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Boltzmann Law

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When Boltzmann's Law is applied to the motion of electrons in an n-p-n transistor, it can be shown that the collector current is given by the equation

Ic = Io exp[(q VBE)/(KB T)]


Io = A(T) exp [(- f/(KB T)]

In the second equiation, A(T) is a slowly varying function of temperature and f is the height of the barrier in the absence of an applied voltage.

In the lab, students test the validity of the first equation by measuring Ic as a function of VBE in an n-p-n transistor at three different temperatures (room temperature, in a dry ice-alcohol mixture and in mineral oil heated to ~91 C). For each temperature, graphs of log(Ic) as a function of VBE are made and the value of the ratio q/kB is computed from the slope of the plotted data. Next, the height of the barrier in electron volts, f/q , is computed from a plot of ln[IoT-3/2] vs. 1/T . Finally, students are asked to estimate the validity of the assumption that A(T) T-3/2 based on their data.

Course Level

Intermediate: P49

Student Handouts


Number of set-ups available:

Per lab station:

2 multimeters
1 DC power supply - HP Harrison 6201B
1 transistor control box
1 transistor on a rod/associated wiring
6 male/female banana adaptors
1 hot plate - VWR Dylatherm
1 low temperature thermometer (-100 to 50 degrees C)
1 thermometer (-20 to 150 degrees C)
1 styrofoam cylindrical container for dry/alcohol mixture
1 styrofoam container to hold extra dry ice
1 600 ml beaker
1 aluminum pan/stand inside
mineral oil
isopropal alcohol
dry ice
2 pair of safety glasses
2 lab coats
1 MSDS sheet for isopropal alcohol
1 box of Kimwhips
1 pair of gloves for handling hot and cold items
1 ring stand
1 ring stand clamp
1 three pronged claps
5 cycle semi-log graph paper

Charges apparatus

Circuit Diagram

circuit diagram


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Site contact: largent@Dartmouth.EDU

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