Question E6E03:
Which of the following materials supports the highest frequency of operation when used in MMICs?  

Choices:  
A: Silicon  
B: Silicon nitride  
C: Silicon dioxide  
D: Gallium nitride    

Correct Answer is  D: Gallium nitride  

Correct answer: D — Gallium nitride (GaN)

Why D is correct
- GaN is a wide-bandgap III–V semiconductor with high electron saturation velocity and very high critical electric field. These enable very short-channel HEMTs with high transconductance and low transit time, yielding very high cutoff and maximum oscillation frequencies.
- Typical performance: GaN HEMTs achieve $f_t \sim 100$–$200+$ GHz and $f_{\max} \sim 200$–$400+$ GHz, while also handling high power and temperature—ideal for MMICs at microwave to mmWave.

Key ideas and formulas
- Transit-time/velocity limit:
  $$f_t \approx \frac{g_m}{2\pi C_{gg}} \approx \frac{v_{\text{sat}}}{2\pi L_g}$$
  Higher $v_{\text{sat}}$ and shorter $L_g$ give higher $f_t$. GaN has high $v_{\text{sat}} \approx 2$–$2.5\times 10^7\ \text{cm/s}$.
- Johnson’s figure of merit (HF power capability):
  $$\text{JFoM} \propto f_t \cdot V_{\text{br}} \propto v_{\text{sat}} \cdot E_{\text{crit}}$$
  GaN’s wide bandgap ($\sim 3.4$ eV) gives very high $E_{\text{crit}}$, boosting high-frequency, high-voltage operation simultaneously.

Why the other choices are incorrect
- A: Silicon
  - Narrower bandgap and lower $v_{\text{sat}}$ than GaN lead to lower $f_t/f_{\max}$ for comparable device geometries. While advanced SiGe HBTs can reach high $f_t$, “silicon” (CMOS/MOSFET/BJT) generally does not surpass GaN in highest-frequency MMIC power applications.
- B: Silicon nitride (Si3N4)
  - An insulator/dielectric used for passivation, MIM capacitors, and spacers—not an active semiconductor for transistors. It does not set the fundamental frequency limit of the active device.
- C: Silicon dioxide (SiO2)
  - Also an insulator/dielectric (gate oxide, isolation). Not used as the active semiconductor; therefore it does not determine the attainable transistor $f_t/f_{\max}$.

Rules of thumb for exam prep
- Wide bandgap → higher breakdown field and usually higher usable field and temperature.
- Higher $v_{\text{sat}}$ and shorter gate length $L_g$ → higher $f_t$:
  $$f_t \propto \frac{1}{L_g} \quad \text{and} \quad f_t \propto v_{\text{sat}}$$
- For MMICs needing both very high frequency and high power, GaN is the go-to among the listed materials.