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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "#dimensionless formulation, x,L in \+
units of Debye's length" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "L
:=10:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "U0:=0: #normalized
 potential on the boundary" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
49 "#concentration of impurities - region of N-P jump" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "c:=tanh(20*(x/L-1/2)):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Ca0:=subs(x=0,c);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 22 "phiD0:=arcsinh(Ca0/2);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 17 "CaN:=subs(x=L,c);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 22 "phiDN:=arcsinh(CaN/2);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 48 "eq:=diff(phi(x),x,x)=exp(phi(x))-exp(-phi(x))-
c;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "IC1:=phi(0)=phiD0+U0;
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "IC2:=phi(L)=phiDN;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "sol:=dsolve(\{eq,IC1,IC2\},p
hi(x),numeric);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "P1:=plot
s[odeplot](sol,x=0..L):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "
P2:=plot(arcsinh(c/2),x=0..L, color=black, linestyle=2):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "plots[display](\{P1,P2\});" }}}}
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