Log plot and linear plot plotted in one view

Question

I have the following code:

q := 1.6*10^-19;
me := 9.1*10^-31; (* Free electron rest mass in kg *)
h :=  6.63*10^-34;  (* Reduced Planck's constant in J.s *)
kb := 1.38*10^-23;(* Boltzmann constant in J/K *)
Jschottky[V_, T_] := (2 q*(2 \[Pi] me)^0.5 kb^1.5)/h^2*(0.3)^0.5*
  Exp[-0.18/((kb*T)/q)] (Exp[(q*V)/(kb*T)] - 1);
LogPlot[Abs[Jschottky[V, 77]], {V, -0.5, 0.5}, PlotRange -> All, 
 Frame -> True, 
 FrameLabel -> {"Voltage (V)", 
   "\!\(\*FractionBox[\(J\), SuperscriptBox[\(T\), \(3/2\)]]\)"}, 
 BaseStyle -> {FontSize -> 15}, PlotStyle -> {Thick, Red} , 
 AspectRatio -> GoldenRatio, ImageSize -> 400, FrameStyle -> Black, 
 FrameTicks -> {{{#, Superscript[10, Log10@#]} & /@ ({10^-21, 10^-11, 
       10^-1, 10^9, 10^19}), None}, {Automatic, None}}]

Plot[Abs[Jschottky[V, 77]], {V, -0.5, 0.5}, PlotRange -> All, 
 Frame -> True, 
 FrameLabel -> {"Voltage (V)", 
   "\!\(\*FractionBox[\(J\), SuperscriptBox[\(T\), \(3/2\)]]\)"}, 
 BaseStyle -> {FontSize -> 15}, PlotStyle -> {Thick, Blue} , 
 AspectRatio -> GoldenRatio, ImageSize -> 400, FrameStyle -> Black]

I get the following results:

Now I want to plot them on the same plot with the logplot on the left y axis and the linear plot on the right yaxis. What should I do? Also any recommendations for a good grayscale plot of the same?

Answer 1

q := 1.6*10^-19;
me := 9.1*10^-31;(*Free electron rest mass in kg*)h := 
 6.63*10^-34;(*Reduced Planck's constant in J.s*)kb := 
 1.38*10^-23;(*Boltzmann constant in J/K*)
Jschottky[V_, T_] := (2 q*(2 \[Pi] me)^0.5 kb^1.5)/h^2*(0.3)^0.5*
  Exp[-0.18/((kb*T)/q)] (Exp[(q*V)/(kb*T)] - 1);
p1 = LogPlot[Abs[Jschottky[V, 77]], {V, -0.5, 0.5}, PlotRange -> All, 
  Frame -> True, 
  FrameLabel -> {"Voltage (V)", 
    "\!\(\*FractionBox[\(J\), SuperscriptBox[\(T\), \(3/2\)]]\)"}, 
  BaseStyle -> {FontSize -> 15}, PlotStyle -> {Thick, Red}, 
  AspectRatio -> GoldenRatio, ImageSize -> 400, FrameStyle -> Black, 
  ImagePadding -> {{100, 100}, {80, 80}}, FrameTicksStyle -> Red, 
  FrameTicks -> {{{#, Superscript[10, Log10@#]} & /@ ({10^-21, 10^-11,
         10^-1, 10^9, 10^19}), None}, {Automatic, None}}]

p2 = Plot[Abs[Jschottky[V, 77]], {V, -0.5, 0.5}, PlotRange -> All, 
  Frame -> True, 
  FrameLabel -> {{None, 
     "\!\(\*FractionBox[\(J\), SuperscriptBox[\(T\), \(3/2\)]]\)"}, \
{None, None}}, BaseStyle -> {FontSize -> 15}, 
  PlotStyle -> {Thick, Blue}, AspectRatio -> GoldenRatio, 
  ImageSize -> 400, ImagePadding -> {{100, 100}, {80, 80}}, 
  FrameStyle -> Black, FrameTicks -> {{None, All}, {None, None}}, 
  FrameTicksStyle -> Blue]
Overlay[{p1, p2}]

Answer 2

On a side note (but too big to fit in a comment), you can speed up the Jschottky function evaluation by about 13x by using FunctionCompile:

f = Function[{Typed[V, "Real64"], Typed[T, "Integer64"]},
  Module[{q, me, h, kb},
   q = 1.6*10^-19;
   me = 9.1*10^-31;
   h = 6.63*10^-34;
   kb = 1.38*10^-23;
   (2 q*(2 \[Pi] me)^0.5 kb^1.5)/h^2*(0.3)^0.5*
    Exp[-0.18/((kb*T)/q)] (Exp[(q*V)/(kb*T)] - 1)
   ]
  ]

and then:

cf = FunctionCompile[f]

On my machine I get the following timings:

In[.]:= Do[Jschottky[RandomReal[{-0.5, 0.5}], 77], 100000] // AbsoluteTiming
Out[.]= {0.777224, Null}

In[.]:= Do[cf[RandomReal[{-0.5, 0.5}], 77], 100000] // AbsoluteTiming

Out[.]= {0.0563924, Null}