Incomplete Dopant Ionization in 4H-SiC

Dopants atoms in silicon carbide are incorporated substitutionally in place of either a silicon or carbon atom in the hexagonal crystal lattice. Due to the stacking sequence of the polytype, not all silicon or carbon sites are equivalent in terms of their surroundings, and each donor or acceptor can exhibit multiple site-dependent energy levels. Dopants on cubic sites typically have higher ionization energies than dopants on hexagonal sites.

Aluminum is the principal p-type dopant in 4H-SiC, and occupies either a hexagonal or a cubic silicon site, having ionization energies of 197.9 and 201.3 meV respectively [1]. The primary n-type dopants are nitrogen and phosphorus. Nitrogen substitutes for carbon, and on a hexagonal C-site it has an ionization energy of 61.4 meV. Phosphorus substitutes for silicon, and on a cubic Si-site it has an ionization energy of 60.7 meV [1].

Because of its high ionization energy, aluminum acceptors in neutral regions of 4H-SiC are not fully ionized at room temperature. The density of ionized acceptors (and donors) is denoted by (and ), respectively. Incomplete ionization has a profound effect on device performance, and must be taken into consideration in our equations. Nitrogen and phosphorus donors have lower ionization energies and tend to be fully ionized at room temperature, so in most cases . However, it is important to include the correct expression for the ionized acceptor density in all equations.

In depletion regions, the band bending moves the donor and acceptor energy levels far enough from the Fermi energy that even deep aluminum acceptors are fully ionized (occupied by electrons) at room temperature. In determining whether to use the ionized concentration or the total concentration in an equation, we must decide whether the expression refers to the charge density in a depletion region (use ), or to the carrier density in a neutral region (use ). In all equations developed in this book, care has been taken to distinguish these two situations and include the correct representations.

We now consider numerical values typical of 4H-SiC. The equilibrium hole and electron concentrations in extrinsic material ( or ) at moderate temperatures are given by (p-type material) or (n-type material). The ionized dopant concentrations or in a neutral region can be calculated from the charge neutrality condition, and the equilibrium density of holes in p-type material can be written [2]

A1

where is given by

A2

Here is the energy level of the acceptor impurity, is the degeneracy factor for acceptors (typically taken as 4), and is the effective density of states in the valence band, given by

A3

where is the density-of-states effective mass for holes and is Planck's constant. Similarly, the equilibrium density of electrons in n-type material is given by

A4

where

A5

Here is the donor energy level, is the degeneracy factor for donors (typically taken as 2), and is the effective density of states in the conduction band, given by

A6

where is the density-of-states effective mass for electrons.

Figure A.1 shows the ionization fraction for aluminum acceptors in neutral regions of 4H-SiC, computed using an ionization energy of 200 meV. Room temperature is indicated by the dashed line. At a doping of , only about 15% of the acceptors are ionized at room temperature, and the equilibrium hole concentration is only about . The ionization fraction increases with temperature, reaching about 75% at 300 °C.

Figure A.2 shows the ionization fraction for nitrogen or phosphorus donors in 4H-SiC, computed using an ionization energy of 61 meV. At a doping of , approximately 90% of the donor atoms are ionized at room temperature.

Figure A.3 shows the Fermi potential for aluminum-doped 4H-SiC calculated using Equations 8.21 and A1, including the dependence of on temperature. As temperature increases, the Fermi level moves closer to the midgap, and the change is more dramatic for lighter dopings. The reduction in is caused by the rapid increase of with temperature, as shown in Figure A.4. Figure A.5 shows similar calculations for the Fermi potential in nitrogen or phosphorus-doped 4H-SiC.

The above equations assume that the doping is not so high as to create an impurity band. However, at doping levels above the mean spacing between dopant atoms is less than 5 nm, and electron wavefunctions from adjacent atoms overlap, giving rise to an impurity band that reduces the effective bandgap. This reduces the dopant ionization energies , leading to more complete ionization than predicted by Equations A1 and A4.

References

1. [1] Ivanov, I.G., Henry, A. and Janzen, E. (2005) Ionization energies of phosphorus and nitrogen donors and aluminum acceptors in 4H silicon carbide from the donor-acceptor pair emission. Phys. Rev. B, 71 (24), 241201-1–241201-4.
2. [2] Pierret, R.F. (2003) Advanced Semiconductor Fundamentals, Pearson Education, Inc., Upper Saddle River, NJ.