The influence of the columnar structure of heteroepitaxial nitride layers on electronic transport has been described within the model of thermionic emission of carriers through potential barriers formed at grain boundaries. Dependence of the potential barrier height on the material properties and applied external voltage has been calculated. Potential barriers heights for gallium nitride layers grown by the metalorganic vapour phase epitaxy method has been estimated to be in the range of 20-60 meV and 10-40 meV in the dark and under illumination, respectively

A Szyszka

B Paszkiewicz

M Tłaczała

R Paszkiewicz

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Materials Science-Poland, Vol. 26, No. 1, 2008 
Influence of the columnar structure of heteroepitaxial 
nitride layers on the transport of electrons 
A. SZYSZKA*, B. PASZKIEWICZ, R. PASZKIEWICZ, M. TŁACZAŁA 
Faculty of Microsystem Electronics and Photonics, Wrocław University of Technology, 
ul. Janiszewskiego 11/17, 50-372 Wrocław, Poland 
The influence of the columnar structure of heteroepitaxial nitride layers on electronic transport has 
been described within the model of thermionic emission of carriers through potential barriers formed at 
grain boundaries. Dependence of the potential barrier height on the material properties and applied exter-
nal voltage has been calculated. Potential barriers heights for gallium nitride layers grown by the metalor-
ganic vapour phase epitaxy method has been estimated to be in the range of 20–60 meV and 10–40 meV 
in the dark and under illumination, respectively. 
Key words: gallium nitride; columnar structure; electronic transport 
1. Introduction 
Gallium nitride and its alloys are applied for fabrication of UV light detectors and 
emitters and for high frequency, high power field effect transistors. Despite a great 
progress in device technology, the highest predicted and calculated parameters of fab-
ricated structures have not been obtained. Discrepancies between the theoretical and 
obtained parameters of the devices are mainly caused by an assumption that heteroepi-
taxial layers of A(III)N compounds have singlecrystalline structure. This assumption 
neglects the fact that epitaxial layers of nitrides always have columnar structure with 
low angle boundaries. Distribution of sizes of crystallites in heteroepitaxial layers 
grown by metal-organic chemical vapour deposition (MOCVD) method was examined 
by high resolution X-ray diffractometry [1]. It was shown that sizes of crystallites in 
a layer depend on conditions of the growth process and that GaN layers grown on 
sapphire substrates consist of crystallites of various sizes. 
Dangling bonds and atoms of impurities existing in disordered boundary area in-
troduce deep trap levels in the forbidden band of the material. Negatively charged 
 __________  
*E-mail: adam.szyszka@pwr.wroc.pl 
A. SZYSZKA et al. 222
acceptor traps, in n-type material, form potential barriers for a majority of carriers. 
Influence of these barriers on the surface potential in GaN layers was examined by the 
scanning Kelvin probe microscopy [2]. Nonuniformity of photocurrent flow in AlGaN 
MSM detectors, caused by columnar structure of the layer, was observed by the light 
beam induced current technique [3]. 
2. Calculations 
One-dimensional model which allowed the analysis of the formation of potential 
barrier at the grain boundary was evaluated (cf. [4–7]) in order to describe electronic 
properties of polycrystalline silicon. 
 
Fig. 1. Scheme of the energy band diagram of a potential barrier formed at the boundary of two grains:  
Ef  – Fermi energy level, Eb – potential barrier height, Efg – Fermi energy level in the volume of a grain, 
Efb – Fermi energy level in grain boundary in neutral conditions, ΔEf – shift of the Fermi level at the grain 
boundary caused by the excess charge (ΔEf = Efg – Efb), d – width of the space charge region 
The energy band diagram of two adjacent grains in a semiconductor is presented 
in Fig. 1. The model assumes a constant distribution of densities of deep trap states at 
the grain interface. The negative charge associated with interface trap states is ba-
lanced by the positive net charge of uncompensated ionized shallow donor states. Do-
nor states occur in GaN layers mainly due to the presence of N vacancies. Non-
compensated donor states are localized in space charge regions created on both sides 
of the grain boundary. The height of the potential barrier depends on the relation be-
tween density of the interface states and concentration of donor states in the grains. It 
could be concluded (Fig. 2) that for higher values of the concentration of shallow do-
nors in the volume of a grain (Nd), a higher density of acceptor trap states at the grain 
boundary (NT) is needed to form the potential barrier. We have also found that for very 
Transport of electrons in heteroepitaxial nitride layers 223
high values of trap densities at the grain boundary, the potential of the barrier was 
pinned and was dependent only on Efb. 
 
Fig. 2. Dependence of the calculated height of the potential barrier on the trap states density at grains 
boundary for various concentrations of donors in the grains (the calculation was carried out for Efb = 3.1 eV) 
 
Fig. 3. Dependence of the calculated height of the potential barrier on the applied voltage at grains 
boundary for various concentrations of donors in the grains (the calculation was carried out for Efb = 3.02 eV) 
A. SZYSZKA et al. 224
The calculated dependence of the height of the potential barrier on the external vol-
tage is presented in Fig. 3. The NT value at the grain boundary was assumed to be 4×1017 
cm–2·eV–1 based on Refs. [8] and [9]. For small values of the applied voltage the barrier 
height remained constant. Further, with subsequent increase of the voltage, the barrier 
height started to decrease to the point where it vanished for a defined value of voltage. 
The breakdown voltage of the potential barrier was higher for the higher initial barrier 
height. After reaching the breakdown voltage, the conductivity of the layer was con-
trolled only by bulk conductivity of grains. This effect could explain the observed phe-
nomenon that despite small mobility of electrons in heteroepitaxial layers of nitrides, the 
measured drift velocity of electrons in high electric fields is very high [10]. 
 
Fig. 4. Influence of the size of grains on the potential barrier height 
for various concentrations of donors in the grains 
The dependence of the potential barrier height on the sizes of grains is presented 
in Fig. 4. It was observed that decrease of grain sizes did not influence the potential 
barrier height till the point when it reached the value equal to the double width of the 
space charge region. This occurs when the space charge regions occupy the whole 
grain. Further decreasing of the grain sizes caused the decrease of the barrier height 
due to overlapping of the depletion regions. These phenomena could be responsible 
for spatial non-uniformities in photo-response of AlGaN MSM detectors [3]. 
The dependence of the barrier height on the concentration of donors in grains is 
presented in Fig. 5. In the area of small donor concentration, its increase caused the 
increase of the barrier height due to an increase of the number of electrons trapped at 
the grain boundary. When all interface states were completely filled, the potential 
Transport of electrons in heteroepitaxial nitride layers 225
barrier height reaches its maximum. Further, any increase of the concentration of do-
nors results in a decrease of the barrier height due the increase of the compensating 
positive charge of ionized donors in the depletion layer. 
 
Fig. 5. Dependence of the calculated potential barrier height on the concentration 
of donors in the grains (calculation was carried out for Efb = 3.02 eV) 
3. Experiments 
The potential barrier heights in MOVPE gallium nitride layer have been estimated 
based on the measurements of the temperature dependence of conductivity of the epi-
taxial layer (Fig. 6). Assuming a thermionic character of emission through potential 
barriers, their heights could be evaluated from the slope of the Arrhenius plot of the 
conductivity vs. temperature. Two values of barrier heights of the GaN heteroepitaxial 
layer were measured: one for dark conditions, the other for an illuminated sample. 
Potential barrier heights have been estimated to be in the range of 20–60 meV for the 
former case and 10–40 meV for the latter one. The decrease of the potential barrier 
heights for an illuminated sample could be explained by a release of electrons from the 
trap states caused by the incident photons. That also could explain another specific 
behaviour of nitride layers, namely the persistent photoconductivity. Presumably, pho-
to-generated electrons could not re-occupy deep states because of the existence of 
residual negative charge at grain boundaries repelling electrons. Thus grain boundaries 
remain lowered for a long time after switching off the illumination.  
A. SZYSZKA et al. 226
 
Fig. 6. Temperature dependence of conductivity of GaN heteroepitaxial layer 
The nonlinearity of the Arrhenius plot observed in the low temperature region 
could indicate the occurrence of other conduction phenomena in nitride layers such as 
tunneling effect and/or impurity band conduction. 
4. Conclusions 
The model of formation of potential barriers at the grain boundaries of heteroepi-
taxial layers of nitrides has been put forward. The dependence of the barrier height on 
the layer parameters such as the density of deep traps, concentration of shallow do-
nors, energy of Fermi level at grain boundary in neutral conditions and the size of 
grains has been calculated. The presence of potential barriers at grain boundaries al-
lowed us to explain some characteristic properties of nitride heteroepitaxial layers. 
Potential barrier heights of MOVPE GaN layers were calculated based on the depen-
dence of conductivity vs. temperature with an assumption of the thermionic character 
of the emission. 
Acknowledgements 
This work was partially supported by Polish Ministry of Science and Higher Education under Grant 
PBZ/100/1/1/2004, R0201802, PBZ-MEiN-6/2/2006, Wrocław University of Technology statutory grant 
and EU Structural Funds in Poland – Ph.D scholarschip under contract No. 49. 
Transport of electrons in heteroepitaxial nitride layers 227
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Received 28 April 2007 
Revised 16 February 2008 
 


Influence of the columnar structure of heteroepitaxial nitride layers on the transport of electrons

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Influence of the columnar structure of heteroepitaxial nitride layers on the transport of electrons

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