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

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

Current Flow in a pn Junction Diode 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.

Ideal Diode: Assumptions 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.

Current Flow in a pn Junction Diode 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.

Carrier Concentrations at –xp, +xn 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:

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:

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

Example: Carrier Injection 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?

Excess Carrier Distribution 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

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

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

pn Diode I–V Characteristic 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

Diode Saturation Current I0 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,

Diode Carrier Currents 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

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

Carrier Concentration: Reverse Bias 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

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

Homework This time no homework. Prepare well for midterm examination. 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.

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 10 μA/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.

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?