President UniversityErwin SitompulSDP 6/1 Dr.-Ing. Erwin Sitompul President University Lecture 6 Semiconductor Device Physics

President UniversityErwin SitompulSDP 6/2 Majority carriers Majority carriers Qualitative Derivation Chapter 6pn Junction Diodes: I-V Characteristics

President UniversityErwin SitompulSDP 6/3 Current Flow in a pn Junction Diode Chapter 6pn Junction Diodes: I-V Characteristics When a forward bias (V A > 0) is applied, the potential barrier to diffusion across the junction is reduced. Minority carriers are “injected” into the quasi-neutral regions  Δn p > 0, Δp n > 0. Minority carriers diffuse in the quasi-neutral regions, recombining with majority carriers.

President UniversityErwin SitompulSDP 6/4 Ideal Diode: Assumptions Chapter 6pn Junction Diodes: I-V Characteristics 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.

President UniversityErwin SitompulSDP 6/5 Current Flow in a pn Junction Diode Chapter 6pn Junction Diodes: I-V Characteristics Current density J = J N (x) + J P (x) J N (x) and J P (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  J N and J P are therefore determined to be constants independent of position inside the depletion region.

President UniversityErwin SitompulSDP 6/6 n-sidep-side Carrier Concentrations at –x p, +x n Chapter 6pn Junction Diodes: I-V Characteristics Consider the equilibrium carrier concentrations at V A = 0: If low-level injection conditions prevail in the quasi-neutral regions when V A  0, then:

President UniversityErwin SitompulSDP 6/7 “Law of the Junction” Chapter 6pn Junction Diodes: I-V Characteristics The voltage V A 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:

President UniversityErwin SitompulSDP 6/8 n-sidep-side Excess Carrier Concentrations at –x p, x n Chapter 6pn Junction Diodes: I-V Characteristics

President UniversityErwin SitompulSDP 6/9 Example: Carrier Injection Chapter 6pn Junction Diodes: I-V Characteristics A pn junction has N A =10 18 cm –3 and N D =10 16 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?

President UniversityErwin SitompulSDP 6/10 Excess Carrier Distribution Chapter 6pn Junction Diodes: I-V Characteristics From the minority carrier diffusion equation, We have the following boundary conditions: For simplicity, we develop a new coordinate system: Then, the solution is given by: L P : hole minority carrier diffusion length

President UniversityErwin SitompulSDP 6/11 Excess Carrier Distribution Chapter 6pn Junction Diodes: I-V Characteristics New boundary conditions From the x’ → ∞, From the x’ → 0, Therefore Similarly,

President UniversityErwin SitompulSDP 6/12 n-side p-side pn Diode I–V Characteristic Chapter 6pn Junction Diodes: I-V Characteristics

President UniversityErwin SitompulSDP 6/13 pn Diode I–V Characteristic Chapter 6pn Junction Diodes: I-V Characteristics Shockley Equation, for ideal diode I 0 can be viewed as the drift current due to minority carriers generated within the diffusion lengths of the depletion region

President UniversityErwin SitompulSDP 6/14 I 0 can vary by orders of magnitude, depending on the semiconductor material, due to n i 2 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, Diode Saturation Current I 0 Chapter 6pn Junction Diodes: I-V Characteristics

President UniversityErwin SitompulSDP 6/15 Diode Carrier Currents Chapter 6pn Junction Diodes: I-V Characteristics Total current density is constant inside the diode Negligible thermal R-G throughout depletion region  dJ N /dx = dJ P /dx = 0

President UniversityErwin SitompulSDP 6/16 Excess minority carriers Excess minority carriers Carrier Concentration: Forward Bias Chapter 6pn Junction Diodes: I-V Characteristics Law of the Junction Low level injection conditions

President UniversityErwin SitompulSDP 6/17 Carrier Concentration: Reverse Bias Chapter 6pn Junction Diodes: I-V Characteristics Deficit of minority carriers near the depletion region. Depletion region acts like a “sink”, draining carriers from the adjacent quasineutral regions

President UniversityErwin SitompulSDP 6/18 Forward-bias current Reverse-bias current “Breakdown” “Slope over” No saturation Smaller slope Deviations from the Ideal I-V Behavior Chapter 6pn Junction Diodes: I-V Characteristics Si pn-junction Diode, 300 K.

President UniversityErwin SitompulSDP 6/19 This time no homework. Prepare well for midterm examination. Homework Chapter 6pn Junction Diodes: I-V Characteristics