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1.5?010 cm-3 .This discrepancy may arise several sources .First, the values of the effective masses are determined at a low temperature where the cyclotron resonance experiments are performed. Since the effective mass is an experimentally determined parameter, and since the effective mass is a measure of how well a particle moves in a crystal, this parameter may be a slight function of temperature. Next, the density of states function for a semiconductor was obtained by generalizing the model of an electron in a three-dimensional infinite potential well. This theoretical function may also not agree exactly with experiment. However, the difference between the theoretical value and the experimental value of ni is approximately a factor of 2, which, in many cases, is not significant. Table 3.2 lists the commonly accepted values of ni for silicon, gallium arsenide, and germanium at T=300K. The intrinsic carrier concentration is a very strong function of temperature. Figure 3.2 is a plot of ni form Equation (3.23) for silicon, gallium arsenide, and germanium as a function of temperature. As seen in the figure, the value of ni these semiconductors may easily vary over several orders of magnitude as the temperature changes over a reasonable range. EXAMPLE 3.3 OBJECTIVE Calculate the intrinsic carrier concentration in silicon at T=300K and at T=400K. The values of Nc and Nv vary as T3/2.As a first approximation, neglect any variation of bandgap energy with temperature. Assume that bandgap energy of silicon is 1.12 eV. The value of kT at 350 K is kT = (0.0259)(350/300) = 0.0302 eV and the value of kT at 400K is kT = (0.0259)(400/300) = 0.0345eV Solution Using Equation(3.23), we find for T=350K Ni2 =(2.8?019)(1.04?019)(350/300)3exp(-1.12/0.0302) = 3.62?022 00Kso that ni(350K)= 1.90?011cm-3
For T=400K,we find Ni2 =(2.8?019)(1.04?019)(400/300)3exp(-1.12/0.0302) = 5.50?024 00so that ni(400K)= 2.34?012cm-3 Comment We can note from this example that the intrinsic