Physics-Based Intrinsic Model for AlGaN/GaN HEMTs

Abstract

DC and intrinsic small signal parameters are reported for AlGaN/GaN high electron mobility transistors. The calculations are based upon a self-consistent solution of Schrödinger and Poisson’s equation to model the quantum well formed in GaN. Transport parameters are obtained from an ensemble Monte Carlo simulation.

Introduction

AlGaN/GaN high electron mobility transistors (HEMTs) have recently attracted much attention with the large available band gap of the channel material (GaN) and excellent thermal properties for possible applications in high power and high temperature microwave devices.

Some of the HEMT structures reported by Binari et. al. [1-2] and Redwing et. al. [3] had appreciable two dimensional electron gas (2DEG) concentration though the AlGaN supply layer was undoped. Dangling bonds at the AlGaN/GaN heterointerface may give rise to interface charge that could explain the observed 2DEG concentration. Recently, an alternative explanation of the formation of the 2DEG concentration using the piezoelectric effect has been proposed by Asbeck et. al. [4]. However, as shown by the present authors [5] the calculation of 2DEG concentration as a function of Al mole fraction is in excellent agreement with the experimental data, even though the piezoelectric effect was not incorporated in the calculation.

The dc and small signal parameters and the rf performance can be investigated once the quantum well (QW) properties and the transport properties of the channel material are known. In this paper the dc and small signal parameters are calculated using results obtained from an exact quantum calculation modeling the QW formed at the AlGaN/GaN heterointerface along with transport data obtained from an ensemble Monte Carlo simulation. The rf performance can then be obtained by evaluating the small signal model.

Theory

The electron concentration, n_s, in the QW formed in GaN is determined by solving the Schrödinger and Poisson’s equations self-consistently [5]. The calculated average distance of the electron cloud from the heterointerface, x_avg, and the position of the Fermi level, E_F, are expressed by the following functional forms and are used in the evaluation of the dc and small signal parameters [6, 7, 8]:

(1)

(2)

where the constants a, b, E_F(0) and γ are determined from the results of the quantum calculation. The drain-source current I_ds can then be written as [5] :

(3)

where G₀=εZv_s/d_eff, d_eff=d × Δd with d and Δd being the thickness of AlGaN layer and effective channel thickness, respectively. Z is the width of the gate and L₁ is the length of unsaturated region of the channel. The above equation incorporates the effect of the quantum well through eqs. 1 and 2 via reduced potentials, s and p. Also implicit in eq. 3 is the use of a velocity-electric field characteristic of the form v_d=μ₀ E/((v_s/μ₀)²× E)^1/2 where v_d is the drift velocity, μ₀ is the low field mobility, v_s is the saturation velocity and E is the electric field. The velocity-electric field characteristics are obtained from an ensemble Monte Carlo simulation using the following scattering mechanisms: acoustic phonon, optical phonon, intervalley, alloy, ionized impurity and piezoelectric scattering The evaluation of dc and small signal parameters follows the treatment presented in Ref. [5].

Results and Discussion

The QW formed in GaN in an Al_0.25Ga_0.75N/GaN heterostructure is considered. The electron effective masses in GaN and AlN are assumed to be 0.19m₀ and 0.23 m₀, respectively, where m₀ is the free electron mass. The electron effective mass of Al_xGa_1−xN is obtained by a linear interpolation between the values for GaN and AlN. Based on a calculated valence band offset in Al_xGa_1−xN/GaN, it is found that the conduction band offset may be given as: ΔE_c = 0.75ΔE_G, where ΔE_G [5]. is the difference in bandgaps of GaN and Al_xGa_1−xN [5].The temperature dependent bandgap for GaN is given as E_G ^GaN (T) = 3. 056 + 5.08×10⁻⁴T²/(T−996) [9]. The bandgap of AlN is assumed to be 5.1 eV.

Fig.1 shows the conduction band profiles obtained by solving the Schrödinger and Poisson’s equations self-consistently for 300K and 500K. On the same plot the 2DEG distributions are also plotted. The plots are obtained for a 2DEG concentration of 1.8×10¹² cm⁻² and the corresponding positions of the Fermi level are 0.092 eV and 0.052eV above the tip of the conduction band discontinuity at 300K and 500K, respectively. The conduction band profiles can be explained by the fact that n_i (300K) is 12 orders of magnitude less that n_i (500K). This difference in n_i is due to the higher effective density of states at higher temperatures and a decrease in bandgap of GaN with increasing temperature. Moreover, the conduction band offset increases from 0.313eV at room temperature to 0.361eV at 500K. Assuming fully ionized acceptors in GaN at both temperatures, the Fermi level moves closer to the intrinsic Fermi level at the higher temperature. Therefore, less band bending in GaN is required to obtain the same 2DEG concentration at 500K that at 300K. At room temperature a higher fraction of the 2DEG concentration is in the first subband due to the close proximity of the Fermi level to the first eigen energy. On the other hand, at 500K a larger separation between the first eigen energy and the Fermi level implies a lesser degree of occupation of the first subband, allowing the higher subbands to be populated.

Fig. 1 Conduction band profile and 2DEG concentration at 300K and 500K.

In Fig. 2, the average distance of the electron cloud from the first heterointerface, x_av, and the position of the Fermi level, E_F, with respect to the tip of the conduction band are plotted as a function of the 2DEG concentration, n_s. At room temperature for n_s > 1 × 10¹¹ cm⁻² , x_av and E_F can be expressed by the following relationships:

(4)

(5)

Fig. 2 x_av and E_f as a function of the 2DEG concentration.

The simulated electron drift velocity is plotted in Fig. 3 as a function of applied electric field in undoped bulk GaN with temperature as a parameter. A peak velocity of 2.6×10⁷ cm/s is obtained at a field strength of 145 kV/cm for undoped GaN at room temperature . The position of the peak velocity moves from 140 kV/cm at 100K to 170 kV/cm at 500K. It is interesting that the low field mobility increases as the temperature is lowered, whereas, the saturation velocity does not show such a pronounced temperature dependence. This can be explained by noting that the low field mobility, which is dominated by acoustic phonons and polar optical phonon absorption, shows improvement due to the suppression of these scattering process at lower temperatures. The high field transport on the other hand, is dominated by polar optical phonon emission and intervalley scattering, both of which have a weak lattice temperature dependence. The room temperature low field mobility, μ, obtained from the initial slope of the velocity field curves, changes from 590 cm²/V-s at 1×10¹⁷ cm⁻³ to 440 cm²/V-s at 1×10¹⁹ cm^-3 for GaN. The simulations show that the temperature dependence of the low field mobility for a doping level of 1×10¹⁷ cm⁻³ can be given as μ(T)=1156 - 2.75T ⊞ 0.002T² cm²/V-s. With increasing doping he peak in the low field mobility decreases and shifts towards higher temperature. This behavior is attributed to the strong influence of ionized impurity scattering.

Fig. 3 Velocity-electric field characteristics for undoped GaN with temperature as a parameter.

The current voltage characteristics of a 1.2 μm x 20μm Al_0.25Ga_0.75N/GaN HEMT at room temperature are plotted in Fig. 4. A low field mobility of 600 cm²/V-s and a saturation velocity of 1x10⁷ cm/s are assumed for the undoped GaN channel. The AlGaN epilayer thickness is assumed to be 220 Å. The threshold voltage is calculated to be -3.75 V, and the barrier potential, φ_b =1.1eV.

Fig. 4 DC current-voltage characteristics of AlGaN/GaN HEMT.

In Fig. 5, the saturation drain current and the transconductance of a 1.2 μm × 20 μm gate HEMT are plotted as a function of the gate-source potential at V_ds=2.0V. A transconductance of 100 mS/mm is obtained at V_gs =2.0 V. In Fig 5 (b), the small signal gate capacitance and the drain resistance are shown. These small signal parameters predict a maximum unity current gain cutoff frequency, f_T, of 12 GHz at room temperature that reduces to 10 GHz at 500K.

Fig. 5 (a) Saturation drain current and transconductance (b) drain resistance and gate-source capacitance are plotted as a function of gate bias.

Conclusion

A physics based intrinsic model for AlGaN/GaN HEMTs has been presented. The model is based a self-consistent solution the Schrödinger and Poisson’s equations as well as channel material transport properties obtained from a Monte Carlo simulation. The resulting small signal model predicts a high transconductance of 100 mS/mm with a unity current gain cutoff frequency of 12 GHz. Transistors with these characteristics will be useful in microwave applications at high temperatures.