The Closed-Form Solutions for the Breakdown Voltages of 6H-SiC Reachthrough Diodes
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device component that deserves to be researched. Experiments and the analytic formula for the breakdown voltage of 6H-SiC NRTD (non-reachthrough diode) have been reported [3,4,5]. However, any closed-form analytic solutions for the breakdown voltage of 6H-SiC RTD have not been reported. The NRTD has the inevitable trade-off between the low on-resistance at forward bias and the high breakdown voltage at reverse bias. However, though the epitaxial layer thickness, WP,, of RTD is thinner than that of the NRTD, the breakdown voltage of RTD can remain the same to that of NRTD by employing the lower doping concentration of the epitaxial layer. In addition, the on-resistance of RTD can be lower than that of NRTD, if the appropriate design of the doping concentration of epitaxial layer, ND and the thickness of epitaxial layer, Wepi is made. Therefore, the analytic formula for the breakdown voltage of 6H-SiC RTD is indispensable to the optimum design of the thickness, Wep, and the doping concentration of the epitaxial layer. The figure for ideal breakdown voltage for reachthrough device was reported in 'ISPSD 97 [2]. In Fig.2, there is the region where the breakdown voltages increase as the doping concentration of the epitaxial layer increases, which may not be physically sound (See Appendix). 143
Mat. Res. Soc. Symp. Proc. Vol. 512 ©1998 Materials Research Society
These data result from the calculation of the breakdown voltages by using the critical electric field of the NRTD instead of RTD. In this paper, analytic formulas for the breakdown voltage of the RTD are derived in closedform equations by solving the ionization integral with the critical electric field of the RTD. ANALYTIC MODEL FOR BREAKDOWN VOLTAGES The one-dimensional cross-section and the electric field distribution of RTD are shown in Fig. 1.
P+ N-
Epitaxial Layer
N+ Substrate
WB W/ S..........................x
El
E crit
Fig. 1 A cross sectional view and an electric field distribution of the RTD Assuming the one-sided abrupt p+-n junction and depletion approximation, the Poisson's equation is expressed in (1). d2V 2
dx
dE
qN1 •
dx
,SIC
(1)
where q is the electron charge, Es,. is the permmittivity of SiC, and ND is the doping concentration of epitaxial layer. By solving eq.(1) and Fig.1, we obtain eq.(2) and eq.(3) respectively. E(x) = qND x - Ecr..
(2)
VB = I (Ec...t +
2
, SIC
and E, = E(WB),
V - qNDWB 2 Ec... = WB Csc
144
E,)xWB
(3) (4)
To meet the avalanche breakdown condition, the ionization integral equation should be satisfied as follows [1,3].
(5)
01eaf.dx = 1
where
ad
=4.6 xl O- Ecr,, 6 [cm 6 ]
for 6H - SiC
Inserting eq.(2) into eq.(5), solving the eq.(5), and substituting (4), we have the eq.(6). , _ ) Wl
____
V1
qN_ W8)
7qN
=0
(6)
Eq.(6) is plotted in Fig.3. The results of the ref.[2] is plotted in Fig.2. There are relatively large differences between the results of ref.[2] and eq.(6) in the range of the low doping concentration for all the thickness of the epitaxial layer. 10000. Nonl-
......
4H.OiC Aslum
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