1. ECE 333 Linear Electronics
Chapter 3 Semiconductors
§3.6 Capacitive Effects in the pn Junction

2. Two Charge-storage mechanisms in pn Junction
Depletion or Junction capacitance
- associtated with charge stored in the depletion region
Diffusion Capacitance
- associated with the minority-carrier charge stored in the n and p materials as a result of the concentration profiles established by carrier injection

3. 3.6.1 Depletion or Junction Capacitance
The charge stored in either side of the depletion region
𝑄 𝐽 =𝐴 2 𝜖 𝑠 𝑞 𝑁 𝐴 𝑁 𝐷 𝑁 𝐴 + 𝑁 𝐷 ( 𝑉 0 + 𝑉 𝑅 )
We can write it as
𝑄 𝐽 =𝛼 ( 𝑉 0 + 𝑉 𝑅 )
𝛼=𝐴 2 𝜖 𝑠 𝑞 𝑁 𝐴 𝑁 𝐷 𝑁 𝐴 + 𝑁 𝐷
where

4. or graded junction (m=1/3)
Junction Capacitance CJ relates the change in charge QJ to a change in the voltage VR
That is:
𝐶 𝐽 = 𝑑 𝑄 𝐽 𝑑 𝑉 𝑅 | 𝑉 𝑅 = 𝑉 𝑄
because
𝑄 𝐽 =𝛼 ( 𝑉 0 + 𝑉 𝑅 )
𝐶 𝐽 = 𝛼 2 ( 𝑉 0 + 𝑉 𝑅 )
𝐶 𝐽0 = 𝛼 2 𝑉 0
If let
𝐶 𝐽 = 𝐶 𝐽0 (1+ 𝑉 𝑅 𝑉 0 )
For abrupt (m=1/2)
or graded junction (m=1/3)
𝐶 𝐽 = 𝐶 𝐽0 (1+ 𝑉 𝑅 𝑉 0 ) 𝑚

5. Another approach to determine CJ
Use the parallel plate capacitor equation:
𝐶 𝐽 = 𝜖 𝑠 𝐴 𝑊
where A is area and W is depletion width
Remember Eq. (3.31)
W= 2 𝜖 𝑠 𝑞 𝑁 𝐴 + 𝑁 𝐷 𝑁 𝐴 𝑁 𝐷 ( 𝑉 0 + 𝑉 𝑅 )
𝐶 𝐽 =𝐴 𝜖 𝑠 𝑞 2 𝑁 𝐴 𝑁 𝐷 𝑁 𝐴 + 𝑁 𝐷 1 ( 𝑉 0 + 𝑉 𝑅 )

6. 3.6.2 Diffusion Capacitance
It is due to the minority-carrier charges stored in p and n bulk regions (outside the depletion region).
𝑄 𝑝 =𝐴𝑞×𝑠ℎ𝑎𝑑𝑒𝑑 𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑡ℎ𝑒 𝑝 𝑛 𝑥 𝑐𝑢𝑟𝑣𝑒𝑠=𝐴𝑞 𝑝 𝑛 𝑥 𝑛 − 𝑝 𝑛0

7. 3.6.2 Diffusion Capacitance
From Eq. (3.33) 𝑝 𝑛( 𝑥 𝑛 ) = 𝑝 𝑛0 𝑒 𝑉/ 𝑉 𝑇
And Eq. (3.37) 𝐽 𝑝( 𝑥 𝑛 ) = 𝑞( 𝐷 𝑝 𝐿 𝑝 )𝑝 𝑛0 (𝑒 𝑉/ 𝑉 𝑇 −1) so
The minority carrier life time
𝑄 𝑝 = 𝐿 𝑝 2 𝐷 𝑝 𝐼 𝑝
𝜏 𝑝 = 𝐿 𝑝 2 𝐷 𝑝
𝜏 𝑛 = 𝐿 𝑛 2 𝐷 𝑛
𝑄= 𝜏 𝑝 𝐼 𝑝 + 𝜏 𝑛 𝐼 𝑛 = 𝜏 𝑇 𝐼
τT is the mean transit time
𝑠𝑜:
𝐶 𝑑 = 𝑑𝑄 𝑑𝑉 = 𝜏 𝑇 𝑉 𝑇 𝐼