Ch 2a 2006

# Ch 2a 2006 - Chapter 2 Diode Circuits Now we form our first...

This preview shows pages 1–8. Sign up to view the full content.

Chapter 2. Diode Circuits Now we form our first useful semiconductor device, a pn junction in a bar of Si. At first we assume that we have a step junction i.e. the concentration changes abruptly from p to n at the pn junction interface as shown below In real devices we never have a perfectly abrupt junction, but this complicates our analysis of the pn junction needlessly, since we only really need to know what is happening right around the metallurgical junction (where the concentrations are equal). We start our analysis of the pn junction using the Poisson equation from physics Eq. 5.1 0 ε ρ s K E = which simplifies in 1-D to Eq. 5.2 0 s K dx E d = EE 329 Introduction to Electronics 38

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
where Ks is the semiconductor dielectric constant and e 0 is the permittivity of free space, ρ here is NOT the resistivity but the charge density (charge / cm 3 ). Assuming total ionization we get Eq. 5.3 ) ( A D N N n p q - + - = Remember that charge density = 0 in a uniformly doped semiconductor at equilibrium. Also note that is proportional to d E / dx in 1-D. Qualitatively we will look at the pn junction problem and find the appropriate band diagram to represent the situation. Begin with the dopants Now we draw a band diagram for each side assuming that they are not in atomic contact. EE 329 Introduction to Electronics 39
As we move the p and n sides closer together what will happen? First the E F lines up and causes all the other bands to shift up or down in energy accordingly. We then need to connect up Ec, Ev and Ei and we also make the assumption that the variation is monotonic in nature with zero slope at both ends. The exact nature of the bands is not known but the figures below appear to be good representations. EE 329 Introduction to Electronics 40

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
EE 329 Introduction to Electronics 41
This then is the equilibrium band diagram of a pn junction diode. Now look at what is happening inside the semiconductor. Remember from Ch. 3 that we can sketch the voltage potential in the semiconductor simply by inverting one of the bands. This leads to We arbitrarily set V = 0 on the p side of the junction, and we note that there is some type of potential across the pn junction region. Now we want to sketch the electric field in the device. Remember that the electric field is proportional to the derivative of the voltage with respect to x in 1-D EE 329 Introduction to Electronics 42

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Eq. 5.4 dx dV E - = and it is proportional to the integral of the charge density as we saw before since electric fields are caused by separation of charges and we note that the derivative of the electric field (with respect to x 1-D) is proportional to the charge density Eq. 5.2 0 ε ρ s K dx E d = We can see these relationships when we apply Gauss’s law to our situation EE 329 Introduction to Electronics 43
The electric field begins where the bands are bent (i.e. where we have non-zero charge density), with its MAGNITUDE steadily increasing to a maximum value at the metallurgical junction then decreasing back

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 23

Ch 2a 2006 - Chapter 2 Diode Circuits Now we form our first...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online