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TYU 9.1  Cr-Si (n-type) Schottky   Nd=3e15 cm^-3, VR=5 V, 300 K
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quantity            material     recomputed   rel.err  verdict
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phi_BO [V]              0.49           0.49    0.000%  PASS
phi_n [V]              0.237       0.236761    0.101%  PASS
V_bi [V]               0.253       0.253239    0.095%  PASS
x_n [cm]           0.0001505    0.000150547    0.031%  PASS
|E_max| [V/cm]      6.98e+04        69788.6    0.016%  PASS
C' [F/cm^2]         6.88e-09    6.87791e-09    0.030%  PASS
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independent invariant checks (not from the material)
  [PASS] phi_BO == phi_m - chi
  [PASS] C' == eps_s / x_n
  [PASS] q*Nd*x_n == eps_s*E_max
  [PASS] phi_BO unchanged by VR
  [PASS] x_n scales as sqrt(V_tot)
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control case, VR = 0 V (equilibrium)
  x_n = 3.305402e-05 cm   |E_max| = 1.5323e+04 V/cm   C' = 3.1326e-08 F/cm^2
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RESULT: ALL PASS