On the Infrared Thickness Measurement of Epitaxially Grown Silicon Layers

P. J. Severin

doi:10.1364/AO.9.002381

Applied Optics
Vol. 9,
Issue 10,
pp. 2381-2387
(1970)
•https://doi.org/10.1364/AO.9.002381

On the Infrared Thickness Measurement of Epitaxially Grown Silicon Layers

P. J. Severin

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P. J. Severin, "On the Infrared Thickness Measurement of Epitaxially Grown Silicon Layers," Appl. Opt. 9, 2381-2387 (1970)

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Abstract

The thickness of epitaxially grown layers is commonly measured by infrared multiple reflection. The phase shift at the layer–substrate interface is very often neglected. It has been computed as a function of the wavelength, and for accurate measurement it is said to be advisable to apply this correction. By direct calculation from measured spectra, a phase shift independent of wavelength is found. The layer–substrate reflection coefficient, generally assumed to be constant, has been verified to vary exponentially with the wavenumber, yielding another constant phase shift. The measured constant phase shift cannot be explained from this dependence. An alternative procedure for measuring the thickness of epitaxial layers with a precision to within 0.5% is suggested.

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Slice	d[μm]	d₀[μm]	d₀/2π	δ^*/2π
H24-2	15.45	45	0.21	0.235
H24-3	15.45	75	0.24	0.22
H24-4	15.1	100	0.18	0.22
H24-5	15.0	75	0.1	0.23
H24-6	15.4	75	0.1	0.23
H24-7	15.4	60	0.1	0.235
H24-8	12.6	50	0.2	0.23

Ref. Fig. Table	k [cm⁻¹]		2dn [μm]	d [μm]	$l - \frac{1}{2} + \frac{δ_{0}}{2 π}$	$l + \frac{δ_{0}}{2 π}$	$\frac{δ_{0}}{2 π}$	$\frac{δ_{0}}{2 π}$	Correl.
Ref. Fig. Table	Max.	Min.	2dn [μm]	d [μm]	$l - \frac{1}{2} + \frac{δ_{0}}{2 π}$	$l + \frac{δ_{0}}{2 π}$	$\frac{δ_{0}}{2 π}$	$\frac{δ_{0}}{2 π}$	Correl.
10	1120		68.6	10.03	7.68		0.18	0.19	0.99986
3	980				6.72		0.22
	827				5.67		0.17
	685				4.70		0.20
11	358		49.4	7.22	1.77		0.27	0.24	0.9988
		456				2.25	0.25
1	546				2.70		0.20
		649				3.21	0.21
	766				3.78		0.28
13		316	102.4	14.97		3.24	0.24	0.22	0.99987
1	364				3.78		0.23
3		408				4.18	0.18
	460				4.71		0.21
		508				5.20	0.20
	559				5.72		0.22
		609				6.24	0.24
	655				6.71		0.21
14	592		107.1	15.66	6.34		0.84	0.87	0.9997
2		548				5.87	0.87
	505				5.41		0.91
		455				4.87	0.87
	410				4.39		0.89
		358				3.83	0.83
	315				3.37		0.87
16		580	19.66	2.87		1.14	0.14	0.12	0.9997
2	830				1.63		0.13
		1080				2.12	0.12
	1340				2.63		0.13
		1550				3.05	0.05
	1870				3.68		0.18
		2060				4.05	0.05
	2350				4.62		0.12
		2600				5.11	0.11
	2860				5.62		0.12
		3130				6.15	0.15
17	480		68.3	9.99	3.28		0.78	0.78	0.9997
3(a)		552				3.77	0.77
	625				4.27		0.77
		704				4.82	0.82
	770				5.26		0.86
3(b)	500		64.4	9.42	3.22		0.72	0.73	0.9994
		582				3.75	0.75
	655				4.22		0.72
3(c)		461	60.6	8.86		2.79	0.79	0.77	0.9978
	532				3.22		0.72
		625				3.79	0.79
18	961		73.5	10.14	7.06		0.56	0.55	0.9999
		891				6.55	0.55
8a	823				6.05		0.55
		755				5.55	0.55
	687				5.05		0.55
		617				5.53	0.53
	554				4.07		0.57
8(b)		893	75.3	11.01		6.72	0.22	0.20	0.9996
	820				6.17		0.17
		755				5.69	0.19
	690				5.20		0.20
		629				4.74	0.24
	556				4.19		0.19
19	42		582	85.1	2.44		0.94	0.98	0.9997
1		51				2.97	0.97
	60				3.49		0.99
		69				4.02	0.02
	77				4.48		0.98
		86				5.00	0.00
	94				5.47		0.97
		102				5.94	0.94
24	410		145	21.2	5.95		0.45	0.46	0.9999
2	480				6.96		0.46
1	550				7.97		0.47
	615				8.91		0.41
	687				9.96		0.46
25	288		136.5	19.9	3.93		0.43	0.46	0.9998
3		331				4.52	0.52
	362				4.94		0.44
		401				5.47	0.47
	433				5.91		0.41
		475				6.48	0.48
	509				6.95		0.45
		547				7.47	0.47
	581				7.93		0.43
		618				8.44	0.44
	659				8.99		0.49
26		1140	46.2	6.75		5.26	0.26	0.28	0.9998
4	1030				4.76		0.26
		922				4.26	0.26
	820				3.79		0.29
		710				3.28	0.28
	605				2.80		0.30
		485				2.24	0.24

Slice	d[μm]	d₀[μm]	d₀/2π	δ^*/2π
H24-2	15.45	45	0.21	0.235
H24-3	15.45	75	0.24	0.22
H24-4	15.1	100	0.18	0.22
H24-5	15.0	75	0.1	0.23
H24-6	15.4	75	0.1	0.23
H24-7	15.4	60	0.1	0.235
H24-8	12.6	50	0.2	0.23

Ref. Fig. Table	k [cm⁻¹]		2dn [μm]	d [μm]	$l - \frac{1}{2} + \frac{δ_{0}}{2 π}$	$l + \frac{δ_{0}}{2 π}$	$\frac{δ_{0}}{2 π}$	$\frac{δ_{0}}{2 π}$	Correl.
Ref. Fig. Table	Max.	Min.	2dn [μm]	d [μm]	$l - \frac{1}{2} + \frac{δ_{0}}{2 π}$	$l + \frac{δ_{0}}{2 π}$	$\frac{δ_{0}}{2 π}$	$\frac{δ_{0}}{2 π}$	Correl.
10	1120		68.6	10.03	7.68		0.18	0.19	0.99986
3	980				6.72		0.22
	827				5.67		0.17
	685				4.70		0.20
11	358		49.4	7.22	1.77		0.27	0.24	0.9988
		456				2.25	0.25
1	546				2.70		0.20
		649				3.21	0.21
	766				3.78		0.28
13		316	102.4	14.97		3.24	0.24	0.22	0.99987
1	364				3.78		0.23
3		408				4.18	0.18
	460				4.71		0.21
		508				5.20	0.20
	559				5.72		0.22
		609				6.24	0.24
	655				6.71		0.21
14	592		107.1	15.66	6.34		0.84	0.87	0.9997
2		548				5.87	0.87
	505				5.41		0.91
		455				4.87	0.87
	410				4.39		0.89
		358				3.83	0.83
	315				3.37		0.87
16		580	19.66	2.87		1.14	0.14	0.12	0.9997
2	830				1.63		0.13
		1080				2.12	0.12
	1340				2.63		0.13
		1550				3.05	0.05
	1870				3.68		0.18
		2060				4.05	0.05
	2350				4.62		0.12
		2600				5.11	0.11
	2860				5.62		0.12
		3130				6.15	0.15
17	480		68.3	9.99	3.28		0.78	0.78	0.9997
3(a)		552				3.77	0.77
	625				4.27		0.77
		704				4.82	0.82
	770				5.26		0.86
3(b)	500		64.4	9.42	3.22		0.72	0.73	0.9994
		582				3.75	0.75
	655				4.22		0.72
3(c)		461	60.6	8.86		2.79	0.79	0.77	0.9978
	532				3.22		0.72
		625				3.79	0.79
18	961		73.5	10.14	7.06		0.56	0.55	0.9999
		891				6.55	0.55
8a	823				6.05		0.55
		755				5.55	0.55
	687				5.05		0.55
		617				5.53	0.53
	554				4.07		0.57
8(b)		893	75.3	11.01		6.72	0.22	0.20	0.9996
	820				6.17		0.17
		755				5.69	0.19
	690				5.20		0.20
		629				4.74	0.24
	556				4.19		0.19
19	42		582	85.1	2.44		0.94	0.98	0.9997
1		51				2.97	0.97
	60				3.49		0.99
		69				4.02	0.02
	77				4.48		0.98
		86				5.00	0.00
	94				5.47		0.97
		102				5.94	0.94
24	410		145	21.2	5.95		0.45	0.46	0.9999
2	480				6.96		0.46
1	550				7.97		0.47
	615				8.91		0.41
	687				9.96		0.46
25	288		136.5	19.9	3.93		0.43	0.46	0.9998
3		331				4.52	0.52
	362				4.94		0.44
		401				5.47	0.47
	433				5.91		0.41
		475				6.48	0.48
	509				6.95		0.45
		547				7.47	0.47
	581				7.93		0.43
		618				8.44	0.44
	659				8.99		0.49
26		1140	46.2	6.75		5.26	0.26	0.28	0.9998
4	1030				4.76		0.26
		922				4.26	0.26
	820				3.79		0.29
		710				3.28	0.28
	605				2.80		0.30
		485				2.24	0.24

Abstract

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Equations (17)

Applied Optics