Table 1 For each sample, the integrated thermal activation paramter \({{D}}_{{\rm{\Sigma }}}^{\ast }\) is shown in the second column, followed by the aggregate time spent at each 1000 °C, 1100 °C, and 1200 °C. Using the \({D}_{{\rm{\Sigma }}}^{\ast }\) parameter for each sample, we calculate equivalent activation times (t_eq) if the sample had sat at a single temperature of either 1100 °C or 1200 °C. The next two columns provide single dopant bulk and surface diffusion lengths using E_a = 3.5 eV¹² for 3D, E_a = 0.94 eV¹¹ for 2D and D₀ = 3.85 cm²/s¹⁹ for both bulk and surface diffusion. Finally, the equivalent time at 1100 °C is used to estimate the spreading of the implanted dopants “edge” using an online diffusion calculator, corresponding to a dopant density of 3.8 × 10¹⁸ cm³.

Sample	\({{\boldsymbol{D}}}_{{\boldsymbol{\Sigma }}}^{{\boldsymbol{\ast }}}\)	Total time (s)^a			t_eq (min)^b		Diffusion length (μm)^b		l_c (μm)^c
Sample		1000 °C	1100 °C	1200 °C	1100 °C	1200 °C	l _3D	l _2D	l_c (μm)^c
D1	0.084 ± 0.003	60	0	0	0.10	0.01	0.02	2.09 × 10³	—
D2	2.5 ± 0.3	55	48	23	2.81	0.38	0.10	3.99 × 10³	0.23
D3	5.1 ± 0.4	69	54	45	5.86	0.79	0.14	5.73 × 10³	0.34
D4	6.1 ± 0.4	0	97	51	6.97	0.94	0.15	5.78 × 10³	0.37
D5	7.5 ± 0.6	0	7	60	8.56	1.15	0.17	4.53 × 10³	0.43
D6	9.1 ± 0.5	0	151	93	10.34	1.39	0.19	7.04 × 10³	0.46
D7	26.2 ± 0.5	52	1816	23	29.95	4.03	0.32	16.08 × 10³	0.78

^aThe total times reported for each sample for each temperature is the time that the sample reached 95% of the corresponding temperature and we estimate the uncertainty to be ± 2 s. ^bRelative uncertainty for equivalent anneal time (t_eq) and the diffusion lengths (l_3D, and l_2D) are estimated as < 10%. ^cl_c is the broadening of the critical concentration for metal-insulator transition relative to as implanted dopant profile due to annealing at 1100 °C for t = t_eq time using publicly accessible dopant profile calculator²⁰.

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