194
4 Mean Values and Thermodynamics
value I = 510.56 K. Putting all of this information together, we obtain the specific
result
N ce
N d
= 0.1153T
3
2 e
−510.56/T
−1 +
1 + 17.342T
−
3
2 e 510.56/T
for the ratio of the number of donor-generated conduction electrons to the number
of dopant donor atoms in the sample. 6 A plot of N ce /N d vs. T // I is illustrated in
Fig. 4.1.
4.2.2 Fluctuations in the Number of Particles
As we have seen in Eq. (4.2.30a), N is given in the grand ensemble by
Fig. 4.1 Plot showing the dependence of the ratio of the number of donor electrons released into
the conduction band of a Si crystal from dopant P atoms on the temperature of the sample
6 From this expression, we may directly determine the fraction of the dopant P atoms that are
ionized at room temperature (say, T = 294 K) to be 0.9949. That is, approximately 99.5% of the P
atoms are already in their ionized form at room temperature.
4 Mean Values and Thermodynamics
value I = 510.56 K. Putting all of this information together, we obtain the specific
result
N ce
N d
= 0.1153T
3
2 e
−510.56/T
−1 +
1 + 17.342T
−
3
2 e 510.56/T
for the ratio of the number of donor-generated conduction electrons to the number
of dopant donor atoms in the sample. 6 A plot of N ce /N d vs. T // I is illustrated in
Fig. 4.1.
4.2.2 Fluctuations in the Number of Particles
As we have seen in Eq. (4.2.30a), N is given in the grand ensemble by
Fig. 4.1 Plot showing the dependence of the ratio of the number of donor electrons released into
the conduction band of a Si crystal from dopant P atoms on the temperature of the sample
6 From this expression, we may directly determine the fraction of the dopant P atoms that are
ionized at room temperature (say, T = 294 K) to be 0.9949. That is, approximately 99.5% of the P
atoms are already in their ionized form at room temperature.