Materials Science Forum Vols. 527-529 (2006) pp 1055-1058 online at http://www.scientific.net © (2006) Trans Tech Publications, Switzerland Online available since 2006/Oct/15

Determination of the Temperature and Field Dependence of the Interface Conductivity Mobility in 4H-SiC/SiO2 G. Pennington1,a, S. Potbhare1,b, N. Goldsman1,c, D. Habersat2,d, and A. Lelis2,e 1

Department of Electrical Engineering, University of Maryland, College Park, MD 20742, USA 2

U.S. Army Research Laboratory, 2800 Powder Mill Road, Adelphi, MD 20783, USA

a

b

c

d

[email protected], [email protected], [email protected], [email protected], e [email protected]

Keywords: 4H-SiC MOSFET, field-effect mobility, conductivity mobility, compact modeling, and surface phonon scattering.

Abstract. In this work we present a comparison between the field-effect (µFE) and conductivity (µinv) mobilities calculated from ID-VG measurements on a 4H-SiC MOSFET. A compact device model is used to determine µinv. The conductivity mobility is found to be larger than µFE near room temperature, but less than µFE at 500K. These results are due to a reduction in charge trapping at higher temperatures. In strong inversion, µinv decreases markedly with increasing temperature. Modeling indicates that surface phonon scattering dominates in this regime. Introduction Currently, measurements of the field-effect mobility (µFE) in 4H-SiC MOSFETs are typically found to be very small (<40 cm2/Vs). The cause for such small mobilities is believed to be directly related to the very large density of traps measured at the 4H-SiC/SiO2 interface. These traps may reduce µFE through two mechanisms: charge trapping and coulomb scattering. The importance of each mechanism can be deduced by considering the conductivity mobility of free inversion channel carriers (µinv), which is independent of charge trapping. Furthermore, µinv gives insight into the importance of phonon and roughness scattering in 4H-SiC MOSFETs. In this work, a compact device model for determining µinv from experimental ID(drain current)-VG(gate voltage) characteristics is presented. In comparison to Hall measurements [1], the procedure is advantageous since µinv can be calculated without requiring knowledge of the Hall factor. Compact Modeling of Experimental 4H-SiC MOSFET Measurements The device studied is a poly-silicon gated 4H-SiC MOSFET, with a gate thickness of 60nm and a substrate acceptor doping of 5X1015cm-3. The channel length (L) and channel width (W) of the device are both 200µm. From ID-VG measurements at a drain bias of VD=0.25V, µinv is calculated using the expression [2]:

d ( N inv µ inv ) dI D L = µ FE = . d (N inv − N f −t ) WC oxVD dVG

(1)

Here Nf-t is the fixed minus the trapped interface charge density (Nf-Nt), and is assumed to be located exactly at the interface. Ninv is the free mobile charge density at the interface. These charge densities are determined using a compact device model which requires self-consistency of the

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VG above flatband = V drop over oxide and SiC VG - VFB(Nf-t=0) = Vox + ψs Ec

Vox

ZAVG

ψs SiO

2

4H-SiC Subband

EF

tox=60nm

Figure 1: Experimental threshold voltage.

Fixed and trapped interface charge Nf-t = Nf - Nt(ψs)

Figure 2: Band bending diagram.

fields, and potentials across the oxide and semiconductor. The oxide capacitance is given by Cox. An outline of the modeling used to determine Ninv, Nf-t, and thus µinv using Eq. (1) follows. The average inversion layer width Zav is also determined and is used to develop a mobility model. Modeling Threshold Measurements. Threshold voltage (Vth) measurements in the range of 300-500K are shown in Fig. 1. As the temperature increases, the MOSFET turns on at lower gate voltages. This effect is likely due to an increase in the ratio of mobile to total induced charge, f =Ninv/(Ninv+Nt), at higher temperatures. Using Vth measurements in Fig. 1, a determination of Nf-t vs. semiconductor band bending (Ψs) at threshold can be made. This is accomplished by setting the threshold voltage relative to the theoretical flat band voltage equal to the total potential drop over the semiconductor (4H-SiC) and oxide:

 2N f − t N z  + a d . Vth (T) − VFB (T) = Ψs + et ox  ε SiC   ε SiC + ε ox

(2)

Here VFB is the theoretical flat band voltage in the absence of fixed and trapped charge in either the oxide or at the interface. It is determined for a polysilicon gate doping of 1019 cm-3. The band bending and depletion width (Zd) are found by self consistently solving for the mobile surface charge density using the threshold criteria Ninv=NaZav. In the calculations, the subband structure of the first two conduction bands of 4H-SiC are used. The second band is taken to be 0.01 eV higher in energy. Since Ninv is small, the triangular well approximation is used. A diagram of the oxide/4H-SiC interface with subbands is illustrated in Fig. 2. Once Ψs and Zd are found via self-consistent calculations, Eq. (2) can be solved for Nf-t as a function of surface band bending. Results are given in Fig. 3, where Nf-t decreases with increasing Ψs due to an increase in trapped charge Nt. Since Nf is independent of band bending, the curve can be extrapolated to give a fixed charge density of Nf=3.6X1012 cm-2 at low Ψs. Modeling Above Threshold. Once threshold is modeled, further measurements are not needed to model the charge densities above threshold. For gate voltages above threshold, the potential drop due to the mobile inversion charge must be taken into account by replacing NaZd with Ninv+NaZd in Eq. (2). As was the case at threshold, Ψs, Zd, Ninv, and Zav are determined self-consistently. In this case, however, self-consistent calculations also satisfy Eq. (2) with Nf-t found directly from Ψs by extrapolation in Fig. 3.

Materials Science Forum Vols. 527-529

Figure 3: Fixed-trapped charge density.

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Figure 4: µFE and µinv from measurements.

Calculated Mobilities. Upon determination of the charge densities, µinv is found from Eq. (1). Fig. 4 shows µFE and µinv calculated from ID-VG measurements. The field-effect mobility is found to increase with increasing temperature whereas the conductivity mobility decreases with increasing temperature. This indicates that the ratio f increases with temperature as expected. At room temperature the conductivity mobility is 2 to 4 times as large as µFE . Things are reversed at high temperatures (500K) where the field-effect mobility is actually larger than µinv. Insight can be gained by considering the ratio:

 f dµ inv µ FE df  = (VG − Vth ) ⋅ + +f . µ inv  µ inv dVG dVG 

(3)

As an example, analysis of the region of strong inversion at 500K is considered. In Fig. 4, the conductivity mobility in this region can be seen to vary approximately as AVG, where A is a negative constant. The ratio in Eq. (3) is found to be ~ 2f + VG·df/dVG, were we find df/dVG > 0. As the ratio f increases approaching 1/2, as might be expected at high temperatures where charge trapping is diminished, the field-effect mobility can be larger than the conductivity mobility. Mobility Modeling

The conductivity mobility determined from experimental measurements on a 4H-SiC MOSFET, as described in the previous section, is compared with a phonon scattering model [1,3]:

1

µ mod el

=

1

µB

+

1

µS

=

(

1

800 300

)

2 .4

m * ϑ th p + 2eZ AVG

. (4)

T Here µB and µS are the bulk and surface phonon scattering mobilities respectively. Also m*, υth, and e are the effective mass, thermal velocity, and charge of an electron. The average inversion channel width (ZAVG) is determined by the compact device modeling of the previous section. Fuchs parameter in Si has been determined as p=0.09(T/300K)1.5 [3]. A good fit to the conductivity mobility in the region of strong inversion is found here using the same temperature dependence. The constant term is however increased from 0.09 to 0.16 for agreement.

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Figure 5: Conductivity mobilty vs. gate voltage.

Figure 6: Conductivity mobility vs. mobile charge.

In Figs. (5) and (6) the mobility model is compared with µinv calculated from experimental measurements using Eq. (1). Temperatures ranging from 300 to 500K are shown. The model agrees very well with the temperature dependence of µinv in the region of strong inversion. Another scattering mechanism which might be important in strong inversion results from the surface roughness. Surface roughness scattering may be very large in off-axis 4H-SiC MOSFETs due to interface steps resulting from step-flow growth. However, roughness scattering typically decreases with increasing lattice temperature. The temperature dependence of µinv at high gate potentials seems to indicate that surface phonon scattering is dominant. This result is consistent with the analysis of Hall measurements in SiC [1]. As seen in Figs. (5) and (6), the phonon scattering model does not fit µinv as well at lower temperatures, near 300K. This indicates that surface roughness likely contributes to the degradation of the mobility in this temperature regime, with phonon scattering still being the dominant scattering mechanism. As found previously [1], the conductivity mobility in weak inversion decreases with increasing temperature. This dependence does not appear to agree with models for charge or roughness scattering. Furthermore, as found with the analysis of Hall measurements [1], the mobility in weak inversion increases strongly with mobile charge density Ninv. These observations indicate a dominant scattering mechanism in weak inversion which is affected by screening and is coupled to the lattice phonons. A possible mechanism might involve variations in the coulomb field of the trapped charges by surface phonons leading to carrier scattering. Further studies are required. Summary In this work we have presented a comparison between the field-effect (µFE) and conductivity (µinv) mobilities determined from ID-VG measurements on a 4H-SiC MOSFET. Compact device modeling is used to calculated µinv. Near room temperature, µinv is much larger than µFE as a result of charge trapping. A reduction in trapping occurs at high temperatures (500K) where µFE increases above µinv. The conductivity mobility in strong inversion is found to decrease with increasing temperature in accord with a model based on bulk and surface phonon scattering. References [1] N. S. Saks: Mat. Res. Soc. Symp. Proc. Vol. 742 (2001), p. 233 [2] W. Mönch: Semiconductor Surfaces and Interfaces (Springer, Berlin 2001). [3] S. A. Schwarz and S. E. Russek: IEEE Trans. Elect. Dev., Vol. ED-30 (1983), p. 1634

Materials Science Forum Vols. 527-529

Silicon Carbide and Related Materials 2005 doi:10.4028/www.scientific.net/MSF.527-529 Determination of the Temperature and Field Dependence of the Interface Conductivity Mobility in 4H-SiC/SiO₂ doi:10.4028/www.scientific.net/MSF.527-529.1055

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