Materials, Reliability and Failure Analysis

Kinetic thermal energy $$ K_{kin} = \frac{m}{2}v_{th}^2 = \frac{3}{2}kT $$

When an electric field $E$ is applied, each carrier (i.e. electrons and holes) experiences a force $± q \times E$ and is accelerated. These velocities caused by the external electrical field $E$ are called drift velocities ^[1].

The current density $J$, or the current flow of electrons per unit volume, is given by the following:

$$ \begin{align*} J_n &= nqv_d \newline J_n &= nq\dfrac{1}{2} \dfrac{q\tau}{m^{2}}E \end{align*} $$

Electron mobility $\mu_n$ is the ratio of drift velocity to the electric field strength.

$$ \mu_n = \dfrac{\nu_d}{E} = \dfrac{q \tau}{m^*} $$

Hight voltage Shottky diode

• Anisotropic: Sic, GaN. Mobility are different in parallel $\mu_{\parallel}$ and perpendicular $\mu_{\perp}$ direction.
• Phonons: lattice vibration
• Scattering: small amount of things spread over an area.
• More dopping --> more phonons --> $\mu_{n} \downarrow$ and desisty $\downarrow$. However, in combination with thickness and doping density --> Wide Bandgap semiconductors have lower conduction losses.
• Shottky diode: $E_{max}$ at the contact semiconductor and metal or P-N junction.
  • Merged PiN Schottky Diodes (MPS) structure: reduce electrical field stress
• "Trench Oxide Pin Schottky" (TOPS): reduce contact between metal and semiconductor --> prevent the migration of carriers at the anode (metal). The rest of structure is the same as MPS ^[2].
• Soft recovery. Soft factor $s = \cfrac{t_f}{t_s} \gt 0.8$

Cross section of a merged pin Schottky diode in SiC [3]

References

1. 4: Carrier Drift and Mobility ↩

2. Lutz, J., Schlangenotto, H., Scheuermann, U. and De Doncker, R., 2011. Semiconductor power devices. Physics, characteristics, reliability, 2. ↩

3. SiC Semiconductor Devices Technology, Modeling, and Simulation ↩