Carrier Physics and Junction Electrostatics


To understand the operating characteristics of power semiconductor devices well it requires a good background knowledge in semiconductor physics, in particular on carrier transport and junction electrostatics. For this chapter, some important concepts on carrier transport physics and junction electrostatics with breakdown mechanisms of silicon (Si) semiconductor are reviewed. Materials of gallium arsenide (GaAs) and silicon carbide (SiC) are also briefly mentioned. The aim of this chapter is not to treat the semiconductor physics rigorously in fundamental detail. Rather, it is to highlight those properties that are important and needed in understanding the operational characteristics of power semiconductor devices.

Crystal Structure and Energy Bands

Silicon belongs to the group IV element and as such it has four valence electrons in its outermost shell. Silicon crystallizes in a diamond structure in which four atoms are located at the corners of opposite diagonals of the cube and they surround one atom in the center of the cube, as shown in Fig. 2.1. The central atom has four covalent shared-pair electron bonds with the surrounding four atoms. The unit cell lattice constant a is 5.43 A. It has eight corner atoms, six face atoms, and four central atoms for a total of eight atoms in the unit cell. Since there are eight silicon atoms per unit cell and the volume of the unit cell is a3, it follows that there are 5 x 1022 atoms/cm3 in the silicon lattice. It is this structure that gives rise to the many unique properties of silicon. For gallium arsenide, another power semiconductor material, it is a compound semiconductor as it consists of gallium and arsenic atoms crystallizing in a structure similar to the diamond structure called the zinc-blende structure as shown in Fig. 2.2. In the zinc-blende structure, the central atoms are occupied

Silicon atomic structure

Fig. 2.1. Silicon atomic structure.

Atomic structure of GaAs

Fig. 2.2. Atomic structure of GaAs.

by the gallium atoms. Thus, the gallium arsenide unit cell has four gallium atoms and four arsenic atoms. Some physical properties of semiconductor materials can be found in Table 2.1.

Electrons in the outermost shell are shared by many atoms, as such, the energy of each can be grouped into various energy bands. In silicon, the valence electrons group together to occupy a band of energy levels, called the valence band. The next higher band of allowed energy levels, called the conduction

Table 2.1. Some physical properties of semiconductor materials.









Lattice constant (A)












Density (g/cm3)









Energy bandgap (eV)



- 9.0


2.4 to 3.26




Dielectric coefficient (e/eo)





9.6 to 10




Melting point (°C)







- 2200

- 4000

Saturated electron velocity (107cm/s)









Electron mobility (cm2/V • s) @300 K





- 800




Hole mobility (cm2/V • s) @300 K



- 0



- 300



Breakdown field (105 V/cm)






- 33



Thermal conductivity (W/cm • K)









Direct or indirect









Note: ав-SiC denotes either 4H-SiC, 6H-SiC (a), or 3C-SiC(e).

Semiconductor energy band structure

Fig. 2.3. Semiconductor energy band structure.

band, is separated from the valence band by a forbidden energy gap, EG, as shown in Fig. 2.3. The conduction band is partially occupied by the free electrons. The bandgaps for silicon and gallium arsenide are 1.12 eV (electron-volt) and 1.43 eV, respectively around room temperature (T = 300 K). At room temperature, some electrons in the valence band may acquire enough thermal energy (above 26 meV) to traverse from the valence band to the conduction band. For each successful transition of a valence electron to the conduction band, a hole which is an unoccupied or empty energy level is left behind in the valence band. This process is known as the electron-hole pair generation. Under thermal equilibrium state, the number of electrons in the conduction band and holes in the valence band is equal. Thermal equilibrium is defined as the steady-state condition at a given temperature without any external excitation. These electrons and holes are free to move in the crystal lattice, and they are generally known as free electrons and holes.

One of the models described by the quantum mechanics for the energy bands in solids is called the Kronig-Penney model and an E-k (energy- momentum, where carrier momentum a hk) dependence diagram can be drawn as in Fig. 2.4 for the energy bands. The interesting concept to be described here is the effective mass of electron. The effective mass is determined by the radius of curvature of the E-k curve at a given energy level, i.e. the effective mass varies with k value. When the E-k curve is concave as the shape of conduction band, the effective electron mass is positive, whereas, when it is convex as

E-k diagram with different surface curvatures for conduction band and valence band

Fig. 2.4. E-k diagram with different surface curvatures for conduction band and valence band.

The energy band diagrams in momentum space for germanium, silicon, and gallium arsenide at 300 K (from left to right)

Fig. 2.5. The energy band diagrams in momentum space for germanium, silicon, and gallium arsenide at 300 K (from left to right).

the shape of valence band, the effective electron mass is negative. This means that an electron in the valence band will be accelerated by the field as if it is a positively charged particle and mass. This forms the basic concept of hole carrier.

Depending on the structure of the energy band, a semiconductor can be classified as either a direct-gap or an indirect-gap semiconductor, as shown in the E-k diagram of Fig. 2.5 (Bar-Ler, 1984). In a direct-gap semiconductor, the minimum energy of the conduction band coincides with the maximum energy of the valence band in the momentum space, whereas, in an indirect- gap semiconductor, the minimum energy of the conduction band does not align at k = 0 but occurs near the zone edge. With this in mind, germanium and silicon materials are indirect-gap semiconductors while gallium arsenide is a direct-gap semiconductor. As such, they have distinctly different carrier recombination processes. In silicon, electrons make transitions to the valence band by a change of both the momentum and energy simultaneously. This means that other quantum particles, such as phonons which are the vibrational modes of the lattice, must participate to remove or contribute the necessary excess momentum. A phonon has therefore a relatively high momentum but low energy. In GaAs, since the minimum of the conduction band aligns with the maximum of the valence band, electrons in the conduction band recombine with holes in the valence band by making direct transition from the conduction band to the valence band without a change in their momentum. The energy given up by the electron will be emitted as a photon, the quantum of light. Thus, gallium arsenide is the material of choice in photonic devices.

Another material of choice for power semiconductor devices is the silicon carbide, SiC for its larger bandgap and higher thermal conductivity. A unique crystal property of the SiC is on the polytypism. If we designate a SiC atom pair in an A-plane in close packing as Aa, in the B-plane as Bb, and in the C-plane as Cc, then we can generate a series of SiC structures by the variation of stacking along the principal crystal axis (Choyke and Pensl, 1997). For example, by having AaBbAaCcAaBbAaCc ... structure, we generate the 4H-SiC polytype. Or, for AaBbCcAaCcBb ... structure, we can generate the 6H-SiC polytype. They are hexagonally symmetric. Both 4H-SiC and 6H-SiC polytypes are available in bulk wafer form and are useful for power semiconductor device applications (Casady et al., 1998; Ramungul et al., 1996). The 4H-SiC has two equivalent sites with 8 atoms per unit cell while the 6H-SiC has three equivalent sites with 12 atoms per unit cell. Therefore, 4H-SiC has the possibility of two donors or two acceptors for a particular substitutional impurity, while 6H-SiC may have three donors or three acceptors. Both structures have a hexagonal crystal structure. The 6H-SiC has a bandgap energy of

3.03 eV and lattice parameters of 3.081 A and 15.117 A while the 4H-SiC has a bandgap of 3.26 eV and lattice parameters of 3.073 A and 10.053 A. Besides hexagonal (H) polytypes, there are also cubic (C) and rhombohedral (R) polytypes. More than 200 polytypes of SiC have been discovered; among them the common types are 3C, 2H, 4H, 6H, 8H, 9R, 10H, 14H, 15R, 20H, 21H, and 24R. 3C-SiC possesses the smallest bandgap energy of about 2.4 eV and it has the highest electron mobility of 800 cm2 ? V-1 ? s-1 among all polytypes.

Recently, SiC power MOSFETs have achieved a blocking voltage of 6.1 kV and performance figure-of-merit 70 times higher than the ideal silicon counterpart. However, still the current problem faced in the SiC power MOSFET device development is the low carrier mobility at the oxide-SiC interface. This

Lines of ideal silicon and silicon carbine limits for majority carrier devices

Fig. 2.6. Lines of ideal silicon and silicon carbine limits for majority carrier devices.

requires a better understanding of the interface material properties with an incorporation of proper processes for post-oxidation anneal (Cooper et al., 2002). Another important focus on SiC device development is that the SiC bulk breakdown field of 5 MV/cm is close to that of the SiO2 breakdown field. Special protective layers need to be placed to avoid gate oxide breakdown, especially at the corner of a U-MOS gate oxide. Figure 2.6 shows the ideal silicon limit and SiC limit for majority carrier devices, such as the Schottky diodes and MOSFETs. As it can be seen, SiC material has a much better value of merit (the breakdown voltage divided by the on-state resistance) than that of the silicon material.

The (aluminum) gallium nitride power device with the best properties is at the infancy development stage. The progress is slow due to the lack of GaN substrate wafer and due to the high cost in epi-growth. The advantage of having the GaN transistor is its capability of sustaining power density above 10 W/mm of gate width (Eastman and Mishra, 2002), while amplifying signals at 10 GHz. For a brief comparison, the silicon-based power transistors can efficiently handle signals up to 3 GHz but at a lower power density. The silicon carbide devices achieve a power density at 7 W/mm but at a lower frequency of 3.5 GHz operations. Gallium arsenide and silicon germanium devices can handle high-frequency operations over 10 GHz, but they cannot withstand high power.

Silicon is expected to continue to be the dominant material for most of the power semiconductor devices for the next 10 years. However, materials such as SiGe for its higher carrier mobility and tuneable bandgap, GaN for its high piezoelectric constant and good carrier transport properties, etc. are also used to produce power semiconductor devices, e.g. HEMT (High Electron Mobility Transistor) for high performance applications. The major concern on SiGe material is on the critical layer thickness which cannot exceed the critical thickness for a given Ge mole fraction. In the recent times, the SiGe transistor research is driven by the wireless applications where low operating voltage and high power-added efficiency are needed for a frequency range between 2 GHz and 5 GHz. Hybrid-material devices, such as having SiC, SiGeC, and GaN materials can also play another important role in device development when both high thermal conductivity and good current carrying capability are needed in application. The material technology brings forth the possibility of making new SiGe BiCMOS large-scale integrated circuits and high-frequency system-on-chip solutions in future.

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