# Semiconductor theory

Why is there no resistor in the circuit when analyzing hole and electron currents according to semiconductor theory?

• Hoàng Lê - Hi, Please note the site rule which requires that if a post copies or adapts content (e.g. text, image, photo etc.) from elsewhere, that content must be correctly referenced. As a minimum, for online material, the original source webpage / PDF / video etc. should be named & linked (see that rule regarding references for books / articles etc.). Therefore please edit your question to add the original image source name & link (and please remember it's your responsibility to do that in future). Thanks. Commented Nov 13, 2023 at 10:39
• Question (with regard to Graham Nyes answer): Does your problem desription involves the INTERNAL resistor of the device or EXTERNAL parts (resistors) in some application circuits?
– LvW
Commented Nov 13, 2023 at 17:41
• it is a reistor in circuit in some application Commented Nov 14, 2023 at 1:22

Whilst the semiconductor block will have some resistance these diagrams are not intended to represent realistic circuits.

The battery exists to show a bias of a specific polarity across the junction to allow discussion of how the semiconductor works. Real world requirements like external resistors have been omitted to focus on the semiconductor action. The diagram shows you that forward bias is defined as having an external voltage with the positive side connected to the p layer and the negative side connected to the n layer (and that the depletion region narrows under forward bias). The diagram isn't there to tell you anything else.

A real circuit will have some external load so that the semiconductor action can be put to some practical use. In a practical circuit forward biasing a semiconductor junction with no external resistance to limit the current flow may result in such a high current flowing that the junction will be damaged.

Once a textbook has covered the fundamental operation of a p-n junction individually and in combination to form more complex semiconductor devices (e.g. transistors, thyristors) it will hopefully go on to explain how semiconductor devices are used in practical circuits.

The resistance is there. I remind you that the current density J in the semiconductor subjected to a potential difference at two ends is given by the conductivity σ, reciprocal of the resistivity, of the semiconductor for the electric field intensity E, i.e.: J=σE. The conductivity σ depends on the concentration n of electrons and p of holes but also on their mobility μ1 and μ2 constants at T constant , i.e. σ=nμ1+pμ2.

The shown figure represents the classical pn-junction (diode). The corresponding V-I relationship is given by the well-known exponenetial Shockley-equation.

Such a non-linear function current I versus voltage V always allows to specify two resistances:

• The static resistance is defined as the ratio of the two DC quantities: Rstat=V/I. This resistance is identical to the inverse slope of the line between the origin and the actual working point on the curve I=f(V).

• The dynamic (differential) resistance rd=d(V)/d(I) is identical to the inverse slope of the function I=f(V) at the actual working point.