1. Introduction

Most metal-semiconductor contacts are rectifying. The electronic transport across such Schottky contacts is characterized by their barrier heights. The barrier height is the energy distance between the Fermi level W_F and the respective majority carrier band edge at the interface (respectively, the valence-band maximum W_vi for p- and the conduction-band minimum W_ci for n-type semiconductors). The famous Schottky-Mott rule Reference Schottky[1] Reference Mott[2] predicts the barrier height to be equal to the difference between the electron affinity of the semiconductor and the work function of the metal. Schweikert (see Reference Schottky[3]) was the first to test this rule. He found the barrier heights of metal-Se contacts to vary proportional to the work functions of the metals used but with a slope much smaller than unity. This strong deviation from what is predicted by the Schottky-Mott rule was explained by interface states Reference Bardeen[4]. At metal-semiconductor interfaces, the wavefunctions of the metal electrons decay exponentially into the semiconductor in the energy range where the metal conduction band overlaps the semiconductor band gap. These wavefunction tails form the continuum of the metal-induced gap states (MIGS) Reference Heine[5] which are the intrinsic interface states in such contacts.

The character of the metal-induced gap states varies across the bandgap from mostly donor-like to predominantly acceptor-like closer to the valence and the conduction band, respectively. When the respective branch point is above, coincides with, or below the Fermi level, then the corresponding net charge-density in the metal-induced gap states is positive, zero, or negative.Therefore, these branch points are also called the charge neutrality levels (CNL) of the MIG states. The energy position of the Fermi level at a metal-semiconductor interface, and by this its barrier height, depends on the occupation of the MIGS.

Interfaces are electrically neutral. Therefore, the charge densities on both sides of an interface are of equal magnitude but opposite sign. Pauling Reference Pauling[6] described the ionicity of diatomic molecules by the difference of the atomic electronegativities. A generalization of this concept models the charge transfer across metal-semiconductor interfaces by the difference X_m - X_s of the electronegativities of the metal and thesemiconductor in contact.

The MIGS-and-electronegativity model predicts barrier heights to vary as Reference Monch[7]

on semiconductors doped n-type. The zero-charge transfer barrier height ϕ _cnt = W _ci − W _cnt results when the electronegativity difference X _m − X _s is zero. As a consequence of this, the Fermi level coincides with the charge neutrality level of the MIGS. The MIGS-and-electronegativity model predicts the barrier heights of ideal metal-semiconductor contacts to be determined by two parameters: the energy position W _cnt − W _v (Γ) of the charge neutrality level of the MIGS with regard to the valence-band maximum and the slope parameter S _x = ∂ϕ _Bn / ∂X _m .

The MIG states represent the primary mechanism which determines the barrier heights in ideal, i.e., intimate, abrupt, defect-free, and laterally homogenous metal-semiconductor contacts. Deviations from what is predicted by the MIGS are then caused by secondarymechanisms, e.g. interface dipoles induced by specific interface structures or layers of foreign atoms and interface defects Reference Kampen and Mönch[8].

Research on both ohmic and Schottky contacts are of current interest for GaN. Khan et al. Reference Khan, Detchprom, Hacke, Hiramatsu and Sawaki[9] measured 0.91 eV Schottky barrier height for Au/GaN contacts. The barrier heights of Ti and Au contacts on GaN were determined by Binari et al to be 0.59 eV and 1.19 eV, respectively Reference Binari, Dietrich, Kelner, Rowland, Doverspike and Gaskill[10]. For Pt and Pd contacts, barrier heights of 1.04 eV and 0.94 eV, respectively, were reported Reference Guo, Feng, Guo, Pan and Chang[11].

In the present study, Pb and Ag were evaporated on n-type α-GaN epilayers grown on sapphire. These contacts are rectifying.Their zero-bias barrier heights ϕ _bn were evaluated from the current-voltage (I/V) characteristics. Our experimental data and those previously published by others are analyzed by applying the MIGS-and-electronegativity model.

2. Experimental

The substrates used were cut from n-type α-GaN epilayers on sapphire (Cree Research Inc.). The doping level of these layers is below 5x10¹⁶ cm^-3. The following cleaning procedure was applied. The samples were first dipped for 1 min into hydrofluoric acid which was then diluted by a buffered HF-solution (HF:NH₄F:NH₄OH) having pH = 9, then rinsed in de-ionized water, blown dry with N₂ gas, and transferred into the UHV system. There they were heated to a temperature of about 800° C and simultaneously exposed to a Ga flux with a rate of 1x10¹⁶ cm^-2 s^-1. The Ga flux was shut off after 10 min of exposure and the samples were further heated for 30 min. The surface cleanliness was checked by photoemission excited with Mg(Kα) radiation. The spectra recorded showed no trace of residual surface impurities. All surfaces showed sharp 1x1 LEED patterns.

After surface preparation, Pb or Ag was evaporated onto the clean GaN surfaces from Knudsen cells. In front of the samples a mask was placed which had circular openings with nominal diameters of approximately 1 mm. The exact diameter of the diodes was evaluated by using a microscope. The metal evaporation rate was monitored by a quartz-crystal thickness monitor and adjusted to 0.05 nm/s. Usually, a total of 150 nm of metal was deposited. The I/V measurements were performed outside the UHV system at room temperature in the dark. Ohmic contacts were achieved by rubbing Ga into the GaN with an Al-pencil.

3. Results

The Ag and Pb/n-α-GaN contacts were always rectifying. Figure 1 shows the forward I/V characteristics of one diode each at T=296 K. For thermionic emission over the barrier the current density of Schottky contacts as a function of applied voltage V_a is given by Reference Rhoderick and Williams[12],

Figure 1. I/Vcharacteristics of Ag- and Pb/n-α-GaN Schottky diodes at room temperature.

where nis the ideality factor, A^** is the effective Richardson constant, and k_B and e₀ are Boltzmann`s constant and the elementary charge, respectively. The effective mass of the conduction electrons in GaN, m^* = 0.22 m₀ Reference Drechsler, Hofmann, Meyer, Detchprohm, Amano and Akasaki[13], gives an effective Richardson constant A^**  = 26.4x10⁴ A/cm²K. This value is used here. For applied voltages larger than 3k _BT/e₀ ≈ 0.08 V the data displayed in Figure 1 exhibit the semilogarithmic behavior expected from equation 2. The deviation from the straight line for applied voltages larger than 0.15 V is due to the sample series resistance, the back contact, and the external electrical connections. Least-squares fits of equation 2 to the linear portions of the I/V curves shown in Figure 1 give barrier heights of 0.7 eV and 0.72 eV and ideality factors of 1.57 and 1.28 for the Ag and the Pb contacts, respectively.

Barrier heights and ideality factors vary from diode to diode. However, a linear correlation between both quantities was observed for Ag/S/n-GaAs(001) Reference Monch, Schmitsdorf, Kampen, Stockhausen and Lockwood[14], Ag/n-Si(111)-“7×7”, Ag/n-Si(111)-1x1 Reference Schmitsdorf, Kampen and Mönch[15], Ag/n-Si(111):H-1x1 Reference Kampen, Schmitsdorf and Mönch[16], Pb/H:p-Si(111) and Pb/n-Si(111) Schottky diodes Reference Kampen and Mönch[8]. Therefore, the barrier heights of all our Ag- and Pb/n-αGaN contacts are plotted in Figure 2 versus their ideality factors. The straight lines are least-squares fits to the data.

Figure 2. Zero-bias barrier heights of Ag- and Pb/n-α-GaN Schottky diodes as a function of the respective ideality factor.

4. Discussion

Tung Reference Tung[17] studied the potential distribution and the current transport in Schottky contacts with non-uniform barrier heights along the interface. He calculated effective barrier heights and ideality factors of such patchy contacts as a function of the shape and size of the inhomogeneities and the deviations of their barrier heights from the value of the homogenous interface. A combination of two relations derived by Tung indeed gives a linear correlation between effective barrier heights and ideality factors of nonuniform contacts. Interface defects, for example,may induce a non-uniform distribution of barrier heights and increase the ideality factor.

The barrier height of homogeneous metal-semiconductor contacts are lowered and become voltage-dependent due to the image-force or Schottky effect. For the GaN samples used the respective ideality factor results as n_if =1.01 Reference Schmitsdorf, Kampen and Mönch[15] Reference Kampen, Schmitsdorf and Mönch[16].The extrapolation of the least-squares fits in Figure 2 to this ideality factor gives zero-bias barrier heights of 0.82 eV and 0.73 eV for uniform Ag and Pb contacts, respectively. The two important parameters of the MIGS-and-electronegativity model are the CNL and the slope parameter. The slope parameters are given by the optical dielectric constant ε _∞ of the respective semiconductor Reference Monch[18]

The parameter A_x  = 0.86 accounts for the use of Miedema's electronegativity scale. The MIG states derive from the virtual gap states of the complex semiconductor band structure. Their branch points are given by Reference Monch[19] Reference Monch[20]

where W_dg is the dielectric band gap Reference Penn[21] and

is the position of the valence band at the mean-value or Baldereschi point in the Brillouin zone Reference Baldereschi[22] with regard to the valence band maximum. This energy difference is calculated using the empirical tight-binding method. Equation 4 was derived for zincblende-structure semiconductors.

From equations (3) and (4) one obtains a slope parameter S_x  = 0.29 eV/Miedema-unit. and W _bp − W _v (Γ) = 2.35 eV for cubic ß-GaN. However, the barrier heights reported here and by others Reference Khan, Detchprom, Hacke, Hiramatsu and Sawaki[9] Reference Binari, Dietrich, Kelner, Rowland, Doverspike and Gaskill[10] Reference Guo, Feng, Guo, Pan and Chang[11] were all obtained with wurtzite rather than zincblende GaN. SiC is another example for such polytypism. Barrier heights were reported for Schottky contacts on the cubic 3C- and hexagonal 6H-SiC. Mönch Reference Monch, Ohdomari, Oshima and Hiraki[23] analyzed these data and found the energy position of the CNL with regard to the valence band maximum to be the same with both SiC polytypes.Therefore, the positions of the CNLs in β- and α-GaN with regard to the valence band maximum are also assumed to be identical.

Figure 3 displays the barrier heights of uniform Ag and Pb contactson n-type α-GaN which were obtained by extrapolation of the experimental data to n_if  = 1.01. The MIGS line of GaN, which results from equations (3) and (4), is also shown in Figure 3. The Ag and Pb/GaN data agree with the predictions from the MIGS model. Therefore, these values are characteristic not only of uniform but also of ideal α-GaN Schottky contacts. Figure 3 also displays the experimental data published by Khan et al. Reference Khan, Detchprom, Hacke, Hiramatsu and Sawaki[9], Binary et al. Reference Binari, Dietrich, Kelner, Rowland, Doverspike and Gaskill[10], and Guo et al. Reference Guo, Feng, Guo, Pan and Chang[11]. These data also confirm the predictions of the MIGS-and-electronegativity model. From Figure 3 it follows that ideal metal-GaN contacts are rectifying. In this respect GaN exhibits the same behavior as almost all metal-semiconductor contacts. Genuinely ohmic contacts are only observed with metal contacts on n-InAs and p-GaSb. Therefore, ohmic contacts on GaN require specific preparational methods which e.g. produce tunnel contacts with apparently ohmic I/V characteristics.

Figure 3. Barrier heights of α-GaN Schottky contacts as a function of the electronegativity difference X _m − X _GaN . (O) data from Refs. Reference Monch, Schmitsdorf, Kampen, Stockhausen and Lockwood[14], Reference Schmitsdorf, Kampen and Mönch[15], Reference Kampen, Schmitsdorf and Mönch[16].