The spatial and energy distribution of oxide trap responsible for 1/f noise in 4H-SiC MOSFETs

Low-frequency noise is one of the important characteristics of 4H-SiC metal-oxide-semiconductor field-effect transistors (MOSFETs) that is susceptible to oxide traps. Drain-source voltage noise models of 4H-SiC MOSFETs under low–drain-voltage and inverse condition were proposed by considering the spatial and energy non-uniform distribution of the oxide trap, based on the McWhoter model for uniform trap distribution. This study performed noise experiments on commercial 4H-SiC MOSFETs, and revealed that the non-uniform spatial and non-uniform energy distribution caused new 1/f noise phenomenon, different from that under uniform spatial and energy distribution. By combining experimental data and theoretical models, the spatial and energy distribution of oxide traps of these samples were determined.

There are mainly two models to describe the origin of the carrier number dependent 1/f noise, McWhoter model and thermal activation model. Zhang et al [5,6] used thermal activation model, the first principle simulation, and noise and threshold voltage experiments of 4H-SiC MOSFETs to conclude that low frequency noise was mainly induced by slow-speed interface traps at a temperature of below 370 K, whereas by border traps at a temperature of over 370 K, and the interface state might originated from carbon vacancy clusters and N-dopant atoms at or near the interface. However, in thermal activation model, the capture cross-section around the bottom of the conduction band of 4H-SiC MOS devices ranged from 10 -18 to 10 -20 cm 2 using AC conductance method [4]. Since the physical area of atoms is approximately 10 -15 cm 2 , these capture crosssections are too small and make no practical sense. The McWhoter noise model now has been extensively used in BSIM model for SPICE circuit simulation [14]. As described in [3], in 4H-SiC DMOSFET, S , I d the noise of drain current I d was measured, and the dependence of the relative spectral noise density S I band; E f is a position of the Fermi level). In this paper, we will consider the details of the distribution of oxide traps. The noise characteristics reported by [3] may be explained by the non-uniform energy distribution of traps, and the noise characteristics reported by [7] may be explained by the uniform energy distribution of traps.
In this study, the McWhoter noise model was improved for examining the effect of the spatial and energy distribution of the oxide traps on noise. It should be noted that this study assumed both interface traps and border traps were included in oxide traps. Spectral noise density S V d experiments were implemented on commercial 4H-SiC MOSFETs devices. The extraction method of the spatial and energy distribution of oxide traps based on the curve of low-frequency noise was explored. The spatial and energy distribution of oxide traps responsible for 1/f noise in 4H-SiC MOSFETs were obtained and discussed.

Noise model
Under moderate to strong inversion with low drain voltage, the relative spectral noise density S I can be expressed as [8,15,16], where, I d denotes the drain current, S I d denotes the drain current noise, g denotes the tunneling coefficient, W and L denote width and length of the channel, respectively, n s denotes the number of carriers per unit area of channel, f denotes frequency and D S N t denotes the power spectral density of the fluctuation of the occupiedtrap number in a small neighborhood Dx along the channel direction x, as shown in figure 1.
Traps are assumed to be uniformly distributed in the entire oxide layer along the channel direction and to be non-uniformly distributed in the direction perpendicular to the channel. It should be noted that this assumption is reasonable for large-size devices. Assuming that D S N t can be written as [17]: where, N fn is fermi energy level, k is Boltzmann constant, T is absolute temperature, t is time constant and Tox is oxide layer thickness. In equation (2), g denotes the tunneling coefficient, and the typical value of t 0 is 10 -10 s [8,17].
The charge pumping measurements show that trap density in SiO 2 within a nanometer range may vary by nearly two or even more than two orders of magnitude [18]. Accordingly, the trap distribution is described in the following exponential form: in which = z 0 denotes the interface position and N t,0 denotes the density of traps at the interface. By substituting ( into equation (1) and integrating, the following expression can be derived: where, b = q kT, N sub denotes the substrate doping concentration, j f denotes the Fermi potential of the substrate and E i denotes the mid-value of the forbidden band. With equation (5), N t,0 can be obtained from the measured curve of S , V d and with equations (6) and (7), -E E fn i also can be acquired.

Experimental details
Threshold voltage test and drain voltage noise test were performed on 4H-SiC MOSFETs, C2M0160120D, manufactured by CREE Corporation. Three samples of C2M0160120D were labeled as 120-1, 120-2 and 120-3, respectively. The MOSFETs are n-type channel with planar architecture and SiO 2 gate dielectric. Keithley 4200-SCS was used to measure theĨ V g g curve and extract the threshold voltage V . T As shown in the noise test diagram of figure 3, an adaptive circuit for 4H-SiC MOSFET noise measurement was built, in which the sample could be in a setting bias condition, the fluctuation of V d was transmitted to the pre-voltage amplifier by AC coupling, a data acquisition card collected the amplified signal and a computer transformed time series into noise power spectral density S . V d The noise test was performed under room temperature. The amplifier gain was set as 5000, the measuring frequency ranged from 1 Hz ∼ 10 KHz. Figure 4 shows that the I d -V g curves of these devices are normal and figure 5 shows the variations of S V d with frequency in low-frequency range (1 Hz ∼ 1000 Hz) under linear mode. The absolute value of the spectrum slope in the log-log coordinate system reflects the frequency exponent, r. It can be observed that all curves of the same sample exhibit nearly similar slopes at different bias conditions. As shown in figure 5, the fitted values of r approximately are 0.83 and 0.84, respectively, consistent with the general range of the r of 1/f noise (   r 0.8 1.
1 ,the traps are uniformly distributed, and equation (5) is converted to  figure 7. The oxide trap has a uniform energy distribution, and then = m 2, which has been reported by [20]. But the results in figure 6 are more relatively complex. For 120-type samples, we can observe < m 2 for all the samples. The difference of     m reflects the different trends of the trap density with energy. For Sample 120-1, the density of oxide traps decreased as the energy shifts further away from the bottom of the conduction band, and similar trend has been reported in [5]]. The m value of Sample 120-2 is closest to 2, i.e. the traps in Sample 120-2 have an approximately uniform energy distribution.
With the methods described in noise model and N sub assumed as´-1 10 cm , 15 3 the trends of trap energy distribution are calculated and shown in figure 7. If the structure parameters of devices such as C ox and WL can be obtained, the horizontal and vertical coordinates of the figure can be completely determined, that is to say, the change of trap density with energy can be accurately measured. Sample 120-2 is chosen as an example to compute the trap density distribution. The measurement capacitance of 120-2 is´-F 1.2 10 , 9 by assuming that oxide thickness is 50nm, then, 2 and the average of N t,0 is ( ) / 5.4857 10 eV cm . 21 3 By multiplying N t,0 with the spatial distribution ( ) -´z exp 1. 15 10 , 7 the final distribution could be obtained, which is If the sample trap has a non-uniform energy distribution, the trap density as a linear function of energy, can be gotten to use the least square method for linear fitting.

Conclusions
The McWhoter model for uniform trap distribution was modified, to investigate non-uniformities in spatial and energy distributions of oxide traps in 4H-SiC MOSFETs. For two kinds of sample, the characteristics of drain voltage noise with frequency and gate voltage were examined experimentally. By combining experimental data and theoretical models, the spatial and energy distribution of oxide traps in these samples were determined. The values of the parameter b in the trap spatial expression were -´-1.1 10 cm 7 1 for Sample 120-1. A negative value of b was suggestive of the fact that the density of traps in the oxide layer further away from the SiC/SiO 2 interface was lower. The exponent of S V d dependence on -V V g t was denoted as m. = m 2 was the sign of the uniform energy distribution of oxide trap, while the m value deviating from 2 meant a non-uniform energy distribution. For three 120 samples decreased slightly as the energy shifted further away from the bottom of the conduction band, and among them, the energy distribution of sample 120-2 and sample 120-3 were the closest to an uniform distribution.