rel="nofollow" href="#ulink_18ecf7dd-6169-5d60-9c93-d3b15711afb8">14]. The current-voltage (I-V) and the capacitance-voltage (C-V) measurements are basic methods to assess the materials electrical properties, to be further refined in the corresponding spectroscopies. All these methods in one or another variation, require a fabrication of the ohmic and rectifying contacts.
Specifically, in a non-degenerate semiconductor, the electron and hole concentrations are given by:
where EF is the Fermi level, NC and NV are the effective densities of states for the conduction band and valence band respectively. Notably, the np product is given by
i.e., independent of EF, with ni labelling the intrinsic carrier concentration.
A donor D donates an electron to the conduction band, i.e. D0 ⇋ D+ + e−. The neutral donor D0 and ionized donor D+ concentrations are respectively:
if the degeneracy (g) of the donor is taken into account.
Assuming reverse bias conditions in a Schottky diode fabricated on n-type semiconductor with the donor concentration much exceeding the acceptor concentration (i.e. ND ≫ NA), the diode depletion width W is given by:
where Vbi is the built-in potential and VR is the applied bias. The corresponding junction capacitance C is given by:
where A is the area of the metal contact. Notably,
Thus, the ND can be found from the slope of the 1/C2 against the VR plot. Similar discussions hold for the acceptor doped p-type semiconductors.
Temperature dependent dc conductivity measurement can be used to determine the energy levels of the defect in the band gap. This method requires good ohmic contacts fabricated on the sample. The dc conductivity is given by:
where k is the Boltzmann constant, T is the temperature, EDi is the ionization energy of the ith defect. The ionization energies of the defects can be obtained via the Arrhenius plot log σ(T) against 1/T.
Hall effect measurement can be used to distinguish type of carriers (i.e. electron or hole), and to obtain the materials’ carrier concentration and carrier mobility. Ohmic contacts in the van-der-Pauw configuration are needed for Hall effect measurement. The Hall coefficient for n-type materials (n ≫ p) is RH = −r/en and that for p-type material (p ≫ n) is RH = r/ep, with r being the scattering factor depending on the magnetic field and temperature; conventionally r = 1. The Hall coefficient can be found experimentally by: RH = tVH/BI, where t is the sample thickness, VH is the Hall voltage, B is the magnetic field and I is the current. The Hall mobility is given by: μH = RHσH, where σH is the conductivity. The above description of Hall-effect measurement applies for homogeneous sample structures. The interpretation of the Hall-effect data for non-homogeneous and/or multi-layered samples is possible too as developed by Look [16].
Deep level transient spectroscopy (DLTS) is used to identify deep traps in the materials and devices. A rectifying contact (for example a Schottky junction or a p–n junction) is needed for the DLTS characterization. The concentration, energy level and capture cross section of the deep trap can be obtained from the DLTS study. A forward bias is applied to fill all the traps (for simplicity assuming one deep donor trap of density of NT0). A reverse bias is then applied to create a depletion region at the rectifying contact. The filled traps in the depletion region will emit electrons to the conduction band depending on the temperature with the emission rate of: en = σcapvNC exp[−(EC − ET)/kT], where σcap is the electron capture cross section of the trap,
The rate-window approach is usually adopted to extract the emission rate from the capacitance transient [17, 18]. The DLTS signal is defined as a difference of the capacitance taken at two consecutive times t1 and t2 (with t2 > t1):
Figure 1. Schematics of the capacitance transient resulted from thermally excited deep electron traps in the depletion region while applying the reverse bias. Three cases with different emission rates namely en = 0.01, 0.1 and 1
