Introduction to Semiconductor Devices and Circuit Model

Transcription

1 Itroductio to Semicoductor Devices ad Circuit Model Readig: Chater 2 of Howe ad Sodii Electrical Resistace I + V _ W homogeeous samle t L Resistace R V I L = ρ Wt (Uits: Ω) where ρ is the resistivity (Uits: Ω-cm) EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 2 1

2 What is a Semicoductor? Low resistivity => coductor High resistivity => isulator Itermediate resistivity => semicoductor Geerally, the semicoductor material used i itegrated-circuit devices is crystallie I recet years, however, o-crystallie semicoductors have become commercially very imortat olycrystallie amorhous crystallie EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 3 Semicoductor Materials Elemetal: Comoud: EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 4 2

3 The Silico Atom 14 electros occuyig the 1st 3 eergy levels: 1s, 2s, 2 orbitals filled by 10 electros 3s, 3 orbitals filled by 4 electros To miimize the overall eergy, the 3s ad 3 orbitals hybridize to form 4 tetrahedral 3s orbitals Each has oe electro ad is caable of formig a bod with a eighborig atom EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 5 The Si Crystal diamod cubic lattice Each Si atom has 4 earest eighbors lattice costat = 5.431Å EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 6 3

4 Comoud Semicoductors Ga As zic blede structure III-V comoud semicoductors: GaAs, GaP, GaN, etc. imortat for otoelectroics ad high-seed ICs EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 7 Electroic Proerties of Si Silico is a semicoductor material. Pure Si has relatively high resistivity at room temerature. There are 2 tyes of mobile charge-carriers i Si: Coductio electros are egatively charged. Holes are ositively charged. They are a absece of electros. The cocetratio of coductio electros & holes i a semicoductor ca be affected i several ways: 1. by addig secial imurity atoms (doats) 2. by alyig a electric field 3. by chagig the temerature 4. by irradiatio EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 8 4

5 Coductio Electros ad Holes 2-D reresetatio Whe a electro breaks loose ad becomes a coductio electro, a hole is also created. Si Si Si Si Si Si Si Si Si Note: A hole (alog with its associated ositive charge) is mobile! EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 9 Defiitio of Parameters = umber of mobile electros er cm 3 = umber of holes er cm 3 i = itrisic carrier cocetratio (#/cm 3 ) I a ure semicoductor, = = i EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 10 5

6 Geeratio We have see that coductio (mobile) electros ad holes ca be created i ure (itrisic) silico by thermal geeratio. Thermal geeratio rate icreases exoetially with temerature T Aother tye of geeratio rocess which ca occur is otical geeratio The eergy absorbed from a hoto frees a electro from covalet bod I Si, the miimum eergy required is 1.1eV, which corresods to ~1 μm wavelegth (ifrared regio). 1 ev = eergy gaied by a electro fallig through 1 V otetial = q e V = 1.6 x C x 1 V = 1.6 x J. Note that coductio electros ad holes are cotiuously geerated, if T > 0 EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 11 Recombiatio Whe a coductio electro ad hole meet, each oe is elimiated, a rocess called recombiatio. The eergy lost by the coductio electro (whe it falls back ito the covalet bod) ca be released i two ways: 1. to the semicoductor lattice (vibratios) thermal recombiatio semicoductor is heated 2. to hoto emissio otical recombiatio light is emitted Otical recombiatio is egligible i Si. It is sigificat i comoud semicoductor materials, ad is the basis for light-emittig diodes ad laser diodes. EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 12 6

7 Pure Si coductio i cm -3 at room temerature EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 13 Doig By substitutig a Si atom with a secial imurity atom (Colum V or Colum III elemet), a coductio electro or hole is created. Doors: P, As, Sb Accetors: B, Al, Ga, I Doat cocetratios tyically rage from cm -3 to cm -3 EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 14 7

8 Charge-Carrier Cocetratios N D : ioized door cocetratio (cm -3 ) N A : ioized accetor cocetratio (cm -3 ) Charge eutrality coditio: At thermal equilibrium, = i 2 N D + = N A + ( Law of Mass Actio ) Note: Carrier cocetratios deed o et doat cocetratio (N D - N A )! EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 15 N-tye ad P-tye Material If N D >> N A (so that N D N A >> i ): N D N A ad N D 2 i N >> material is -tye A If N A >> N D (so that N A N D >> i ): N A N D ad N A 2 i N >> material is -tye D EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 16 8

9 Termiology itrisic semicoductor: udoed semicoductor electrical roerties are ative to the material extrisic semicoductor: doed semicoductor electrical roerties are cotrolled by the added imurity atoms door: imurity atom that icreases the electro cocetratio grou V elemets (P, As) accetor: imurity atom that icreases the hole cocetratio grou III elemets (B, I) -tye material: semicoductor cotaiig more electros tha holes -tye material: semicoductor cotaiig more holes tha electros majority carrier: the most abudat carrier i a semicoductor samle miority carrier: the least abudat carrier i a semicoductor samle EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 17 Carrier Scatterig Mobile electros ad atoms i the Si lattice are always i radom thermal motio. Average velocity of thermal motio for electros i Si: ~ K Electros make frequet collisios with the vibratig atoms lattice scatterig or hoo scatterig Other scatterig mechaisms: deflectio by ioized imurity atoms deflectio due to Coulombic force betwee carriers The average curret i ay directio is zero, if 3 2 o electric field is alied. 1 EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu electro 9

10 Carrier Drift Whe a electric field (e.g., due to a exterally alied voltage) is alied to a semicoductor, mobile charge-carriers will be accelerated by the electrostatic force. This force suerimoses o the radom motio of electros: E 1 electro Electros drift i the directio oosite to the E-field Curret flows Because of scatterig, electros i a semicoductor do ot achieve costat acceleratio. However, they ca be viewed as classical articles movig at a costat average drift velocity. EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 19 Drift Velocity ad Carrier Mobility Mobile charge-carrier drift velocity is roortioal to alied E-field: v = μ E μ is the mobility (Uits: cm 2 /V s) μ Note: Carrier mobility deeds o total doat cocetratio (N D + N A )! μ EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 20 10

11 Curret Desity The curret desity J is the curret er uit area (J = I / A ; A is the cross-sectioal area of the coductor) If we have N ositive charges er uit volume movig with average seed v i the +x directio, the the curret desity i the +x directio is just J = qnv v Examle: 2 x10 16 holes/cm 3 movig to the right at 2 x10 4 cm/sec J = 1.6x10-19 x2x10 16 x 2x10 4 = 64 A/cm 2 Suose this occurs i a coductor 2 μm wide ad 1 μm thick: I = J x A = 64 x (2x10-4 x1x10-4 ) = 1.28 μa EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 21 Electrical Coductivity σ Whe a electric field is alied, curret flows due to drift of mobile electros ad holes: electro curret desity: J = ( q) v = qμ E hole curret desity: J = ( + q) v = qμ E total curret desity: J = J + J = ( qμ + qμ ) E J = σe σ qμ + qμ coductivity (Uits: Ω-cm -1 ) EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 22 11

12 Electrical Resistivity ρ 1 ρ = σ ρ ρ 1 qμ 1 qμ 1 qμ + qμ (Uits: ohm-cm) for -tye mat l for -tye mat l EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 23 Examle Cosider a Si samle doed with /cm 3 Boro. What is its resistivity? Aswer: N A = /cm 3, N D = 0 (N A >> N D -tye) /cm 3 ad 10 4 /cm ρ = qμ + qμ qμ = [( )(10 )(450)] = 1.4 Ω cm From μ vs. ( N A + N D ) lot EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 24 12

13 Examle (cot d) Cosider the same Si samle, doed additioally with /cm 3 Arseic. What is its resistivity? Aswer: N A = /cm 3, N D = /cm 3 (N D >>N A -tye) 9x10 16 /cm 3 ad 1.1x10 3 /cm ρ = qμ + qμ qμ = [( )(9 10 )(700)] = 0.10 Ω cm The samle is coverted to -tye material by addig more doors tha accetors, ad is said to be comesated. EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 25 Sheet Resistace R s L L ρ R = ρ = Rs Rs (Uit: ohms/square) Wt W t (L, W, t = legth, width, thickess) R s is the resistace whe W = L The R s value for a give layer i a IC techology is used for desig ad layout of resistors for estimatig values of arasitic resistace i a circuit R = R s R = R s /2 R = 2R s R = 3R s R 2.6R s Metallic cotacts EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 26 13

14 Itegrated-Circuit Resistors The resistivity ρ ad thickess t are fixed for each layer i a give maufacturig rocess A circuit desiger secifies the legth L ad width W, to achieve a desired resistace R R = R fixed desigable Examle: Suose we wat to desig a 5 kω resistor usig a layer of material with R s = 200 Ω/ Resistor layout (to view) s L W Sace-efficiet layout t EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 27 Summary Crystallie Si: 4 valece electros er atom diamod lattice: each atom has 4 earest eighbors 5 x atoms/cm 3 I a ure Si crystal, coductio electros ad holes are formed i airs. Holes ca be cosidered as ositively charged mobile articles which exist iside a semicoductor. Both holes ad electros ca coduct curret. Doats i Si: Reside o lattice sites (substitutig for Si) Grou V elemets cotribute coductio electros, ad are called doors Grou III elemets cotribute holes, ad are called accetors EE40 Summer 2005: Lecture 10 Istructor: Octavia Florescu 28 14