Semiconductor Device Physics Lecture 6 Dr Ing Erwin

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Semiconductor Device Physics Lecture 6 Dr. -Ing. Erwin Sitompul President University http: //zitompul. wordpress.

Semiconductor Device Physics Lecture 6 Dr. -Ing. Erwin Sitompul President University http: //zitompul. wordpress. com 2 President University 0 1 3 Erwin Sitompul SDP 6/1

Semiconductor Device Physics Chapter 6 pn Junction Diodes: I-V Characteristics President University Erwin Sitompul

Semiconductor Device Physics Chapter 6 pn Junction Diodes: I-V Characteristics President University Erwin Sitompul SDP 6/2

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

Chapter 6 pn Junction Diodes: I-V Characteristics Qualitative Derivation Majority carriers President University Erwin Sitompul SDP 6/3

Chapter 6 pn Junction Diodes: I-V Characteristics Current Flow in a pn Junction Diode

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

Chapter 6 pn Junction Diodes: I-V Characteristics Ideal Diode: Assumptions n Steady-state conditions. n

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

Chapter 6 pn Junction Diodes: I-V Characteristics Current Flow in a pn Junction Diode

Chapter 6 pn Junction Diodes: I-V Characteristics Current Flow in a pn Junction Diode n Current density J = JN(x) + JP(x) n JN(x) and JP(x) may vary with position, but J is constant throughout the diode. n 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. President University Erwin Sitompul SDP 6/6

Chapter 6 pn Junction Diodes: I-V Characteristics Carrier Concentrations at –xp, +xn n Consider

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

Chapter 6 pn Junction Diodes: I-V Characteristics “Law of the Junction” n The voltage

Chapter 6 pn Junction Diodes: I-V Characteristics “Law of the Junction” n 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). n Two quasi-Fermi levels is drawn in the depletion region: President University Erwin Sitompul SDP 6/8

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

Chapter 6 pn Junction Diodes: I-V Characteristics Excess Carrier Concentrations at –xp, xn p-side President University n-side Erwin Sitompul SDP 6/9

Chapter 6 pn Junction Diodes: I-V Characteristics Example: Carrier Injection n A pn junction

Chapter 6 pn Junction Diodes: I-V Characteristics Example: Carrier Injection n 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? President University Erwin Sitompul SDP 6/10

Chapter 6 pn Junction Diodes: I-V Characteristics Excess Carrier Distribution n From the minority

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

Chapter 6 pn Junction Diodes: I-V Characteristics Excess Carrier Distribution n New boundary conditions

Chapter 6 pn Junction Diodes: I-V Characteristics Excess Carrier Distribution n New boundary conditions n From the x’ → ∞, From the x’ → 0, n Therefore n Similarly, President University Erwin Sitompul SDP 6/12

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

Chapter 6 pn Junction Diodes: I-V Characteristics pn Diode I–V Characteristic n-side p-side President University Erwin Sitompul SDP 6/13

Chapter 6 pn Junction Diodes: I-V Characteristics pn Diode I–V Characteristic • Shockley Equation,

Chapter 6 pn Junction Diodes: I-V Characteristics pn Diode I–V Characteristic • Shockley Equation, • President University 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 Erwin Sitompul SDP 6/14

Chapter 6 pn Junction Diodes: I-V Characteristics Diode Saturation Current I 0 n I

Chapter 6 pn Junction Diodes: I-V Characteristics Diode Saturation Current I 0 n I 0 can vary by orders of magnitude, depending on the semiconductor material, due to ni 2 factor. n In an asymmetrically doped pn junction, the term associated with the more heavily doped side is negligible. n If the p side is much more heavily doped, n If the n side is much more heavily doped, President University Erwin Sitompul SDP 6/15

Chapter 6 pn Junction Diodes: I-V Characteristics Diode Carrier Currents • Total current density

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 d. JN/dx = d. JP/dx = 0 President University Erwin Sitompul SDP 6/16

Chapter 6 pn Junction Diodes: I-V Characteristics Carrier Concentration: Forward Bias n Law of

Chapter 6 pn Junction Diodes: I-V Characteristics Carrier Concentration: Forward Bias n Law of the Junction n Low level injection conditions Excess minority carriers President University Erwin Sitompul Excess minority carriers SDP 6/17

Chapter 6 pn Junction Diodes: I-V Characteristics Carrier Concentration: Reverse Bias n Deficit of

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

Chapter 6 pn Junction Diodes: I-V Characteristics Deviations from the Ideal I-V Behavior n

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

Chapter 6 pn Junction Diodes: I-V Characteristics Homework n This time no homework. n

Chapter 6 pn Junction Diodes: I-V Characteristics Homework n This time no homework. n Prepare well for midterm examination. • Midterm examination covers material of • • • Lecture 1 until Lecture 6. Two A 4 - 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. President University Erwin Sitompul SDP 6/20

Chapter 6 pn Junction Diodes: I-V Characteristics Exercise Problems 1. A certain Silicon sample

Chapter 6 pn Junction Diodes: I-V Characteristics Exercise Problems 1. 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. 2. 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/cm 2. 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. President University Erwin Sitompul SDP 6/21

Chapter 6 pn Junction Diodes: I-V Characteristics Exercise Problems 3. A certain Si pn-junction

Chapter 6 pn Junction Diodes: I-V Characteristics Exercise Problems 3. 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 cm 2/s, DP = 12 cm 2/s, and τp = τn = 10– 7 s. (a) 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 nside? (b) Determine Jdiff if VA = 0. 5 V? What is the change if VA = – 0. 2 V? President University Erwin Sitompul SDP 6/22