Ab initio calculation of valley splitting in monolayer δ-doped phosphorus in silicon

Table 2 Valley splitting values of 1/4 ML P-doped silicon obtained using different techniques

Technique	Number of	Valley
	layers	splitting
		(meV)
Planar Wannier orbital^a[30]	1,000	20
Tight binding (4 K)^b[34]	∼150	∼17
Tight binding (4 K)^b[37]	120	25
Tight binding (300 K)^b[36]	∼150	∼17
	40	7
	80	6
DFT, SZP basis set ^a[32]	120	6
	160	6
	200	6
DFT, SZP: ordered ^b[31]	40	120
DFT, SZP: random disorder ^b[31]	40	∼70
DFT, SZP: [110] direction alignment ^b[32]	40	∼270
DFT, SZP: dimers ^b[32]	40	∼85
DFT, SZP: random disorder ^b[32]	40	∼80
DFT, SZP: clusters ^b[32]	40	∼65
DFT, SZP: [100] direction alignment ^b[32]	40	∼50
DFT, SZP: ordered, M=4^b,c[32]	80	153
DFT, SZP: ordered, M=6^b,c[32]	80	147
DFT, SZP: ordered, M=10^b,c[32]	80	147
	40	145.1
	60	144.7
SZP, M=9 (this work)^b,c	80	144.8
	120	144.7
	160	144.7
	200	144.7
	16	118.6
	32	94.1
PW, M=9 (this work)^b,d	40	93.5
	60	93.3
	80	93.2
	40	100
	60	99.5
DZP, M=9 (this work)^b,c	80	99.5
	120	99.3
	160	99.6

Techniques are grouped by similarity. ^aImplicit doping; ^bExplicit doping; ^cM × M × 1k-points; ^dM × M × N k-points; N as in Appendix 1.