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Lecture 11. OUTLINE pn Junction Diodes (cont’ d) Narrow-base diode Junction breakdown Reading : Pierret 6.3.2, 6.2.2; Hu 4.5. Introduction.

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Lecture 11
Lecture 11

OUTLINE

  • pn Junction Diodes (cont’d)

    • Narrow-base diode

    • Junction breakdown

      Reading: Pierret 6.3.2, 6.2.2; Hu 4.5


Introduction
Introduction

  • The ideal diode equation was derived assuming that the lengths of the quasi-neutral p-type & n-type regions (WP’ , WN’) are much greater than the minority-carrier diffusion lengths (Ln , Lp) in these regions.

    • Excess carrier concentrations decay exponentially to 0.

    • Minority carrier diffusion currents decay exponentially to 0.

  • In modern IC devices, however, it is common for one side of a pn junction to be shorter than the minority-carrier diffusion length, so that a significant fraction of the “injected” minority carriers reach the end of the quasi-neutral region, at the metal contact.

    Recall that Dp = Dn = 0 at an ohmic contact

     In this lecture we re-derive the diode I-V equation with the boundary condition that Dp = 0 at a distance xc’ (rather than ) from the edge of the depletion region.

  • EE130/230A Fall 2013

    Lecture 11, Slide 2


    Excess carrier distribution n side
    Excess Carrier Distribution (n side)

    • From the minority carrier diffusion equation:

    • For convenience, let’s use the coordinate system:

    • So the solution is of the form:

    • We have the following boundary conditions:

    x’’ 0

    0 x’

    xc'

    EE130/230A Fall 2013

    Lecture 11, Slide 3


    Applying the boundary conditions, we have:

    Therefore

    Since this can be rewritten as

    We need to take the derivative of Dpn’ to obtain the hole diffusion current within the quasi-neutral n region:

    EE130/230A Fall 2013

    Lecture 11, Slide 4


    Thus, for a one-sided p+n junction (in which the current is dominated by injection of holes into the n-side) with a short n-side:

    Evaluate Jp at x=xn (x’=0) to find the injected hole current:

    EE130/230A Fall 2013

    Lecture 11, Slide 5


    and

    Therefore if xc’ << LP:

    For a one-sided p+n junction, then:

    EE130/230A Fall 2013

    Lecture 11, Slide 6


    Excess hole concentration profile
    Excess Hole Concentration Profile

    If xc’ << LP:

    Dpn is a linear function:

    • Jp is constant

      (No holes are lost due to recombination as they diffuse to the metal contact.)

    Dpn(x)

    slope is

    constant

    x'

    0

    x'c

    0

    EE130/230A Fall 2013

    Lecture 11, Slide 7


    General narrow base diode i v
    General Narrow-Base Diode I-V

    • Define WP‘ and WN’ to be the widths of the quasi-neutral regions.

    • If both sides of a pn junction are narrow (i.e. much shorter than the minority carrier diffusion lengths in the respective regions):

    e.g. if hole injection into the n side is greater than electron injection into the p side:

    J

    JP

    JN

    x

    xn

    -xp

    EE130/230A Fall 2013

    Lecture 11, Slide 8


    Summary narrow base diode
    Summary: Narrow-Base Diode

    • If the length of the quasi-neutral region is much shorter than the minority-carrier diffusion length, then there will be negligible recombination within the quasi-neutral region and hence all of the injected minority carriers will “survive” to reach the metal contact.

      • The excess carrier concentration is a linear function of distance.

        For example, within a narrow n-type quasi-neutral region:

      • The minority-carrier diffusion current is constant within the narrow quasi-neutral region.

        Shorter quasi-neutral region  steeper concentration gradient  higher diffusion current

    Dpn(x)

    location of metal contact

    (Dpn=0)

    x

    0

    xn

    WN’

    EE130/230A Fall 2013

    Lecture 11, Slide 9


    Pn junction breakdown
    pn Junction Breakdown

    C. C. Hu, Modern Semiconductor Devices for Integrated Circuits, Figure 4-10

    Breakdown

    voltage, VBR

    VA

    AZener diodeis designed to operate in the breakdown mode:

    EE130/230A Fall 2013

    Lecture 11, Slide 10


    Review peak e field in a pn junction
    Review: Peak E-Field in a pn Junction

    E(x)

    -xp

    xn

    x

    E(0)

    For a one-sided junction,

    where N is the dopant concentration on the lightly doped side

    EE130/230A Fall 2013

    Lecture 11, Slide 11


    Breakdown voltage v br
    Breakdown Voltage, VBR

    • If the reverse bias voltage (-VA) is so large that the peak electric field exceeds a critical value ECR, then the junction will “break down” (i.e. large reverse current will flow)

    • Thus, the reverse bias at which breakdown occurs is

    EE130/230A Fall 2013

    Lecture 11, Slide 12


    Avalanche breakdown mechanism
    Avalanche Breakdown Mechanism

    R. F. Pierret, Semiconductor Device Fundamentals, Figure 6.12

    High E-field:

    if VBR >> Vbi

    Low E-field:

    • ECR increases slightly with N:

      • For 1014 cm-3 < N < 1018 cm-3,

      • 105 V/cm < ECR < 106 V/cm

    EE130/230A Fall 2013

    Lecture 11, Slide 13


    Tunneling zener breakdown mechanism
    Tunneling (Zener) Breakdown Mechanism

    Dominant breakdown mechanism when both sides of a junction are very heavily doped.

    VA = 0

    VA < 0

    Ec

    Ev

    Typically, VBR < 5 V for Zener breakdown

    C. C. Hu, Modern Semiconductor Devices for Integrated Circuits, Figure 4-12

    EE130/230A Fall 2013

    Lecture 11, Slide 14


    Empirical observations of v br
    Empirical Observations of VBR

    R. F. Pierret, Semiconductor Device Fundamentals, Figure 6.11

    • VBR decreases with increasing N

    • VBR decreases with decreasing EG

    EE130/230A Fall 2013

    Lecture 11, Slide 15


    V br temperature dependence
    VBR Temperature Dependence

    • For the avalanche mechanism:

      • VBR increases with increasing T, because the mean free path decreases

    • For the tunneling mechanism:

      • VBRdecreases with increasing T, because the flux of valence-band electrons available for tunneling increases

    EE130/230A Fall 2013

    Lecture 11, Slide 16


    Summary junction breakdown
    Summary: Junction Breakdown

    • If the peak electric field in the depletion region exceeds a critical value ECR, then large reverse current will flow.

      This occurs at a negative bias voltage called the breakdown voltage, VBR:

      where N is the dopant concentration on the more lightly doped side

    • The dominant breakdown mechanism is

      avalanche, if N < ~1018/cm3

      tunneling, if N > ~1018/cm3

    EE130/230A Fall 2013

    Lecture 11, Slide 17


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