EE 330 Lecture 12. Devices in Semiconductor Processes. Resistors Diodes

Transcription

1 EE 330 Lecture 12 evices in Semiconductor Processes Resistors iodes

2 Exam 1 Friday Feb 16 Students may bring 1 page of notes HW assignment of week of Feb 11 due on Wed Sfeb 14 at beginning of class No 5:00 p.m extension so solutions can be posted Those with special accommodation needs, please send me an message or contact me so arrangements can be made Review session to be announced

3 Review from Last Lecture Resistivity olumetric measure of conduction capability of a material Area is A units : ohm cm L R AR L for homogeneous material, A, R, L

4 Review from Last Lecture Sheet Resistance W d L R RW R ( for d << w, d << L ) units : ohms / L for homogeneous materials, R is independent of W, L, R

5 Review from Last Lecture Resistivity of Materials used in Semiconductor Processing Cu: Al: Gold: Platinum: 1.7E-6 cm 2.7E-4 cm 2.4E-6 cm 3.0E-6 cm Polysilicon: 1E-2 to 1E4 cm* n-si: intrinsic Si: SiO 2 : typically.25 to 5 cm* (but larger range possible) 2.5E5 cm E14 cm * But fixed in a given process

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9 Temperature Coefficients Used for indicating temperature sensitivity of resistors & capacitors For a resistor: 1 dr R dt 6 TCR 10 ppm C op. temp This diff eqn can easily be solved if TCR is a constant R R T RT 2 1 e T 2 T TCR T R T 1 T T TCR 10 dentical Expressions for Capacitors

10 oltage Coefficients Used for indicating voltage sensitivity of resistors & capacitors For a resistor: 1 dr CR R d ref voltage 6 10 ppm This diff eqn can easily be solved if CR is a constant R R 2 1 e CR R R CR dentical Expressions for Capacitors

11 Temperature and oltage Coefficients Temperature and voltage coefficients often quite large for diffused resistors Temperature and voltage coefficients often quite small for poly and metal resistors

12 From:F. Maloberti : esign of CMOS Analog ntegrated Circuits - Resistors, Capacitors, Switches

13 Example: etermine the percent change in resistance of a 5K Polysilicon resistor as the temperature increases from 30 o C to 60 o C if the TCR is constant and equal to 1500 ppm/ o C R T R T T T 1 TCR o 130 R T R T C R T R T 2 1 R T R T Thus the resistor increases by 4.5%

14 Basic evices and evice Models Resistor iode Capacitor MOSFET BJT

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17 group (or family) 4 valence-band Electrons All elements in group have 4 valence-band electrons

18 Serves as an acceptor of electrons Acts as a p-type impurity when used as a silicon dopant All elements in group have 3 valence-band electrons Only 3 alenceband Electrons

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20 Serves as an donor of electrons Acts as an n-type impurity when used as a silicon dopant All elements in group have 5 valence-band electrons Five alenceband Electrons

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23 Silicon opants in Semiconductor Processes B (Boron) widely used a dopant for creating p-type regions P (Phosphorus) widely used a dopant for creating n-type regions (bulk doping, diffuses fast) As (Arsenic) widely used a dopant for creating n-type regions (Active region doping, diffuses slower)

24 iodes (pn junctions) epletion region created that is ionized but void of carriers

25 pn Junctions Physical Boundary Separating n-type and p-type regions f doping levels identical, depletion region extends equally into n-type and p-type regions

26 pn Junctions Physical Boundary Separating n-type and p-type regions Extends farther into p-type region if p-doping lower than n-doping

27 pn Junctions Physical Boundary Separating n-type and p-type regions Extends farther into n-type region if n-doping lower than p-doping

28 pn Junctions Positive voltages across the p to n junction are referred to forward bias Negative voltages across the p to n junction are referred to reverse bias As forward bias increases, depletion region thins and current starts to flow Current grows very rapidly as forward bias increases Current is very small under revere bias

29 pn Junctions Anode Anode Cathode Cathode Circuit Symbol

30 pn Junctions As forward bias increases, depletion region thins and current starts to flow Current grows very rapidly as forward bias increases Anode Cathode Simple iode Model: =0 >0 =0 <0 Simple model often referred to as the deal diode model

31 pn Junctions Simple iode Model: pn junction serves as a rectifier passing current in one direction and blocking it n the other direction

32 Rectifier Application: 1 OUT Simple iode Model: N 1K N = M sinωt M N t OUT M t

33 - characteristics of pn junction mproved iode Model: (signal or rectifier diode) d S in the 10fA to 100fA range d kt = t q iode Equation d t e 1 S What is t at room temp? t is about 26m at room temp k= (24) JK -1 q = (40) C k/q= K -1 iode equation due to William Schockley, inventor of BJT n 1919, William Henry Eccles coined the term diode n 1940, Russell Ohl stumbled upon the p-n junction diode

34 - characteristics of pn junction mproved iode Model: (signal or rectifier diode) iode Characteristics 0.01 d d d (amps) d (volts) iode Equation Under reverse bias ( d <0), Under forward bias ( d >0), d t e 1 S Simplification of iode Equation: S Se d t S in the 10fA to 100fA range kt = t q k= (24) JK -1 q = (40) C k/q= K -1 t is about 26m at room temp Simplification essentially identical model except for d very close to 0 iode Equation or forward bias simplification is unwieldy to work with analytically

35 - characteristics of pn junction mproved iode Model: iode Equation Simplification of iode Equation: Under reverse bias, Under forward bias, (signal or rectifier diode) d t e 1 S S S e d t S often in the 10fA to 100fA range S proportional to junction area t is about 26m at room temp How much error is introduced using the simplification for d > 0.5? d t S e 1 Se d t e 1 S d t e How much error is introduced using the simplification for d < - 0.5? e Simplification almost never introduces any significant error 9 9

36 Will you impress your colleagues or your boss if you use the more exact diode equation when d < -0.5 or d > +0.5? Will your colleagues or your boss be unimpressed if you use the more exact diode equation when d < -0.5 or d > +0.5?

37 pn Junctions Anode Cathode iode Equation: (good enough for most applications) JSAe 0 n T 0 0 Note: S =J s A J S = Sat Current ensity (in the 1aA/u 2 to 1fA/u 2 range) A= Junction Cross Section Area T =kt/q (k/q=1.381x10-23 C/ K/1.6x10-19 C=8.62x10-5 / K) n is approximately 1

38 pn Junctions iode Equation: J 0 S Ae n T 0 0 Anode J S is strongly temperature dependent With n=1, for >0, Cathode - G0 (T) J T m e Ae t t SX Typical values for key parameters: J SX =0.5A/μ 2, G0 =1.17, m=2.3

39 Example: pn Junctions - G0 (T) J m t T e Ae SX t What percent change in S will occur for a 1 C change in temperature at room temperature? - -G G0 G0 G0 G0 (T ) t T1 (T ) (T ) m m m m t T1 t 2 t t 2 t 2 J T e Ae - J T e Ae T e - T e SX T SX T T S S -G0 - - G0 G0 m t T1 (T ) m t T1 t 2 J T e Ae T e SX T T x x x10 S % 21% S

40 pn Junctions Anode Cathode iode Equation: (good enough for most applications) JSAe 0 n T 0 0 S =J s A Simple iode Model: Often termed the conducting or ON state Often termed the nonconducting or OFF state

41 Consider again the basic rectifier circuit OUT N R Previously considered sinusoidal excitation Previously gave qualitative analysis Rigorous analysis method is essential? O U T

42 Analysis of Nonlinear Circuits (Circuits with one or more nonlinear devices) What analysis tools or methods can be used? KCL? KL? Superposition? Nodal Analysis Mesh Analysis Two-Port Subcircuits oltage ivider? Current ivider? Thevenin and Norton Equivalent Circuits?

43 Consider again the basic rectifier circuit OUT N R N OUT R R d t e 1 S OUT S R e N t O U T 1 Even the simplest diode circuit does not have a closed-form solution when diode equation is used to model the diode!! ue to the nonlinear nature of the diode equation Simplifications are essential if analytical results are to be obtained

44 Lets study the diode equation a little further d t d S e 1 iode Characteristics d (amps) Linear-Linear Axis d (volts) Power issipation Becomes estructive if d > 0.85 (actually less)

45 Lets study the diode equation a little further d t e 1 d S iode Characteristics d (amps) E-06 1E-08 1E-10 1E-12 Linear-Log Axis d (volts) For two decades of current change, d is close to 0.6 This is the most useful current range for many applications

46 Lets study the diode equation a little further d t e 1 d S iode Characteristics 0.01 d (amps) d (volts) For two decades of current change, d is close to 0.6 This is the most useful current range when conducting for many applications

47 Lets study the diode equation a little further d d t e 1 S iode Characteristics d 0 d 0.6 d d d (amps) d (volts) Widely Used Piecewise Linear Model

48 Lets study the diode equation a little further d d t e 1 S iode Characteristics d (amps) d (volts) Better model in ON state though often not needed ncludes iode ON resistance

49 Lets study the diode equation a little further d t e 1 d S Piecewise Linear Model with iode Resistance d d 0 if 0.6 d R d d (R is rather small: often in the 20Ώ to 100Ώ range): if Equivalent Circuit A d C A C Off State d d A C d 0.6 R On State

50 The deal iode 0 if 0 0 if 0

51 The deal iode 0 if 0 0 if 0 OFF ON ON OFF alid for >0 0

52 iode Models d (amps) iode Characteristics d (volts) d (amps) iode Characteristics d (volts) iode Characteristics d (amps) d (volts) Which model should be used? The simplest model that will give acceptable results in the analysis of a circuit

53 iode Models iode Characteristics iode Equation d t e 1 S d (amps) d (volts) iode Characteristics d 0 d 0.6 if d if d d (amps) d (volts) iode Characteristics Piecewise Linear Models d d d R d if if d d d (amps) d (volts) 0 if 0 0 if 0

54 End of Lecture 12