Memories Bipolar Transistors

Technische Universität Graz nstitute of Solid State Physics Memories Bipolar Transistors

Technische Universität Graz nstitute of Solid State Physics Exams February 5 March 7 April 18 June 27

Exam Four questions, two from the online list. Calculator is ok. No notes. Explain some concept: (tunnel contact, indirect band gap, thermionic emission, inversion, threshold voltage,...) Perform a calculation: (concentration of minority carriers, integrate charge density to find electric field,...) Explain how a device works: (JFET, MESFET, MOSFET, laser diode, bipolar transistor, LED, Schottky diode, Heterojunction bipolar transistor,...)

Gate delay Gate delay is limited by C gate V dd /. Ring oscillator

SRAM Static random access memory No refresh circuitry needed.

DRAM Dynamic random access memory

DRAM Read and refresh DRAM with a SRAM cell

Flash memory Charge is stored on a floating gate nonvolatile

Phase change memory Phase-change memory (PRAM) uses chalcogenide materials. These can be switched between a low resistance crystalline state and a high resistance amorphous state. GeSbTe is melted by a laser in rewritable DVDs and by a current in PRAM. nonvolatile

High Bandwidth Memory AMD to launch its HBM graphics cards on 16 June 2015.

Technische Universität Graz nstitute of Solid State Physics bipolar transistors npn transistor collector base emitter n+ n p+ p n + lightly doped p substrate Used in front-end high-frequency receivers (mobile telephones).

bipolar transistors p+

abrupt junction de dx E dv dx E en A + -x p - x n en D x A E xxp -x p x n x ev bi D A kbt ln 2 ni en en D E xxn 2 en A x V xxp xp x0 2 2 en D x V xxn 0 x x 2 N N x x0 p 0 x x n n

Forward bias, V > 0 n p0 N A n N 2 i A ND p n0 n p (x p ) p n (x n ) + n N 2 i D Electrons and holes are driven towards the junction. The depletion region becomes narrower evbi V np( xp) NDexp kt B ev np0 exp kt B evbi V pn( xn) NAexp kt B ev pn0 exp kt B Minority electrons are injected into the p-region Minority holes are injected into the n-region

Reverse bias, V < 0 n p0 N A n N 2 i A n p (x p ) p n (x n ) + p ND n0 n N 2 i D Electrons and holes are driven away from the junction. The depletion region becomes wider evbi V np( xp) NDexp kt B ev np0 exp kt B ev bi V pn( xn) NAexp kt B ev pn0 exp kt B Minority electrons are extracted from the p-region by the electric field Minority holes are extracted from the n-region by the electric field

pnp transistor, no bias

pnp transistor, forward active bias The base-emitter voltage controls the minority carriers injected from the emitter to the base. These diffuse to the base-collector junction and are swept into the collector. Always dissipate power due to the forward bias

Long/Short diode p n (x n ) Long diode d n >> L p p n (x n ) p n0 p n (x) d n n-type dp J ed ed dx diff, p p p x Short diode d n << L p Metal contact is much closer to the depletion region than the diffusion length J diff, p p ( x ) p n n n0 d n dp edp dx

Minority carrier concentration contact p emitter (n+) base (p) collector (n) exp ev be nb0 ev kt B kt B e0 exp be contact n b0 p c0 p exp ev bc nb0 e0 kt B x e We W eb W bc W x c c evbe / kbt pe0 e 1 exp ev bc pc0 kt B Ep eabedp W x ea D En be n b0 n e e e e ev / k T ev / k T be B bc B W bc W be

Emitter current ea D p ea D n e ea D n e be B bc B 1 1 be p e 0 be n b0 ev / k T be n b0 ev / k T E En Ep Web xe Wbc Wbe Wbc Wbe evbe / kbt / 1 evbc kbt 1 e e E ES R CS p ev kt B e0 exp be n ev kt B b0 exp be p e0 n b0 exp ev bc nb0 kt B x e We W eb W x bc W c c p c0

Collector current contact p emitter (n+) base (p) collector (n) exp ev be nb0 ev kt B kt B e0 exp be contact n b0 p c0 p exp ev bc nb0 e0 kt B x e We W eb W bc W x c c evbc / kbt pc0 e 1 exp ev bc pc0 kt B cp eabcdp x W ea D cn bc n b0 n e e c ev / k T ev / k T c be B bc B W bc W eb

Collector current ea D n ea D p ea D n evbe / kbt bc p c0 evbc 1 / kbt 1 bc n b0 bc n b0 c cp cn e e Wbc Wbe xc Wc Wbc Wbe evbe / kt B / 1 evbc kt B 1 e e c cp cn F ES CS p ev kt B e0 exp be n ev kt B b0 exp be p e0 n b0 exp ev bc nb0 kt B x e We W eb W x bc W c c p c0

Not an npn transistor contact p e0 exp be emitter (n+) base (p) collector (n) exp ev be nb0 ev kt B kt B contact n b0 p c0 p exp ev bc nb0 e0 kt B x e We W eb W x bc W c c exp ev bc pc0 kt B

Ebers-Moll model evbe / kbt / 1 evbc kbt 1 e e E ES R CS evbe / kbt / 1 evbc kbt 1 e e C F ES CS B E C B E R F F R C F evbe / kbt evbc / kbt ES 1 R CS e 1 e

Emitter efficiency e En 1 1 / En Ep Ep En for npn ea D Ep be p ea D En be n b0 p evbe / kbt e0 e 1 W eb x n e e e ev / k T ev / k T be B bc B W bc W be For e ~ 1, W bc -W be << L b, W eb -x e and n b0 >> p e0 neutral base width Small base width and heavy emitter doping n N 2 i Ab n N 2 i De

Base transport factor B c En ratio of the injected current to the collected current recombination in the base would reduce the base transport factor A thin base with low doping results in a base transport factor ~ 1

Current transfer ratio C E B e ~ 1 for a good BJT

Transistor modes 1. Forward active: emitter-base forward, base-collector reverse 2. Saturation: emitter-base forward, base-collector forward 3. Reverse active: emitter-base reverse, base-collector forward 4. Cut-off: emitter-base reverse, base-collector reverse

Common base configuration evbe / kbt / 1 evbc kbt 1 e e E ES R CS solve for V be e e evbe / kt B / 1 evbc kt B 1 c F ES CS saturation active http://lamp.tu-graz.ac.at/~hadley/psd/l13/commonbase/pnp_current.html cutoff E < 0

Common base configuration c C ~ E buffer circuit: the output current is constant over a wide range of output voltages

Ebers - Moll Model ea D p ea D n ES W x W W eabednnb 0 RCS W W be p e0 be n b0 eb e bc be bc be F CS ES ea D n W W bc n b0 bc be ea D p ea D n x W W W bc p c0 bc n b0 c c bc be

Common emitter configuration evbe / kbt / 1 evbc kbt 1 e e E ES R CS evbe / kbt / 1 evbc kbt 1 e e c F ES CS current amplification ~100 B E C http://lamp.tu-graz.ac.at/~hadley/psd/l13/commonemitter.php

Current amplification factor C fe B h B E C 1 1 B C 1 1 C e B e B B ~ 50-500 C E

The Art of Electronics Horowitz and Hill for common emitter configuration

Transconductance g m V C be evbe / kt B / 1 evbc kt B 1 e e c F ES CS The first term depends on V be g m e e e e kt kt kt be B F ES ev / k T C B B B B The transconductance can be very high.

Early effect Ebers - Moll: evbe / kbt / 1 evbc kbt 1 e e E ES R CS evbe / kt B / 1 evbc kt B 1 e e c F ES CS B E C ES ea D p ea D n W x W W be p e0 be n b0 eb e bc be CS ea D p ea D n x W W W bc p c0 bc n b0 c c bc be ES and CS are treated as constants but the depletion widths W bc, W be, W c, and W e depend on the voltages. p ev kt B e0 exp be n ev kt B b0 exp be p ev kt B c0 exp bc n b0 p c0 p exp evbc nb 0 e0 kt B x e W e W eb W x bc W c c

Early effect Common emitter configuration Base width modulation: smaller width increases the diffusion current and increases the gain. Punchthrough: The neutral base width goes to zero and all gain is lost. Lightly dope the collector -> voltage drops in collector. Makes circuit slower.

Common emitter configuration C ~ B amplifier