• To initiate the junction formation:
• click the FormJunction button, or
• mouse drag one object toward the other.
• To return the PN junction to separate pieces:
• click the Separate button, or
• mouse drag one object away from the other

Equilibrium band diagrams appear below the semiconductor. The green horizontal line is the Fermi level. Initiate the pn junction formation by clicking the 'FormJunction' button or using mouse drag and watch the physical system approach a new (electro-thermal) equilibrium which is characterized by a constant Fermi level throughout the material. The white region between the red (p-type) and blue (n-type) regions is the transition (or depletion) region where most of the free carriers are depleted. This white region is the space charge region with uncompensated ionized impurity charges which produce electric field in this region.

Repeat formation and separation of the PN junction several times trying out different doping values. When you become sufficietly familiar with the equilibrium band diagram and its formation principles, do the following quiz.

Quiz:

1. Depletion thickness
• The depletion thicknesses, xp and xn, represent the distance of the depeletion edge from the junction.  
• Change the doping level of one side at steps of a factor ten. Record on paper both depletion thicknesses at each doping level.
• Based on your data, what is the mathematical relationship of xp and xn to Na and Nd ?  Write down a single equation that involves all these four parameters.  Check your answer.
• What does this relation mean physically about the toal space charge ?  Check your answer.
2. Band diagram
• Hide the applet page by scrolling down the text or minimizing your web browser.
• Draw on paper the band diagram of PN junction for Na = 1E16 and Nd = 1E15. Make the band diagram correct both quantitatively (in the relative depletion thickness of the two sides) and qualitatively (shape of band diagram).
• Use the applet to check if your diagram is correct.
• Can you draw the band diagram for a PNP structure where Na = 1E18, Nd = 1E17, and Na = 1E15 ? Assume that the N-layer thickness is greater than the sum of the depletion thicknesses from the two junctions.

PROBLEMS:

1. By mouse drag of the rectangles toward each other or clicking on the "formTheJunction" button, you can bring the two 'bulk' semiconductors to form the junction.  This applet visualizes the hypothetical, initial transient process during junction formation, and the band stabilizes when the junction arrives at a new thermal equilibrium (for the combined physical system).  
• From observing the band as the junction is being formed, state the condition for a new equilibrium of the combined physical system (ie, the p- and n-materials joined together) ?   Is this condition satisfied separately for the two semiconductor pieces before the pn junction formation ?   
• For a Si pn junction, keep the doping level constant for one-side and vary the doping level for the other side. Make a record of (N, V₀) for a series of N (the varying doping level)-values.  From this record, find (or verify) the Mathematical relationship between V₀ and N.  Do it for the other dopant also, and combine the two results.  Did you verify the commonly found relationship between V₀ and the doping levels (such as eq.3-15 of Yang, p.74).
2. Comment on how this problem can be better formulated to assist you to learn better, conceptually and mathematically.
3. Comment on what additions (ie, graphical presentations) to this applet will be helpful for learning the space charge (and total charge = 0), electric field, and potential drop on each side of the junction.
4. Any other related applet programs do you desire ??

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Copyright (c) C.R.Wie, SUNY-Buffalo, 1996-1997

Space charge and electric field

Diffusion and drift currents

Applied bias and current flow

Diffusion currents and the recombination in the neutral regions

The SPICE device model for junction diode

Answer to the quiz:

1.

• N_d x_n = N_a x_p.
  
  
  
  
  
• Space charge neutrality: that is, the total positive charge ( N_d x_n ) due to the uncompensated ionized donors is equal to the total negative charge ( N_a x_p ) due to the uncompensated ionized acceptors.