1. 1 Chapter 5-2 Quantitative electrostatic relationships We make the analysis in 1 dimension, even though actual diode as shown may not be a one-dimensional system. This makes the analysis simple. The metallurgical junction is located at x = 0.

2. 2 Quantitative analysis: Electric field E p n NANA NDND  x p 0x n W E max =  q N A x p /  =  q N D x n / 

3. 3 Relationship between x n and x p E max =  q N A x p /  =  q N D x n /  N A x p = N D x n Net charge on p-side = Net charge on n-side Depletion layer width: W = x n + x p If N A >> N D, then W  x n and if N A << N D, then W  x p

4. 4 Built-in voltage: V bi V bi =  {area under E versus x curve} =  (1/2) [ W (– q N D x n /  ) ] = [q / (2  )] N D x n W

5. 5 Quantitative analysis: Electrostatic potential V x V bi

6. 6 Step junction with V A  0 The equation for W is similar to the earlier equation except that V bi is replaced by V bi  V A ; (V A is restricted to V A < V bi ). V A = Applied Voltage

7. 7 Effects of forward and reverse bias

8. 8 PN-junction energy-band diagrams

9. 9 Example 1 N D = 2  10 16 cm –3 N A = 3  10 17 cm –3 N A = 1  10 16 cm –3 N D = 2  10 17 cm –3 Consider the following diode. Calculate the maximum electric field, E max, the location of E max, the depletion layer width W, x n and x p and the built-in voltage, V bi. Carefully plot the charge density, electric field, and the potential as a function of x. Also, calculate the depletion layer width and the maximum electric field if a reverse voltage of 10 V is applied across the diode. What will be W if V A = 0.5 V?

10. 10 Example 2 Consider the diode of Example 1. Calculate the depletion layer width and the maximum electric field if a reverse voltage of 10 V is applied across the diode. Calculate the depletion layer width in the n-side and p-side under this biased condition. What will be W if V A = 0.5 V? What happens if we apply V A > V bi ?