD. However, HEMT devices are not bound only by the AlGaAs/GaAs heterostructure. The game changes when we use an AlGaN/GaN heterostructure instead.

Conditions for forming 2DEG.

The conduction channel in a HEMT is called the two-dimensional electron gas (2DEG) created by the heterojunction formed by the AlGaN/GaN interface. Its formation requires the presence of a triangular quantum well. The triangular quantum well is formed by the conduction band offset created by the difference in the band structures of the two semiconductor materials, particularly their electron affinities and band gaps. The conduction band goes below the Fermi level. The Fermi level is where the probability of finding electrons is 50%.

The conduction band can be thought of as a range of houses available for electrons. The density of states tells us how many houses are available at each energy. The conduction-band edge $E_C$ represents the lowest energy at which conduction-band states become available. Whether an electron actually occupies a particular house depends on the probability of occupation, which is determined by the Fermi–Dirac distribution. The probability is given by:

f(E) = \frac{1}{1 + \exp\left(\frac{E-E_F}{k_BT}\right)}

Graph illustrating the Fermi-Dirac occupation probability, showing the relationship between energy (E) and occupancy probability (f(E)). The curve approaches 1 at lower energies and decreases sharply, crossing the 0.5 line at the Fermi energy (EF). — Figure 1: Fermi-Dirac probability graph.

The problem in the AlGaAs/GaAs interface is that while there is a conduction band offset, it does not bend sufficiently downward to go below the Fermi level. The probability of an electron taking residence in the conduction band remains low. Therefore, there is no significant electron accumulation at the interface and a 2DEG does not form.

Graph illustrating the band alignment of AlGaAs/GaAs across three stages: separate AlGaAs, separate GaAs, and a joined type-I heterostructure. The energy levels (Ec, Ef, Ev) and the energy gaps (Eg) are labeled, with values noted for each material. — Figure 2: Band diagram of joining the two compounds to create a heterostructure.

When the gate metal forms a contact with the semiconductor, charges are redistributed until the metal and semiconductor reach Fermi-level equilibrium. This establishes a common Fermi level and causes band bending in the semiconductor. The band bends due to the presence of electric fields generated by charge redistribution.

Graph depicting the band alignment between Metal, AlGaAs, and GaAs, showing energy levels (EC, EF, EV) and energy differences (ΔEC = 0.23 eV, ΔEV = 0.15 eV) across the x-axis. — Figure 3: Band alignment due to gate metal contact.

As you can see, the band does not bend enough to go beyond the fermi level. N-type doping allows us to shift the fermi level near the conduction band.

Energy band diagram of an n-type semiconductor showing the conduction band (EC), Fermi level (EF), and valence band (EV) as functions of position. — Figure 4: N-type semiconductor band diagram.

The proper amount of doping will allow us to create the triangular quantum well required for the formation of 2DEG. These free electrons due to modulation doping transfer to the lower-energy GaAs side, leaving positively charged donor ions in the AlGaAs. The resulting charge separation produces band bending in the GaAs, and together with the conduction-band offset, this creates a triangular quantum well at the AlGaAs/GaAs interface where the 2DEG forms.

Energy band diagram for Modulation-Doped AlGaN/GaN HEMT, showing conduction band (blue), valence band (orange), and electron quasi-Fermi level (dashed line) over distance in nanometers. — Figure 5: Modulation-doped CB going under the fermi level.

The AlGaN/GaN heterostructure does not require the help of modulation doping for sufficient band bending.

How does the AlGaN/GaN heterostructure differ from AlGaAs/GaAs?

The presence of a large amount of polarization in charges allows the 2DEG to form without the help of modulation doping. III-nitride compound semiconductors can be found in three crystal structures: wurtzite, zinc blende, and rock salt. GaAs has the zinc-blende structure while GaN forms a wurtzite structure at roon temperature and atmosphere.

Isometric view of a crystal structure with labeled spheres representing different elements (Ga0, Ga1, Ga2, Ga3, As4, As5, As6, As7) connected by lines. — Figure 6: GaAs zinc-blende structure (Vesta view).

An isometric view and a top view diagram showing a molecular structure with green spheres labeled Ga and N, representing gallium and nitrogen atoms, respectively. — Figure 7: GaN wurtzite structure (Vesta view).

The wurtzite structure allows two types of polarization to take place: a) spontaneous, and b) piezoelectric.

Spontaneous polarization

It arises due to the asymmetry of the wurtzite crystal and the differences in electronegativity between Ga and N. The bond made by Ga and N is polar due to N pulling the electrons towards it.

Where is the electron density?

Increase nitrogen’s electron attraction and watch the bonding electron density shift toward nitrogen.

Electron attraction

A larger value represents a stronger tendency for the bonding electrons to shift toward N.

N electron attraction 50%

Electron-density shift Moderate

Bond polarity δ⁺ — δ⁻

Conceptual bond dipole 0.50

Increasing the slider represents a larger electronegativity difference. In real GaN, the electron distribution is determined by the electronic structure of the crystal, not by a single adjustable parameter.

All atoms on the same plane at each side of a bond are the same. Hence, the wurtzite GaN crystal shows two distinct faces, commonly known as Ga-face and N-face. Conventional GaN devices use Ga-face to make a HEMT.

Schematic representation of the crystal structures of Ga-face and N-face, showing atomic arrangements with labeled planes and atomic elements. — Figure 8: Ga- and N-face wurtzite structures.

So now we have two main points, the wurtzite structure and the polar Ga-N bond. Wurtzite GaN has the property of being non-centrosymmetric. This means that it does not have a center of symmetry. A centrosymmetric structure would have a center of symmetry. If you take every atom and reflect it through the center, you find an equivalent atom at the opposite position. Centrosymmetric crystals cancel out the net dipole moment.

The spontaneous polarization for Ga-face AlGaN grown on GaN is negative because of the direction along the vector from substrate to the surface. In contrast, spontaneous polarization direction vector is away from the substrate for N-face III-nitrides. We need the the vector towards the substrate so that we get a net positive polarization induced sheet charge so free electrons can compensate for these charges.

Spontaneous polarization is given by:

P_{\mathrm{sp}}(x) = (-0.52x - 0.029)\ \mathrm{C/m^2}

where x is the composition of Al in Al_xGa_1-xN.

Piezoelectric polarization

This results from the lattice mismatch between two materials. Lattice mismatch causes atoms to be pulled away from each other leading to an electrostatic force imbalance.

Parameter	AlN	GaN
a₀ (Å)	3.112	3.189
c₀ (Å)	4.982	5.185

AlN has a lower a₀ than GaN. Al brings the nitrogen atoms closer together. The Al_xGa_1-xN layer will have a lattice constant in between 3.112 Å and 3.189 Å. This layer will try to conform to the GaN layer below it. The N atoms will have to shift from their positions.

Diagram illustrating the combination of two layers of GaN and AlGaN, showing the atomic structure and orientation with labeled axes. — Figure 9: Piezoelectric polarization in AlGaN/GaN interface.

The N atom on top will push downwards because the three N atoms countering it have been shifted from their positions. This will cause a separation of charge, leading to piezoelectric polarization.

A very important point to note is that if the barrier layer becomes thick then you lose piezoelectric polarization due to the Al_xGa_1-xN layer relaxing. The layer needs to be kept under tensile strain for it to have its intended effect.

Piezoelectric polarization can be calculated by:

\begin{aligned} P_{\mathrm{PE}} = 2 \left( \frac{a(0)-a(x)}{a(x)} \right)\left[ e_{31}(x) - e_{33}(x) \frac{C_{13}(x)}{C_{33}(x)}\right]\ \mathrm{C/m^2} \end{aligned}

Where a is lattice constant, C is elastic constant, and e is piezoelectric constant. We will talk more about this in the upcoming section.

Total polarization

Moving on to adding both types of polarizations to get the desired HEMT structure. In figure 10, try and identify the structure that will give us the best 2DEG. The total amount of polarization is given by:

P = P_{sp}+P_{PE}

Diagram illustrating the layers and strain conditions in GaN and AlGaN on substrates, with labeled components for Ga-face (a-c) and N-face (d-f) configurations. — Figure 10: Polarization directions of different structure configurations

The total amount of polarization induced sheet charge density for an undoped AlxGa(1-x)N/GaN heterostructure can be calculated:

\begin{aligned} \lvert \sigma(x) \rvert = \lvert P_{\mathrm{PE}}\left(\mathrm{Al}_x\mathrm{Ga}_{1-x}\mathrm{N}\right) + P_{\mathrm{sp}}\left(\mathrm{Al}_x\mathrm{Ga}_{1-x}\mathrm{N}\right) - P_{\mathrm{sp}}(\mathrm{GaN})\rvert \end{aligned}

Important formulae for 2DEG calculation in GaN HEMT

We looked upon some formulae in the previous section about polarization but did not relate it to the total sheet carrier concentration. Before that let us summarize all the formulae in a table (Reference: O. Ambacher et. al. 1999). Use the slider at the bottom to navigate.

Name	Formula	Related Formulae	Variables
Polarization induced sheet charge density for an undoped Al_xGa_(1-x)N/GaN heterostructure	\[ \begin{aligned} \|\sigma(x)\| = \left\| P_{\mathrm{PE}}\left(\mathrm{Al}_x\mathrm{Ga}_{1-x}\mathrm{N}\right) + P_{\mathrm{sp}}\left(\mathrm{Al}_x\mathrm{Ga}_{1-x}\mathrm{N}\right) - P_{\mathrm{sp}}(\mathrm{GaN}) \right\| \end{aligned} \]	\[ P_{\mathrm{sp}}(x)=(-0.52x-0.029) \quad \mathrm{C/m^2} \] \[ \begin{aligned} P_{\mathrm{PE}} = 2 \left( \frac{a(0)-a(x)}{a(x)} \right) \left[ e_{31}(x) - e_{33}(x) \frac{C_{13}(x)}{C_{33}(x)} \right] \quad \mathrm{C/m^2} \end{aligned} \] \[ e_{31}(x)=-0.11x-0.49 \] \[ e_{33}(x)=0.73x+0.73 \] \[ a(x)=(-0.77x+3.189)\times10^{-10} \] \[ C_{13}(x)=5x+103 \] \[ C_{33}(x)=-32x+405 \]	$x$: Al composition $e$: Polarization constants $e_{31}$: coupling between in-plane strain and polarization along the c-axis $e_{33}$: coupling between strain along the c-axis and polarization along the c-axis $a$: lattice constant $C$: Elastic stiffness constants $C_{13}$: coupling between in-plane strain and the c-axis direction $C_{33}$: stiffness against strain along the c-axis
2DEG sheet carrier concentration	\[ n_s(x) = \frac{\sigma(x)}{e} - \frac{\varepsilon_0\varepsilon(x)} {d e^2} \left[ e\phi_b(x) + E_F(x) - \Delta E_C(x) \right] \]	\[ \varepsilon(x)=-0.3x+10.4 \] \[ e\phi_b(x)=1.3x+0.84\ \mathrm{eV} \] \[ E_F(x) = E_0(x) + \frac{\pi\hbar^2}{m^(x)} n_s(x) \quad \mathrm{eV} \] \[ E_0(x) = \left[ \frac{9\pi\hbar e^2} {8\varepsilon_0\sqrt{8m^(x)}} \frac{n_s(x)}{\varepsilon(x)} \right]^{2/3} \quad \mathrm{eV} \] \[ m^*(x)=0.22m_e \] \[ \Delta E_C(x) = 0.7 \left[ E_g(x)-E_g(0) \right] \quad \mathrm{eV} \] \[ E_g(x) = xE_g(\mathrm{AlN}) + (1-x)E_g(\mathrm{GaN}) - x(1-x)b \quad \mathrm{eV} \]	$\varepsilon$: dielectric constant $\phi_b$: Schottky barrier height $E_F$: Fermi energy $E_0$: Ground sub-band energy $\hbar$: Reduced Planck's constant $\left(\frac{h}{2\pi}\right)$ $m^*$: effective mass $m_e$: mass of electron $e$: electron charge $\varepsilon_0$: permittivity of free space $\Delta E_C$: Conduction band offset $E_g$: Bandgap energy $b$: Bowing parameter (1.0 eV)

The 2DEG sheet carrier concentration will give us the final value for the number of electrons near the interface area. The bandgap and lattice constant of the AlxGa(1-x)N compound keeps changing as we vary the composition of aluminium.

Conclusion

GaN HEMTs do not require the help of modulation doping due to the presence of piezoelectric and spontaneous polarization. Polarization causes charge transport resulting in electric fields. These electric fields can cause band bending which allows the conduction band to go under the fermi level creating the triangular quantum well required for 2DEG formation.

Frequently Asked Questions (FAQ)

Ques: Why is N so electronegative?

Nitrogen is highly electronegative because it has a relatively small atomic radius and a strong effective nuclear attraction for its valence electrons. It also has five valence electrons, so it strongly attracts electrons to complete its outer shell. Nitrogen therefore has an electronegativity of about 3.0 on the Pauling scale, much higher than Ga.

Ques: How does N possess higher electronegativity than Ga?

Nitrogen is much smaller than gallium and its valence electrons are closer to the nucleus. Therefore, the nucleus of N exerts a stronger attractive force on bonding electrons. Gallium is larger and its valence electrons experience more shielding from inner electrons, resulting in a lower electronegativity.

Ques: What wurtzite face is used in GaN HEMT?

GaN HEMTs are commonly grown on the c-plane (0001) (Ga face) of wurtzite GaN. This orientation is important because the crystal's spontaneous and piezoelectric polarization have a component along the c-axis, allowing a strong polarization discontinuity to form at the AlGaN/GaN interface and generate the 2DEG.

Ques: What is non-centrosymmetric?

A non-centrosymmetric crystal does not have a center of inversion. In other words, if you take a point in the crystal and invert it through the center, the resulting atomic arrangement is not identical to the original arrangement. Wurtzite GaN is non-centrosymmetric, which allows it to exhibit properties such as spontaneous polarization and piezoelectricity.

Ques: Why is the AlGaN layer kept under tensile strain in GaN HEMT?

AlGaN has a different lattice constant from GaN. When AlGaN is grown pseudomorphically on GaN, it is forced to match the smaller in-plane lattice constant of GaN, producing tensile in-plane strain in the AlGaN layer. This strain generates piezoelectric polarization, which adds to the spontaneous polarization difference between AlGaN and GaN and contributes to the formation of the high-density 2DEG.

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How does the composition of aluminium in the barrier layer of a GaN HEMT affect its characteristics?