3.2.3.3 Effective Carrier Masses

The effective carrier masses for basic semiconductors of electrons and holes are given in Table 3.9. The temperature dependence of the relative carrier mass is modeled according to:

$$m_n = m_{n,0} + m_{n,1} \cdot \bigg(\frac{{\it T}_\mathrm{L}}{300 K}\bigg)$$ (3.27)

$$m_p = m_{p,0} + m_{p,1}\cdot \bigg(\frac{{\it T}_\mathrm{L}}{300 K}\bigg) + m_{p,2} \cdot \bigg(\frac{{\it T}_\mathrm{L}}{300 K}\bigg)^2$$ (3.28)

for electrons and holes, respectively. Again, a k-valley dependent model is introduced which reads:

$$m_{0,n} = \left\{ \begin{array}{r@{\quad:\quad}l} m_{\Gamma} & \text {... ...)^{1/3} & \text {for Si, AlAs, and AlN} \\ \end{array} \right.$$ (3.29)

$$m_{0,p} = \big( m_{pl}^{(3/2)}+ m_{ph}^{(3/2)}\big)^{(2/3)}$$ (3.30)

The parameter values are given in Table 3.9.

Table 3.9: Effective carrier masses for binary III-V semiconductors at $T_L$= 300 K.

Material	m$_{\Gamma}$	m$_{X}$	m$_{L}$	m$_{nt}$	m$_{nl}$	m$_{0,p}$	m$_{ph}$	m$_{pl}$	References
GaAs	0.067	0.471	0.23	0.229	1.987	0.49	0.50	0.074	[194]
AlAs	0.15	0.38	-	0.19	1.5	0.81	0.76	0.16	[4]
InAs	0.0237	0.64	0.286	0.271	3.619	0.41	0.39	0.055	[41,52,91]
									[194,284]
InP	0.078	0.262	0.325	0.273	1.321	0.64	0.56	0.12	[52,85,91]
	also 0.073								[143,294]
GaN	0.20	-	-	0.2283	0.1846	0.6	-	0.259	[103,259]
	also 0.19								[284]
AlN	0.314	-	-	0.3433	0.2938	-	-	0.471	[103,259]
InN	0.11	-	-	0.1311	0.1190	-	-	-	[103,259]
Si	-	0.328	-	0.19	0.98	0.55	0.49	0.16	[194,284]

Table 3.10: Model parameters of the relative carrier masses for the temperature dependence and for the ternary III-V semiconductors at $T_L$= 300 K.

Material	Valley	m$_{n,0}$	m$_{n,1}$	m$_{p,0}$	m$_{p,1}$	m$_{p,2}$	References
GaAs	$\Gamma$	0.067 (0.471)	-0.0036	0.49	-	-	-
AlAs	X ($\Gamma$)	0.38 (0.15)	-0.0036	0.8	-	-	-
InAs	$\Gamma$ (X)	0.0237 (0.64)	-0.0027	0.41	-	-	-
InP	$\Gamma$ (X)	0.077 (0.462)	-0.004	0.64	-	-	-
GaN	$\Gamma$	0.20 $\pm$ 0.005	-	-	-	-	[78]
AlN	$\Gamma$	0.48	-	-	-	-	[259]
InN	$\Gamma$	0.11	-	-	-	-	-
Si	X	0.321	0.009	0.55	0.6	-0.1	-

The values for the nitrides are preliminary results. Direct measurements of the effective conduction band mass in  [78] confirm the value for GaN within an accuracy of $\pm$ 0.005. For the use in ternary semiconductors the values for the combination are given in Table. 3.10. For the ternary semiconductors the values are composed from the binary constituents as follows:

$$m_{\nu}^{AB} = x \cdot m^A_{\nu} + (1-x) \cdot m^B_{\nu} + x \cdot (1-x) \cdot C_{m \nu}$$ (3.31)

For the bowing parameters values from Table 3.11 were used.

Table 3.11: Model parameters of the relative carrier masses for ternary III-V semiconductors.

Material	C$_{m,n}$	C$_{m,p}$	Reported Range m$_n$	References
Al$_x$Ga$_{1-x}$As	0.0	0.0	0.07-0.08 ($x$= 0.2)	[4]
In$_x$Ga$_{1-x}$As	-0.012	-0.03	0.041 ($x$= 0.53)	[163]
In$_x$Al$_{1-x}$As	0.0	0.0	0.070 ($x$= 0.52), 0.081 ($x$= 0.52)	[163,250]
Al$_x$Ga$_{1-x}$N	0.0	0.0	-	[158]