# Space Charge Effect and Resistance Switching in Doped Monocrystalline Silicones
## 3 Results  
In our experiments, two-terminal devices were fabricated by making indium (In) ohmic contacts on the phosphorus-doped n-type-silicon (n-Si). Figure 1a illustrates the schematic measurement configuration. \(L\) is the spacing between two electrodes. Figure 1b shows the I-V curve of device 0129-1# measured by the two-terminal method at room temperature. The I-V curve can be divided into three distinct regimes: Ohmic regime (0-3 V), ETF regime in-between (3-18 V), and MG regime (18-50 V). The upper-limit voltage is the value of voltage that can be accurately measured by the instrument, rather than the upper-limit voltage in the MG state. In other words, traps are filled with carriers under an external electric field, which leads to a deviation in the I-V curve from [PERSON]'s law. While the I-V curve enters into an ETF regime, a critical voltage \(V_{\mathrm{L}}\) can be evaluated. In an ETF regime, the trap-filling effect is strengthened through the increase in voltage. When all available states in the band gap are filled with carriers, the I-V curve rises up and conforms to the square law (I\(\propto\)V\({}^{2}\)). Hence, another critical voltage \(V_{\mathrm{U}}\) for the ETF regime is defined [1; 2; 3; 4; 5; 6], and the MG regime can be identified. Two critical voltages, \(V_{\mathrm{L}}\) and \(V_{\mathrm{U}}\), are the lower and upper limitations of the ETF regime. Both the EFT and MG regimes are induced by SCE. In the experiment, \(V_{\mathrm{L}}\) is defined as the intersection of the tangent extension cords of the I-V curve in the Ohmic and ETF regimes; likewise, \(V_{\mathrm{U}}\) is the intersection of those in ETF and MG. In Figure 1b, \(V_{\mathrm{L}}\) and \(V_{\mathrm{U}}\) are labeled by the intersection of red and purple dash lines, respectively. Figure 1: _Cont._The samples were heavily doped n-Si with resistivity 10-20 \(\Omega\)-cm and carrier density \(\sim\)\(2.1\times 10^{14}\) cm\({}^{-3}\) at room temperature. We considered that the observed SCE manifested the role of dopants on the motions of injected carriers under an external electric field [1; 2; 3; 4; 5; 6]. The ionized dopants, which were in fact the effective traps for carriers in a band gap, exert a push-back effect on the motions of carriers. Therefore, under a high electric field, the effect of a space charge limitation on the conduction band is much more significant [1; 2]. However, while dopants dominate the dynamics of carrier transport, SCE may hardly be observed at low voltages in light-doped semiconductors due to the absence of effective traps. Figure 1c demonstrates an I-V curve observed in In/n-Si/In device 0114-1\(\mu\), with the resistivity of n-Si being higher than 1000 \(\Omega\)-cm. The linear Ohmic regime holds up to 200 V, reaching the maximum output voltage of Keithley 4200. These observations are different from the report by [PERSON] et al. for light-doped silicon [7]. The discrepancy may be attributed to the distribution of dopants along the surface and the energy level of dopants in the band gap. Our previous work showed that a large magnetoresistance and the successive Ohmic and MG regimes could be observed in a current perpendicular to plane (CPP) configuration [6], which can be well simulated by a model proposed by [PERSON] and [PERSON] [2]. In fact, it has been predicted in theory that an ETF regime could be \"stretched\" to different voltage ranges by the concentration of dopants [1]. More detailed work may be able to probe a single, deep, trap level with various concentrations of dopants from multiple ETF regimes as suggested by [PERSON] and [PERSON] [2]. SCE leads to a non-uniform distribution of internal voltages between electrodes [1; 2; 3; 4; 5; 6; 7]. Figure 2a shows I-V curves of device 0129-7\(\mu\) with a different \(L\) value. A longer \(L\) corresponds to higher resistance; hence, the I-V curve shifts down with an increase in \(L\). With the same definition for the two critical voltages as marked in Figure 1, \(V_{\rm L}\) and \(V_{\rm U}\) versus \(L\) are obtained, as shown in Figure 2b.