Chapter 6 pn Junction Diodes: I - V Characteristics

2. Semiconductor Device Physics Chapter 6 pn Junction Diodes: I-V Characteristics

3. Chapter 6 pn Junction Diodes: I-V Characteristics Majority carriers Majority carriers Qualitative Derivation

4. Chapter 6 pn Junction Diodes: I-V Characteristics Current Flow in a pn Junction Diode • When a forward bias (VA > 0) is applied, the potential barrier to diffusion across the junction is reduced. • Minority carriers are “injected” into the quasi-neutral regions Δnp > 0, Δpn > 0. • Minority carriers diffuse in the quasi-neutral regions, recombining with majority carriers.

5. Chapter 6 pn Junction Diodes: I-V Characteristics Ideal Diode: Assumptions • Steady-state conditions. • Non-degenerately doped step junction. • One-dimensional diode. • Low-level injection conditions prevail in the quasi-neutral regions. • No processes other than drift, diffusion, and thermal R–G take place inside the diode.

6. Chapter 6 pn Junction Diodes: I-V Characteristics Current Flow in a pn Junction Diode • Current density J = JN(x) + JP(x) • JN(x) and JP(x) may vary with position, but J is constant throughout the diode. • Yet an additional assumption is now made, that thermal recombination-generation is negligible throughout the depletion region  JN and JP are therefore determined to be constants independent of position inside the depletion region.

7. Chapter 6 pn Junction Diodes: I-V Characteristics Carrier Concentrations at –xp, +xn • Consider the equilibrium carrier concentrations at VA = 0: p-side n-side • If low-level injection conditions prevail in the quasi-neutral regions when VA 0, then:

8. Chapter 6 pn Junction Diodes: I-V Characteristics “Law of the Junction” • The voltage VA applied to a pn junction falls mostly across the depletion region (assuming that low-level injection conditions prevail in the quasi-neutral regions). • Two quasi-Fermi levels is drawn in the depletion region:

9. Chapter 6 pn Junction Diodes: I-V Characteristics Excess Carrier Concentrations at –xp, xn p-side n-side

10. Chapter 6 pn Junction Diodes: I-V Characteristics Example: Carrier Injection • A pn junction has NA=1018 cm–3 and ND=1016 cm–3. The applied voltage is 0.6 V. • a) What are the minority carrier concentrations at the depletion-region edges? • b) What are the excess minority carrier concentrations?

11. Chapter 6 pn Junction Diodes: I-V Characteristics Excess Carrier Distribution • From the minority carrier diffusion equation, • For simplicity, we develop a new coordinate system: • We have the following boundary conditions: • Then, the solution is given by: • LP : hole minority carrier diffusion length

12. Chapter 6 pn Junction Diodes: I-V Characteristics Excess Carrier Distribution • New boundary conditions • From the x’ → ∞, • From the x’ → 0, • Therefore • Similarly,

13. Chapter 6 pn Junction Diodes: I-V Characteristics pn Diode I–V Characteristic n-side p-side

14. Chapter 6 pn Junction Diodes: I-V Characteristics pn Diode I–V Characteristic • Shockley Equation,for ideal diode • I0 can be viewed as the drift current due to minority carriers generated within the diffusion lengths of the depletion region

15. Chapter 6 pn Junction Diodes: I-V Characteristics Diode Saturation Current I0 • I0 can vary by orders of magnitude, depending on the semiconductor material, due to ni2 factor. • In an asymmetrically doped pn junction, the term associated with the more heavily doped side is negligible. • If the p side is much more heavily doped, • If the n side is much more heavily doped,

16. Chapter 6 pn Junction Diodes: I-V Characteristics Diode Carrier Currents • Total current density is constant inside the diode • Negligible thermal R-G throughout depletion region  dJN/dx = dJP/dx = 0

17. Chapter 6 pn Junction Diodes: I-V Characteristics Excess minority carriers Excess minority carriers Carrier Concentration: Forward Bias • Law of the Junction • Low level injection conditions

18. Chapter 6 pn Junction Diodes: I-V Characteristics Carrier Concentration: Reverse Bias • Deficit of minority carriers near the depletion region. • Depletion region acts like a “sink”, draining carriers from the adjacent quasineutral regions

19. Chapter 6 pn Junction Diodes: I-V Characteristics No saturation “Slope over” “Breakdown” Smaller slope Deviations from the Ideal I-V Behavior • Si pn-junction Diode, 300 K. Forward-bias current Reverse-bias current

20. Chapter 6 pn Junction Diodes: I-V Characteristics Homework • This time no homework. • Prepare well for midterm examination. • Midterm examination covers material of Lecture 1 until Lecture 6. • Two A4- formula sheets may be used during exam. Formula sheets may not contain problems and solutions. • The use of calculator is allowed. • No notebooks, tablets, smart phones, nor any other electronics may be used during exam.

21. Chapter 6 pn Junction Diodes: I-V Characteristics Exercise Problems A certain Silicon sample is doped differently in two regions. Region A is doped with Boron (7×1016 cm–3) and Arsenic (3×1016 cm–3) while Region B only with Arsenic (1018 cm–3). At 300 K, calculate the resistance of the block. An Si sample is given with ND = 1018 cm–3. The minority carrier lifetimes are given by 10–7 s. Holes are injected at x=0 to generate a certain hole diffusion current density of 10μA/cm2. Low level injection condition is assumed to be prevailed. If the hole concentration decays exponentially as x increases with a certain diffusion length constant, determine the excess concentration required to be supplied at x=0.

22. Chapter 6 pn Junction Diodes: I-V Characteristics Exercise Problems A certain Si pn-junction diode is doped with NA=2×1018 cm–3 and ND= 4×1018 cm–3. The constants are given by DN = 18 cm2/s, DP = 12 cm2/s, and τp = τn = 10–7 s. Calculate the built-in voltage Vbi and the depletion width W at T = 300 K. Which side of the depletion layer will be wider, on the p-side or on the n-side? Determine Jdiff if VA=0.5 V? What is the change if VA=–0.2 V?