B. Schineller

M. Germain

M. Heuken

M. Schmeits

N.D. Nguyen

English

Crossref

Investigation of Defect Levels in Mg-Doped GaN Schottky Structures by 
Thermal Admittance Spectroscopy
N. D. NGUYEN (a), M. GERMAIN (a), M. SCHMEITS (a), B. SCHINELLER (b), and M. HEUKEN (b, c)
(a)  Institut de Physique, Université de Liège, B5, B-4000 Liège, Belgium
(b) AIXTRON AG, Kackerstr. 15-17, D-52072 Aachen, Germany
(c)  Institut für Halbleitertechnik, RWTH Aachen, Templergraben 55, D-52056 Aachen, Germany
Schottky structures based on Mg-doped GaN layers grown by metalorganic chemical vapor deposition 
(MOCVD) on sapphire substrate are studied by thermal admittance spectroscopy from 90 K to room 
temperature. Evidence of two impurity levels results from the analysis of the observed peaks in the conductance 
curves, whose positions and strengths are temperature dependent. The experimental results are analyzed within a 
detailed theoretical study of the steady-state and small-signal electrical characteristics of the structure. Numerical 
simulations are based on the solution of the basic semiconductor equations for the structure consisting of two 
Schottky diodes connected back-to-back by a conduction channel formed by the GaN layer.
Introduction 
Successful Mg-doping of GaN has led to a breakthrough in the use of this wide band-gap compound 
semiconductor both for optoelectronics and for high-power, high-frequency electronic devices. As Schottky-type 
junctions are the building blocks of these devices, we have performed a thorough analysis of the conduction 
mechanism in GaN : Mg double Schottky structures. We use numerical simulation to fully explain the 
experimental results obtained by thermal admittance spectroscopy. It is shown that, due to the simultaneous role 
of Mg both as a dopant and as a deep impurity, the classical analysis of the Arrhenius plot underestimates the 
defect ionization energy. Moreover, we show the existence of a second shallow acceptor state with an activation 
energy of several tens of meV.
Experimental Results 
Epitaxial growth by metalorganic chemical vapor deposition (MOCVD) of the GaN layers studied in this work 
has been detailed elsewhere [1]. The structures consist of a nucleation layer grown directly on top of the sapphire 
substrate, followed by a 1 µm thick undoped buffer layer and a 2 µm thick Mg-doped layer. Coplanar metallic 
contacts (Ni/Au) of 0.5 mm diameter and separated by 2 mm, were evaporated on top of the layers.
In Fig. 1, frequency responses of the conductance G divided by ω = 2πf, where ƒ is the measurement frequency, 
of a typical sample, are shown for temperatures ranging from room temperature (RT) down to 90 K. Between 
RT and 200 K, the G/ω curves show a large peak at the cutoff frequencies fc in C-f curves (not shown here). The 
amplitude of this peak decreases as the temperature is lowered. At around 200 K, a shoulder emerges from the 
high-frequency side of the mentioned peak and is resolved into another peak for temperatures below 170 K. Its 
position is also temperature dependent.
Published in : Physica Status Solidi B. Basic Research (2001), vol. 228, iss. 2, pp. 385-389.
Authors : N. D. Nguyen, M. Germain, M. Schmeits, B. Schineller, and M. Heuken
Status : Postprint (Author’s version)
Fig. 1. Experimental curves of conductance G divided by ω = 2πf as function of frequency ƒ for temperatures 
ranging from a) 293 (RT) to 210 K and b) 190 to 90 K (curves from top to bottom)
Numerical Simulation 
It is known that Mg gives rise to an acceptor-type energy level in the GaN bandgap. Values ranging from 100 to 
250 meV above the valence band edge EV are reported [2-6]. We denote by EtA and NtA the energy position and 
the total concentration of the level corresponding to the acceptor Mg impurity. In the same way, we introduce EtB 
and NtB, the energy position and the total concentration of the acceptor level whose existence is suggested by the 
experimental characteristics at low temperature. To investigate their role in the electrical characteristics of the 
Schottky diodes, explicit inclusion of the related active population in the semiconductor equations is necessary 
[7].
The classical basic semiconductor equations are solved numerically in order to obtain as function of the one-
dimensional x-coordinate, the hole concentration p, and the occupied level concentrations ntA and ntB which are, 
with the electrical potential, the primary unknowns involved in the as-formulated system of equations. After 
solving the latter for the steady-state conditions, the small-signal amplitudes resulting from the application of an 
ac voltage of frequency ƒ = ω/2π are calculated. A fixed Schottky barrier height qφb, which is chosen identical 
for both contacts, is imposed in the expression of the boundary conditions. As a result of the ac calculation, the 
total current density, composed of the hole current density and the displacement current, is obtained. In a final 
step, we determine the conductance G and the capacitance C from the complex admittance Y = G + iωC [7]. 
Further physical parameters are necessary to effectively reproduce the experimental admittance curves. In 
addition to qφb, EtA and EtB, NtA and NtB, which have already been introduced, one needs the values of the defect 
thermal capture cross sections, ΣA and ΣB. The hole effective mass is taken as mh = 0.8m0. The value of the hole 
mobility µh is fixed at 10 cm2/Vs above T0 = 150 K and given a (T/T0)a dependence below that temperature, with 
α being a free parameter. This T-dependence reproduces the decrease of µh with temperature which has been 
observed experimentally [4]. In order to reproduce with a one-dimensional formalism the electrical 
characteristics of a structure which is three-dimensional by nature, we have introduced a geometrical parameter 
Rµ multiplying the carrier mobilities and whose value is of the order of the ratio between the GaN layer 
thickness, which is in the micrometer range, and the contact diameter, which is in the millimeter range.
Discussion 
With the numerical procedure explained above, the electrical characteristics can be calculated at various 
temperatures, starting from an initial guess for the free parameters. A least-square fit procedure, based on the 
comparison of the electrical characteristics obtained from the numerical calculation to the experimental data, is 
used to determine the best values of the parameters. This optimization procedure yields the following values: 
(EtA - EV) = 210 meV, (EtB - EV) = 30 meV, NtA = 1 × 1019 cm-3, NtB = 2 × 1016 cm-3, σA = 2 × 10-19 cm2, σB = 2 × 
10-19 cm2, qφb = 1.05 eV, Rµ = 0.007, and α = 3. The resulting G/ω curves for six temperatures are shown in Fig. 
2a. The as-obtained values of the parameters are comparable to those found in the literature for the Schottky 
barrier height [8, 9] in Au-Ni/p-GaN contacts, the activation energy of the Mg-related acceptor level determined 
by admittance spectroscopy [2, 3] or by Hall measurements [3, 4], and the thermal capture cross section of the 
defect A level [3]. The small values obtained for the activation energy and the total concentration of the defect B 
level, combined with the fact that its effect only appears below 150 K with a weaker amplitude than for level A, 
may greatly reduce the possibility to easily detect such a level. Nevertheless, more than one acceptor level has 
been observed in experimental works [2].
Published in : Physica Status Solidi B. Basic Research (2001), vol. 228, iss. 2, pp. 385-389.
Authors : N. D. Nguyen, M. Germain, M. Schmeits, B. Schineller, and M. Heuken
Status : Postprint (Author’s version)
Fig. 2. a) Theoretical G/ω curves as function of frequency for temperatures between RT and 90 K. b) to g) 
Theoretical capacitance C (dashed lines) and conductance G/ω (dotted lines) curves for the short diode (SD) 
case, and calculated capacitance C (dash-dotted lines) and conductance G/ω (full lines) curves for the long 
diode (LD) case. Results are shown for temperatures between 350 and 100 K. The curves are magnified for 
temperatures of 150 K (× 2) and 100 K (× 10). Positions of the cutoff frequencies fc and of the defect transition 
frequencies ftA and ftB are shown for some G/ω curves
In Figs. 2b to g, we show the calculated capacitance and conductance (G/ω) curves of two different structure 
types between 350 and 100 K.  One (labeled LD, for "long diode") is the complete double Schottky diode 
structure which has been studied up to now. The other one is essentially the same structure but with a total length 
of 1 µm and Rµ = 1 (labeled SD, for "short diode"). In this case, series resistance effects, which are explained 
below, are expected to play no role. The electrical characteristics for temperatures above 200 K are first 
discussed. In Figs. 2b, c, d and e, the cutoff frequency in the capacitance curve and the peak in the G/ω curve for 
the SD case are the signature of the Mg-related defect whose transition frequency is denoted by ftA. Starting with 
this observation, we found that for T > 240 K, the cutoff frequency fc in the LD case is mainly due to an 
electrical cutoff mechanism, i.e. fc ≈ fRC, with fRC = 1/(2πRSC), where RS is the series resistance of the structure 
and C the low-frequency value of the capacitance, while for T < 240 K, fc can be identified with ftA. The cutoff 
frequency for the LD case is therefore the feature resulting from the combination of two mechanisms which are 
both present in the 200-350 K temperature range. An Arrhenius plot based on the temperature dependence of the 
peak position between 200 and 300 K yields activation energies of 176 and 107 meV, respectively, for the SD 
case and the LD case, which are both distinct from the input value of 210 meV. This is partly explained by the 
fact that the Mg impurity plays a double role: it acts as a dopant and as a deep impurity. The assumptions leading 
to the identification of the defect transition frequency with the thermal emission rate are not fulfilled [7, 10], 
even when resistance effects do not take place, i.e. in the SD case.
Below 200 K, the main peak in G/ω moves below the 100 Hz limit of the measurement equipment. A shoulder 
appears in the 103-104 Hz frequency range and leads to a second resolved peak around 4 × 104 Hz for 
temperatures around 150 K (Fig. 2f). The position of the latter is once more that of a RSC electrical cutoff whose 
evolution with temperature is mainly due to the variation of the series resistance RS. The related cutoff frequency 
1/(2πRSC) is proportional to the conductivity of the layer and therefore proportional to p and µh. The calculated 
bulk concentration of holes p between 130 and 160 K varies only weakly with temperature, this explains why the 
displacement of this peak is small in this temperature range. Below 130 K, the displacement of the cutoff 
frequency is explained by the decrease of p due to the variation of the bulk value of (EF - EtB), where EF is the 
Fermi energy, and by the reduction of µh due to various scattering mechanisms. In Fig. 2g, the transition 
frequency ftB of defect B appears at 104 Hz in the admittance curves of the SD case at 100 K.
Conclusion 
This work shows that only a complete numerical study allows a correct interpretation of the admittance curves. 
In particular, it is shown that deducing activation energies from an Arrhenius plot of the cutoff frequencies would 
lead, in the case of the system we have studied, to an underestimation of the activation energies.
Acknowledgements 
Financial support by the Belgian Fonds National de la Recherche Scientifique (Contract No. 9.4565.96F) and by 
an INTAS grant No. N97-0995 are gratefully acknowledged.
Published in : Physica Status Solidi B. Basic Research (2001), vol. 228, iss. 2, pp. 385-389.
Authors : N. D. Nguyen, M. Germain, M. Schmeits, B. Schineller, and M. Heuken
Status : Postprint (Author’s version)
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Published in : Physica Status Solidi B. Basic Research (2001), vol. 228, iss. 2, pp. 385-389.
Authors : N. D. Nguyen, M. Germain, M. Schmeits, B. Schineller, and M. Heuken
Status : Postprint (Author’s version)


Investigation of Defect Levels in Mg-Doped GaN Schottky Structures by Thermal Admittance Spectroscopy

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Investigation of Defect Levels in Mg-Doped GaN Schottky Structures by Thermal Admittance Spectroscopy

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