Physics-Based Intrinsic Model for AlGaN/GaN HEMTs
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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 AIGaN/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•, in the QW formed in GaN is determined by solving the Schrbdinger and Poisson's equations self-consistently [5]. The calculated average distance of the electron cloud from the heterointerface, xag, and the position of the Fermi level, EF, are expressed by the following functional forms and are used in the evaluation of the dc and small signal
parameters [6, 7, 8]: x.,, =a+ bb.ln(n,) EF= EF(0) + y . ln(n,)
(A) (eV)
G 6.58
Mat. Res. Soc. Symp. Proc. Vol. 537 ©1999 Materials Research Society
(1) (2)
where the constants a, b, EF(O) and y are determined from the results of the quantum calculation. The drain-source current lds can then be written as [5]
2
.('I2 Id, =OVi g L
-p
0 1
-2P2
[V_s_ co-I P
2
2 "
F
P2)
S
P
rF ý 2 TsI
2
p
-Cos 1()]
(3)
where Go = CZvJdeff, deff = d + Ad with d and Ad being the thickness of AIGaN layer and effective channel thickness, respectively. Z is the width of the gate and L, is the length of unsaturated region of the channel. The above equation incorporates the effect of the quantum well through eqs. I and 2 via reduced potentials, s and p. Also implicit in eq. 3 is the use of a velocityelectric field characteristic of the form vd=to E/((Vjst0) 2+ E)" 2 where v, is the drift velocity, lto is the low field mobility, v, 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 A10.25Gao.75N/GaN heterostructure is considered. The electron effective masses in GaN and AIN are assumed to be 0.19m0 and 0.23 ino, respectively, where m0 is the free electron mass. The electron effective mass of AlxGa, xN is obtained by a linear interpolation between the values for GaN and AIN. Based on a calculated valence band offset in AlxGa1 _xN/GaN, it is found that the conduction band offset may be given as: AE, =-0.75AEG, where AEG is the difference in bandgaps of GaN and AlxGa, xN [5]. The temperature dependent bandgap for GaN is given as EGN (T) = 3.056 + 5.08 x 10 4T 2 /(T -996) [9]. The bandgap of AIN is assumed to be 5.1 eV. Fig. 1 shows the conduction band profiles obtained by solving the Schr•dinger and Poisson's equations self-consistently for 300K and 500K. On the
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