Physics of Semiconductors 8 th

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1 Physics of Semiconductors 8 th Shingo Katsumoto Department of Physics, Institute for Solid State Physics University of Tokyo

2 Review of pn junction Estimation of builtin potential Depletion layer width Injection of minority carriers Bipolar junction transistor BaseCollector characteristics CollectorEmitter characteristics Depletion layer with reverse bias voltage Effective capacitance and reverse bias voltage pn junction FET Schottky barrier MES FET MOS FET Outline today

3 p n Review of pn junctions w p + + w n Balance of diffusion and drift currents. Minimize F = U TS E x Depletion layer Space charge E F Builtin electric field Builtin potential V bi

4 electrons concentration holes Estimation of builtin potential nlayer player number of sites: N number of sites: N particle number: N 1 particle number: N 2 Number of cases:

5 Estimation of builtin potential (2) Stirling approximation: ln N! NlnN N :Mixing entropy

6 w p E w n x Depletion layer width N A N D

7 Electrons Current voltage characteristics Equilibrium Current balance External voltage V Forward bias (against V bi ) : lowers barrier for diffusion current n n

8 J Injection of minority carriers 0 minority carrier current Barrier overflow 0 V Fate of injected minority carriers: Radiative recombination Nonradiative recombination Diffusion with lifetime: Minority carrier diffusion length hν light emitting diode electron phonon

9 J A question for you J V 1 E g e V Consider an ideal light emitting diode, which has no nonradiative recombination. Every injected carrier emits a photon with the energy E g. Now apply a voltage V 1 < E g /e and a current J 1 flows. The power of light emission is P L = E g J 1 /e. On the other hand, the electric power source gives the power P S = J 1 V 1, which is smaller than P L! Does the LED create energy? Or what is happening inside the LED?

10 External injection of minority carriers: Solar Cells J 0 ev n Δn p dark 0 illuminated V External injection

11 Two types of transistors Bipolar junction transistor n p n Field effect transistor p John Bardeen, William Shockley, Walter Brattain 1948 Bell Labs. n

12 Bipolar transistor structures and symbols Bipolar transistor structures and symbols PNP type NPN type Similar characteristics PNP and NPN: complementary

13 E B C n p n BaseCollector characteristics J E J C J C V BC J E V BC

14 n p BaseCollector characteristics n e+ e+ e+ e+ e+ e e e e e e J E J C V BC

15 n p n E B C J C CollectorEmitter characteristics

16 Current amplification : Linearize with quantity selection J C = h FE J B Emittercommon current gain

17 Linear approximation of bipolar transistor Hybrid matrix j 2 j 1 hparameters V 1 (lower case: local linear approximation) V 2

18 Depletion layer width with reverse bias voltage V bi + V Poisson equation p w p w n n

19 Depletion layer width with reverse bias voltage (2) Charge per unit area:

20 Effective capacitance and reverse bias voltage Doping profiler V bi V Varicap diode KB505 Frequency modulation Phase lock loop

21 pn junction field effect transistor (JFET) Circuit symbols D D G G S nchannel S pchannel

22 p+ L G pn junction FET w d (y) S n N D e V ch (y) 2w t D p+ G V g y conductivity electric field channel width pinch off (internal) voltage: Only valid for w d < w t /2.

23 IV characteristics of JFET From Wikipedia R(V g ) is nonlinear 2N5459

24 Walter Schottky Schottky barrier metal eφ M semiconductor eφ S E c E D E F Q 0 E c x E F E F w d E v E v Charge balance: Voltage V > barrier height e(v s V)

25 MESFET

26 MOSFET enhancement Simplified CMOS inverter circuit depletion Low leakage current Single gate input both on/off switch inversion

27 Exercise A A1. pge has Seebeck coefficient of 300mV/K and ntype Bi 2 Te 3 230mV/K. If one makes a thermocouple from these two materials, how high is the voltage caused by the temperature difference of 50K. A2. Obtain expressions for electron mobility and for diffusion constant in terms of the conductivity and the Hall coefficient. Submission deadline:

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