1. Introduction

Numerous attempts at investigating the shallow donor states in GaN have been made Reference Meyer, Volm, Graber, Alt, Detchprohm, Amano and Akasaki[1] Reference Wang, Kaplan, Ng, Doverspike, Gaskill, Ikedo, Akasaki and Amono[2] Reference Moore, Freitas and Molnar[3], but there is no clear conclusion about the properties and origin of such centers. The subject therefore still remains of interest. We try to investigate the problem by means of far infrared (FIR) magnetospectroscopy. The investigated samples were in the form of epitaxial MOCVD gallium nitride layers grown on an oriented (0001) sapphire substrate, with c-axis perpendicular to the sample substrate. The atmospheric pressure MOCVD technique starting from TMG, NH₃ and SiH₄ was used. The method used is described in detail elsewhere Reference Pakula, Baranowski, Leszczynski, Suchanek and Wojdak[4]. Using different substrate and buffer layer preparation methods two types of material were grown: relaxed (SAP) and strained (MAR). The strain in the layer is determined from the donor bound exciton spectra Reference Pakula, Wojdak, Palczewska, Suchanek and Baranowski[5]. Some of the MAR type samples were intentionally doped with silicon. The thickness of the layers varied from 2 μm to 8 μm. Prior to the optical measurements, the samples where characterized using classical transport. The temperature dependence of electron concentration and mobility is presented in Figure 1. As one can see, we are able to obtain a free carrier concentration one order of magnitude lower in MAR samples than in SAP samples. The lowest investigated concentration (sample MAR51) is about 2×10¹⁶ cm⁻³ in an 8 μm layer. We have therefore been able to dope such layers with silicon donors at the level of 10¹⁷ cm⁻³ (see Figure 1).

Figure 1. Temperature dependence of concentration and mobility for GaN epilayers grown on sapphire.

We chose the following samples for magnetooptical studies:

• • SAP119 (2 μm thick) with n_300K = 2×10¹⁷ cm⁻³, mobility μ_300K = 490 cm²/Vs;

• • MAR51 (8 μm thick) with n_300K = 2×10¹⁶ cm⁻³, mobility μ_300K = 540 cm²/Vs;

• • MAR70 (Si doped, 6 μm thick) with n_300K = 2×10¹⁷ cm⁻³,mobility μ_300K = 740 cm²/Vs.

2. Experimental results

The FIR magnetophotoconductivity and magnetotransmission were measured using a Bruker FTIR 113V Fourier transform spectrometer at magnetic fields up to 13T and temperatures of 4.3K and 2K. In the SAP sample a magnetic field dependent structure was observed at about 213 cm⁻¹ at zero field (see Figure 2). Other features are due to the optical properties of the sapphire and GaN, multilayer structure, and can be interpreted without the existence of shallow states. The magnetic field splitting and the energies of the lines (Figure 2) can be found after a careful recalculation of the experimental data. These suggest that it is a shallow donor, but with a quite large chemical shift (20 cm⁻¹ = 2.5 meV). The estimated ionization energy is about 35 meV, in agreement with previously reported data Reference Meyer, Volm, Graber, Alt, Detchprohm, Amano and Akasaki[1]. It is worth noting that the high field slope is equal to the cyclotron resonance slope with m* = 0.222 m₀.

Figure 2. (top) Photocurrent for SAP 119 at different magnetic fields. (bottom) Position of PC lines vs. magnetic field. Lines represent theoretical calculations.

A different and clearer photocurrent response can be observed for MAR samples (Figure 3). There, a sharp line is observed at 187 cm⁻¹. It splits in a magnetic field into three components, whose energy positions vs. magnetic field show a strong non-linear dependence. We assign them to inter-donor transitions from 1s to split 2p_± states.

Figure 3. (top) Photocurrent for MAR 51 at different magnetic fields. (bottom) Position of PC lines vs. magnetic field. Lines represent theoretical calculations.

The positions of the observed lines can be described using a simple model of a hydrogen-like center in a magnetic field. The splitting of 2p₋₁ 2p₊₁ states is directly related to the cyclotron energy, so one can establish the effective mass to be 0.222 m_o, which agrees very well with previously reported data Reference Wang, Kaplan, Ng, Doverspike, Gaskill, Ikedo, Akasaki and Amono[2] Reference Moore, Freitas and Molnar[3]. The high quality of the data (sharp lines) reveals a strong diamagnetic shift for all transitions, which has to be included in the description. The same behavior was measured for samples intentionally doped with silicon. The conclusion is therefore that the native donor in this group of samples has the same chemical shift (less than −0.5 meV) as a silicon donor (ionization energy of about 260 cm⁻¹ = 32.5 meV).

The structure observed in the relaxed sample is probably related to a donor with a different physical origin, with a much larger chemical shift (about 2.5 meV).

3. Theoretical description

To describe the magnetic field dependence of the transitions we used a model developed by Wheeler and Dimmock Reference Wheeler and Dimmock[6] for excitons in CdS, which takes into account both the diamagnetic shift and a correction due to the uniaxial symmetry. In this case the energies of the levels are given by the following formulas:

where

We assume that the conduction band is spherically symmetric, and therefore the electron effective mass is a scalar. We allow for differences between longitudinal (ε_z) and perpendicular (ε_x) dielectric constants. For calculations we have taken values of ε_z and ε_x from reflectivity data given in Reference Barker and Ilegems[7]. With a small adjustment of the values of ε (within experimental error) we obtained an excellent description of the experimental points (Figure 2 and Figure 3).

4. Conclusions

The following conclusions can be drawn:

• • The shallow donors in strained and relaxed GaN layers grown by MOCVD on sapphire have different origins, leading to different chemical shifts;

• • The splitting of 2p states at higher fields is equal to the cyclotron energy, which allows to determine the effective mass as m* = 0.222 m₀.

• • The energy of shallow donor states is strongly affected by the diamagnetic shift.

Some speculation can be made in this point. In strained, undoped samples the donors are silicon impurities introduced on the level of 10¹⁵ cm⁻³ during the growth procedure. In the case of unstrained samples another impurity is responsible for the creation of the donor centers. Due to the polarity of the layer Reference Pakula, Wojdak, Palczewska, Suchanek and Baranowski[5] one of the possibilities is oxygen impurities.