1. EE105 Fall 2011Lecture 3, Slide 1Prof. Salahuddin, UC Berkeley Lecture 3 OUTLINE Semiconductor Basics (cont’d) – Carrier drift and diffusion PN Junction Diodes – Electrostatics – Capacitance Reading: Chapter 2.1-2.2

2. EE105 Fall 2011Lecture 3, Slide 2Prof. Salahuddin, UC Berkeley Recap: Drift Current Drift current is proportional to the carrier velocity and carrier concentration:  Hole current per unit area (i.e. current density) J p,drift = q p v h Total current J p,drift = Q/t Q= total charge contained in the volume shown to the right t= time taken by Q to cross the volume Q=qp(in cm 3 )X Volume=qpAL=qpAv h t

3. EE105 Fall 2011Lecture 3, Slide 3Prof. Salahuddin, UC Berkeley Recap: Conductivity and Resistivity In a semiconductor, both electrons and holes conduct current: The conductivity of a semiconductor is – Unit: mho/cm The resistivity of a semiconductor is – Unit: ohm-cm

4. EE105 Fall 2011Lecture 3, Slide 4Prof. Salahuddin, UC Berkeley Electrical Resistance where  is the resistivity Resistance (Unit: ohms) V + _ L t W I homogeneously doped sample

5. EE105 Fall 2011Lecture 3, Slide 5Prof. Salahuddin, UC Berkeley Resistivity Example

6. EE105 Fall 2011Lecture 3, Slide 6Prof. Salahuddin, UC Berkeley A Second Mechanism of Current Flow is Diffusion

7. EE105 Fall 2011Lecture 3, Slide 7Prof. Salahuddin, UC Berkeley Carrier Diffusion Due to thermally induced random motion, mobile particles tend to move from a region of high concentration to a region of low concentration. – Analogy: ink droplet in water

8. EE105 Fall 2011Lecture 3, Slide 8Prof. Salahuddin, UC Berkeley Carrier Diffusion Current flow due to mobile charge diffusion is proportional to the carrier concentration gradient. – The proportionality constant is the diffusion constant. Notation: D p  hole diffusion constant (cm 2 /s) D n  electron diffusion constant (cm 2 /s)

9. EE105 Fall 2011Lecture 3, Slide 9Prof. Salahuddin, UC Berkeley Diffusion Examples Non-linear concentration profile  varying diffusion current Linear concentration profile  constant diffusion current

10. EE105 Fall 2011Lecture 3, Slide 10Prof. Salahuddin, UC Berkeley Diffusion Current Diffusion current within a semiconductor consists of hole and electron components: The total current flowing in a semiconductor is the sum of drift current and diffusion current:

11. EE105 Fall 2011Lecture 3, Slide 11Prof. Salahuddin, UC Berkeley The Einstein Relation The characteristic constants for drift and diffusion are related: Note that at room temperature (300K) – This is often referred to as the “thermal voltage”.

12. EE105 Fall 2011Lecture 3, Slide 12Prof. Salahuddin, UC Berkeley The PN Junction Diode When a P-type semiconductor region and an N-type semiconductor region are in contact, a PN junction diode is formed. VDVD IDID +–

13. EE105 Fall 2011Lecture 3, Slide 13Prof. Salahuddin, UC Berkeley Diode Operating Regions In order to understand the operation of a diode, it is necessary to study its behavior in three operation regions: equilibrium, reverse bias, and forward bias. V D = 0V D > 0V D < 0

14. EE105 Fall 2011Lecture 3, Slide 14Prof. Salahuddin, UC Berkeley Carrier Diffusion across the Junction Because of the differences in hole and electron concentrations on each side of the junction, carriers diffuse across the junction: Notation: n n  electron concentration on N-type side (cm -3 ) p n  hole concentration on N-type side (cm -3 ) p p  hole concentration on P-type side (cm -3 ) n p  electron concentration on P-type side (cm -3 )

15. EE105 Fall 2011Lecture 3, Slide 15Prof. Salahuddin, UC Berkeley Depletion Region As conduction electrons and holes diffuse across the junction, they leave behind ionized dopants. Thus, a region that is depleted of mobile carriers is formed. – The charge density in the depletion region is not zero. – The carriers which diffuse across the junction recombine with majority carriers, i.e. they are annihilated. width=W dep quasi- neutral region

16. EE105 Fall 2011Lecture 3, Slide 16Prof. Salahuddin, UC Berkeley Some Important Relations Energy=-qV

17. EE105 Fall 2011Lecture 3, Slide 17Prof. Salahuddin, UC Berkeley The Depletion Approximation In the depletion region on the N side: (x)(x) x -qN A qN D In the depletion region on the P side: a -b Because charge density ≠ 0 in the depletion region, a large E-field exists in this region:

18. EE105 Fall 2011Lecture 3, Slide 18Prof. Salahuddin, UC Berkeley Carrier Drift across the Junction

19. EE105 Fall 2011Lecture 3, Slide 19Prof. Salahuddin, UC Berkeley PN Junction in Equilibrium In equilibrium, the drift and diffusion components of current are balanced; therefore the net current flowing across the junction is zero.

20. EE105 Fall 2011Lecture 3, Slide 20Prof. Salahuddin, UC Berkeley Built-in Potential, V 0 Because there is a large electric field in the depletion region, there is a significant potential drop across this region: (Unit: Volts)

21. EE105 Fall 2011Lecture 3, Slide 21Prof. Salahuddin, UC Berkeley Built-In Potential Example Estimate the built-in potential for PN junction below. – Note that NP N D = 10 18 cm -3 N A = 10 15 cm -3

22. EE105 Fall 2011Lecture 3, Slide 22Prof. Salahuddin, UC Berkeley A forward bias decreases the potential drop across the junction. As a result, the magnitude of the electric field decreases and the width of the depletion region narrows. PN Junction under Forward Bias (x)(x) x -qN A qN D a -b V(x)V(x) x a V0V0 IDID 0