President UniversityErwin SitompulSDP 8/1 Dr.-Ing. Erwin Sitompul President University Lecture 8 Semiconductor Device Physics

President UniversityErwin SitompulSDP 8/2 Majority carriers Majority carriers Qualitative Derivation Chapter 6pn Junction Diodes: I-V Characteristics

President UniversityErwin SitompulSDP 8/3 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. M inority carriers are “injected” into the quasi-neutral regions  Δn p > 0, Δp n > 0. M inority carriers diffuse in the quasi-neutral regions, recombining with majority carriers.

President UniversityErwin SitompulSDP 8/4 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 8/5 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.

President UniversityErwin SitompulSDP 8/6 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 8/7 “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 8/8 n-sidep-side Excess Carrier Concentrations at –x p, x n Chapter 6pn Junction Diodes: I-V Characteristics

President UniversityErwin SitompulSDP 8/9 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 8/10 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 8/11 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 8/12 n-side p-side pn Diode I–V Characteristic Chapter 6pn Junction Diodes: I-V Characteristics

President UniversityErwin SitompulSDP 8/13 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 8/14 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 8/15 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 8/16 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 8/17 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 8/18 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 8/19 Dominant breakdown mechanism is tunneling Empirical Observations of V BR Chapter 6pn Junction Diodes: I-V Characteristics V BR : breakdown voltage V BR decreases with increasing N, V BR decreases with decreasing E G.

President UniversityErwin SitompulSDP 8/20 At breakdown, V A =–V BR Breakdown Voltage, V BR Chapter 6pn Junction Diodes: I-V Characteristics If the reverse bias voltage (–V A ) is so large that the peak electric field exceeds a critical value E CR, then the junction will “break down” and large reverse current will flow Thus, the reverse bias at which breakdown occurs is

President UniversityErwin SitompulSDP 8/21 Small E-field: High E-field: Low energy, causing lattice vibration and localized heating High energy, enabling impact ionization which causing avalanche, at doping level N < cm –3 Breakdown Mechanism: Avalanching Chapter 6pn Junction Diodes: I-V Characteristics E CR : critical electric field in the depletion region

President UniversityErwin SitompulSDP 8/22 Breakdown Mechanism: Zener Process Chapter 6pn Junction Diodes: I-V Characteristics Zener process is the tunneling mechanism in a reverse-biased diode. Energy barrier is higher than the kinetic energy of the particle The particle energy remains constant during the tunneling process Barrier must be thin  dominant breakdown mechanism when both junction sides are heavily doped Typically, Zener process dominates when V BR cm –3.

President UniversityErwin SitompulSDP 8/23 Effect of R–G in Depletion Region Chapter 6pn Junction Diodes: I-V Characteristics R–G in the depletion region contributes an additional component of diode current I R–G. The net generation rate is given by E T : trap-state energy level

President UniversityErwin SitompulSDP 8/24 For reverse bias, with the carrier concentrations n and p being negligible, Effect of R–G in Depletion Region Chapter 6pn Junction Diodes: I-V Characteristics Continuing, Reverse biases with V A < – few kT/q

President UniversityErwin SitompulSDP 8/25 Effect of R–G in Depletion Region Chapter 6pn Junction Diodes: I-V Characteristics Continuing, For forward bias, the carrier concentrations n and p cannot be neglected,

President UniversityErwin SitompulSDP 8/26 Diffusion, ideal diode Effect of R–G in Depletion Region Chapter 6pn Junction Diodes: I-V Characteristics

President UniversityErwin SitompulSDP 8/27 Voltage drop, significant for high I R S can be determined experimentally Effect of Series Resistance Chapter 6pn Junction Diodes: I-V Characteristics

President UniversityErwin SitompulSDP 8/28 (for a p + n junction) (for a pn + junction) Effect of High-Level Injection Chapter 6pn Junction Diodes: I-V Characteristics As V A increases and about to reach V bi, the side of the junction which is more lightly doped will eventually reach high-level injection: This means that the minority carrier concentration approaches the majority doping concentration. Then, the majority carrier concentration must increase to maintain the neutrality. This majority-carrier diffusion current reduces the diode current from the ideal.

President UniversityErwin SitompulSDP 8/29 Perturbation of both minority and majority carrier High-Level Injection Effect Chapter 6pn Junction Diodes: I-V Characteristics

President UniversityErwin SitompulSDP 8/30 Forward-bias current Reverse-bias current Deviations from ideal I-V Due to avalanching and Zener process Due to high-level injection and series resistance in quasineutral regions Due to thermal generation in depletion region Due to thermal recombination in depletion region Summary Chapter 6pn Junction Diodes: I-V Characteristics

President UniversityErwin SitompulSDP 8/31 This time no homework. Prepare well for Quiz 2. Chapter 5pn Junction Electrostatics Homework