Homoepitxially growing layers on semi-insulating substrates are normally not influ-enced by the substrate in the sense of electrical properties. Since β-Ga2O3 is a wide band gap semiconductor, the difference in ionization energy of the shallow donor in the layer to that of the deep compensating acceptor of semi-insulating substrates can be larger then in common semiconductors. Moreover, a quite low doping con-centration of ND = 1016cm−3 is possible in these layers. Since the width of the band alignment between the layer and the substrate increases with decreasing shallow donor concentration, this has to be taken into account when growing homoepitaxi-ally a wide band gap semiconductor. Consequently, the substrate may influence the electrical properties of layers grown homoepitaxially if they are thin.
In Fig. 6.1(a)&(b) the band alignment of homoepitaxial β-Ga2O3 layers on semi-insulating substrates doped with Mg or Fe is shown. This band alignment is calculated using the Schrödinger-Poisson solver of G. L. Snider.[130] Magnesium and iron are deep acceptors compensating the unitentional n-type doping during the bulk crystal growth leading to semi-insulating substrates. Mg and Fe are supposed to have their acceptor level atEc−ET(Mg) = 3.7 eV [131, 132] and at Ec−ET(Fe) = 0.7 eV
6.1 Band alignment on semi-insulating substrates
[133], respectively. An acceptor concentration of NA = 1018cm−3 is enough to fully compensate the unintentional doping of ND = 5×1017cm−3 in the crystals.
These values for ND and NA were also applied for the calculation of the band dia-gram. In Fig. 6.1(a) the band diagram of layers with shallow donor concentrations of 1016cm−3 to 1018cm−3 on Mg doped substrates is shown. Hereby, the shallow donor ionization energy is assumed to be 36 meV and independent of the doping concentration. It is shown, that a charge depletion layer forms at the interface of the substrate and the layer due to the Fermi level adjustment. The charge deple-tion layer width is 675 nm, 225 nm, and 75 nm for shallow donor concentradeple-tions of 1016cm−3, 1017cm−3, and 1018cm−3, respectively. In Fig. 6.1(b) the same situation for layers on iron doped substrates are shown. Since the acceptor level of Fe is 3 eV closer to the conduction band than this of Mg, the charge depletion layer is much smaller. The charge depletion layer width on iron doped substrates is 360 nm, 120 nm, and 40 nm for shallow donor concentrations of 1016cm−3, 1017cm−3, and 1018cm−3, respectively. The electric field of the charge depletion layer presses the charge carriers to the surface leading to a reduced effective layer thickness and may increase surface scattering mechanisms. Consequently, it is crucial to know the layer thickness, the shallow donor concentration and the kind of acceptor impurity com-pensating the substrate to calculate the effective layer thickness for the Hall effect characterization ofβ-Ga2O3. If I want to grow a layer with ND = 1016cm−3 on a Mg doped substrate, I suppose to grow at least 1 µm thick layers and take the charge depletion layer of 675 nm into account.
Figure 6.1: Band diagram of homoepitaxial β-Ga2O3 layers with shallow donor concentrations of ND = 1016cm−3 (red), ND = 1017cm−3 (black), and ND = 1018cm−3 (blue) on semi-insulating substrates calculated with the Schrödinger-Poisson solver of G. L.
Snider.[130]
(a)Layer on a Mg doped, semi-insulating, (100) oriented substrate. Mg is assumed to have its acceptor level atEc−ET(Mg) = 3.7 eV.[131, 132]
(b)Layer on an Fe doped, semi-insulating, (010) oriented substrate. Fe is assumed to have its acceptor level atEc−ET(Fe) = 0.7 eV.[133]
In Fig. 6.2 SIMS profiles of silicon in layers with a thickness of 200 nm grown on either (100)-oriented, Mg doped substrates or (010)-oriented Fe doped substrates are shown. In both cases, at the interface between the layer and the substrate a silicon peak of 3×1018cm−3 is visible. Since silicon is supposed to be a shallow donor in β-Ga2O3,[54] if it is incorporated on an electrically active site, the interface peak will
6.1 Band alignment on semi-insulating substrates
influence the just calculated band diagram. To check if the silicon is incorporated on an electrically active site, I performed C-V measurements on a 125 nm thick layer grown on a (100)-oriented, conductive substrate. The net doping (ND−NA) profile of the layer is shown in Fig. 6.3. A shallow donor peak of 1018cm−3 at the interface between substrate and layer is visible. The shallow donor peak shows an ionization energy of 30 meV to 40 meV derived from an Arrhenius plot of the peak maximum concentrations over the inverse temperature. I attribute this shallow donor peak to the silicon peak in the SIMS measurements. Consequently, the Schrödinger-Poisson calculations of the band diagram have to be adjusted by an interface layer with ND = 3×1018cm−3 and a thickness of 10 nm and 15 nm for (100)-oriented and (010)-oriented substrates, respectively.
Figure 6.2: SIMS profile of silicon in homoepitaxial β-Ga2O3 layers on either semi-insulating, (100)-oriented, Mg doped substrates (red) or semi-insulating, (010)-oriented, Fe doped substrates (black).
Figure 6.3: Net doping profile measured by C-V measurements of aβ-Ga2O3layer homoepitax-ially grown by MOVPE on a conductive, (100)-oriented substrate at 100 K (blue), 200 K(cyan), 250 K (green), 300 K (yellow), 400 K(orange), and 450 K(red). A donor interface peak occurs with an ionization energy of30 meV to40 meV.
Fig. 6.3(a)&(b) shows the band diagrams of layers on either (100)-oriented, Mg doped substrates or (010)-oriented Fe doped substrates adjusted by a Si interface
6.1 Band alignment on semi-insulating substrates
peak. For the Mg doped substrate (Fig. 6.3(a)), the charge depletion layer width is just reduced due to the interface peak to 520 nm, 160 nm, and 35 nm for shallow donor concentrations of 1016cm−3, 1017cm−3, and 1018cm−3, respectively. In this case a silicon interface peak helps to grow thinner layers. This can be also applied to the growth process by growing a δ-doped interface layer to reduce the charge depletion layer width. For the Fe doped substrate (Fig. 6.3(b)), the charge depletion layer vanishes due to the Si interface peak. The inset of Fig. 6.3(b) shows that a conductive channel forms at the interface of layer and substrate. Consequently, a two channel model has to be applied for the Hall characterization. I also want to note here that lateral devices may fail due to leakage current flowing over the conductive interface channel.
Figure 6.4: Band diagram of homoepitaxial β-Ga2O3 layers with shallow donor concentrations of ND = 1016cm−3 (red), ND = 1017cm−3 (black), and ND = 1018cm−3 (blue) on semi-insulating substrates including a Si interface peak calculated with the Schrödinger-Poisson solver of G. L. Snider.[130]
(a)Layer on a Mg doped, semi-insulating, (100) oriented substrate, including a Si interface peak of10 nm thickness and ND= 3×1018cm−3 from Fig. 6.3.
(b) Layer on a Fe doped, semi-insulating, (010) oriented substrate, including a Si interface peak of15 nm thickness and ND= 3×1018cm−3 from Fig. 6.3.
In conclusion, the substrates influences the electrical properties of thin layers due to the kind of acceptor impurity compensating the unintentional n-type doping of the crystals. For characterization of homoepitaxialβ-Ga2O3 layers and device design all circumstances like shallow donor doping, interface donor peaks and the substrates have to be taken into account. Due to a reduced effective thickness the calculated charge concentration from Hall effect measurements may be underestimated. By reducing the effective thickness of the channel there can be surface scattering effects, which can reduce the charge carrier mobility in the layers. The thicker the layers are grown, the less effect the substrate has. However, for lateral devices thin layers are needed. Here, the investigation of an acceptor with its deep level in the middle of the band gap will reduce the effect of the substrate, since the depletion layer width will be smaller than for Mg doped substrates, but the conductive interface layer is still depleted. Potential candidates could be nickel or cobalt.[134]