Strain groups in database{ …_zb{} } and database{ …_wz{} }

Note

This section is under construction

There are about 18 identicall groups available directly under all zincblende- and wurtzite-related groups. In this section we describe four of them, specifically all groups related to strain parameters:

• lattice_consts{}

• elastic_consts{}

• piezoelectric_consts{}

• pyroelectric_consts{} (only wurtzite)

Strain for zincblende

database{ …{ lattice_consts{} } } for zincblende

a

type:

double

unit:

Angstrom

Specify lattice constant at 300K. In a cubic crystal system (like diamond and zincblende), the lattice constants in all three crystal axes are equal.

a_expansion

type:

double

unit:

Angstom/K

The lattice constants are temperature dependent. The lattice constant a in the database should be given for 300 K. For all other temperatures, the lattice constant is calculated by the following formula:

\[\mathrm{a(T) = a_{300 K} + a\_expansion \cdot (T - 300 K)}\]

where T is the temperatue in units of K.

database{ …{ elastic_consts{} } } for zincblade

Specify elastic constants:

c11

type:

double

unit:

GPa

c12

type:

double

unit:

GPa

c44

type:

double

unit:

GPa

database{ …{ piezoelectric_consts{} } } for zincblade

Specify piezoelectric constants (If strain is present, then generally piezoelectric charges and thus piezoelectric fields arise):

e14

type:

double

unit:

C/m\(^2\)

B114 (optional)

\(\mathrm{2^{nd}}\) order piezoelectric constant

type:

double

unit:

C/m\(^2\)

B124 (optional)

\(\mathrm{2^{nd}}\) order piezoelectric constant

type:

double

unit:

C/m\(^2\)

B156 (optional)

\(\mathrm{2^{nd}}\) order piezoelectric constant

type:

double

unit:

C/m\(^2\)

Note

For silicon and germanium there is no piezoelectric effect at all, thus the constants are zero in this case.

Strain for wurtzite

database{ …{ lattice_consts{} } } for wurtzite

a

Lattice constant at 300 K (perpendicular to hexagonal c axis). In a hexagonal crystal system, the two lattice constants perpendicular to the hexagonal c axis are equal.

type:

double

unit:

Angstrom

c

Lattice constant at 300 K (along hexagonal c axis)

type:

double

unit:

Angstrom

a_expansion

type:

double

unit:

Angstrom/K

c_expansion

type:

double

unit:

Angstrom/K

The formaula for the temperature dependency of the lattice constants a and c in wurtzite is the same as for a in zincblende.

database{ …{ elastic_consts{} } } for wurtzite

Specify elastic constants:

c11

type:

double

unit:

GPa

c12

type:

double

unit:

GPa

c13

type:

double

unit:

GPa

c33

type:

double

unit:

GPa

c44

type:

double

unit:

GPa

database{ …{ piezoelectric_consts{} } } for wurtzite

Specify piezoelectric constants (If strain is present, then generally piezoelectric charges and thus piezoelectric fields arise):

e31

type:

double

unit:

C/m\(^2\)

e33

type:

double

unit:

C/m\(^2\)

e15

type:

double

unit:

C/m\(^2\)

B311 (optional)

\(\mathrm{2^{nd}}\) order piezoelectric constant

type:

double

unit:

C/m\(^2\)

B312 (optional)

\(\mathrm{2^{nd}}\) order piezoelectric constant

type:

double

unit:

C/m\(^2\)

B313 (optional)

\(\mathrm{2^{nd}}\) order piezoelectric constant

type:

double

unit:

C/m\(^2\)

B333 (optional)

\(\mathrm{2^{nd}}\) order piezoelectric constant

type:

double

unit:

C/m\(^2\)

B115 (optional)

\(\mathrm{2^{nd}}\) order piezoelectric constant

type:

double

unit:

C/m\(^2\)

B125 (optional)

\(\mathrm{2^{nd}}\) order piezoelectric constant

type:

double

unit:

C/m\(^2\)

B135 (optional)

\(\mathrm{2^{nd}}\) order piezoelectric constant

type:

double

unit:

C/m\(^2\)

B344 (optional)

\(\mathrm{2^{nd}}\) order piezoelectric constant

type:

double

unit:

C/m\(^2\)

database{ …{ pyroelectric_consts{} } } for wurtzite

Specify pyroelectric constants (for spontaneous polarization).

p1

type:

double

unit:

C/m\(^2\)

The pyroelectric field is directed along the hexagonal c axis ([0 0 0 1] direction).