/* Carrier equilibrium identities. Every printed residual must be zero. */
kill(all)$
assume(Nc>0,Nv>0,k>0,T>0)$
n : Nc*exp(-(Ec-Ef)/(k*T))$
p : Nv*exp(-(Ef-Ev)/(k*T))$
ni2 : Nc*Nv*exp(-(Ec-Ev)/(k*T))$
print("mass-action residual =", ratsimp(n*p-ni2))$
Ef_i : (Ec+Ev)/2 + k*T*log(Nv/Nc)/2$
print("intrinsic neutrality residual =", ratsimp(subst(Ef_i,Ef,n)-subst(Ef_i,Ef,p)))$