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Excerpt Edition
This PDF is an excerpt from Chapter 7
of the Parametric Measurement Handbook.
                                          The
                                          Parametric Measurement
                                          Handbook




                                                 Third Edition
                                                 March 2012
Chapter 7: Diode and Transistor Measurement
                        "Choose a job you love, and you will never have to work a day in your life"
                        -- Confucius

                        Introduction
                        It is not the intent of this handbook to teach a course on semiconductor device
                        physics as there are already an abundance of excellent textbooks available on
                        this subject. However, it is difficult to discuss making parametric diode and
                        transistor measurements without first spending a little time understanding their
                        operation. Therefore, we will give a brief review of pn junctions, diodes, and
                        MOS and bipolar transistor operation with an emphasis on how we characterize
                        them in parametric test as opposed to detailed theoretical derivations.


                        PN junctions and diodes
                        Review of PN diode operation
                        Intrinsic semiconductor materials (such as silicon) do not have an abundance
                        of either electrons or electron holes. However, silicon can be doped with other
                        materials such that it becomes either n-type (possessing excess electrons) or
                        p-type (possessing excess electron holes). When considered individually these
                        materials are not particularly interesting. However, consider the case shown
                        below when these two materials are brought into close contact.



                              p                    n


                                         Q

                                         +
                               xp
                                    -        xn        x



                                              E
                        Figure 7.1. The cross section of a pn junction assuming an abrupt change from p-doped
                        to n-doped material. The graph shows the fixed charge remaining after the mobile carrier
                        diffusion has stabilized.

                        Assuming the extremely idealized case of an abrupt junction (i.e. one that
                        instantaneously transitions from p to n material) as shown in Figure 7.1, we can
                        see that something very interesting happens. The force of diffusion causes holes
                        from the p-type material to flow into the n-type material (leaving behind fixed
                        negative charge), and similarly the force of diffusion causes electrons from the
                        n-type material to flow into the p-type material (leaving behind fixed positive
                        charge). This diffusion process will continue until the electric field created by the
                        fixed charge in what is normally called the space-charge region becomes strong
                        enough to exactly balance the diffusion tendencies of the mobile carriers.




                                             126
The one-dimensional (x-axis) equations defining current flow in semiconductor
are shown below.
                            dn
          Jn = qnx + qDn                                          (Equation 7.1)
                            dx

                                 dp
           Jp = q p x - qD p                                          (Equation 7.2)
                                 dx
Where J is the current density of electrons (n) and holes (p)
      q is the electron charge
      xis the electric field in the x-dimension
       is the mobility of electrons (n) and holes (p)
      D is the diffusion constant for electrons (n) and holes (p)
      n is the electron density
      p is the hole density

These equations basically state what was alluded to in the previous discussion
of an abrupt pn junction. Namely, current flow in a semiconductor consists of
two parts: a drift current proportional to the applied electric field and a diffusion
current proportional to the spatial first derivative of the mobile carrier density. In
addition to the above current flow equations we also have the Einstein relation-
ship which relates the ratios of the mobility and diffusions constants as shown
below.
        Dn       Dp         kT
             =        =                                               (Equation 7.3)
        n        p          q

Where q is the magnitude of the electron charge (1.602 

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