Lecture 6 - PN Junction and MOS Electrostatics (III) Electrostatics of pn Junction under Bias February 27, 2001

Transcription

1 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture 61 Lecture 6 PN Junction and MOS Electrostatics (III) Electrostatics of pn Junction under Bias February 27, 2001 Contents: 1. electrostatics of pn junction under bias 2. depletion capacitance Reading assignment: Howe and Sodini, Ch. 3,

2 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture 62 Key questions What happens to the electrostatics of a pn junction if a voltage is applied across its terminals? Why does a pn junction behave in some way like a capacitor?

3 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture Electrostatics of pn junction under bias Bias convention for pn junction: p n >0 forward bias <0 reverse bias

4 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture 64 Potential distribution across pn junction in thermal equilibrium: p + n pqnr SCR φ nqnr φ mp φ B po 0 no φ mn Apply voltage to pside with respect to nside: p + n pqnr SCR φ nqnr φ B po 0 no Battery imposes a potential difference across diode

5 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture 65 How does potential distribution inside junction change as a result of bias? p + n pqnr SCR nqnr φ >0? =0 can drop across five regions: metal/pqnr contact pqnr SCR nqnr metal/nqnr contact In which region does drop most?

6 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture 66 Essentially, all applied voltage drops across SCR: p + n pqnr SCR nqnr φ >0 =0 φ B φ B Potential difference across junction (potential barrier ): in equilibrium: φ B in forward bias: φ B <φ B in reverse bias: φ B >φ B (since <0) What happens to SCR electrostatics?

7 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture 67 SCR electrostatics under bias: φ φ B φ B φ B >0 =0 <0 E E() ρ qnd p() n() qna forward bias: builtin potential E d reverse bias: builtin potential E d

8 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture 68 Fundamentally, electrostatics of SCR under bias unchanged from thermal equilibrium SCR dipole of charge modulated to accommodate modified potential build up across junction Useful consequence: Analytical formulation of electrostatics of SCR identical to that of thermal equilibrium if: Then: φ B φ B n ( )= 2ɛ(φ B )N a p ( )= q(n a + N d )N d 2ɛ(φ B )N d q(n a + N d )N a d ( )= 2ɛ(φ B )(N a + N d ) qn a N d E ( )= 2q(φ B )N a N d ɛ(n a + N d )

9 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture 69 Can all be rewritten as: n ( )= no 1 φ B p ( )= po 1 φ B d ( )= do 1 φ B E ( )= E o 1 φ B In strongly asymmetric junction, all changes take place in lowly doped side: φ E ρ φ B φ B φ B >0 qnd n() =0 <0 E() qna

10 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture Depletion capacitance Apply small signal on top of bias: p n ρ qn d p() Q Q +Q qna Q n() + + Q ρ p() n() Q Change in across diode: change of Q at p change of Q at n

11 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture 611 Looks like parallelplate capacitor: ε t ins ρ + Q +Q Q Q ρ + Q Q Capacitance per unit area: C = ɛ t ins

12 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture 612 In analogy, in pn junction: p n ρ qn d p() Q Q +Q qna Q n() + + Q ρ p() n() Q Depletion capacitance per unit area: C j ( )= ɛ d ( ) = qɛn a N d 2(φ B )(N a + N d ) = C jo 1 φ B

13 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture 613 C j ( )= ɛ d ( ) = qɛn a N d 2(φ B )(N a + N d ) = C jo 1 φ B Key dependencies of C j : C j depends on bias (because d depends on bias) C j C jo 0 φ B C j depends on doping: N a,n d C j In strongly asymmetric junction (i.e. p + n junction): C j ( ) qɛn d 2(φ B ) capacitance dominated by lowlydoped side.

14 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture 614 Relevance of capacitancevoltage characteristics of diode: 1. pn diode= variable capacitor (varactor): useful for voltagecontrolled oscillators (CO) 2. C j : important consideration in dynamics of pn diode 3. powerful characterization technique: i.e. 1/C 2 j vs. yields φ B and N d in strongly asymmetric p + n junction: 1 C 2 j 2(φ B ) qɛn d 1 C j 2 2 εqn d 0 φ B

15 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture 615 Eperimental data [from Fortini et al., IEEE Trans. Electron Dev. ED29, 1604 (1982)]:

16 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture 616 Alternative view of capacitance: depletion charge p n ρ qn d p() Q Q +Q qna Q n() + + Q ρ p() n() Q Q j ( )= 2qɛN a N d (φ B ) N a + N d = Q jo 1 φ B

17 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture 617 Q j ( )= 2qɛN a N d (φ B ) N a + N d = Q jo 1 φ B Qj Qjo C j 0 φ B C j is slope of Q j vs. characteristics: but not: C j = dq j d C j = Q j

18 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture 618 Application of voltage to pn junction also results in current: pn diode. I log I 0.43 q kt IS IS linear scale semilogarithmic scale Will study after MOSFET and CMOS digital circuits.

19 6.012 Microelectronic Devices and Circuits Spring 2001 Lecture 619 Key conclusions oltage applied to pn junction drops across SCR: SCR electrostatics modified in forward bias: d, E in reverse bias: d, E Analytical formulation for SCR electrostatics in thermal equilibrium valid under bias if: φ B φ B As changes, SCR charge changes too: depletion capacitance pn junction depletion capacitance depends on bias