Electrical Properties of Oxygen Doped GaN Grown by Metalorganic Vapor Phase Epitaxy
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and 420-500 cm2V-1s-1, respectively. Two oxygen-nitrogen gas mixtures were used as a dopant source (20 and 520 ppm of oxygen in nitrogen, respectively). The epitaxial layer consisted of a 20 nm GaN nucleation layer, a thin 50 nm undoped layer, and a two micron thick oxygen doped layer. Doped layers were grown at 1060°C. Hall measurements were performed using the van der Pauw geometry over the temperature range of 77-330 K. The ohmicity of the indium contacts were verified over all temperatures. DEPENDENCE OF CARRIER CONCENTRATION ON OXYGEN PARTIAL PRESSURE For substitution of oxygen on a nitrogen site the defect equilibrium equation is given by:
[O ] 1 O2 → O N , → K O = 1N/ 2 2 p O2
(1)
where K0 is the equilibrium constant and is given by exp[- GF/kT] . The free energy GF = EF- TSF for oxygen substitution can be obtained using first principles, total energy calculations. The value of EF is given by [17]:
(
)
(
)
E F GaN : O Nq = Etot GaN : O Nq − µ O + µ N + qE F
(2)
where Etot is the energy of the neutral defect, µO and µN are the chemical potentials of oxygen and nitrogen , q is a charge state of defect and EF is the Fermi energy. The chemical potential of oxygen is given by µO = kTlnfO= kTln(K0P(O2)1/2). The ON concentration is thus given by:
EF = exp(E tot − µ N + qE F )Kp 1O/22 = K * pO1 /22 exp − k kT
[O N ] = N sites exp S
F
(3)
where Nsite is the substitional oxygen site density and T is the growth temperature. The entropy contribution is assumed to be small. The carrier concentration and its dependence on oxygen partial pressure can be obtained from the charge neutrality condition:
n = N D − N A = N D (1 − Θ ) = [O N ](1 − Θ) and n = K * (1 − Θ) pO1 /22
(4)
-where Θ is the compensation ratio NA/ND. Since the oxygen donor is shallow, n ≈ ND - NA. The carrier concentration can be calculated once the compensation ratio Θ is known. It has been shown for n-type GaN the compensation ratio is nearly independent of donor concentration and is of the order of 0.4 [10]. The theoretical expression of the free electron concentration versus oxygen partial pressure can be calculated at growth temperature [9-10] using Eqns. 1-4, where the site density Nsite= 4.4×1022 cm-3 and the effective density of states is given by Nc = 4.98×1014T3/2. Fig. 1 shows the dependence of carrier concentration on oxygen dopant partial pressure. The carrier concentration increases as the square root of oxygen partial pressure up to 7×1018 cm-3. The solid line is the calculated dependence of the free electron concentration on oxygen partial pressure using the formation energy as a fitting parameter. There is good agreement between theory and
F99W3.80
experimental data up to 7×1018 cm-3, as seen in Fig. 1 for a formation energy of 1.3 eV. Since the measured electron concentration is directly proportional to the square root of the oxygen partial pressure and proportional to the oxygen donor concentration, it can be concluded that oxygen is a simple donor in GaN. The measured oxygen solubility, how
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