3.4 Aluminum Nitride

Material parameters as used by different group are given in Table 3.7, while Table 3.8 summarizes the experimental and theoretical values of the elastic constants $c_{11}$, $c_{12}$, and $c_{44}$, available for wurtzite AlN in the literature. From these the corresponding $c_\ensuremath{\mathrm{L}}$, $c_\ensuremath{\mathrm{T}}$, $v_\ensuremath{\mathrm{sl}}$, and $v_\ensuremath{\mathrm{st}}$ are calculated. The experimental values from [165] are adopted in the MC simulation.

Table 3.7: Summary of material parameters of wurtzite AlN for Monte Carlo
simulation.

Bandgap energy			Electron mass			Non-parabolicity			Scattering models						Ref.
$\Gamma_{1}$	U	$\Gamma_{3}$	$\ensuremath{\mathrm{m}}_{\Gamma 1}$	$\ensuremath{\mathrm{m}}_\ensuremath{\mathrm{U}}$	$\ensuremath{\mathrm{m}}_{\Gamma 3}$	$\alpha_{\Gamma 1}$	$\alpha_\ensuremath{\mathrm{U}}$	$\alpha_{\Gamma 3}$	ADP	$\hbar \omega _\ensuremath{\mathrm{ij}}$	$\hbar \omega _\ensuremath{\mathrm{LO}}$	$\rho$	$\ensuremath{\ensuremath{\epsilon}_\ensuremath{\mathrm{r}}}$	$\ensuremath{\ensuremath{\epsilon}_{\infty}}$
eV	eV	eV	m$_0$	m$_0$	m$_0$	1/eV	1/eV	1/eV	eV	meV	meV	g/cm$^2$	-	-
6.20	6.90	-	0.48	1.0	-	0.044	0	-	9.5	99.2	99.2	3.23	8.5	4.77	[246]
5.84	7.00	8.29	0.326	0.384	0.473	0.29	-	-	9.5	75.8	110.3	3.23	8.5	4.46	[153]
6.00	7.05	8.49	0.26	0.495	0.55	0.207	0.035	0.023	-	76.1	110.7	-	-	4.68	[247]
6.20	6.90	8.20	0.33	0.40	0.50	0.044	0	0	9.5	99.2	99.2	3.23	8.5	4.77

Table 3.8: Summary of elastic constants of AlN and the resulting longitudinal and transverse elastic constants and sound velocities.

$c_{11}$	$c_{12}$	$c_{44}$	Data	Refs.	$c_\ensuremath{\mathrm{L}}$	$c_\ensuremath{\mathrm{T}}$	$v_\ensuremath{\mathrm{sl}}$	$v_\ensuremath{\mathrm{st}}$
GPa	GPa	GPa			GPa	GPa	m/s	m/s
345	125	118	exp.	[248]	351	115	10430	5962
411	149	125	exp.	[249]	406	127	11214	6280
410	140	120	exp.	[165]	398	126	11100	6246
380	114	109	calc.	[250]	361	119	10569	6060
464	149	128	calc.	[251]	440	140	11677	6579
424	103	138	calc.	[166]	406	147	11211	6746
398	140	96	calc.	[167]	372	109	10726	5814
396	137	116	calc.	[168]	385	121	10920	6131
398	142	127	calc.	[169]	397	127	11089	6280

Table 3.9 summarizes the experimental and theoretical values of the piezoelectric coefficients $e_{15}$, $e_{31}$, and $e_{33}$.

Table 3.9: Summary of piezoelectric coefficients of AlN for Monte Carlo simulation of
piezoelectric scattering.

$e_{15}$	$e_{31}$	$e_{33}$	Data	Refs.	$\langle e_\ensuremath{\mathrm{L}}^2 \rangle$	$\langle e_\ensuremath{\mathrm{T}}^2 \rangle$
C/m$^2$	C/m$^2$	C/m$^2$	Data	Refs.	C$^2$/m$^4$	C$^2$/m$^4$
-0.48	-0.58	1.55	exp.	[248]	0.251	0.304
-	-0.60	1.50	exp.	[171]	0.260	0.334
-0.29	-0.58	1.39	exp.	[252]	0.102	0.230
-	-0.60	1.46	calc.	[172]	0.251	0.326
-	-0.38	1.29	calc.	[169]	0.169	0.187
-	-0.64	1.80	calc.	[174]	0.349	0.429

Fig. 3.14 compares the MC simulation result for AlN against others from [253,246,254]. The simulation results are in good agreement with [253,246], since similar MC parameters are used as shown in Table 3.7. The difference visible at high fields can be explained by different effective electron masses used in the higher valleys. The simulation of [254] differs at low fields, since it ignores some mechanisms, e.g. ionized-impurity scattering.

Figure 3.14: Drift velocity versus electric field in wurtzite AlN: Comparison of MC simulation results.