This is a introduction or review of pn junction diodes. All semiconductors

and microchips have pn junctions either as part of the device itself or

between the device and the substrate. Every pn junction has a space

charge layer or depletion region that is determined by the doping

concentrations and the applied voltages. The size of the space charge

layer determines the size of the transistor. Every pn junction has

capacitance which is important determining the speed or frequency

response of the circuit.

This is a table of constants that you will need for some of your

homework problems.

Semiconductors are materials that can have their resistivity

(1/conductivity) changed over several orders of magnitude by small

amounts (parts per million) of impurities (dopants). The most common

semiconductors are the single crystal version of the elements in column

4 or binary combinations of elements in column 3 and 5 shown in the

color above. Or example Silicon (the second most abundant element

on earth) in its single crystal form is the most common semiconductor.

Germanium is another semiconductor. Gallium Arsenide is an example

of a binary mixture of elements to make a semiconductor. Many other

materials have semiconducting properties.

This table shows some of the properties of selected semiconductors

and insulators. We will be most interested in the Energy Gap, relative

permittivity, electron and hole mobility, intrinsic carrier concentration and

breakdown electric field. There are some things we can learn from this

table. One is that the electron mobility is always higher than the hole

mobility. That is because electron mobility is the movement of free

electrons, hole mobility is the movement of bound electrons (which is

harder to achieve). Pay attention to the units for the values in the chart.

This illustrates the uniformly doped pn junction. The dotted line is the

metallurgical junction between the p-side (on the left) and the n-side (on

the right) The p-side is doped with Boron atoms. This is shown as a

circle with a B- inside, the B is for Boron and the – sign is an extra

electron that is accepted in the valence level of the Boron atom,

creating a hole else ware in the Silicon. The n-side is doped with

Phosphorous atoms. This is shown as a circle with a P+ inside, the P is

for Phosphorous and the + sign represents a free electron else ware in

the Silicon, from the valence level of the Phosphorous atom. Holes and

free electrons can move creating current flow. Near the metallurgical

junction holes and free electrons cross over the metallurgical junction

leaving behind the ionized immobile Boron or Phosphorous atoms

which is the space charge layer. The space charge layer will be

negative on the left and positive on the right. Separated charge creates

and electric field shown as pointing to the left. The electric field creates

a voltage difference or potential. This is an important figure… please

study everything in this figure carefully.

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These are some of the equations from Semiconductor Physics or from

Electric and Magnetic Fields theory. They provide mathematical

relationship between space charge, electric field and potential.

Semiconductor physics theory gives the relationship between doping

concentration (NA and ND) and the potential.

This is the derivation of the build in voltage shown in the box above.

This slide gives the mathematical expressions for the most important

quantities (shown in red) for the uniformly doped pn junction.

This example is to illustrate the use of the equations on the previous

page. Pay attention to the units for each item in the equation to get the

correct answer. You will be asked to do this on homework and exams.

The equations on the pages above are used in this Excel spread sheet.

You enter variables in the white boxes and the results are calculated in

the blue boxes. It also plots the diode I-V characteristic and will show

changes as a function of temperature. You can check your answers for

the example on the previous page. This spread sheet can be down

loaded from the course webpage.

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The figure show might represent a pn junction formed by diffusion of p-

type impurities (NA) into a uniformly doped n-type wafer ND. The

metallurgical junction is the point in X where the p-type doping is equal

to the n-type doping., Xj. The cross hatched areas form the space

charge layer. The width of the space charge layer on the p-side and n-

side add to give the total width, W.

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We are still interested in calculating the width of the space charge layer,

width on p-side and width on n side, junction capacitance as a function

of the doping concentrations and the reverse bias voltage. We know

the equation for the doping concentration on both sides of the

metallurgical junction from diffusion and ion implant theory (not covered

in this course). We can set the equations equal to each other and solve

for Xj. Then we follow the calculations described in this flow chart. This

is something you may do in other courses you may take.

The ideal diode equation is shown in the box. The ideal diode equation

does not give the reverse breakdown voltage. The reverse breakdown

voltage can be found from the equation for the max electric field in the

space charge region and solving for the reverse bias voltage that gives

an electric field equal to the material breakdown electric field. For

example in silicon Emax is 3E5 V/cm from page 5. Used with the

equation for maximum electric field shown on page 9. you can solve

for VR. The diode reverse leakage current Is is a strong function of

temperature.

This figure shows a cross section of a diode created in a p-type wafer

by doing three diffusions and/or ion implants. The orange region is

doped n-type, the green region is doped p-type. The green to orange

boundary is the diode. The red region is n-type into lighter doped n-

type region so there is no junction but the red area is heavily doped

making a better contact with the aluminum shown in dark blue. A

second diode could be made on the same wafer and the pn junction

between the orange and gray regions is always reverse biased

preventing current flow one diode to a neighboring diode.

This shows a layout of a PN junction made at RIT in the Semiconductor

and Microsystems Fabrication Laboratory, SMFL. The diode I-V

characteristic was measured as shown. The reverse breakdown

voltage is not shown because we measured out to 100 volts reverse

bias and still did not see breakdown. A photo of the diode is show with

two probes touching the aluminum contacts to the p and n side. We

also measured series resistance, junction capacitance, and reverse

leakage current.

A diode SPICE model was created with measured values from the

diode shown on the previous page.

These next three pages derive the temperature dependence of current

in a forward biased pn diode. It starts with the ideal diode equation

shown in the box. In forward bias the -1 term can be neglected. We see

temperature, T, in the exponent, thermal voltage KT/q but not shown is

the temperature dependence of Is which is actually more important. We

take the derivative with respect to Temperature remembering that Is is

also a function of temperature to get to equation 2. The Is term is

expanded as shown in eq. 3, Note diffusion lengths, Dp and Dn, and

the intrinsic carrier concentration, ni, are functions of temperature.

The equation for ni2 is shown with its temperature depencence in eq.4.

(Eg aslo has a small temperature dependence). The constant A and C

lump together some other variables that do not change with

temperature. The result is an equation for Is that has the important

temperature dependence shown in the box. We can now take the

derivative of Is with respect to T and use it in equation 2 on the previous

page. The final result is shown in the box at the bottom of the page.

The temperature dependence of a forward biased diode with a constant

current is shown in the box. For example for silicon pn diode the Eg is

~1.2, the forward bias to give a constant current is 0.6 volts at room

temperature of 300 K. The change in forward bias voltage to have the

same current will be -2.2mV / °

This page shows a diode made at RIT in the SMFL. The diode also has

a polysilicon resistor on top of the pn diode separated by an oxide layer

to be used as a heater. The figure on the right is measured diode

current versus diode voltage. We see the diode characteristic shift to

the levt by 0.16 volts from the starting value of 0.64V at room

temperature when 0.3 watts of power is applied to the polysilicon

heater. Using the -2.2mV/° we calculate the diode temperature to be

72.7 °C above room temperature when heated.

Diodes also make great light detectors as long as the light can

penetrate into the space charge region of the diode. Most diodes are

packaged in a black opaque package to prevent unwanted effects of

light. Some are packaged in a glass package where it is possible to get

some response to light. Good photodiodes have large area pn junctions

where the top layer is thin and the space charge layer is wide. When

photons (light) are adsorbed they generate electron and hole pairs. The

Electric field in the space charge layer moves the holes in the direction

of the E field and electrons in the opposite direction. I a current meter

was connected to the p and n sides of the photodetector there will be

current flow in the directions shown that is proportional to the light

intensity.

In order to generate electron hole pairs the energy of the photon needs

to be greater than the energy gap of the semiconductor. Photon energy

depends on the wavelength of the photon and is given in the equation at

the top of this page. For example green light has a wavelength of

550nm so the energy of a green photon is ~ 2.5eV. Since

This slide above shows a picture of the photodiode and its measured I-

V characteristics at no light, room lights on, and microscope light on at

Max.

Although all visible light can generate electron hole pairs in silicon,

different wavelength photons have different absorption coefficients and

go different distances into silicon. As illustrated above red light goes

furthest into silicon before it is all absorbed, violet light goes the shortest

distance into silicon before it is all absorbed. The absorption coefficient

is explained on the next page.

The yellow chart gives the adsorption coefficient vs. wavelength. For

example at 550nm wavelength (green) the adsorption coefficient is

approximately 1.00E4/cm. In the equation in the box, Phi(0) is the light

intensity at x=0… ie at the surface, Phi(x) is the light intensity and

distance x into the silicon. Alpha is the adsorption coefficient. The

equation gives the amount of light remaining from the starting value

Phi(0) of 100%

Do the calculation asked for on the slide.

Answer: 99% and 39%

This slide explains where the light comes from. The light is generated

near the edges of the space charge layer. Electrons are injected into

the p-side when the diode is forward biased they diffuse away from the

junction and recombine with holes in p-type silicon before traveling far

into the p-type silicon. The electron concentration decays exponentially

and is described by a diffusion length. Depending on the doping the

distance might be a few micrometers or less. A similar thing happens

with holes injected into the n-side,

The turn on voltage is different for each color LED because the energy

gap is different for the different type of semiconductor used.

This homework is due one week after finishing this topic in class.