Schematic of a band diagram of the p-side of an abrupt n+-p junction (such as in ZnO/Cu2O). The shaded region represents the region contributing to the capacitance when measuring at a frequency (ω) during admittance spectroscopy. The frequency translates into an energy (Eω) which represents the difference between the Fermi level and the valence band at a location (xω). Here, a bulk trap state is shown to exist at an energy (E0) above the valence band and cross the Fermi level at a position (x0). A trap state will only contribute to the capacitance response if the frequency is low enough to encompass a region stretching to x0 from the depletion width edge (W). Additionally, it can be seen that the energy at the interface (Efpi) is equal to the built-in potential energy (qVbi) plus the bulk Fermi level position (Efp∞).
Equivalent circuit model of a pn junction with a trap state in series with a Schottky barrier contact. Cj is the junction capacitance and Rj is the parallel resistance of the pn junction depletion region. Ct is the trap state capacitance and Rt is the resistance to recombination. CSB is the capacitance and RSB is the parallel resistance of the Schottky barrier depletion region.
(a) Modeled differential capacitance for a device with a trap state in the absence and presence of a Schottky barrier contact. In the absence of a Schottky barrier, the trap state peak magnitude and frequency exist at the location (ω0,P). In the presence of a Schottky barrier, the apparent trap state peak moves to a location (ω0′,P′). (b) Capacitance versus frequency for the same devices modeled in (a).
Modeled differential capacitance plots of the equivalent circuit in Figure 2 considering (a) temperature dependent Ct, CSB, and Cj and (b) temperature independent Ct(T), CSB(T), and Cj(T). For both (a) and (b), the plots show the differential capacitance at different temperatures in the presence (blue) and absence (red) of the Schottky barrier. Arrhenius plots based onEq. (1) of the four scenarios are given in (c). For the temperature independent scenarios, Ct = 9.8 × 10−8 F cm−2, CSB = 4.3 × 10−9 F cm−2, Cj = 2.6 × 10−6 F cm−2. Model parameters were used to give roughly equivalent capacitance and resistance values between the temperature independent and dependent scenarios at 300 K. Model parameters are At,C = 9.9 × 10−10 F cm−2 K−2, Efpi = 0.61 eV, σC = 6.3 × 10−13 cm2, ASB,C = 4.3 × 10−9 F cm−2 K4/3, Efn∞ = 0.1 eV, ΦSB = 0.6 eV, ASB,R = 3.4 × 10−4 Ω cm2 K, Cj,C = 1.4 × 10−8 Fcm−2 K4/3, E fp∞ = 0.37 eV, Aj,R = 1 × 10−9 Ω cm2, Tj,R = 30 K.
(a)-(c) Equivalent circuit models and (d) percent error (100% * |Model − Data|/Data) of the magnitude of admittance versus frequency at 300 K. Circuit model (a) uses a pure capacitor for Ct and CSB. Circuit model (b) uses a CPE to replace CSB and a Gaussian distribution of states for Ct. Circuit model (c) uses a CPE for Ct and CSB.
(a) Admittance spectroscopy data of a ZnO/Cu2O device with an ITO/ZnO Schottky barrier measured from 290-320 K (open circles). The full modeled data (blue lines) and modeled data without CPESB, RSB, RS, and L (red lines) are also presented. (b) Arrhenius plot of the trap state peak of the raw data (blue) and modeled data with the Schottky barrier, series resistance, or inductance contributions (red). (c) Correlation of the interface trap state energy with bias.
Comparison of the trap state energy (E0), capture cross section (σC), and density of states (Nt) for different models considering temperature independent and dependent capacitance in the presence and absence of a Schottky barrier contact.
Summarized admittance spectroscopy results averaged (±1 standard deviation) for 3 ZnO/Cu2O devices. Raw data include an ITO/ZnO Schottky barrier. Modeled data subtract the Schottky barrier contact as well as the additional series resistance and inductance.
Resulting circuit model fit parameters (using the model in Figure 4(c) ) of data for a ZnO/Cu2O device for different measurement temperatures. Fit parameters were obtained using the LEVMW nonlinear linear least squares regression fitting software. 17 The resulting differential capacitance using these parameters is laid over the data in Figure 5(a) . Q and n are components of the CPE from Eq. (15) . The device area was 0.15 cm2.
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