Announcements HW1 is posted due Tuesday 9 4 Discussion Section 102 We 9 10 moved to 289 Cory Lab sections If a section is over subscribed then priority will be given to students officially registered for this section Paid position for videotaping EE105 lectures is available EE105 Fall 2007 Lecture 2 1 Slide 1 Prof Liu UC Berkeley Lecture 2 OUTLINE Basic Semiconductor Physics cont d Carrier drift and diffusion PN Junction Diodes Electrostatics Capacitance Reading Chapter 2 1 2 2 EE105 Fall 2007 Lecture 2 1 Slide 2 Prof Liu UC Berkeley Dopant Compensation An N type semiconductor can be converted into Ptype material by counter doping it with acceptors such that NA ND A compensated semiconductor material has both acceptors and donors N type material ND NA P type material NA ND n ND N A p N A ND 2 2 ni p ND N A EE105 Fall 2007 ni n N A ND Lecture 2 Slide 3 Prof Liu UC Berkeley Types of Charge in a Semiconductor Negative charges Conduction electrons density n Ionized donor atoms density ND Positive charges Holes density p Ionized acceptor atoms density NA The net charge density C cm3 in a semiconductor is q p n N D N A EE105 Fall 2007 Lecture 2 Slide 4 Prof Liu UC Berkeley Carrier Drift The process in which charged particles move because of an electric field is called drift Charged particles within a semiconductor move with an average velocity proportional to the electric field The proportionality constant is the carrier mobility Hole velocity vh p E Electron velocity ve n E Notation p hole mobility cm2 V s n electron mobility cm2 V s EE105 Fall 2007 Lecture 2 Slide 5 Prof Liu UC Berkeley Velocity Saturation In reality carrier velocities saturate at an upper limit called the saturation velocity vsat 0 1 bE vsat 0 b v 1 EE105 Fall 2007 Lecture 2 Slide 6 0 E 0 E vsat Prof Liu UC Berkeley Drift Current Drift current is proportional to the carrier velocity and carrier concentration vh t A volume from which all holes cross plane in time t p vh t A of holes crossing plane in time t q p vh t A charge crossing plane in time t q p vh A charge crossing plane per unit time hole current Hole current per unit area i e current density Jp drift q p vh EE105 Fall 2007 Lecture 2 Slide 7 Prof Liu UC Berkeley Conductivity and Resistivity In a semiconductor both electrons and holes conduct current J p drift qp p E J n drift qn n E J tot drift J p drift J n drift qp p E qn n E J tot drift q p p n n E E The conductivity of a semiconductor is qp p qn n Unit mho cm The resistivity of a semiconductor is Unit ohm cm EE105 Fall 2007 Lecture 2 Slide 8 1 Prof Liu UC Berkeley Resistivity Example Estimate the resistivity of a Si sample doped with phosphorus to a concentration of 1015 cm 3 and boron to a concentration of 1017 cm 3 The electron mobility and hole mobility are 700 cm2 Vs and 300 cm2 Vs respectively EE105 Fall 2007 Lecture 2 Slide 9 Prof Liu UC Berkeley Electrical Resistance I V W t homogeneously doped sample L V L Resistance R I Wt Unit ohms where is the resistivity EE105 Fall 2007 Lecture 2 Slide 10 Prof Liu 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 Current flow due to mobile charge diffusion is proportional to the carrier concentration gradient The proportionality constant is the diffusion constant dp J p qD p dx Notation Dp hole diffusion constant cm2 s Dn electron diffusion constant cm2 s EE105 Fall 2007 Lecture 2 Slide 11 Prof Liu UC Berkeley Diffusion Examples Linear concentration profile constant diffusion current Non linear concentration profile varying diffusion current x p N 1 L J p diff EE105 Fall 2007 p N exp dp qD p dx N qD p L J p diff Lecture 2 Slide 12 x Ld dp qD p dx qD p N x exp Ld Ld Prof Liu UC Berkeley Diffusion Current Diffusion current within a semiconductor consists of hole and electron components dp dn J p diff qD p J n diff qDn dx dx dn dp J tot diff q Dn Dp dx dx The total current flowing in a semiconductor is the sum of drift current and diffusion current J tot J p drift J n drift J p diff J n diff EE105 Fall 2007 Lecture 2 Slide 13 Prof Liu UC Berkeley The Einstein Relation The characteristic constants for drift and diffusion are related D kT q kT Note that 26mV at room temperature 300K q This is often referred to as the thermal voltage EE105 Fall 2007 Lecture 2 Slide 14 Prof Liu 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 VD ID EE105 Fall 2007 Lecture 2 Slide 15 Prof Liu 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 VD 0 EE105 Fall 2007 VD 0 Lecture 2 Slide 16 VD 0 Prof Liu UC Berkeley Carrier Diffusion across the Junction Because of the difference in hole and electron concentrations on each side of the junction carriers diffuse across the junction Notation nn electron concentration on N type side cm 3 pn hole concentration on N type side cm 3 pp hole concentration on P type side cm 3 np electron concentration on P type side cm 3 EE105 Fall 2007 Lecture 2 Slide 17 Prof Liu 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 quasiquasineutral neutral region width Wdep region EE105 Fall 2007 Lecture 2 Slide 18 Prof Liu UC Berkeley Carrier Drift across the Junction Because charge density 0 in the depletion region an electric field exists hence there is drift current EE105 Fall 2007 Lecture 2 Slide 19 Prof Liu 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 J p drift J p diff J n drift J n diff J tot J p drift J n drift J p diff J n diff 0 EE105 Fall 2007 Lecture 2 Slide 20 Prof Liu UC Berkeley Built in Potential V0 Because of the electric field in the depletion region there exists a potential drop across the junction qp p E qD p …
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