Electrical characterization and generation of EL in SBDs on

On the sample with NCr = 6×10¹⁹cm⁻³ and due to silicon co-doping a charge carrier density ofn= 1×10¹⁸cm⁻³, Schottky barrier diodes (SBDs) were prepared by electron beam evaporation of Ni in vacuum at a pressure of few 10⁻⁶mbar on freshly cleaved (100) β-Ga2O3 surfaces using a shadow mask with circular holes

5.3 Chromium as an example for optical active ions in the wide band gap semiconductor β-Ga2O3

of 0.4 mm and 0.8 mm diameter. To obtain semi-transparent Ni contacts, their thickness was limited to 20 nm. Ohmic contacts were formed by painting a film of InGa eutectic on whole the sample’s back side area of 5×5 mm². No annealing was necessary to obtain acceptable ohmic behavior, i.e. the back side contacts were not current limiting. Capacitance-voltage (C-V) measurements reveal a net donor concentration of N_D−N_A = 10¹⁸cm⁻³, which is consistent with the Hall charge carrier concentration and a built-in voltage V_bi= 0.9 V.

A typical current-voltage (I-V) characteristic of the Ni onβ-Ga2O3:Cr,Si SBDs is shown in Fig. 5.11(a). The SBDs show a rectification ratio ofIforward/Ireverse ≈10⁶ at

±1 V. Although this is four orders of magnitude lower compared to SBD prototypes for power electronics,[92] it is not unexpected for our SBDs since they were fabricated on base material of hundred times higher net donor concentration and without any precautions for edge terminations. However, we will explain in the following why the high leakage currents of the SBDs are essential for observing the EL. For this purpose, we need to introduce the following two parameters. First, the depletion layer width W of the SBD which is calculated by:[63]

W =

where e is the elementary charge, N_D = 10¹⁸cm⁻³ is the donor concentration mea-sured, ε_r = 10.2 is the relative static dielectric constant perpendicular to the (100) plane,[1] ε0 is the vacuum permittivity, V is the applied bias voltage, Vbi = 0.9 V is the built-in voltage obtained from C-V measurements for the actual Ni Schot-tky contacts and T = 300 K is the temperature. Second, the average electric field hFi = ¹₂Fmax, which can be derived from the electric field distribution F(x) in the depletion layer (0≤x≤W) of a homogenously doped SBD:[63]

F(x) = eN_D

ε_rε₀(W −x) =Fmax− eN_D

ε_rε₀x . (5.4)

In Fig. 5.11 the leakage current density is plotted versusV,W andhFi, whereby the calculated values of W given in Fig. 5.11(a) are consistent with the measured ones from the C-V measurements. The leakage current density increases by several orders of magnitude with increasing bias while the average electric field and the depletion layer width only increase by factor 2 and 3, respectively. For current densities above 0.1 A/cm² (reverse biases > 9 V) red EL occurs with an intensity well visible to the naked eye (see Fig. 5.12(a)). The spectrum of the EL at room temperature is shown in Fig. 5.12(b) for bias voltages from −4 V to −10 V. The EL spectrum is similar to the reported PL of Cr³⁺ inβ-Ga2O3 at room temperature. It is characterized by a broad but structured band around 700 nm (≈ 1.8 eV), which is featured by two lines related to the well-known R1 and R2 transitions.[117–120] This EL is caused by electron impact excitation in the space charge region under the Ni Schottky contact what we conclude from the following facts:

• The intensity of the EL linearly increases with increasing current density under reverse biasing conditions (see Fig. 5.12(c)).

5.3 Chromium as an example for optical active ions in the wide band gap semiconductor β-Ga2O3

• The EL can be only obtained under reverse bias, although similar current densities can be achieved under forward bias (see Fig. 5.11(a)).

• Under reverse bias, the electrons get accelerated in the space charge region and may take up a maximum energy of E_e =eWhFi =eV_bi−V − ^kB_e^T, which is already above 2 eV at V =−1.2 V, and therefore large enough to populate the luminescent state (≈1.8 eV) by impact excitation.

Figure 5.11: (a)Characteristic curve of the current density over the voltage of a nickel Schottky diode on β-Ga₂O₃:Cr,Si at room temperature. The inset shows a scheme of the device structure.

(b)The current density over the average electric field in the SBD is shown for the reverse bias voltages interesting for the generation of the EL.

Therefore, the reverse leakage current of the SBDs is indispensable for the gen-eration of the EL. Such a light-emitting device has to be optimized on it which leads to the following prerequisites. Since the higher the shallow donor concentration, the higher the electric field, and the higher the acceleration of electrons in the depletion layer of the SBD needed for the impact excitation, the shallow donor concentra-tion must be as high as possible. The impact excitaconcentra-tion necessary for the EL is most effective when the charge carriers are injected by thermionic emission over the Schottky barrier. Then the charge carriers can take up the highest possible energy by starting their travel through the depletion layer of the reverse biased SBD at the

5.3 Chromium as an example for optical active ions in the wide band gap semiconductor β-Ga2O3

metal-semiconductor interface where they are subjected to the maximum electric field. Charge carriers injected by tunneling (or field emission, FE) and by thermally assisted tunneling (or thermionic-field emission, TFE) start acceleration inside the depletion layer at a lower electric field strength since they tunnel through the Schot-tky barrier (in case of TFE at different heights). Hence, TFE and FE injected carriers may also contribute to impact excitation if taking up enough energy in the remaining electric field region. In particular, we expect that at the rim of our SBDs, which do not have an edge termination, TFE and FE currents contribute to the total leakage current and likewise, to impact excitation of EL.

The Cr concentration is optimal as long as it is high enough for a linear correla-tion between optical emission with current density, since in this case each conduccorrela-tion electron has the possibility to excite the luminescence in a Cr³⁺ ion. Hence, the cur-rent density is in this case the limiting factor. If the Cr concentration is too low and thus the limiting factor, the optical emission with current would saturate since not each conduction electron has the probability to excite the luminescence. Con-cluding, the chromium concentration is with 6×10¹⁹cm⁻³ in our case high enough since the intensity of the EL correlates with the leakage current (see Fig. 5.12(c)).

The optimal silicon concentration was in our case ND ≈ 10¹⁸cm⁻³, since simple Schottky structures were used. For higher charge carrier concentrations the inten-sity of the EL was lower, probably due to leakage current which is not fully related to thermionic emission. The fabrication of more advanced SBDs with a guard ring and high quality layers with clean surface may lead to the possibility to use even higher shallow donor concentrations.

Figure 5.12: (a)Photographic image of the electroluminescence (EL) at room temperature gen-erated in a reverse biased Ni Schottky barrier diode.

(b)The room temperature spectrum of the EL under different biasing conditions.

(c) The peak intensity (at 712.5 nm) of the EL versus the current density in the Schottky diode in logarithmic scale. The inset shows the same measurement in linear scale including a linear fit.