EECS130 Integrated Circuit Devices Professor Ali Javey 9/18/2007 P Junctions Lecture 1 Reading: Chapter 5
Announcements For THIS WEEK OLY, Prof. Javey's office hours will be held on Tuesday, Sept 18 3:30-4:30 pm and Wednesday, Sept 19 5-6 pm. Exam 1 (Oct 4) will cover Semiconductor Fundamentals, Fabrication, and P junctions. HW2 is due right now. HW3 is now posted on the web. You can check your grades on bspace. Check out the group discussion board.
P Junctions Donors -type P-type I V + I Reverse bias V Forward bias P diode symbol A P junction is present in every semiconductor device.
Energy Band Diagram and Depletion Layer of a P Junction -region P-region (a) E f E c (b) E c E f E v E v E c (c) (d) eutral -region Depletion layer eutral P-region E f E v E c E f E v A depletion layer exists at the P junction. n 0 and p 0 in the depletion layer.
Doping Profile of Idealized Junctions p n p n
Qualitative Electrostatics Band diagram Built in-potential From ε-dv/dx
Formation of pn junctions When the junction is formed, electrons from the n-side and holes from the p-side will diffuse leaving behind charged dopant atoms. Remember that the dopant atoms cannot move! Electrons will leave behind positively charged donor atoms and holes will leave behind negatively charged acceptor atoms. The net result is the build up of an electric field from the positively charged atoms to the negatively charged atoms, i.e., from the n- side to p-side. When steady state condition is reached after the formation of junction (how long this takes?) the net electric field (or the built in potential) will prevent further diffusion of electrons and holes. In other words, there will be drift and diffusion currents such that net electron and hole currents will be zero.
Equilibrium Conditions Under equilibrium conditions, the net electron current and hole current will be zero. E-field P-type -type A 10 17 cm 3 D 10 16 cm 3 hole diffusion current hole drift current net current 0
2 ln i a d bi n q kt V Built-in Potential d c kt q A c d q kt A e n ln 2 2 ln i a c kt qb c a i n q kt B e n n d c i a c bi n q kt A B V ln ln 2 -region P-region (b) E f E c E v qv bi qb qa
Built-in Potential as a function of a and d
Poisson s Equation What can Poisson s equation tell us? ) ε s : semiconductor permittivity (~12ε o for Si) ρ: charge density (C/cm 3 )
The Depletion Approximation We assume that the free carrier concentration inside the depletion region is zero. We assume that the charge density outside the depletion region is zero and q( d - a ) inside the depletion.
Field in the Depletion Layer eutral Region Depletion Layer eutral Region P On the P-side of the depletion layer, ρ q a x 0 n x p ρ d dx q a ε s x n q d q a x p x qa qa ( x) x + C 1 ( x p x) ε ε s s E On the -side, ρ q d x x n 0 p x qd ( x ) ( x + xn ) ε s
Field in the Depletion Layer eutral Region Depletion Layer x 0 n x p eutral Region P The electric field is continuous at x 0. a x p d x n A one-sided junction is called a + P junction or P + junction
Potential in the Depletion Layer D 1 0
Depletion Width
Depletion Width
EXAMPLE: A P + junction has a 10 20 cm -3 and d 10 17 cm -3. What is a) its built in potential, b)w dep, c)x n, and d) x p? Solution: a) kt φbi q b) W 20 17 d a 10 10 cm ln 0.026V ln 20 6 n 10 cm 6 2 i dep 2ε sφbi q d 2 12 8.85 10 19 1.6 10 10 14 17 1 1/ 2 1V 0.12 μm c) x n W dep 0.12 μm d) x p x n d a 1.2 10 4 μm 1.2 Å 0
V + Reverse-Biased P Junction P qv bi (a) E c W dep 2ε s ( Vbi + VA ) 2ε s q potential q barrier E c E f E f E v E v (b) V 0 E c 1 1 d + 1 a lighter 1 dopant density E c E fn qv bi + qv A qv A E fp E v Does the depletion layer widen or shrink with increasing reverse bias? E v (c) reverse-biased
Reverse-Biased P Junction
Forward Biased P Junction
ote: simply replace Vbi with Vbi-VA
Capacitance-Voltage Characteristics d a P C dep ε s A W dep Conductor Insulator Conductor W dep Is C dep a good thing? What are three ways to reduce C dep?
Capacitance-Voltage Characteristics 1/C dep 2 Capacitance data C 1 2 dep W A 2 dep 2 2 ε s 2( φbi + V ) 2 qε A S Slope 2/qε s A 2 φ bi Increasing reverse bias V r
Junction Breakdown I V B, breakdown voltage Forward Current V Small leakage Current A Zener diode is designed to operate in the breakdown mode.
Peak Electric Field + a eutral Region increasing reverse bias P 0 x p p (a) increasing reverse bias p 2q ( 0) ( φ + bi V ) ε s r 1/ 2 x p (b) x
Tunneling Breakdown (a) E c E f E v Dominant breakdown cause when both sides of a junction are very heavily doped. (b) Filled States - Empty States E c E v V B ε 2 s crit 2 q φ bi (c) I V p crit 10 6 V/cm Breakdown
Avalanche Breakdown E c E fp E v original electron impact ionization avalanche breakdown electron-hole pair generation V B ε s 2 crit 2q E c E fn 1 1 V B + a 1 d